ARMYBR~1

130237643.xls.ms_office

A. Structural Picture of Bridge (Superstructure & Substructure). X 12750 1250 1250

10250 450

0

0

0

0

1250 9350

0

0

450

1250 Toe 2525

5500

450

2525

300

0

BF - 01

1775

450

BF-02

0

BF-03

0

0 0

1250

450

3450

2450 12750

X Abutment Plan

3450

450

1250

130237643.xls.ms_office 375 300 700

150

Toe 0

0

0

450

0

0

0

450

1775 1775

300

0 300

450

2525

450

2525

H1 6147

4947

400 450

H

130237643.xls.ms_office 5500 A1 and A2

y

X

y

X

0

25.000

0.300

0

24.400

0.300

25.000 PC Girder Plan

1

0

3

4

4

2000

2

800

2

150

3

200

200

2000

130237643.xls.ms_office

0

350

5

7 0

7

6

0

350

0

6

0

350 PC Girder Section X-X Mid Section

0

0

0

1

2

2

100

100 0

0

3

0

0

0

2000

150

1800

150

1650

0

0 130237643.xls.ms_office

0

0

0

PC Girder Section Y-Y End Section

75

2

2

1625

1

1700

250

75

75

PC Cross Girder Section

3570

1070

300 200

Girder

2000 4000

Curb Slab and wearing

3570

130237643.xls.ms_office 1070

4000

24,400 Effect area =

Toe

87.11 m2

Wind Action Area

B

H1 Ka.g.H1 ka.g.H1 H2 Ka.g.H2

Sylhet

18.833

Earth Pressure

19.592

19.592

18.833

Balagonj

130237643.xls.ms_office

16.556

16.86

17.315

P1

A1 13.683

16.556 A2

6.3

6.3

15.080

17.315

P2

42.68

36.6 RL

16.86

3.716

36.6 6.200

13.657

10000 1750

150 600

5000

2500

4

455

1 3

2

1200 3

300 6500

1750

11015

1750

600

8015 4007.5

700

300

130237643.xls.ms_office

1200

11000 2100

3000

5000

Pile Cap

11000

3000

6000

130237643.xls.ms_office

1800

A1P1 P1P2

1800

300

300

60

1200

15

1200

130237643.xls.ms_office

Strap Beam

8615

1200 dia circular column

Pile Cap

1200

10560

Tie Beam

11015

10000

8160

1200

11000 Pier P1

Mid Span / 2

1070

Railing

Railing

1070

300 200

curb slab

curb slab Girder

300 200

Girder 1830

1254

1200

1200 300

300 12769

2206

P1P2 Span

11,015

A1P1 Span

8615 1500

1500 300 1200

3776

3400

End Span / 2

130237643.xls.ms_office 1200

Pier P1

Railing

Railing

1070

300 200

curb slab

curb slab Girder

300 200

Girder 1600

1145

1254

P1P2 Span

P2A2 Span

0

1200

Pier P2

2715

End Span / 2

1070

4039.00

3170

Mid Span / 2

130237643.xls.ms_office

5500

130237643.xls.ms_office

2147

600 300

1900

1200

H2

130237643.xls.ms_office

130237643.xls.ms_office

130237643.xls.ms_office

130237643.xls.ms_office

130237643.xls.ms_office

900

900

4 1

2, 3 1800

130237643.xls.ms_office

300 2100

1200 1800

6000

300 2100

130237643.xls.ms_office

12957

130237643.xls.ms_office

3812

130237643.xls.ms_office

130237643.xls.ms_office

B. Load Analusis of Bridge Structure : a. National Highway b. Regional Highway working stress for pile load bearing capacity calc c. District Road 3 d. Bridge Type Simple Supported Single Span T- Girder e. End Span Length,C/C 24.400 m f. Total Girder Length 25.000 m g. Cross Section Category RCC h. Stem Height 1.900 m i. H1, Back wall top to Well cap top 4.947 m j. H2, Well cap height 1.200 m k. H, Back wall top to Well cap bottom (Toe) 6.147 m l. Ko , Co-efficient of Active Horizontal Earth Pressure , 0.441 (AASHTO-LRFD-3.11.5.3 ;Table 3.11.5.3-1.) kN/m2 m) Dp-ES, DL Surcgarge Horizontal Pressure Intensiy (ES) 7.935 2. Calculations for Dead Loads Of Super-structure : A. Super Imposed Loads on Girders : i. Exterior Girder Cross Section m m 0.225 0.225

Item 1.Railing Post

Height m 1.070

2. Railing Beam 0.175

0.175

3Curb (a). Side walk (b). (-)Conduit

0.300 0.925

1.475 0.225

4. Slab

0.200

2.125

Interval (m) 2.000

Load kN/m 0.650

number 3.000

2.205 10.620 (4.995)

Total for (1+2+3+4)= 5. Wearing Course

0.075

0.650

6.Conduit (For Utility)

0.925

0.225

1.121

Total for (5+6)= Sub - total =

ii. Interior Girder 1. Slab

2. Wearing Course Sub - total =

10.200 18.680

2.081 3.203 43.765

Height m 0.200 -

Width m 2.000 -

0.075

2.000

m

Volume m2 0.400 0.150

Load kN/m 9.600

3.450 13.050

130237643.xls.ms_office

B. Self-Weight of RCC Girders & X-Girders: i. Exterior Girder Item i. Central Section Section 1 Section 2 Section 3 Section 4 Section 5 Section 6 Section 7 Sub - total =

nos

Length m

Width m

Height m

Volume m3

0.00 0.00 0.00 2.00 1.00 2.00 2.00

25.000 25 25 25 25 25 25

2.000 0.000 0.150 0.150 0.350 0.000 0.000

0.200 0.000 0.000 0.150 1.800 0.000 0.000

0.000 0.000 0.000 0.563 15.750 0.000 0.000

13.500 378.000 391.500

0.000 0.000 0.000

ii. End Section Section 1 Section 2 Section 3 Sub - total =

1.000 2.000 1.000

0 0 0

-

-

Weight kN

Exterior Girder

Self weight

kN

=

391.50

Interior Girder

Self weight

kN

=

391.50

ii. Interior Girder

iii. Cross Girder Cross Girder

nos

Section 1 Section 2 Sub - total =

1.000 2.000

Number of Cross Girder = Length of Cross Girder = Length width m m 6.600 0.250 6.600 0.075 Cross Girder Self weight

5.00 6.60 Height m 1.700 0.075 kN

nos m Volume m3 2.805 0.037 =

Weight KN 67.320 0.891 68.211 68.211

3. Dead Load Reaction for Abutment Item i. Exterior Girder a. Super Imposed without WC & Utility b. Self Weight c. Wt. from X-Girder d. Total from (a+b+c) e. Super Imposed only WC & Utility f. Total Load from Exterior Girder ii. Interior Girder a. Super Imposed without WC. b. Self Weight c. Wt. from X-Girder d. Total from (a+b+c) e. Super Imposed only WC. d. Total for Int.-Girder

nos

Length m

2 2 5

25.000 25.000 0.825

2 2

25.000

3 3 5

25.000 25.000 1.650

3 3

25.000

LOAD/METER Load for 1 no. Total Load kN/m kN kN

Reaction kN

18.680 15.660 10.335 36.045 3.203

467.001 391.500 42.632 901.133 80.063 1,023.827

934.001 783.000 85.264 1,802.265 160.125 2,047.654

467.001 391.500 42.632 901.133 80.063 981.195

9.600 15.660 10.335 28.671 3.450

240.000 391.500 85.264 716.764 86.250 803.014

720.000 1,174.500 255.791 2,150.291 258.750 2,409.041

360.000 587.250 127.896 1,075.146 129.375 1,204.521

130237643.xls.ms_office

Total Dead Load Reaction for Abutment

(kN) =

2185.715625

i. Wheel load 145.000 kN

145.000 kN

4.300 Ra =

35.000 kN

4.300 24.400

15.800

287.111 kN

Wheel load Reaction for 2 Lane on Each Abutment Dynamic Load Allowance Factor (DLAF) (Applicable only for Truck/Wheel Load & Tandem Loading & Tandem Loading) Wheel Load Reaction on Each Abutment including DLAF (IM)

Rb =

37.889 kN

Ra = Rb = RWheel = IM

=

287.111 kN 37.889 kN 574.221 kN 1.330

RWheel-F =

763.714 kN

iii. Lane Load on Bridge Deck a. Lane Load Intensity = 9.300 kN/m/Lane b. Length of Bridge Deck = 25.000 m c.Lane Load for 1(One) Lane Bridge = 232.500 kN Reaction on each Abutment due to Lane Load for 2 Lane Bridge Deck

RLane =

232.500 kN

iv. Pedestrian Load 2 a. Pedestrian Load Intensity = 3.600 kN/m b. Width of Each Sidewalk = 1.250 m c. Length of Sidewalk = 25.000 m d. Pedestrian Load on 1no Sidewalk = 112.500 kN Reaction on each Abutment due to Pedestrian Load on 2nos Sidewalk Total Live Load Reaction for Abutment

RPedestrain = RLL =

112.500 kN 1,108.714 KN

5. Calculations for Vertical Load and Resisting Moment from Abutment Components, Soil & Also Resisting Moment from Superstructure Loads (Live & Dead) : Arm from Height Width Length Weight Components Toe m m m KN m i. Back Wall 2.147 0.300 9.350 144.536 3.225 ii. Bridge Seat-Rect.-1 0.600 1.000 9.350 134.640 2.875 " Rect.-2 0.300 0.450 9.350 30.294 2.750 " Tri -1 0.300 0.400 9.350 13.464 3.108 " Tri-2 0.300 0.150 9.350 5.049 2.475 iii. Stem-i 1.900 0.450 9.350 95.931 2.750 Stem-ii 1.900 0.300 9.350 127.908 3.075 Sub Total for i + ii + iii = 551.822

Resisting Moment KN-m 466.129 387.090 83.309 41.851 12.496 263.810 393.317 1,648.001

130237643.xls.ms_office

iv.Wing Wall -Well Part-2 nos 4.947 0.450 Cantilever Part-1,Rect-2 nos 2.000 0.450 Cantilever Part-2,Trin-2 nos 1.500 0.450 Sub Total for iv = v.Counterfort Wall Abutment- (3 nos) WingWall-1 (2 nos) 4.947 0.450 WingWall-2 (2 nos) WingWall-3 (2 nos) Sub Total for v = vi. Well Cap-Part-1(Rectangular) 1.200 12.750 Part-2 (Rectangular) 1.200 7.250 Part-3 (Semi Circular) 2nos. 1.200 2.750 Sub Total for vi = Total for Substructure Components= vii. Back Fill (BF-1) 4.947 9.350 " (BF-2) " (BF-3) Sub Total for vii = Vertical load components of Abutment (sub-structure)

2.975 3.000 3.000

317.894 129.600 48.600 366.494

4.013 7.000 7.500

1,275.551 907.200 364.500 1,640.051

3.450 -

5.275 -

vii.Dead Load Reaction & Moment from Superstructure

184.325 184.325 1,009.800 574.200 940.950 2,524.950 3,627.592 2,102.265 2,102.265 5,729.857 KN 2,185.716

972.316 972.316 4,165.425 789.525 1,940.710 6,895.660 11,156.028 8,908.347 8,908.347 20,064.375 KN-m 6,010.718

vii. Live Load Reaction & Moment from Superstructure

1,108.714

Total Vertical Load & Moment from Structure

2.750 2.750 2.750

2.525 Total (KN)=

PV

=

4.125 1.375 2.063

4.238 Total (KN-m) = m 2.750 2.750 =

3,048.964

9,024.287

MR

29,124.057

KN KN KN KN KN

2.849 0.600 0.400 3.674 0.600

m m m m m

2,836.490 360.492 29.148 1,477.974 72.839

KN

7.947

m

1,291.388

KN

2.000

m

54.530

KN

4.000

m

278.746

KN

7.947

m

109.271

6. Calculation of Horizontal Loads (Pressures) & Overturning Moments i. Earth Pressure, P (AASHTO-LRFD-3.11.5.3 ;Table 3.11.5.3-1.) ii. Horizontal Surcharge Load on Abutment (AASHTO-LRFD-3.11.5.3 ;Table 3.11.5.3-1.)

995.609 600.820 72.871 402.334 121.398

ii. Braking Force (25% of Truck Weight 162.500 = 162.500kNActing at1.800m Above Deck ; AASHTO-LRFD-3.6.4) iii. Wind Load on Substructure (0.950kN/m2 27.265 on Vertical Faces Perpendicular to Traffic. AASHTO-LRFD-3.8.1.2.3). iv. Wind Load on Superstructure (0.800kN/m2 69.686 on Vertical Surface of all Supperstructure Elements. AASHTO-LRFD-3.8.1.2.2; Table-3.8.1.2.2-1.) v. Wind Load on Live Load ( 0.550kN/m Acting at 13.750 1.800 m Above Deck ; AASHTO-LRFD-3.8.1.3) Total Horizontal Forces VH = (KN)

2,466.234

KN

Total Overturning Moment, MO =(KN-m)

6,510.878 KN-m

130237643.xls.ms_office

7. Calculations for Factor of Safety Against Overturning & Factor of Safety Against Sliding Abutment Structure Against Imposed Vertical Loads/Forces & Horizontal Forces/Pressure on Abutment & Also Location of Rsultant Forces in Y-Y Direction Well Cap Toe i. Factor of Safety Against Overturning

Mr / Mo

ii. Factor of Safety Against Sliding

0.4 * Pv / Vh

iii. Location of Resultant Force,Lr

(Mr - Mo) / Pv

4.473 OK, FS more than 2 1.464 Not OK 2.506 m

130237643.xls.ms_office

130237643.xls.ms_office

130237643.xls.ms_office

130237643.xls.ms_office

ainst Y-Y

130237643.xls.ms_office

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

C. Checking of Stability for Abutment & Well Cap Against Loads of Different Components & Applied Forces on Structural Elements : 1 Information about Soil, Foundation, Abutment & Wing-walls: a) Type of Sub-soil

:

a) At Borehole No-BH07 (Cox's Bazar End), from GL (GL is - 2.25m from Road Top Level) up to 2.50m depth Sub-soil posses Loss gray fine Silty sand having SPT Value ranging 7 to 12. Whereas in next 0.75m from depth 2.50m to 3.75m there exists Medium dense gray fine sand with SPT value ranging from 12 to 40. From depth about 3.75m there exists Bed-rock (Gray Shale) having 50 and over SPT values . b) At Borehole No-BH08 (Teknuf End), from GL (GL is - 2.25m from Road Top Level) upto 2.75m depth Sub-soil posses Medium dency gray sandy silt having SPT Value renging 12 to 37. In next 2.15m (About depth 2.75m to 4.80m) there exists Medum densey gray fine sand with SPT value renging from 37 to 50. From depth about 4.80m there exists Bed rock (Gray Shale) having SPT value 50 over.

b) Type of Foundation

:

Due to its Geographical position, Marin Drive Road have every risk to effected by Wave action & Cyclonic Strom from Sea. More over the Slain Water is also an important factor for RCC Construction Works in these area. In Designing of any Permanent Bridge/Structure on this Road, specially in Foundation Design all the prevalling adverse situations should be considered for their Survival and Durability. Though as per Soil Investigation Report there exist Loss to Medium dency gray sandy silt on Seashore Sub-soil, but due to ground their formation those posses a very poor Mechanical bonding among it contitutent.But there exites Bed-rock at a considerably short depth (About 3.75m to 4.80m) from the Ground Level.Presence of Bed-rock is an important for the Foundation of any Structue on this Road. To encounter all mentioned adverse situations Provision of RCC Caissons embedded into the Bed-rock will be best one as Foundation of Bridges on this Road. RCC Caissons embedded into the Bed-rock will be a Solid mass to save guard the Structure against Errosion, Sliding, Overturning etc. which caused by the Wave action & Cyclonic Strom. More over against Salinity effect necessary meassary can provide for RCC Caissions. Thus it is recommended to Provide RCC Caissions embedded into the Bed-rock at least 1.50m into Bed-rock as Foundation of Delpara Bridge.

c) Type of Abutment

:

Wall Type Abutment.

d) Type of Wing-walls

:

Wall Type Wing Walls Integrated with Abutment Wall having Counterforts over Well & Cantilever Wings beyond Well.

e) Design Criteria

:

Ultimate Stress Design (AASHTO-LRFD-2004).

2 Design Data in Respect of Unit Weight, Strength of Materials, Soil Pressure & Multiplier Factors : Description

Notation Dimensions

3 i) Unit Weight of Different Materials in kg/m :

Page 33

Unit.

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

(Having value of Gravitional Acceleration, g = a) b) c) d) e)

2 9.807 m/sec )

gW-Nor. gW-Sali. gs

2,447.23 2,345.26 1,019.68 1,045.17 1,835.42

kg/m3 kg/m3 kg/m3 kg/m3 kg/m3

wc wWC wW-Nor. wW-Sali. wE

24.00 23.00 10.00 10.25 18.00

kN/m3 kN/m3 kN/m3 kN/m3 kN/m3

gc gWC

Unit weight of Normal Concrete Unit weight of Wearing Course Unit weight of Normal Water Unit weight of Saline Water Unit weight of Earth (Compected Clay/Sand/Silt)

3 ii) Unit Weight of Different Materials in kN/m :

a) b) c) d) e)

Unit weight of Normal Concrete Unit weight of Wearing Course Unit weight of Normal Water Unit weight of Saline Water Unit weight of Earth (Compected Clay/Sand/Silt)

iii) Strength Data related to Ultimate Strength Design( USD & AASHTO-LRFD-2004) : a) Concrete Ultimate Compressive Strength, f/c (Normal Concrete) b) Concrete Allowable Strength under Service Limit State (WSD) = 0.40f/c c) Modulus of Elasticity of Concrete, Ec = 0.043gc1.50f/c (AASHTO LRFD-5.4.2.4). d) Poisson's Ration = 0.63f/c = 0.63*21^(1/2), subject to cracking and considered to be neglected (AASHTO LRFD-5.4.2.5). e) Modulus of Rupture of Concrete, fr = 0.63f/c Mpa (AASHTO LRFD-5.4.2.6). f) Steel Ultimate strength, fy (60 Grade Steel) g) Steel Allowable Strength under Service Limit State (WSD) = 0.40fy h) Modulus of Elasticity of Reinforcement, Es for fy = 410 MPa

f/c fc Ec

21.00 8.40 23,855.62

MPa MPa MPa

2.89 fr fy fs ES

2.89

MPa

410.00 MPa 164.00 MPa 200000 MPa

iv) Permanent & Dead Load Multiplier Factors for Strength Limit State Design (USD) According to AASHTOLRFD-3.4.1 ; Table 3.4.1-1&2 : a) b) c) d) e)

Modular Ratio, n = Es/Ec  6 = 8.384 Value of Ratio of Steel & Concrete Flexural Strength, r = fs/fc Value of k = n/(n + r) Value of j = 1 - k/3 Value of R = 0.5*(fckj)

Let

n r k j R

8 19.524 0.291 0.903 1.102

v) Sub-soil Investigation Report & Side Codition Data: a) SPT Value as per Soil Boring Test Report, / b) Corrected SPT Value for N>15, N = 15 + 1/2(N - 15) = 15 + 1/2(50 - 15) = 15 + 1/2(50 - 15) = 32.5 . Say N/ = 33 c) Recommended Allowable Bearing Capacity of Soil as per Soil Investigation Report witht SPT Value 50 over, p = 7.2 Ton/ft2. = 770kN/m2

Page 34

N N/

50 Over 33

p

2 770 kN/m

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

d) For Back Filling with Clean fine sand, Silty or clayey fine to medium sand Angle of Friction with Concrete surface, d = 190 to 240, e) AASHTO-LRFD-3.11.5.3 ;Table 3.11.5.3-1. Recommended Co-efficient of Lateral Active Earth Pressure Ka-recom v) = 0.34 to 0.45 (AASHTO-LRFD-3.11.5.3 ;Table 3.11.5.3-1.) Provided Co-efficient of Active Earth Pressure is Average of, Ka-recom

d

Ka-recom Ka

19 to 24

0.34 to 0.45 0.395

vi) Permanent & Dead Load Multiplier Factors Under Strength Limit State (USD) : a) Dead Load Multiplier Factor for Structural Components & Attachments-DC Applicable to All Components Except Wearing Course & Utilities (Max. value of Table 3.4.1-2)

gDC

1.250

b) Dead Load Multiplier Factor for Wearing Course & Utilities- DW , (Max. value of Table 3.4.1-2)

gDW

1.500

c) Multiplier Factor for Horizontal Active Earth Pressure on Substructure Components of Bridge-EH ; Applicable to Abutment & Wing Walls, (Max. value of Table 3.4.1-2)

gEH

1.500

d) Multiplier Factor for Vertical Earth Pressure on Substructure Components of Bridge-EV ; Applicable toAbutment & Wing Walls, (Max. value of Table 3.4.1-2)

gEV

1.350

e) Multiplier Factor for Surchage Pressure on Substructure Components of Bridge-ES ; Horizontal & Vertical Loads on Abutment & Wing Walls, (Max. value of Table 3.4.1-2)

gES

1.500

m

1.000

gLL-Truck

1.750

IM

1.330

d) Multiplier Factor for Lane Loading-LL-Lane

gLL-Lane

1.750

e) Multiplier Factor for Pedestrian Loading-PL.

gLL-PL.

1.750

f) Multiplier Factor for Vehicular Centrifugal Force-CE

gLL-CE.

1.750

g) Multiplier Factor for Vhecular Breaking Force-BR .

gLL-BR.

1.750

h) Multiplier Factor for Live Load Surcharge-LS

gLL-LS.

1.750

gLL-WA.

1.000

gLL-WS.

1.400

vii) Live Load Multiplier Factors : a) Multiplier Factor for Multiple Presence of Live Load ( No of Lane = 2)-m (ASSHTO LRFD-3.6.1.1.1) b) Multiplier Factor for Truck Loading (HS20 only)-LL-Truck . c) Multiplier Factor for Vhecular Dynamic Load Allowence-IM as per Provision of ASSHTO LRFD-3.6.2.1, Table 3.6.2.1-1; (Applicable only for Truck Loading & Tandem Loading)

i) Multiplier Factor for Water Load & Stream Pressure-WA j) Multiplier Factor for Wind Load on Structure-WS

STRENGTH - III

Page 35

O

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

gLL-WL

1.000

gLL-FR.

1.000

gLL-TU.

1.000

gLL-CR.

1.000

n) Multiplier Factor for deformation due to Shrinkage of Concrete-SH (With Elastomeric Bearing).

gLL-SH.

1.000

o) Multiplier Factor for Temperature Gradient-TG (With Elastomeric Bearing).

gLL-TG.

1.000

p) Multiplier Factor for Settlement of Concrete-SE (With Elastomeric Bearing).

gLL-SE.

1.000

q) Multiplier Factor for Earthquake -EQ

gLL-EQ.

-

r) Multiplier Factor for Vehicular Collision Force-CT

gLL-CT.

-

t) Multiplier Factor for Vessel Collision Force-CV

gLL-CV.

1.000

l) Multiplier Factor for Wind Load on Live Load-WL

STRENGTH - V

k) Multiplier Factor for Water Load & Stream Pressure-FR l) Multiplier Factor for deformation due to Uniform Temperature Change -TU (With Elastomeric Bearing). m) Multiplier Factor for deformation due to Creep on Concrete-CR (With Elastomeric Bearing).

vii) Permanent & Dead Load Multiplier Factors for Service Limit State Design (WSD) According to AASHTOLRFD-3.4.1 ; Table 3.4.1-1&2 : a) Dead Load Multiplier Factor for Structural Components & Attachments-DC Applicable to All Components Except Wearing Course & Utilities (Max. value of Table 3.4.1-2)

gDC

1.000

b) Dead Load Multiplier Factor for Wearing Course & Utilities- DW , (Max. value of Table 3.4.1-2)

gDW

1.000

c) Multiplier Factor for Horizontal Active Earth Pressure on Substructure Components of Bridge-EH ; Applicable to Abutment & Wing Walls, (Max. value of Table 3.4.1-2)

gEH

1.000

d) Multiplier Factor for Vertical Earth Pressure on Substructure Components of Bridge-EV ; Applicable toAbutment & Wing Walls, (Max. value of Table 3.4.1-2)

gEV

1.000

e) Multiplier Factor for Surchage Pressure on Substructure Components of Bridge-ES ; Horizontal & Vertical Loads on Abutment & Wing Walls, (Max. value of Table 3.4.1-2)

gES

1.000

ii) Live Load Multiplier Factors for Service Limit State Design (WSD) According to AASHTO-LRFD-3.4.1; Table 3.4.1-1&2 :

Page 36

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

a) Multiplier Factor for Multiple Presence of Live Load ( No of Lane = 2)-m (ASSHTO LRFD-3.6.1.1.1)

m

1.000

gLL-Truck

1.000

IM

1.300

d) Multiplier Factor for Lane Loading-LL-Lane

gLL-Lane

1.000

e) Multiplier Factor for Pedestrian Loading-PL.

gLL-PL.

1.000

b) Multiplier Factor for Truck Loading (HS20 only)-LL-Truck . c) Multiplier Factor for Vhecular Dynamic Load Allowence-IM as per Provision of ASSHTO LRFD-3.6.2.1, Table 3.6.2.1-1 ; SERVICE - II (Applicable only for Truck Loading & Tandem Loading)

f) Multiplier Factor for Vehicular Centrifugal Force-CE

SERVICE - II

gLL-CE.

1.300

g) Multiplier Factor for Vhecular Breaking Force-BR .

SERVICE - II

gLL-BR.

1.300

gLL-LS.

1.000

gLL-WA.

1.000

h) Multiplier Factor for Live Load Surcharge-LS i) Multiplier Factor for Water Load & Stream Pressure-WA j) Multiplier Factor for Wind Load on Structure-WS

SERVICE - IV

gLL-WS.

0.700

l) Multiplier Factor for Wind Load on Live Load-WL

SERVICE - II

gLL-WL

1.300

gLL-FR.

1.000

gLL-TU.

1.000

gLL-CR.

1.000

n) Multiplier Factor for deformation due to Shrinkage of Concrete-SH (With Elastomeric Bearing).

gLL-SH.

1.000

o) Multiplier Factor for Temperature Gradient-TG (With Elastomeric Bearing).

gLL-TG.

1.000

p) Multiplier Factor for Settlement of Concrete-SE (With Elastomeric Bearing).

gLL-SE.

1.000

q) Multiplier Factor for Earthquake -EQ

gLL-EQ.

-

r) Multiplier Factor for Vehicular Collision Force-CT

gLL-CT.

-

t) Multiplier Factor for Vessel Collision Force-CV

gLL-CV.

1.000

k) Multiplier Factor for Water Load & Stream Pressure-FR l) Multiplier Factor for deformation due to Uniform Temperature Change -TU (With Elastomeric Bearing). m) Multiplier Factor for deformation due to Creep on Concrete-CR (With Elastomeric Bearing).

5225

Page 37

300

3 Sketch Diagram of Abutment & Wing wall:

5225

12750 3000 600

3450

600 C 2000

RL-5.00m

A

2750

2150

2525

600 450

300 1900

1500

750

2525 1200

1775

1200

3000

RL-2.20m

450

1447

2750

600 2150

1775 450

3000

3450

9350

6350

2450

450

3450 450

5500

450 300

B

10250

C

600

4300

600

5500

4 Dimension of Different Sub-Structural Components & RCC Well for Foundation: i) Dimensions of Sub-Structure. a) Height of Abutment Wall from Bottom of Well Cap up to Top of Back Wall,

H

6.147 m

b) Height of Abutment Wall from Top of Well Cap up to Top of Back Wall,

H1

4.947 m

hWell-Cap.

1.200 m

hSteam.

1.900 m

hGir.

2.000 m

hBearing

0.147 m

hb-wall

2.147 m

H-W-Wall

4.947 m

c) Height of Abutment Well Cap, d) Height of Abutment Steam e) Depth of Girder including Deck Slab f) Height of Bearing Seat g) Height of Back Wall = hGir. + hBearing h) Height of Wing Wall i) Length of Wing Walls upon Well cap

LW-W-Well-Cap

Page 38

2.975 m

H = 6147

3450

H1 = 4947

600

700

2100

2147

3450

600

600

300

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

j) Width (Longitudinal Length) of Abutment Well Cap, Length (Transverse Length) of Abutment Well Cap,

WAb-Cap

5.500

m

LAb-T-W-Cap

12.750 m

LAB-Trans.

10.250 m

LWW-T-Inner

9.350 m

n) Thickness of Abutment Wall (Stem) at Bottom

t.-Ab-wal-Bot.

0.750

o) Thickness of Abutment Wall (Stem) at Top

t.-Ab-wal-Top.

0.450 m

p) Thickness of Counterfort Wall (For Wing Wall)

tWW-Countf.

0.450 m

q) Number of Wing-Wall Counterforts (on each side)

NW-W-count

1.000 No's

k) Transverse Length of Abutment Wall (Outer Face to Outer Face) in X-X l) Direction. m) Inner Distance in between Wing Walls (Transverse),

r) Clear Spacing between Counerfort & Abutment Wall at Bottom

m

SClear-Count& Ab-Bot.

1.775 m

SAver-Count&Ab.

2.375 m

SEfft-Count.

2.825 m

t-Wing-wall

0.450 m

v) Thickness of Cantilever Wing Walls

tw-wall-Cant.

0.450 m

w) Length of Cantilever Wing Walls

Lw-wall-Cant.

3.000 m

hw-wall-Cant.-Rec.

2.000 m

hw-wall-Cant.-Tri.

1.500 m

L-W-Cap-Toe.

2.525 m

L-W-Cap-Heel-Aver.

2.825 m

a) Width of Well in Y-Y Direction (In Longitudinal Direction)

WWell-Y-Y

5.500 m

b) Length of Well in X-X Direction (In Transverse Direction)

LWell-X-X

12.750 m

c) Depth of Well from Bottom of Well Cap up to Bottom of Well Curb

HWell-pro.

6.325 m

s) Average Spacing between Counerfort & Abutment Wall = (tAB-Wall-Bot + tAb-Wall-Top)/2+SClear-Count& Ab-Bot. t) Effective Span of Wing Wall Counterfort = SAver-Count + tWW-Countf u) Thickness of Wing Walls within Well Cap,

x) Height of Rectangular Portion of Cantilever Wing Walls y) Height of Triangular Portion of Cantilever Wing Walls z) Longitudinal Length of Well Cap on Toe Side from Abutment Wall Outer Face. z-i) Average Length (Longitudinal) of Well Cap on Heel Side from Abutment Wall Face.= SAver.-Count.& Ab. + tWW-Count. ii) Dimensions of RCC Well for Foundation.

Page 39

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

d) Wall thickness of Well,

tWall.

0.600 m

tWall-Perti

0.600 m

g) Diameter of Outer Circle,

DOuter.

5.500 m

h) Diameter of Inner Circle = DOuter - 2* tWall

DInner.

4.300 m

i) Transverse Length of Rectangular Portion of Well Cap =LWell-X-X - DOuter

LRect.

7.250 m

j) Length of Partition Walls = DOuter - 2*tWall

LParti.

4.300 m

k) Number of Pockets within Well

NPock.

3.000 Nos

f) Thickness of Partition Walls of Well,

l) Distance between Inner Faces of Pockets in Y-Y Direction (Longitudinal Span Length).

SPock-Y-Y.

4.300 m

m) Distance between Inner Faces of Outer Pockets in X-X Direction (Transverse Span Length).

SPock-X-X-Outer.

3.450 m

n) Distance between Inner Faces of Central Pocket in X-X Direction (Transverse Span Length).

SPocket-X-X-Central.

3.450 m

W1/2-Well-Y-Y

2.750 m

o) Width of Well from its c.g. Line in X-X. = WWell-Y-Y/2

2 63.633 m

p) Surface Area of Well at Top & Bottom Level = pDOuter2/4 + LRect*DOuter

AWell.

q) Total Length of Staining of Well (Main & Partitions) through Center line = p*(DOuter+ DInner)/2 + 2*LRect. + 2*LParti

LStaining.

38.494 m

r) Surface Area of Well Cap = LAb-T-W-Cap*W1/2-Well-Y-Y + 0.5*pDOuter2/4 + LRect*W1/2-Well-Y-Y

AWell-Cap.

2 66.879 m

s) Distance of c.g. (X-X) Line from Well Cap Toe Face = (LAb-T-W-Cap*(W1/2-Well-Y-Y)2*1.50+ (0.5*pDOuter2/4)*0.50*DOuter*3/4 + LRect*W1/2-Well-Y-Y2/2)/AWell-Cap.

bc.g.-Y-Y.

2.939 m

t) RL of Highest Flood Level (HFL)

HFLRL

2.100 m

u) RL of Maximum Scoring Level (MSL)

MSLRL

(4.750) m

5 Calculations for Safe Bearing Capacity (S.B.C.) of Soil for Well (Caisson) as Abutment Foundation . a) Height between RL of HFL & RL of MSL = HFLRL - MSLRL x = (2.100- (-)4.75)m

Page 40

h

6.850 m

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

b) Minimum Depth required for Bottom Level of Well from MSL= h/3

HWell-req

2.283 m

c) Provided Depth from Well Cap Bottom up to Bottom Level of Well

H-Well-pro.

6.325 m

d) Calculated Soil Bearing Capacity at Bottom Level of Well Foundation pCal = 3.5(N-3)*{(B+0.3)/2B}*a*b + W; Where N = 50 over, the Field SPT value;

pCal

2 164.811 kN/m

N/ = 33,the Corrected SPT value; f = 36.900, the Angle of Shearing Resistance of Soil; B =5.000m,Width of Well for Foundation; D = 6.250m, Depth of Well; a = 0.50, for Submerge of Well Bottom; b = (1+D/5B) > 1.20 = (1+6.25/5*5) = 1.2 and W = Soil Pressure per m2 at Bottom Level of Well = D*g = 6.250*18.00kN/m2 = 112.500kN/m2 Thus the Calculated Soil Bearing Capacity pCal = 3.5(N-3)*{(B+0.3)/2B}*a*b + W, = (3.5*(50-3)*((5.00+0.3)/(2*5))*0.50*1.20 + 112.500)kN/m 2 = 164.811kN/m2 e) Since the Soil Bearing Capacity as per Soil Investigation Report, Since the Soil Bearing Capacity as per Soil Investigation Report, p = 770kN/m2 > pCal = 164.811kN/m2, thusthe Well Foundation is OK in respect of S.B.C. 6 Checking for Stability of Well Cap as Abutment Base against all applied Forces: i) Imposed Vertical Loads/Forces upon Abutment Well Cap (As per Design Calculation Sheet - C) : a) Dead Load Reaction from Super-Structure

RDL-Supr.

2,185.716 kN

b) Live Load Reaction from Super-Structure (Pedestrians, Wheel & Lane Load)

RLL-Supr.

1,108.714 kN

c) Dead Load Reaction from Sub-Structure & Earth Pressure,

RDL-Sub.

5,729.857 kN

PV

9,024.287 kN

d) Total Vertical Forces due to Dead & Live Load (Super-Structure + Sub-Structure) e) Moment due to Dead Load Reaction from Super-Structure

MDL-Supr.

6,010.718 kN-m

f) Moment due to Live Load Reaction from Super-Structure

MLL-Supr.

3,048.964 kN-m

g) Moment due to Dead Load & Soil Pressure for Sub-Structure

MDL-Sub.

20,064.375 kN-m

MR

29,124.057 kN-m

h) Total Resisting Moment due to Vertical Forces (Dead & Live Load from Super-Structure + Sub-Structure, Earth Pressure) i) Total Horizontal Forces due to Earth Pressure, Surcharge, Braking, WindLoad, Dead Load Friction etc.

PH

2,466.234 kN

j) Total Overturning Moments due to Horizontal Forces

MO

6,510.878 kN-m

ii) Checking Against Overturning.

Page 41

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

a) Factor of Safety against Overturning, FSOverturn = MR/MO  2.

FSOverturn

4.473

OK

FSSlid

1.464

Not OK

b) Since FSO > 2 , thus the Structure is safe in respect of Overturning. iii) Checking Against Sliding. a) Factor of Safety against Sliding, FSSlid = 0.4*PV / PH  1.50. b) Since FSSlid > 1.50, thus the Structure is safe in respect of Sliding. iv) Calculation of Eccentricity in respect of c.g. Line of Pile Cap in X-X Direction due to Applied Loads & Moments ( Vertical & Horizontal): a) Net Moment or Algebraic sum of Moment about 'B' = MR - MO b) Distance of Resultant Forces from Well Cap Toe Face, x = MN /PV c) Distance of c.g. (X-X) Line from Well Cap Toe Face d) Eccentricity, e = bc.g.-Y-Y. - x e) 1/6th Distance of bc.g.-Y-Y. from c.g. towards Well Wall Cap Toe = bc.g.-Y-Y./6

MN

22,613.179 kN-m

x

2.506 m

bc.g.-Y-Y.

2.939 m

e

0.433 m

1/6th

0.490 m

f) Since the Calculated Eccentricity has (+) ve value & its Location is within Middle 1/3rd Portion of the Pile Cap in Y-Y direction, Factor of Safety against Overturning & Sliding are within limit range, Thus the Structure is a Stable One in all respect. 7 Checking for Stability of Well Cap as Abutment Base Without Superstrucre Loads (DL & LL) : i) Applied Loads Moments : a) Dead Load Reaction from Sub-Structure & Earth Pressure,

RDL-Sub.

b) Moment due to Dead Load & Soil Pressure for Sub-Structure

MDL-Sub.

5,729.857 kN 20,064.375 kN-m

c) Total Horizontal Forces due to Earth Pressure, Surcharge & Wind Load on Substructure.

PH

2,220.297 kN

d) Total Overturning Moments due to Horizontal Forces

MO

4,831.474 kN-m

ii) Checking Against Overturning. a) Factor of Safety against Overturning, FSOverturn = MR/MO  2.

FSOverturn

4.153

FSSlid

1.032

b) Since FSOvertur > 2 , thus the Structure is safe in respect of Overturning. iii) Checking Against Sliding. a) Factor of Safety against Sliding, FSSlid = 0.4*PV / PH  1.50.

Page 42

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

b) Though FSSlid < 1.50, but the Well Cap would be a Integrated Component of the RCC Well, which will make the Structure a Safe one in respect of Sliding. iv) Calculation of Eccentricity in respect of c.g. Line of Pile Cap in X-X Direction due to Applied Loads & Moments ( Vertical & Horizontal): a) Net Moment or Algebraic sum of Moment about 'B' = MR - MO b) Distance of Resultant Forces from Well Cap Toe Face, x = MN /PV c) Distance of c.g. (X-X) Line from Well Cap Toe Face d) Eccentricity, e = bc.g.-Y-Y. - x e) 1/6th Distance of bc.g.-Y-Y. from c.g. towards Well Wall Cap Toe = bc.g.-Y-Y./6

MN

14,334.518 kN-m

x

2.502 m

bc.g.-Y-Y.

2.939 m

e

0.437 m

1/6th

0.490 m

f) The Calculated Eccentricity has (+) ve value & its Location is within Middle 1/3rd Portion of the Well Cap in Y-Y direction, Factor of Safety against Overturning is within limit range, though Safety Factor against Sliding is less than limit range but the Well Cap is Integrated with RCC Well Structure, thus the Structure is a Stable One in all respect without Superstructure Loads also.

Page 43

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 44

D. Design Data, Factors & Methods for Analysis of Flexural Design of Structural Elements: 1 General Data for Construction Materials of Different Structural Components : Description 3 i) Unit Weight of Different Materials in kg/m : (Having value of Gravitional Acceleration, g =

a) b) c) d) e)

Notation Dimensions

Unit.

2 9.807 m/sec )

gW-Nor. gW-Sali. gs

2,447.232 2,345.264 1,019.680 1,045.172 1,835.424

kg/m3 kg/m3 kg/m3 kg/m3 kg/m3

wc wWC wW-Nor. wW-Sali. wE

24.000 23.000 10.000 10.250 18.000

kN/m3 kN/m3 kN/m3 kN/m3 kN/m3

gc gWC

Unit weight of Normal Concrete Unit weight of Wearing Course Unit weight of Normal Water Unit weight of Saline Water Unit weight of Earth (Compected Clay/Sand/Silt)

3 ii) Unit Weight of Different Materials in kN/m :

a) b) c) d) e)

Unit weight of Normal Concrete Unit weight of Wearing Course Unit weight of Normal Water Unit weight of Saline Water Unit weight of Earth (Compected Clay/Sand/Silt)

iii) Strength Data related to Ultimate Strength Design( USD & AASHTO-LRFD-2004) : a) Concrete Ultimate Compressive Strength, f/c (Normal Concrete) b) Concrete Allowable Strength under Service Limit State (WSD) = 0.40f/c c) Modulus of Elasticity of Concrete, Ec = 0.043gc1.50f/c (AASHTO LRFD-5.4.2.4). d) Poisson's Ration = 0.63f/c = 0.63*21^(1/2), subject to cracking and considered to be neglected (AASHTO LRFD-5.4.2.5). e) Modulus of Rupture of Concrete, fr = 0.63f/c = 0.63*21^(1/2)Mpa (AASHTO LRFD-5.4.2.6). f) Steel Ultimate strength, fy (60 Grade Steel) g) Steel Allowable Strength under Service Limit State (WSD) = 0.40fy h) Modulus of Elasticity of Reinforcement, Es for fy = 410 MPa

f/c fc Ec

21.000 8.400 23,855.620 2.887

fr fy fs ES

2.887

Modular Ratio, n = Es/Ec  6 = 8.384 Value of Ratio of Steel & Concrete Flexural Strength, r = fs/fc Value of k = n/(n + r) Value of j = 1 - k/3 Value of R = 0.5*(fckj)

Say

n r k j R

MPa

410.000 MPa 164.000 MPa 200000.000 MPa

iv) Strength Data related to Working Stress Design & Service Load Condition ( WSD & AASHTO-SLS ) : a) b) c) d) e)

MPa MPa MPa

8 19.524 0.291 0.903 1.102

v) Design Data for Resistance Factors for Conventional Construction (AASHTO LRFD-5.5.4.2.1). :

(Respective Resistance Factors are mentioned as f ) a) b) c) d)

e) f) g) h) i) j)

For Flexural & Tension in Reinforced Concrete fFlx-Rin. 0.90 For Flexural & Tension in Prestressed Concrete fFlx-Pres. 1.00 For Shear & Torsion of Normal Concrete fShear. 0.90 For Axil Comression with Spirals or Ties & Seismic Zones at Extreme fSpir/Tie/Seim. 0.75 Limit State (Zone 3 & 4). Flexural value of f of Compression Member will Increase Linearly as the Factored Axil Load Resitance, fPn, Decreases from 0.10f/cAg to 0. For Bearing on Concrete fBearig. 0.70 For Compression in Strut-and-Tie Modeis fStrut&Tie. 0.70 For Compression in Anchorage Zones with Normal Concrete fAnc-Copm-Conc. 0.80 For Tension in Steel in Anchorage Zones fAnc-Ten-Steel. 1.00 For resistance during Pile Driving fPile-Resistanc. 1.00 For Partially Prestressed Components in Flexural with or without Tension fFlx-PPR. 1.00 Resistance Factor f = 0.90 + 0.10*(PPR) in which, PPR = Apsfpy/(Apsfpy + Asfy), where; PPR is Partial Prestress Retio. PPR 2 As = Steel Area of Nonprestressing Tinsion Reinforcement in mm As 2 Aps = Steel Area of Prestressing Steel mm Aps fy = Yeiled Strength of Nonprestressing Bar in MPa. fy 410.00 fpy = Yeiled Strength of Prestressing Steel in MPa. fpy

mm2 mm2 N/mm2 N/mm2

vi) b Factors for Conventional RCC & Prestressed Concrete Design (AASHTO LRFD-5.7.2.2). : a) Flexural value of b1, the Factor of Compression Block in Reinforced Concrete up to 28 MPa. i) For Further increases of Strength of Concrete after 28 MPa agaunst each 7MPa the value of b1 will decrese by 0.05 & the Minimum Value of b1 will be 0.65.

b1

0.85

b

0.85

ii) For Composite Concrete Structure, b1avg = Σ(f/cAccb1)/Σ(f/cAcc); where, Acc =Area of Concrete Element in Compression of Crresponding Strength. b) Value of b for Flexural Tension of Reinforcement in Concrete

vii) Ultimate Strength Data for Design of Prestressing Components ( USD & AASHTO-LRFD-2004) : a) For Uncoated & Stress-relieved 7 (Seven) Wire according to AASHTO-LRFD Bridge Construction Specifications (AASHTO-LRFD-5.4.4) will be; i) AASHTO M 203/M 203M (ASTM A 416/A 416M), or ii) AASHTO M 275/M 275M (ASTM A 722/A 722M). b) Tensial Strength for Strand with Grade 250 having Diameter 6.35 to 15.24mm,

fpu-250-Str.

1,725 Mpa

c) Tensial Strength for Strand with Grade 270 having Diameter 9.37 to 15.24mm,

fpu-270-Str.

1,860 Mpa

d) Tensial Strength for Type-1 Plain Bar having Diameter 19 to 35mm,

fpu-Ty-1-P-Bar

1,035 Mpa

e) Tensial Strength for Type-2 Deformed Bar having Diameter 16 to 35mm,

fpu-Ty-1-P-Bar

1,035 Mpa

f) Yield Strength for Strand with Grade 250 having Diameter 6.35 to 15.24mm, = 85% of Tensial Strength (fpu).

fpy-250-Str.

1,466 Mpa

g) Yield Strength for Strand with Grade 270 having Diameter 9.37 to 15.24mm, = 85% of Tensial Strength (fpu).

fpy-270-Str.

1,581 Mpa

h) Yield Strength for Type-1 Plain Bar having Diameter 19 to 35mm, = 85% of Tensial Strength (fpu). i) Yield Strength for Type-2 Deformed Bar having Diameter 16 to 35mm, = 80% of Tensial Strength (fpu). j) Modulus of Elastacity for Strand j) Modulus of Elastacity for Bar

fpy-Ty-1-P-Bar

880 Mpa

fpy-Ty-1-P-Bar

828 Mpa

Ep-Strandy

197,000 MPa

Ep-Bar

207,000 MPa

2 Different Load Multiplying Fatcors for Strength Limit State Design (USD) & Load Combination : i) Formula for Load Factors & Selection of Load Combination : a) Formula for Load Factors Q = Σ ηigiQi  f Rn = Rr; (ASSHTO LRFD-1.3.2.1-1 & 3.4.1-1) Where, ηi is Load Modifier having values ηi = ηD ηR ηI  0.95 in which for Loads a Maximum value of gi Applicable; (ASSHTO LRFD-1.3.2.1-2), & ηi = 1/(ηD ηR ηI )  1.00 in which for Loads a Minimum value of gi Allpicable; (ASSHTO LRFD-1.3.2.1-3) Here: gi = Load Factor; a statistically based multiplier Applied to Force Effect, f = Resistance Factor; a statistically based multiplier Applied to Nominal Resitance, ηi = Load Modifier; a Factor related to Ductility, Redundancy and Operational Functions, For Strength Limit State; ηD ηi = ηD = 1.00 for Conventional Design related to Ductility, 1.000 ηR ηi = ηR = 1.00 for Conventional Levels of Redundancy , 1.000 ηi = ηI = 1.00 for Typical Bridges related to Operational Functions,

ηl

1.000

Qi = Force Effect, Rn = Nominal Resitance, Ri = Factored Resitance = fRn. ii) Permanent & Dead Load Multiplier Factors for Strength Limit State Design (USD) According to AASHTOLRFD-3.4.1 ; Table 3.4.1-1&2 : a) Dead Load Multiplier Factor for Structural Components & Attachments-DC Applicable to All Components Except Wearing Course & Utilities (Max. value of Table 3.4.1-2)

gDC

1.250

b) Dead Load Multiplier Factor for Wearing Course & Utilities- DW , (Max. value of Table 3.4.1-2)

gDW

1.500

c) Multiplier Factor for Horizontal Active Earth Pressure on Substructure Components of Bridge-EH ; Applicable to Abutment & Wing Walls, (Max. value of Table 3.4.1-2)

gEH

1.500

d) Multiplier Factor for Vertical Earth Pressure on Substructure Components of Bridge-EV ; Applicable toAbutment & Wing Walls, (Max. value of Table 3.4.1-2)

gEV

1.350

e) Multiplier Factor for Surchage Pressure on Substructure Components of Bridge-ES ; Horizontal & Vertical Loads on Abutment & Wing Walls, (Max. value of Table 3.4.1-2)

gES

1.500

iii) Live Load Multiplier Factors for Strength Limit State Design (USD) According to AASHTO-LRFD-3.4.1; Table 3.4.1-1&2 : a) Multiplier Factor for Multiple Presence of Live Load ( No of Lane = 2)-m (ASSHTO LRFD-3.6.1.1.1)

m

1.000

gLL-Truck

1.750

IM

1.330

d) Multiplier Factor for Lane Loading-LL-Lane

gLL-Lane

1.750

e) Multiplier Factor for Pedestrian Loading-PL.

gLL-PL.

1.750

f) Multiplier Factor for Vehicular Centrifugal Force-CE

gLL-CE.

1.750

g) Multiplier Factor for Vhecular Breaking Force-BR .

gLL-BR.

1.750

h) Multiplier Factor for Live Load Surcharge-LS

gLL-LS.

1.750

gLL-WA.

1.000

b) Multiplier Factor for Truck Loading (HS20 only)-LL-Truck . c) Multiplier Factor for Vhecular Dynamic Load Allowence-IM as per Provision of ASSHTO LRFD-3.6.2.1, Table 3.6.2.1-1; (Applicable only for Truck Loading & Tandem Loading)

i) Multiplier Factor for Water Load & Stream Pressure-WA j) Multiplier Factor for Wind Load on Structure-WS

STRENGTH - III

gLL-WS.

1.400

l) Multiplier Factor for Wind Load on Live Load-WL

STRENGTH - V

gLL-WL

1.000

gLL-FR.

1.000

gLL-TU.

1.000

gLL-CR.

1.000

gLL-SH.

1.000

k) Multiplier Factor for Water Load & Stream Pressure-FR l) Multiplier Factor for deformation due to Uniform Temperature Change -TU (With Elastomeric Bearing). m) Multiplier Factor for deformation due to Creep on Concrete-CR (With Elastomeric Bearing). n) Multiplier Factor for deformation due to Shrinkage of Concrete-SH

(With Elastomeric Bearing). o) Multiplier Factor for Temperature Gradient-TG (With Elastomeric Bearing).

gLL-TG.

1.000

p) Multiplier Factor for Settlement of Concrete-SE (With Elastomeric Bearing).

gLL-SE.

1.000

q) Multiplier Factor for Earthquake -EQ

gLL-EQ.

-

r) Multiplier Factor for Vehicular Collision Force-CT

gLL-CT.

-

t) Multiplier Factor for Vessel Collision Force-CV

gLL-CV.

1.000

3 Different Load Multiplying Fatcors for Service Limit State Design (WSD) & Load Combination : i) Permanent & Dead Load Multiplier Factors for Service Limit State Design (WSD) According to AASHTOLRFD-3.4.1 ; Table 3.4.1-1&2 : a) Dead Load Multiplier Factor for Structural Components & Attachments-DC Applicable to All Components Except Wearing Course & Utilities (Max. value of Table 3.4.1-2)

gDC

1.000

b) Dead Load Multiplier Factor for Wearing Course & Utilities- DW , (Max. value of Table 3.4.1-2)

gDW

1.000

c) Multiplier Factor for Horizontal Active Earth Pressure on Substructure Components of Bridge-EH ; Applicable to Abutment & Wing Walls, (Max. value of Table 3.4.1-2)

gEH

1.000

d) Multiplier Factor for Vertical Earth Pressure on Substructure Components of Bridge-EV ; Applicable toAbutment & Wing Walls, (Max. value of Table 3.4.1-2)

gEV

1.000

e) Multiplier Factor for Surchage Pressure on Substructure Components of Bridge-ES ; Horizontal & Vertical Loads on Abutment & Wing Walls, (Max. value of Table 3.4.1-2)

gES

1.000

ii) Live Load Multiplier Factors for Service Limit State Design (WSD) According to AASHTO-LRFD-3.4.1; Table 3.4.1-1&2 : a) Multiplier Factor for Multiple Presence of Live Load ( No of Lane = 2)-m (ASSHTO LRFD-3.6.1.1.1) b) Multiplier Factor for Truck Loading (HS20 only)-LL-Truck . c) Multiplier Factor for Vhecular Dynamic Load Allowence-IM as per Provision of ASSHTO LRFD-3.6.2.1, Table 3.6.2.1-1 (SERVICE - I); (Applicable only for Truck Loading & Tandem Loading)

m

1.000

gLL-Truck

1.000

IM

1.000

d) Multiplier Factor for Lane Loading-LL-Lane

gLL-Lane

1.000

e) Multiplier Factor for Pedestrian Loading-PL.

gLL-PL.

1.000

f) Multiplier Factor for Vehicular Centrifugal Force-CE

SERVICE - II

gLL-CE.

1.300

g) Multiplier Factor for Vhecular Breaking Force-BR .

SERVICE - II

gLL-BR.

1.300

gLL-LS.

1.000

gLL-WA.

1.000

h) Multiplier Factor for Live Load Surcharge-LS i) Multiplier Factor for Water Load & Stream Pressure-WA j) Multiplier Factor for Wind Load on Structure-WS

SERVICE - IV

gLL-WS.

0.700

l) Multiplier Factor for Wind Load on Live Load-WL

SERVICE - II

gLL-WL

1.300

gLL-FR.

1.000

gLL-TU.

1.000

gLL-CR.

1.000

n) Multiplier Factor for deformation due to Shrinkage of Concrete-SH (With Elastomeric Bearing).

gLL-SH.

1.000

o) Multiplier Factor for Temperature Gradient-TG (With Elastomeric Bearing).

gLL-TG.

1.000

p) Multiplier Factor for Settlement of Concrete-SE (With Elastomeric Bearing).

gLL-SE.

1.000

q) Multiplier Factor for Earthquake -EQ

gLL-EQ.

-

r) Multiplier Factor for Vehicular Collision Force-CT

gLL-CT.

-

t) Multiplier Factor for Vessel Collision Force-CV

gLL-CV.

1.000

a) Coefficient of Active Horizontal Earth Pressure, ko = (1-sinff ) ,Where; f is Effective Friction Angle of Soil

ko

0.441

b) For Back Filling with Clean fine sand, Silty or clayey fine to medium sand

f

34.000

k) Multiplier Factor for Water Load & Stream Pressure-FR l) Multiplier Factor for deformation due to Uniform Temperature Change -TU (With Elastomeric Bearing). m) Multiplier Factor for deformation due to Creep on Concrete-CR (With Elastomeric Bearing).

3 Intensity of Different Imposed Loads (DL & LL) & Load Coefficients : i) Coefficient for Lateral Earth Pressure (EH) :

O

Effective Friction Angle of Soil, f = 340 .(Table 12.9, Page-138, RAINA,s Book) c) Angle of Friction with Concrete surface & Soli AASHTO-LRFD-3.11.5.3 ;Table 3.11.5.3-1. d) Value of Tan d (dim) for Coefficient of Friction. = 0.34 to 0.45 (AASHTO-LRFD-3.11.5.3 ;Table 3.11.5.3-1.)

d

Tan d

19 to 24

O

0.34 to 0.45 dim

ii) Dead Load Surcharge Lateral/Horizontal Pressure Intensity (ES); AASHTO-LRFD-3.11.6.1. : a) Constant Horizontal Earth Pressur due to Uniform Surcharge, Dp-ES = ksqs in Mpa. Where; b) ks is Coefficien of Earth Pressure due to Surcharge = ko for Active Earth Pressure, c) qs is Uniform Surcharge applied to upper surface of Active Earth Wedge(Mpa) = wE*10-3N/mm2

Dp-ES

2 0.007935 N/mm 2 7.935 kN/m

ks

0.441

qS

2 0.018 N/mm

iii) Live Load Surcharge Vertical & Horizontal Pressure Intensity (LS); AASHTO-LRFD-3.11.6.4. : a) Constant Earth Pressur both Vertical & Horizontal for Live Load Surcharge on Abutment Wall (Perpendicular to Traffic), Where; Dp-LS = kgsgheq*10-9

b) Constant Horizontal Earth Pressur due to Live Load Surcharge for Wing Walls (Parallel to Traffic), Where; Dp-LS = kgsgheq*10-9 ,

c) d) e) f)

Dp-LL-Ab 1100 but < 4900; ts = 200 > 110 but < 300 ; L =24400 > 6000 but < 76000; Nb (Nos. of Girder) = 5 > 4 ).

gInt.-V

0.635

v) Distribution Factor Method for Analysis of Shear for Deck Overhanging under the Provisions of AASHTO -LRFD-4.6.2.2.3b : a) According to Article-4.6.2.2.3b in Concrete Bridges having Multi Lane with More than 4 Main Girders & Linked by Cross-Girders, the Live Load (Truck/Tandem) Shear for Deck Overhanging should be based upon the Distribution Factor as mentioned in Equation of Table- 4.6.2.2.3a-2. b) The Distribution Factor for Live Loads Per Lane for Shear on Deck Overhanging on face of Exterior Longitudinal Girder of Multi Lane RCC T-Girder Bridge is being Expressed by gExt-V = egInt-V ; where, c) e is Correction Factor having value = 0.60 + de/3000; Here ,

e

d) de is a Distance in mm from Exterior Face/Web of Exterior Girder up to the Interior Edge of Curb or Traffic Barrier = WEdge-to-Curb. - SCant. Since Position of Exterior Face/Web of Exterior Girder is within Inboard of Slab's Outer Edge-to-Curb, thus de is of (+) ve value.

de

e) Thus Calculated value of Distribution Factor for Overhanging gExt.= egInt-V (Having value of de = 575 > (-)300 but < 1700; ts = 200 > 110 but < 300 ; L =24400 > 6000 but < 76000; Nb (Nos. of Girder) = 5 > 4 ).

gExt.-V

0.775 525.000 mm

0.492

vi) Computation of Equivalent Strip Width for Live Load Moment for Interior Deck According to Provisions of AASHTO-LRFD-4.6.2.1.3 : a) According to Article - 4.6.2.1.3 in a Concrete Bridges having More than 4 Main Girders & Linked by Cross-Girders, the Live Load (Truck/Tandem) Moments for Interior Deck Spans should be Calculated in respect of the Strip Width as mentioned in Equation of Table- 4.6.2.1.3-1. b) For Cast in Place PC-Girder Concrete Bridge with Considered Strip Perpendicular to Traffic, Equivalent Strip Width for (+) ve Moment is being Expressed by the Equation, (+)XInt. = 660 + 0.55S in mm.& that for (-) ve Moment is being Expressed by the Equation, (-)XInt. = 1220 + 0.25S in mm. Here, c) S is Spacing of Supporting Components in mm (Here PC-Girders) = LC/C-Gir.

S

2,000.000 mm

d) Thus Equivalent Strip Width for (+) ve Moment

(+)XInt.

1,760.000 mm

e) Thus Equivalent Strip Width for (-) ve Moment

(-)XInt.

1,720.000 mm

vii) Computation of Equivalent Strip Width for Live Load Moment for Deck Overhanging under Provisions of AASHTO-LRFD-4.6.2.1.3 : a) Since the Provisions of Article-4.6.2.1.3 have Recommended to use Provisions of Article-3.6.1.3.4 for Applied Live Load & Calculation of respective Moments on Cantilever/Overhanging Portion of Deck Slab, thus Provisions of this Article is not Applicable.

12 Moment Arms for Calculation of Moments at Different Sections due to Applied Loads : i) Computation of Moment Arms for the Components Resting upon the Overhanging/Cantilever Deck Slab & Live Loads in Respect of Section 1-1 (On outer Face of Exterior Girder) : a) Moment Arm for Railing = LCant-Ext. -bRailing/2

LRailing

0.863 m

b) Moment Arm for Railing Post = LCant-Ext. - WPost-Trans./2

LR-Post

0.823 m

LR-Post-Base

0.813 m

d) Moment Arm for Sidewalk Slab = WSidewalk/2 - bGir-Main - LCurb-inner-Ext.

LS-walk

0.100 m

e) Moment Arm for Utility/Fluid Space = WFluid/2 - LCurb-Outer-Ext.

LUtility.

0.213 m

f) Moment Arm for Pedestrian Live Load = WSidewalk/2 - LCurb-Outer-Ext.

LPedes

0.375 m

LLine

0.700 m

c) Moment Arm for Raining Post Base = LCant-Ext. - bCurb/Guard./2

g) Moment Arm for Line Live Load = WSidewalk - LCurb-Outer-Ext. - 0.300

ii) Computation of Moment Arms for the Components Resting upon the Deck Slab on Inner Side of Exterior Girder & Live Loads in Respect of Section 2-2 (On Inner Face of Exterior Girder) : a) Moment Arm for Curb/Wheel Guard (Part) = LCurb-inner-Ext./2 b) Moment Arm for Pedestrian Live Load on Curb = LCurb-Inner-Ext. c) Moment Arm for Wearing Course & Lane Live Load on Deck in between Exterior Girder & 1st. Interior Girder = (SInter - LCurb-Inner-Ext.)/2 + LCurb-Inner-Ext.

LCurb

0.088 m

LPedes-Curb

0.088 m

LWC/Lane

0.913 m

13 Calculation of (-) Moments (DL & LL) of Overhanging Span at Section 1-1 (Exterior Girder Outer Face) Based Distribution Factor or Lever Rule under Provisions Strength Limit State (USD); AASHTO-LRFD-2004 : i) Since the Span is Overhanging/Cantilever, thus Moment value is of (-) ve in Nature. ii) Calculation of Factored Dead Load (DL) Moments for Overhanging/Cantilever Span at Section 1-1 (Outer Face of Exterior Girder) : 2 a) Moment due to Self Weight of Deck Slab = WDL-Self.-USD*(SCanti.) /2

MDL-Self-USD

2.708 kN-m/m

b) Moment due to Railing = WDL-Railing-USD*LRailing

MDL-Railing-USD

1.902 kN-m/m

c) Moment due to Railing Post = WDL-R-Post-USD*LR-Post

MDL-R-Post-USD

0.668 kN-m/m

MDL-R-Post-base-USD

2.011 kN-m/m

d) Moment due to Railing Post Base = WDL-R-Post-Base-USD*LR-Post-Base

e) Moment due to Curb/Wheel Guard, since it is Outboard of Overhanging thus calculation of Moment is not required.

f) Moment due to Sidewalk Slab = WDL-S-Walk.-USD*LS-Walk. g) Moment due to Utility = WDL-Utility.-USD*LUtility. h) Total Factored Dead Load (-) Moments at Section 1-1 for Overhanging.

MDL-S-Walk.-USD

0.225 kN-m/m

MDL-Utility.-USD

0.663 kN-m/m

(-)MDL-Total-1-1-USD

8.177 kN-m/m

iii) Calculation of Factored Live Load (LL) Moments for Overhanging/Cantilever Span at Section 1-1 (Outer Face of Exterior Girder) : a) Moment due to Pedestrian on Sidewalk = PLL-Pedst.-USD*WSidewalk*LPedes

MLL-Pedst-USD

5.513 kN-m/m

MLL-Line-USD

17.885 kN-m/m

(-) MLL-Total-1-1-USD

23.398 kN-m/m

iv) Calculated Total Factored (-)Moments at Section 1-1 due to (-) MDL+LL-1-1-USD Applied Loads (DL + LL) on Overhanging/Cantilever Span of Deck.

31.574 kN-m/m

b) Moment due to Line load on Sidewalk = PLL-Line.-USD*LLine c) Total Factored Live Load (-) Moments at Section 1-1 for Overhanging.

14 Calculation of (-) Moments (DL & LL) of Interior Span at Section 2-2 (Exterior Girder Inner Face) Based Distribution Factor or Lever Rule under Provisions Strength Limit State (USD); AASHTO-LRFD-2004 : i) For Continuous Span at Support Position Moment value is of (-) ve in Nature. ii) Calculation of Factored Dead Load (DL) Moments Interior Continuous Span at Section 2-2 (Inner Face of Exterior Girder) : 2 a) Moment due to Self Weight of Deck Slab = WDL-Self.-USD*(SInter.) /9

MDL-Self-USD

1.815 kN-m/m

b) Moment due to Wearing Course = WDL-WC.-USD*(SInter)2/9

MDL-WC-USD

0.783 kN-m/m

MDL-Curb.-USD

0.217 kN-m/m

(-)MDL-Total-2-2-USD

2.814 kN-m/m

c) Moment due to Curb/Wheel Guard Portion , = WDL-Curb.-USD*LCurb. d) Total Factored Dead Load (-) Moments at Section 2-2 for Interior Span.

iii) Calculation of Factored Live Load (DL) Moments Interior Continuous Span at Section 2-2 (Inner Face of Exterior Girder) : a) Moment due to Live Truck Wheel Load = PLL-Truck.-USD*gInt.-M

MLL-Truck-USD

82.849 kN-m/m

b) Moment due to Live Lane load on Sidewalk = PLL-Lane.-USD*(SInter.)2/9

MLL-Lane-USD

0.938 kN-m/m

(-)MLL-Total-2-2-USD

83.787 kN-m/m

(-)MDL+LL-2-2-USD

86.602 kN-m/m

c) Total Factored Live Load (-)Moments at Section 2-2 for Interior Span iv) Calculated Total Factored (-) Moments at Section 2-2 due to Applied Loads (DL + LL) on Interior Span of Deck.

15 Calculation of (+) Moments (DL & LL) of Interior Span at Section 3-3 (On Middle between Interior Girders) Based Distribution Factor or Lever Rule under Provisions Strength Limit State (USD); AASHTO-LRFD-2004 : i) For Continuous Span at Middle Position the Moment value is of (+) ve in Nature. ii) Calculation of Factored Dead Load (DL) Moments Interior Continuous Span at Section 3-3 (On Middle of Interior Girders) : 2 a) Moment due to Self Weight of Deck Slab = WDL-Self.-USD*(SInter.) /14

MDL-Self-USD

1.167 kN-m/m

b) Moment due to Wearing Course = WDL-WC.-USD*(SInter)2/14

MDL-WC-USD

0.503 kN-m/m

(+)MDL-Total-3-3-USD

1.670 kN-m/m

c) Total Factored Dead Load (+) Moments at Section 3-3 for Interior Span.

iii) Calculation of Factored Live Load (DL) Moments Interior Continuous Span at Section 3-3 (On Middle of Interior Girders) : a) Moment due to Live Truck Wheel Load = PLL-Truck.-USD*gInt.-M

MLL-Truck-USD

82.849 kN-m/m

b) Moment due to Live Lane load on Sidewalk = FPLL-Lane.-USD*(SInter.)2/9

MLL-Lane-USD

0.603 kN-m/m

c) Total Factored Live Load (+)Moments at Section 3-3 for Interior Span.

(+)MLL-Total-3-3-USD

83.452 kN-m/m

iv) Calculated Total Factored (+) Moments at Section 3-3 due to Applied Loads (DL + LL) on Interior Span of Deck.

(+)MDL+LL-3-3-USD

85.122 kN-m/m

16 Calculation of (-) Moments (DL & LL) of Interior Span at Section 4-4 (On Face of Interior Girder) Based Distribution Factor or Lever Rule under Provisions Strength Limit State (USD); AASHTO-LRFD-2004 : i) For Continuous Span at Support Position Moment value is of (-) ve in Nature. ii) Calculation of Factored Dead Load (DL) Moments Interior Continuous Span at Section 4-4(On Face of Interior Girder) : 2 a) Moment due to Self Weight of Deck Slab = WDL-Self-USD.*(SInter.) /9

MDL-Self-USD

1.815 kN-m/m

b) Moment due to Wearing Course = WDL-WC.-USD*(SInter)2/9

MDL-WC-USD

0.783 kN-m/m

(-)MDL-Total-4-4-USD

2.598 kN-m/m

c) Total Factored Dead Load (-) Moments at Section 4-4 for Interior Span.

iii) Calculation of Factored Live Load (DL) Moments Interior Continuous Span at Section 4-4 (Inner Face of Exterior Girder) : a) Moment due to Live Truck Wheel Load = PLL-Truck.-USD*gInt.-M

MLL-Truck-USD

82.849 kN-m/m

b) Moment due to Live Lane load on Sidewalk = PLL-Lane.-USD*(SInter.)2/9

MLL-Lane-USD

0.938 kN-m/m

c) Total Factored Live Load (-)Moments at Section 4-4 for Interior Span.

(-)MLL-Total-4-4-USD

83.787 kN-m/m

iv) Calculated Total Factored (-) Moments at Section 4-4 due to Applied Loads (DL + LL) on Interior Span of Deck.

(-)MDL+LL-4-4-USD

86.385 kN-m/m

17 Calculated Highest (-) ve Moment value for Distribution Factor Method under Strength Limit Stalt (USD): i) Section on Which Calculated (-) Moment is Highest; ii) The Calculated value of Highest (-) ve Moment

Section 2-2 is highest (-)MDL+LL-2-2-USD

86.602 kN-m/m

18 Selecton of Approprate (-) Moments & (+) Moments (DL+LL) for Flexural Design of Reinforcements of the Bridge Deck Slab from the Calculated Values of Approximate Method & Distribution Factor Method under Provisions of Strength Limit State (USD); AASHTO-LRFD-2004 : i) The Highest of Calculated (+) ve Moment Either Approximate Method or Distribution Factor Method. Distribution Factor Method Highest ii) The Highest of Calculated (-) ve Moment Either Approximate Method or Distribution Factor Method. Approximate Method Higer iii) The Calculated Values of Factored Moments according to Distribution Factor Methods for (+) ve Moments at Sections 3-3 & that for (-) ve Moments at Section 2-2 both are Heigher than the Calculated Factored Moments According to Provisions under Approximate Methods. Thus the Calculated Factored Moments According to Provisions of Distribution Factor Methods at Section 3-3 & 2-2 are the Governing Moments for Flexural Design of Deck Slab Reinforcements. iv) Total Factored Flexural Design (+) ve Moments (DL + LL) for Deck

(+)MDesign-USD

85.122 kN-m/m

v) Total Factored Flexural Design (-) ve Moments (DL + LL) for Deck

(-)MDesign-USD

87.014 kN-m/m

18 Calculation of (+) Moments (DL & LL) of Interior Span at Section 3-3 (On Middle between Interior Girders) Based Distribution Factor or Lever Rule under Provisions Service Limit State (WSD); AASHTO-LRFD-2004 : i) For Continuous Span at Middle Position the Moment value is of (+) ve in Nature. ii) Calculation of Factored Dead Load (DL) Moments Interior Continuous Span at Section 3-3 (On Middle of Interior Girders) : 2 a) Moment due to Self Weight of Deck Slab = WDL-Self.-WSD*(SInter.) /14

MDL-Self-WSD

0.933 kN-m/m

b) Moment due to Wearing Course = WDL-WC.-WSD*(SInter)2/14

MDL-WC-WSD

0.335 kN-m/m

(+)MDL-Total-3-3-WSD

1.269 kN-m/m

c) Total Factored Dead Load (+) Moments at Section 3-3 of Interior Span.

iii) Calculation of Factored Live Load (DL) Moments Interior Continuous Span at Section 3-3 (On Middle of Interior Girders) : a) Moment due to Live Truck Wheel Load = PLL-Truck.-WSD*gInt.-M

MLL-Truck-WSD

35.596 kN-m/m

b) Moment due to Live Lane load on Sidewalk = PLL-Lane.-WSD*(SInter.)2/9

MLL-Lane-WSD

0.603 kN-m/m

(+)MLL-Total-3-3-WSD

36.199 kN-m/m

(+)MSDL+LL-3-3-WSD

37.468 kN-m/m

c) Total Factored Live Load (+)Moments at Section 3-3 for Interior Span. iv) Calculated Total Factored (+) Moments at Section 3-3 due to Applied Loads (DL + LL) on Interior Span of Deck.

19 Calculation of (-) Moments (DL & LL) of Interior Span at Section 4-4 (On Face of Interior Girder) Based Distribution Factor or Lever Rule under Provisions Service Limit State (WSD); AASHTO-LRFD-2004 : i) For Continuous Span at Support Position Moment value is of (-) ve in Nature. ii) Calculation of Factored Dead Load (DL) Moments Interior Continuous Span at Section 4-4(On Face of Interior Girder) : 2 a) Moment due to Self Weight of Deck Slab = WDL-Self.-WSD*(SInter.) /9

MDL-Self-WSD

1.452 kN-m/m

b) Moment due to Wearing Course = WDL-WC.*(SInter)2/9

MDL-WC-WSD

0.522 kN-m/m

(-)MDL-Total-2-2-WSD

1.974 kN-m/m

c) Total Factored Dead Load (-) Moments at Section 4-4 for Interior Span

iii) Calculation of Factored Live Load (DL) Moments Interior Continuous Span at Section 4-4 (Inner Face of Exterior Girder) : a) Moment due to Live Truck Wheel Load = PLL-Truck.-WSD*gInt.-M

MLL-Truck-WSD

35.596 kN-m/m

b) Moment due to Live Lane load on Sidewalk = PLL-Lane.-WSD*(SInter.)2/9

MLL-Lane-WSD

0.938 kN-m/m

(-)MLL-Total-4-4-WSD

36.534 kN-m/m

(-)MSDL+LL-4-4-WSD

38.507 kN-m/m

c) Total Factored Live Load (-)Moments at Section 4-4 for Interior Span. iv) Calculated Total Factored (-) Moments at Section 4-4 due to Applied Loads (DL + LL) on Interior Span of Deck.

20 Unfactored (+) ve & (-) ve Dead Load Moments under Provisions of AASHTO-LRFD-2004 : i) For Continuous Span at Middle Position the Moment value is of (+) ve & on Support is (-) ve. ii) Calculation of Unfactored Dead Load (+)Moments of Interior Continuous Span at Middle : 2 a) Moment due to Self Weight of Deck Slab = WDL-Self.*(SInter.) /14

MDL-Self-UF

0.933 kN-m/m

b) Moment due to Wearing Course = WDL-WC.*(SInter)2/14 c) Total Factored Dead Load (+) Moments at Middle of Interior Span.

MDL-WC-UF

0.335 kN-m/m

(+)MDL-Total-UF

1.269 kN-m/m

iii) Calculation of Unfactored Dead Load (-)Moments of Interior Continuous Span at Support : 2 a) Moment due to Self Weight of Deck Slab = WDL-Self.*(SInter.) /9

MDL-Self-UF

1.452 kN-m/m

b) Moment due to Wearing Course = WDL-WC.*(SInter)2/9

MDL-WC-UF

0.522 kN-m/m

(-)MDL-Total-UF

1.974 kN-m/m

c) Total Unfactored Dead Load (-) Moments at Middle of Interior Span.

21 Calculation of Factored Shearing Forces on Interior Span Faces According to Distribution Factor & Lever Rule under Provisions Strength Limit State (USD); i) Calculation of Factored Dead Load (DL) Shearing Forces on Faces of Interior Span at Grider Faces : a) Shearing Forces due to Self Weight of Deck Slab = WDL-Self.-USD*SInter./2 b) Shearing Forces due to Wearing Course = WDL-WC.-USD*SInter/2 c) Total Factored Dead Load (-) Shearin Forcets at Faces of Interior Girder.

VDL-Self--USD

4.950 kN/m

VDL-WC-USD

2.135 kN-m/m

VDL-Total-USD

7.085 kN-m/m

ii) Calculation of Factored Live Load (DL) Shearing Forces on Faces of Interior Span at Grider Faces : a) Shearing Forces due to Live Truck Wheel Load = PLL-Truck-USD.*gInt.-V

VLL-Truck-USD

107.077 kN/m

b) Shearing Forces due to Live Lane Load = FSPLL-Lane.*SInter./2

VLL-Lane-USD

4.476 kN/m

c) Total Factored Live Load (-)Moments at Section 4-4 for Interior Span

VLL-Total-USD

111.553 kN/m

VDL+LL-USD

118.637 kN/m

iii) Tatal Factored Shearing Forces On Interior Girder Feces due to Applied Loads :

22 Computation of Related Features required for Flexural Design of Top & Bottom Reinforcements for Deck Slab Against Calculated Design (-) ve & (+) ve Moments : i) Design Strip Width for Deck Slab in Transverse Horizontal Direction & Clear Cover on Different Faces: a) Let Consider the Design Width in Transverse Directions is = 1000mm b) Let the Clear Cover on Bottom Surface of Decl Slab, C-Cov.Bot. = 25mm, Let the Clear Cover on Top Surface of Decl Slab, C-Cov.Top = 38mm,

b

1.000 m

C-Cov-Bot. C-Cov-Top.

ii) Calculations of Limits For Maximum Reinforcement, (AASHTO-LRFD-5.7.3.3.1) : . a) With Maximum Amount of Prestressed & Nonprestressed Reinforcement for c/de-Max. a Section c/de  0.42 in which;

25 mm 38 mm

0.42

b) c is the distance from extreme Compression Fiber to the Neutral Axis in mm

c

Variable

c) de is the corresponding Effective Depth from extreme Compression Fiber to the Centroid of Tensial Forces in Tensial Reinforcements in mm. Here; i) de = (Apsfpsdp + Asfyds)/(Apsfps + Asfy), where ; ii) As = Steel Area of Nonprestressing Tinsion Reinforcement in mm2 iii) Aps = Area of Prestressing Steel in mm2 iv) fy = Yeiled Strength of Nonprestressing Tension Bar in MPa. vi) fps = Average Strength of Prestressing Steel in MPa. xi) dp = Distance of Extreme Compression Fiber from Prestressing Tendon Centroid in mm. xii) ds = Distance of Centroid of Nonprestressed Tensial Reinforcement from the Extreme Compression Fiber in mm.

de

Variable

As Aps fy fps dp

Variable Variable 410.00 Variable Variable

mm2 mm2 N/mm2 N/mm2 mm

ds

Variable

mm

d) For a Structure having only Nonprestressed Tensial Reinforcement the values of Aps, fps & dp are = 0. Thus Equation for value of de stands to de = Asfyds/Asfy & thus de = ds . iii) Limits For Manimum Reinforcement, (AASHTO-LRFD-5.7.3.3.2) : a) For Section of a Flexural Component having both Prestressed & Nonprestressed Tensile Reinforcements should have Minimum Resisting Moment Mr  1.2*Mcr or 1.33 Times the Calculated Factored Moment for the Section Based on AASHTO-LRFD-3.4.1-Table-3.4.1-1, which one is less.For Compnents having Nonprestressed Tensile Reinforcements only Mr = 1.2Mcr. b) The Cracking Moment of a Section Mcr = Sc(fr + fcpe) - Mdnc(Sc/Snc -1)  Scfr where; i) fcpe = Compressive Stress in Concrete due to Effective Prestress Forces at Extreme Fiber only where Tensile Stress is caused by Externally Applied Forces after allowance of all Prestressing Losses in MPa. In Nonprestressing RCC Components value of fcpe = 0.

Mcr

Variable

fcpe

-

Mdnc

Variable

N-mm

iii) Sc = Section Modulus for the Extreme Fiber of the Composite Section where Tensile Stress Caused by Externally Applied Loads in mm3.

Sc

Variable

mm3

iv) Snc = Section Modulus of Extreme Fiber of the Monolithic/Noncomposite Section where Tensile Stress Caused by Externally Applied Loads in mm3. For the Rectangular RCC Section value of Snc = (b*tSlab.3/12)/(tSlab./2)

Snc

ii) Mdnc = Total Unfactored Dead Load Moment acting on the Monolithic or Noncomposite Section in N-mm.

v) fr = Modulus of Rupture of Concrete in Mpa,(AASHTO LRFD-5.4.2.6). c) For Nonprestressing & Monolithic or Noncomposite Beam or Elements,

fr Mcr

N-mm N/mm2

3 0.006667 m 3 6.667/10^3 m 3 6.667*10^6 mm

2 2.887 N/mm

19.247 kN-m

Sc = Snc & fcpe = 0, thus Equation for Cracking Moment Stands to Mcr = Sncfr

19246817.919 N-mm

d) Thus Calculated value of Mcr according to respective values of Equation

Mcr-1

Variable

N-mm

e) The value of Mcr = Scfr

Mcr-2

Variable

N-mm

f) Cpoputed value of Mcr = 1.33*MExt Factored Moment due to External Forces

Mcr-3

Variable

N-mm

g) Table-1 Showing Allowable Resistance Moment M r for Minimum Reinforcement of Different Surface & Direction Position Value of Value of Actuat Acceptable 1.2 Times M & Nature Unfactored Mcr-1 Cracking Mcr of Mcr Factored of Moment Dead Load As per Moment Cracking Cracking Moment on Moment Equation Value Moment Moment of Section Back MDL-UF 5.7.3.3.2-1 Sncfr (Mcr-1Sncfr) (1.2*Mcr) M Wall kN-m kN-m kN-m kN-m kN-m kN-m (-)ve Face

Mr of M, Allowable Factored Min. Moment for RCC Moment 1.2Mcr (1.33*M) kN-m kN-m

1.33 Times

Maximum Flexural Moment Mu (M  Mr) kN-m

1.269

19.247

19.247

19.247

23.096

87.014

115.728

23.096

87.014

1.974

19.247

19.247

19.247

23.096

85.122

113.213

23.096

85.122

of Girder (+)ve Mid. of Span

iv) Calculations for Balanced Steel Ratio- pb & Max. Steel Ratio- pmax according to AASHTO-1996-8.16.2.2 : a) Balanced Steel Ratio or the Section, pb = b*b1*((f/c/fy)*(599.843/(599.843 + fy))), b) Max. Steel Ratio, pmax. = f *pb , (Here f = 0.75)

pb

0.022

pmax.

0.016

23 Flexural Design of Reinforcements on Bottom Surface of Deck Slab Against Calculated (-) ve Moment on Interior Span Strip : i) Design Moment for the Section : a) The Calculated Flexural (-) ve Moment on Interior Span Strip of (-)MDL+LL-USD 87.014 kN-m/m Deck Slab is Greater than the Allowable Minimum Moment Mr. Thus Calculated 87.014*10^6 N-mm/m Moment Governs the Provision of Reinforcement against (-) ve Moment Mr 23.096 kN-m/m value. For (-) ve value the required Reinforcement will be on Top Surface. 23.096*10^6 N-mm/m b) Since (-)MDL+LL-USD > Mr, the Allowable Minimum Moment for the Section thus MDL+LL-USD is the Design Moment MU.

MU

87.014 kN-m/m 87.014*10^6 N-mm/m

ii) Provision of Reinforcement for the Section : a) Let provide 16f Bars as Reinforcement on Top Surface of Deck Slab

DDect-Top

b) X-Sectional of 16f Bars = p*DDect-Top2/4

Af-16.

2 201.062 mm

c) The provided Effective Depth for the Section with Reinforcement on Top

de-pro.

154.000 mm

16 mm

Surface, dpro = (tSlab-CCov-Top. -DDect-Top/2) d) With Design Moment MU , Design Strip Width b & Effective Depth dpro; the required value of a = dpro*(1 - (1 - (2MU)/(b1f/cbdpro2))(1/2)) e) Steel Area required for the Section, As-req. = MU/(ffy(dpro - a/2))

areq.

As-req-Top

f) Spacing of Reinforcement with 16f bars = Af-16b/As-req-Top

sreq

g) Let the provided Spacing of Reinforcement with 16f bars for the Section spro = 100mm,C/C

spro.

h) The provided Steel Area with 16f bars having Spacing 100mm,C/C = Af-16.b/spro

As-pro-Top.

35.820 mm

1,732.750 116.036

mm2/m mm,C/C

100 mm,C/C

2,010.619

mm2/m

iii) Chacking in respect of Design Moment & Max. Steel Ratio : a) Steel Ratio for the Section, ppro = As-pro/bdpro

ppro

/ b) With provided Steel Area the value of 'a' = As-pro*fy/(b1*f c*b)

apro

c) Resisting Moment for the Section with provided Steel Area, = As-pro*fy(d - apro/2)/10^6

Mpro

d) Relation between Resisting Moment Mpro & Designed Moment MU. e) Relation between Provided Steel Ration rpro & Allowable Max. Steel Ratio rMax.

0.013 46.182 mm 107.915 kN-m/m

Mpro>Mu

OK

p-pro VU or Vn < VU & Provisions of AASHTO-LRFD-5.8.3 have Satisfied or Not). e) Since Nominal Shear Resitance for the Section Vn > VU the Calculated Ultimate Shearing Force for the Section, thus the Abutment Wall does not require any Shear Reinforcement. f) Since Resisting Moment > Designed Moment, Provided Steel Ratio < Max. Steel Ratio, the Back Wall on its Bottom Section does not Require any Shear Reinforcement, thus Flexural Design of Vertical Reinforcement on Earth Face of Back Wall is OK.

vi) Checking for Factored Flexural Resistance under Provision of AASHTO-LRFD-5.7.3.2: a) Factored Flexural Resistance for any Section of Component, Mr = fMn, where; i) Mn is Nominal Resistance Moment for the Section in N-mm ii) f is Resistance Factor of Flexural in Tension of Reinforcement/Prestressing.

Mr

97.124 N-mm 97.124*10^6 kN-m

Mn

107.915 N-mm 107.915*10^6 kN-m

f

0.90

b) The Nominal Resistance of Rectangular Section with One Axis Stress having both Prestressing & Nonprestessing AASHTO-LRFD-5.7.3.2.3 is Mn = Apsfps(dp-a/2) + Asfy(ds-a/2) - A/sf/y(d/s-a/2) c) In a Nonprestressing Structural Component having Rectangular Elements, at any Section the Nominal Resistance, Mn = Asfy(ds-a/2) d) Since Deck Slab is being a Continuous Sturucture & for Design purpose it is being considered as Constituents of 1.000 m Wide Strips. The Steel Area against Factored Max. Moments on Main Girder Face will have the value of Nominal Resistance, Mn = Asfy(ds-a/2)

Mn-Top

SMDL+LL-USD

e) Calculated Factored Moment MU on Face of Main Girder of Continuous Span Strip = (-) MDL+LL-USD

f) Relation between the Computed Factored Flexural Resistance Mr & the Actual Factored Moment MU at Mid Span ( Which one is Greater, if Mr  MU the Flexural Design for the Section has Satisfied otherwise Not Satisfied)

107.915 kN-m 107.915*10^6 N-mm

87.014 kN-m 87.014*10^6 N-mm Mr>Mu

Satisfied

vii) Checking in respect of Control of Cracking By Distribution of Reinforcement, (AASHTO-LRFD-5.7.3.4) : a) Under Service Limit State Load Condition, Developed Tensile Stress of Reinforcement fs-Dev. of Concrete Elements, should not exceed fs the Computed Tensile Stress of Reinforcement under provision of AASHTO-LRFD-5.7.3.4. Where; b) fs-Dev. is Developed Tensile Stress in Provided Reinforcements of Section under the Service Limit State of Loads = M/As-prode in which, i) M is Calculated Moment for the Section under Service Limit State at Section 4-4, which is the Highest one of (-) WSD values.

(-)MDL+LL-4-4-WSD

ii) As-pro is the Steel Area for the Section under USD Design Calculation. iii) de is Effective Depth between Extreme Compression Fiber to Centroid of the Tensile Reinforcement for the Section. c) fsa is Computed Tensile Stress of Reinforcement having its value = Z/(dcA)1/3  0.6fy, in Which;

fs-Dev.

As-pro de

fsa

2 124.364 N/mm

38.507 kN-m 38.507*10^6 N-mm 2 2,010.619 mm

154.000 mm

2 1.419 N/mm

i) dc= Depth of Concrete Extreme Tension Face from the Center of the Closest dc Tension Bar. The Depth is Summation Earth/Water Clear Cover & Radius of the Closest Bar to Tension Face. The Max. Clear Cover = 50mm. In a Component of Rectangular Section, dc = DBar/2 + CCov-Top. Since Clear Cover on Earth Face of Back Wall, CCov-Earth = 50mm & Bar Dia, DBar = 16f ; thus dc = (16/2 + 50)mm

58.000 mm

ii) A = Area of Concrete Surrounding a Single Tension Bar, which is Calculated A by Dividing the Total Concrete Area bounded in between Extreme Tension Face & a Straight Line parallel to Neutral Axis of Component having equal distance from the Centrioed of Main Tension Reinforcement Bars on both side & Diving the Area by the total Number of Main Bars as Tensile Reinforcement having Max. Clear Cover = 50mm.In Abutment Wall the Tension Bars in One Layer & as per Condition Distance of Neutral Axis from Tension Face = dc, thus Area of Concrete that Surrounding a Single Tension Bar can Compute by A = 2dc*spro. Here spro is Spacing between Provided Tension Bars.

2 11,600.000 mm

iii) Z = Crack Width Parameter for Cast In Place Components in N/mm. For a) Structure with Moderate Exposure Components the Max. value of Z = 30000 b) Structure with Severe Exposure Components the Max. value of Z = 23000 c) Structure with Buried Components the Max. value of Z = 17000 Since the Structure is very close to Sea, thus it’s Components are of Severe Exposure Category having Allowable Max. value of ZMax. = 23000N/mm

ZMax.

23,000.000 N/mm

iv) The Computed value of 0.6*fy for the Concrete Element.

0.6*fy

2 246.000 N/mm

d) Since the Calculated value of fs-Dev. is responsible for Controlling the formation of Cracks under Applied Loads to the Back Wall Structure, thus value of the Crack Width Parameter Z should calculate based the value of fs-Dve. e) Based on fs-Dve. the value of Crack Width Parameter ZDev. = fs-Dev.*(dcA)1/3

ZDev.

124.364 N/mm

f) Relation between of Developed Tensile Stress fs-Dev. & Allowable Tensile Stress fs

fs-Dev.< fs

Satisfy

g) Relation between Computed Tensile Stress fsa & Calculated value of 0.6fy

fsa< 0.6fy

Satisfy

Zdev.< Zmax.

Satisfy

h) Relation between Allowable Max. value of ZMax. & Developed value ZDev.

i) Since Developed Tensile Stress of Tension Reinforcement of Back Wall fs-Dev.< fsa Computed Tensile Stress; the Computed Tensile Stress fsa < 0.6fy ;the Developed Crack Width Parameter ZDev. < ZMax. Allowable Max. Crack Width Parameter, thus Provisions of Tensile Reinforcement in Vertical on Back Wall Earth Surface in respect of Control of Cracking & Distribution of Reinforcement are OK. j) More over though the Structure is a Nonprestressed one & value of dc have not Exceeds 900 mm, thus Component does require any Longitudinal Skein Reinforcement. m) Since Resisting Moment > Designed Moment, Provided Steel Ratio < Max. Steel Ratio, the Flexural Design of Cantilever Slab section of Bridge Deck Slab is OK.

23 Flexural Design of Reinforcements on Bottom Surface of Deck Slab Against the (+) ve Moment on its Interior Span Strip : i) Design Moment for the Section : a) The Calculated Flexural (+ ve Moment on Interior Span Strip of Deck (+)MDL+LL-3-3 85.122 kN-m/m Slab is Greater than the Allowable Minimum Moment Mr. Thus Calculated 85.122*10^6 N-mm/m Moment Governs the Provision of Reinforcement against (+) ve Moment Mr 23.096 kN-m/m value. For (+) ve value the required Reinforcement will be on Bottom Surface. 23.096*10^6 N-mm/m b) Since (+)MDL+LL-3-3 > Mr, the Allowable Minimum Moment for the Section, thus SMDL+LL-3-3 is the Design Moment MU.

MU

85.122 kN-m/m 85.122*10^6 N-mm/m

ii) Provision of Reinforcement for the Section : a) Let provide 16f Bars as Bottom Reinforcement on Bridge Decl Slab.

DBottom.

b) X-Sectional of 16f Bars = p*DBottom2/4

Af-16.

2 201.062 mm

c) The provided Effective Depth for the Section with Reinforcement on Water Face, dpro = (tSlab.-CCov-Bot. -DBottom./2)

de-pro.

167.000 mm

areq.

31.532 mm

d) With Design Moment MU , Design Strip Width b & Effective Depth dpro; the required value of a = dpro*(1 - (1 - (2MU)/(b1f/cbdpro2))(1/2)) e) Steel Area required for the Section, As-req. = MU/(ffy(dpro - a/2))

As-req-Bot.

f) Spacing of Reinforcement with 16f bars = Af-16b/As-req-Bot.

sreq

g) Let the provided Spacing of Reinforcement with 16f bars for the Section spro = 100mm,C/C

spro.

h) The provided Steel Area with 16f bars having Spacing 100mm,C/C = Af-16.b/spro

As-pro-Bot.

16 mm

1,525.344 131.814

mm2/m mm,C/C

100 mm,C/C

2,010.619

mm2/m

iii) Chacking in respect of Design Moment & Max. Steel Ratio : a) Steel Ratio for the Section, ppro = As-pro/bdpro

ppro

/ b) With provided Steel Area the value of 'a' = As-pro*fy/(b1*f c*b)

apro

c) Resisting Moment for the Section with provided Steel Area, = As-pro*fy(d - apro/2)/10^6

Mpro

d) Relation between Resisting Moment Mpro & Designed Moment MU. e) Relation between Provided Steel Ration rpro & Allowable Max. Steel Ratio rMax.

0.012 46.182 mm

118.632 kN-m/m Mpro>Mu

OK

p-pro VU or Vn < VU & Provisions of AASHTO-LRFD-5.8.3 have Satisfied or Not). e) Since Nominal Shear Resitance for the Section Vn > VU the Calculated Ultimate Shearing Force for the Section, thus the Abutment Wall does not require any Shear Reinforcement. f) Since Resisting Moment > Designed Moment, Provided Steel Ratio < Max. Steel Ratio, the Back Wall on its Bottom Section does not Require any Shear Reinforcement, thus Flexural Design of Vertical Reinforcement on Earth Face of Back Wall is OK. vi) Checking for Factored Flexural Resistance under Provision of AASHTO-LRFD-5.7.3.2: a) Factored Flexural Resistance for any Section of Component, Mr = fMn, where; i) Mn is Nominal Resistance Moment for the Section in N-mm ii) f is Resistance Factor of Flexural in Tension of Reinforcement/Prestressing.

Mr

106.769 N-mm 106.769*10^6 kN-m

Mn

118.632 N-mm 118.632*10^6 kN-m

f

0.90

b) The Nominal Resistance of Rectangular Section with One Axis Stress having both Prestressing & Nonprestessing AASHTO-LRFD-5.7.3.2.3 is Mn = Apsfps(dp-a/2) + Asfy(ds-a/2) - A/sf/y(d/s-a/2) c) In a Nonprestressing Structural Component having Rectangular Elements, at any Section the Nominal Resistance, Mn = Asfy(ds-a/2) d) Since Deck Slab is being a Continuous Sturucture & for Design purpose it is being considered as Constituents of 1.000 m Wide Strips. The Steel Area against Factored Max. Moments on Main Girder Face will have the value of Nominal Resistance, Mn = Asfy(ds-a/2) e) Calculated Factored Moment MU on Face of Main Girder of Continuous Span Strip = (+) MDL+LL-3-3-USD

Mn-Bot

SMDL+LL-3-3-USD

f) Relation between the Computed Factored Flexural Resistance Mr & the Actual Factored Moment MU at Mid Span ( Which one is Greater, if Mr  MU the Flexural Design for the Section has Satisfied otherwise Not Satisfied)

118.632 kN-m 118.632*10^6 N-mm

85.122 kN-m 85.122*10^6 N-mm Mr>Mu

Satisfied

vii) Checking in respect of Control of Cracking By Distribution of Reinforcement, (AASHTO-LRFD-5.7.3.4) : a) Under Service Limit State Load Condition, Developed Tensile Stress of Reinforcement fs-Dev. of Concrete Elements, should not exceed fs the Computed Tensile Stress of Reinforcement under provision of AASHTO-LRFD-5.7.3.4. Where; b) fs-Dev. is Developed Tensile Stress in Provided Reinforcements of Section under the Service Limit State of Loads = M/As-prode in which, i) M is Calculated Moment for the Section under Service Limit State

fs-Dev.

(-)MDL+LL-3-3-WSD

ii) As-pro is the Steel Area for the Section under USD Design Calculation. iii) de is Effective Depth between Extreme Compression Fiber to Centroid of the Tensile Reinforcement for the Section. c) fsa is Computed Tensile Stress of Reinforcement having its value = Z/(dcA)1/3  0.6fy, in Which;

As-pro de

fsa

i) dc= Depth of Concrete Extreme Tension Face from the Center of the Closest dc Tension Bar. The Depth is Summation Earth/Water Clear Cover & Radius of the Closest Bar to Tension Face. The Max. Clear Cover = 50mm. In a Component of Rectangular Section, dc = DBar/2 + CCov-Top. Since Clear Cover on Earth Face of Back Wall, CCov-Earth = 50mm & Bar Dia, DBar = 16f ; thus dc = (16/2 + 50)mm

2 111.586 N/mm

37.468 kN-m 37.468*10^6 N-mm 2 2,010.619 mm

167.000 mm

2 1.273 N/mm

58.000 mm

ii) A = Area of Concrete Surrounding a Single Tension Bar, which is Calculated A by Dividing the Total Concrete Area bounded in between Extreme Tension Face & a Straight Line parallel to Neutral Axis of Component having equal distance from the Centrioed of Main Tension Reinforcement Bars on both side & Diving the Area by the total Number of Main Bars as Tensile Reinforcement having Max. Clear Cover = 50mm.In Abutment Wall the Tension Bars in One Layer & as per Condition Distance of Neutral Axis from Tension Face = dc, thus Area of Concrete that Surrounding a Single Tension Bar can Compute by A = 2dc*spro. Here spro is Spacing between Provided Tension Bars.

2 11,600.000 mm

iii) Z = Crack Width Parameter for Cast In Place Components in N/mm. For a) Structure with Moderate Exposure Components the Max. value of Z = 30000 b) Structure with Severe Exposure Components the Max. value of Z = 23000 c) Structure with Buried Components the Max. value of Z = 17000 Since the Structure is very close to Sea, thus it’s Components are of Severe Exposure Category having Allowable Max. value of ZMax. = 23000N/mm

ZMax.

23,000.000 N/mm

iv) The Computed value of 0.6*fy for the Concrete Element.

0.6*fy

2 246.000 N/mm

d) Since the Calculated value of fs-Dev. is responsible for Controlling the formation of Cracks under Applied Loads to the Back Wall Structure, thus value of the Crack Width Parameter Z should calculate based the value of fs-Dve.

e) Based on fs-Dve. the value of Crack Width Parameter ZDev. = fs-Dev.*(dcA)1/3

ZDev.

111.586 N/mm

f) Relation between of Developed Tensile Stress fs-Dev. & Allowable Tensile Stress fs

fs-Dev.< fs

Satisfy

g) Relation between Computed Tensile Stress fsa & Calculated value of 0.6fy

fsa< 0.6fy

Satisfy

Zdev.< Zmax.

Satisfy

h) Relation between Allowable Max. value of ZMax. & Developed value ZDev.

i) Since Developed Tensile Stress of Tension Reinforcement of Back Wall fs-Dev.< fsa Computed Tensile Stress; the Computed Tensile Stress fsa < 0.6fy ;the Developed Crack Width Parameter ZDev. < ZMax. Allowable Max. Crack Width Parameter, thus Provisions of Tensile Reinforcement in Vertical on Back Wall Earth Surface in respect of Control of Cracking & Distribution of Reinforcement are OK. j) More over though the Structure is a Nonprestressed one & value of dc have not Exceeds 900 mm, thus Component does require any Longitudinal Skein Reinforcement. 24 Provision of Distribution Reinforcement for Bridge Dack Slab According to AASHTO-LRFD-9.7.3 : i) Calculation of Distribution Reinforcements for Bridge Dack Slab: a) The Bridge Deck Slab in which Reinforcements are being Provided in Primary Direction in both of its Top & Bottom Surfaces, on its Secondary Depiction Reinforcements should arranged according to Provisions of Article -9.7.3..2 on Bottom Surface as Percentage of Primary Reinforcement against Positive Moment. b) For Primary Reinforcement Parallel to Traffic the Distribution Reinforcement will be 1750/(S) ≤ 50 Percent of the Main Reinforcemenr. c) For Primary Reinforcement Perpendicular to Traffic the Distribution Reinforcement will be 3840/(S) ≤ 67 Percent of the Main Reinforcemenr. Where for both cases S is Effective Span Length in mm as per Article-9.7.2.3 d) For Present Case Effective Span Length = 1550 mm

e) Since the Primary Reinforcement Perpendicular to Traffic thus Calculated Percent of Distribution Reinforcement ae per Formula - 3840/(S) f) Allowable Maximum % of Distribution Reinforcement g) Actual % of Distribution Reinforcement h) Provided Main Reinforcement Steel Area in Primary Direction on Bottom Surface of Deck Slab = As-pro-Bot. i) Required Distribution Reinforcement Steel Area for Bottom Surface Against Primary Reinforcement = As-pro-Bot-Main*DRActual*% j) Let proved 16f Bars as Distribution Reinforcement for Bottom Surface

S

1,650.000 mm

DR

94.534 %

DRMax.

67.000 %

DRActual-%

67.000 %

As-pro-Bot-Main.

2 2,010.619 mm /m

As-Bot-Dist.

2 1,347.115 mm /m

DBot-Dist

16.000 mm

k) X-Sectional of 16f Bars = p*DBot-Dist.2/4

Af-16

l) Spacing of Distribution Reinforcement with 16f Bars = Af-16b/As-Bot-Dist.

sreq

k) Let the spacing of Distribution Reinforcement on Bottom with 16f bars,

spro-Bot-Dist

m) Provided Steel Area for Distribution Reinforcement with 16f Bars having 150 mm C/C Spacing = Af-16.b/spro

As-Dist-pro.

n) Percentage of Provided Steel Area for Distribution Reinforcement Against Provided Main Reinforcement Steel Area = (As-Dist-pro./As-pro-Bot-Main)*100

DRpro.-%

2 201.062 mm

149.254

mm,C/C

150 mm-C/C 2 1,340.413 mm /m

66.667 %

Provision Satisfied

OK

o) Since the Provided Steel Area for Distribution Reinforcement is < 67% of Provided Main Reinforcement Steel Area, thus the Provision of Distribution Reinforcement for Deck Slab is OK. 26 Provision of Shrinkage & Temperature Reinforcements in Secondary Direction on Top Surface of Deck Slab : a) On Deck Slab Flexural Reinforcements are being provided in Primary Direction both on Top & Bottom aginest the Calculated Moments, whereas in Secondary Direction on Bottom Surface Reinforcements are being provided under provision of Distribution Reinforcement. Yet Reinforcements are required on Top Surface in Secondary Direction. On Top Surface of Deck Slab in Secondary Direction Reinforcements can Arrange under Provision of Shrinkage & Temperature Reinforcements as Mentioned in Article-5.10.8. b) Since the Thickness of Deck Slab is less than 1200mm, thus to Calculate the Shrinkage & Temperature Reinforcements on both Faces in Primary & Secondary Directions a Strip is being Considered having Length of each Length of each Arm b = 1000mm.

LPrim. LSec. b

c) According to AASHTO-LRFD-5.10.8.1. Steel Area required as Shrinkage Temperature Reinforcement for Structural Components having its Thickness 1200mm or Less; As  0.11Ag/fy in both way.(Here Thickness = 200mm).

As-req-S&T

d) Here Ag is Gross Area of Strip on Deck Slab Surface = LPrim.*LSec.

Ag-Strip

e) Let provide 16f bars as Shrinkage & Temperature in Secondary Direction on Top Surface of Deck Slab. f) X-Sectional Area of 16f bar = pDBar-S&T-V&H2/4 g) Spacing required for 16f Bars as Shrinkage & Temperature in Secondary Direction on Top Surface of Bridge Deck Slab = Af-16*b/As-req-S&T

DTop-S&T-Sec

1.000 m 1.000 m 1.000 m

2 268.293 mm

2 1000000 mm

16 mm

Af-16

2 201.062 mm

sreq-S&T

749.413 nos.

h) According to AASHTO-LRFD-5.10.8.1. In a Component having Less 1200mm Thickness, Shrinkage & Temperature Reinforcements should not Spaced further Apart than 3.00 Times the Component's Thickness or 450mm.

i) 3.00 Times of Cantilever Wing Wall Thickness = 3.00*tSlab ii) Allowable Max. Spacing for Shrinkage & Temperature Reinforcements

3.00*tSlab sAllow-S&T

i) Let provide 200 mm Spacing for Shrinkage & Temperature Reinforcements with 16f Bars in Secondary Direction on Top Surface of Bridge Deck Slab.

spro-S&T

j) The provided Steel Area with 16f Bars as Shrinkage & Temperature Reinforcements having Spacing 200mm,C/C = Af-16.b/spro-S&T

As-pro-S&T-V&H

600.000 mm 450.000 mm 200 mm

1,005.310

mm2/m

k) According to AASHTO-LRFD-5.10.8.1. For Components of Solid Structural Concrete Wall & Footing having Less 1200mm Thickness, the Spacing of Shrinkage & Temperature Reinforcements Bars should not Exceed 300mm in Each Direction on all Faces and Steel Area of Shrinkage & Temperature Reinforcements need not Exceed value of Ab = 0.0015Ag. Since the Bridge Deck Slab is Continuous Concrete Structure, thus i) Allowable Max. Spacing for Shrinkage & Temperature Reinforcements sAllow-S&T-2 300.000 mm 2 Ab = ii) Calculated value of Ab = 0.0015Ag. åAb = 1,500.000 mm /m l) Status between Provided Steel Area of Shrinkage & Temperature Reinforcement & Allowable Max, Steel Area for Shrinkage & Temperature Reinforcement (Whether Ab > As-pro-S&T or not. If Ab < As-pro-S&T-V&H ; then Provisions of Shrinkage & Temperature Reinforcement have Satisfied, otherwise Not Satisfied) åAb > As-pro-S&T Satisfied m) Since Calculated Ab > As-pro-S&T-V&H. > As-req-S&T-V&H. & spro-S&T-V&H. = sAllow-S&T-V&H-2, thus Provisions for the Shrinkage & Temperature on Surfaces of Cantilever Wing Wall is OK.

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

F. Calculations for Load, Shear & Moments of RCC Main Girders under Strength Limit State of Design (USD) : Description

Notation DImentions

Unit.

1 Structural Data : i) Dimentions of Superstructure : a) b) c) d) e) f) g) h) i) j) k) l) m) n) o) p) q) r) s) t) u) v) w) w-i) w-ii) x) y)

Span Length (Clear C/C distance between Bearings) Addl.Length of Girder beyond Bearing Center Line. Total Girder Length (a+2b) Carriageway Width Width of Side Walk on Each Side Width of Curb/Wheel Guard Width of Railing Curb/Post Guard Total Width of Bridge Deck Width & Depth of Railings Width & Breath of Railing Post Height of Railing Post Height of Wheel Guard/Curb Number of Railings on each Side C/C distance between Railing Posts Thickness of Deck Slab Thickness of Wearing Course Number of Main Girders Number of Cross Girders Depth of Main Girders (Including Slab as T-Girder) Depth of Cross Girders (Including Slab as T-Girder) Width of Main Girders Width of Cross Girders C/C Distance between Main Girders & Flange Width C/C Distance between Cross Girders in Longitudinal Direction . Distance of Slab Outer Edge to Exterior Girder Center Clear Distance Between Main Interior Girders Filets : i) Main Girder in Vertical Direction ii) Main Girder in Horizontal Direction iii) X-Girder in Vertical Direction vi) X-Girder in Horizontal Direction z) Vertical Surface Area of Superstructure's Exposed Elements

SL SAddl. LGir. WCarr-Way. WS-Walk. WCurb. WR-Post. WB-Deck. RW&D. PW&B. hR-Post. hCurb. Rnos. C/CD-R-Post. tSlab. tWC NGirder. NX-Girder. hGir. hX-Girder. WGirder. WX-Girder. C/CD-Girder. C/CD-X-Girder. CD-Ext.-Girder-Edg. ClD-Int.-Girder. FM-Girder-V. FM-Girder-H. FX-Girder-V. FX-Girder-H. ASup-Vert.

24.400 m 0.300 m 25.000 m 7.300 m 1.250 m 0.350 m 0.225 m 10.250 m 0.175 m 0.225 m 1.070 m 0.300 m 3.000 nos 2.000 m 0.200 m 0.075 m 5.000 nos 5.000 nos 2.000 m 1.700 m 0.350 m 0.250 m 2.000 m 6.100 m 1.125 m 1.650 m 0.150 m 0.150 m 0.075 m 0.075 m 2 87.108 m

ii) Number of Traffic Lane on Bridge Deck: a) Number of Design Traffic Lane = WCarr.-way/3600 = 7300/3600 Where WCarr.-way is Clear Carriageway Width in between Curbs in mm

Page 131

NLane.

@

2.028

nos

2

nos

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

(ASSHTO LRFD-3.6.1.1.1) 2 Design Data : i) Design Criterion : a) AASHTO Load Resistance Factor Design (LRFD). b) Type of Loads : Combined Application of AASHTO HS20 Truck Loading & Lane Loading. ii) Design AASHTO HS20 Truck Loading : a) b) c) d) e) f) g) h)

Axle to Axle distance Wheel to Wheel distance Rear Wheel axle Load (Two Wheels) Rear Single Wheel Load Middle Wheel axle Load (Two Wheels) Middle Single Wheel Load Front Wheel axle Load (Two Wheels) Front Single Wheel Load

DAxel. DWheel. LLRW-Load LLRS-Load LLMW-Load LLMS-Load LLFW-Load LLFS-Load

1.800 4.300 145.000 72.500 145.000 72.500 35.000 17.500

m m kN kN kN kN kN kN

iii) Design AASHTO Lane Loading : a) Design Lane Loading is an Uniformly Distributed Load having Magnitude of 9.300N/mm through the Length of Bridge for 1 (One) Lane of Bridge & acting over a 3.000m Wide Dcak Strip in Transverse Direction. Thus Lane Load per meter Length of Bridge for 1 (One) Lane = (9.300*1000/1000)kN/m

LLLane

b) Design Lane Loading is an Uniformly Distributed Load having Magnitude of 9.300N/mm through the Length of Gridge for Single and acting over a 3.000m Wide Strip in Transverse Direction. Thus Intensity of Lane Load per meter Length & for per meter Width = 9.300/3.000kN/m/m-Wd.

LLLane-Int.

9.300 9.300

N/mm kN/m

3.100 kN/m/m-Wd. 0.003100 N/mm/mm-Wd.

iv) Design AASHTO Pedestrian Loading : a) Design Pedestrian Loading is an Uniformly Distributed Load having Magnitude of 3.600*10-3MPa through the Length of Sidewalk on both side and acting over the total Wide of Sidewalk. 3 v) Unit Weight of Different Materials in kg/m : (Having value of Gravitional Acceleration, g =

a) b) c) d) e)

LL-Pedest

2 0.003600 N/mm 2 3.600 kN/m

2 9.807 m/sec )

gc gWC

Unit weight of Normal Concrete Unit weight of Wearing Course Unit weight of Normal Water Unit weight of Saline Water Unit weight of Earth (Compected Clay/Sand/Silt)

gW-Nor. gW-Sali. gs

Page 132

2,447.232 2,345.264 1,019.680 1,045.172 1,835.424

kg/m3 kg/m3 kg/m3 kg/m3 kg/m3

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

3 vi) Unit Weight of Materials in kN/m Related to Design Forces :

a) b) c) d) e)

Unit weight of Normal Concrete Unit weight of Wearing Course Unit weight of Normal Water Unit weight of Saline Water Unit weight of Earth (Compected Clay/Sand/Silt)

wc wWC wWater-Nor. wWater-Sali. wEatrh

24.000 23.000 10.000 10.250 18.000

kN/m3 kN/m3 kN/m3 kN/m3 kN/m3

vii) Strength Data related to Ultimate Strength Design( USD & AASHTO-LRFD-2004) : a) Concrete Ultimate Compressive Strength, f/c (Normal Concrete) b) Concrete Allowable Strength under Service Load Condition (SLC) = 0.40f/c c) Modulus of Elasticity of Concrete, Ec = 0.043gc1.50f/c = 0.043*24^(1.50)*21^(1/2) Mpa, (AASHTO LRFD-5.4.2.4). d) Poisson's Ration = 0.63f/c = 0.63*21^(1/2), subject to cracking and considered to be neglected (AASHTO LRFD-5.4.2.5). e) Modulus of Rupture of Concrete, fr = 0.63f/c Mpa (AASHTO LRFD-5.4.2.6). f) Steel Ultimate strength, fy (60 Grade Steel) g) Modulus of Elasticity of Reinforcement, Es for fy = 410 MPa

f/c fc Ec

21.000 8.400 23,855.620

MPa MPa MPa

2.887 fr fy ES

2.887

MPa

410.000 MPa 200000.000 MPa

viii) Other Design Related Data : a) Velocity of Wind Load in Normal Condition b) Velocity of Wind Load in Special Condition c) Velocity of Water/Stream Current Causing Water/Stream Load

VWL-Nor. VWL-Spe. VWA

90.000 260.000 4.200

3 Factors Applicable for Design of Different Structural Components : i) Formula for Load Factors & Selection of Load Combination : a) Formula for Load Factors Q = Σ ηigiQi  f Rn = Rr; (ASSHTO LRFD-1.3.2.1-1 & 3.4.1-1) Where, ηi is Load Modifier having values ηi = ηD ηR ηI  0.95 in which for Loads a Maximum value of gi Applicable; (ASSHTO LRFD-1.3.2.1-2), & ηi = 1/(ηD ηR ηI )  1.00 in which for Loads a Minimum value of gi Allpicable; (ASSHTO LRFD-1.3.2.1-3) Here: gi = Load Factor; a statistically based multiplier Applied to Force Effect, f = Resistance Factor; a statistically based multiplier Applied to Nominal Resitance, ηi = Load Modifier; a Factor related to Ductility, Redundancy and Operational Functions, For Strength Limit State; ηD ηi = ηD = 1.00 for Conventional Design related to Ductility, 1.000 ηR ηi = ηR = 1.00 for Conventional Levels of Redundancy , 1.000 ηi = ηI = 1.00 for Typical Bridges related to Operational Functions, Qi = Force Effect, Rn = Nominal Resitance,

Page 133

ηl

1.000

km/hr km/hr m/s

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Ri = Factored Resitance = fRn. 4 Different Load Multiplying Fatcors for Strength Limit State Design (USD) & Load Combination : a) The Bridge will have to face Cyclonic Storms with very high Intensity of Wind Load (Wind Velocity = 260km/hr), but those would be occasional. Thus the respective Multiplier Factors of Limit State STRENGTH I (Bridge used by Normal Vehicle without wind load) for normal operation, Limit State of STRENGTH-III (Wind Velocity exceeding 90km/hr) for wind load during cyclonic storm condition and Limit State of STRENGTH-IV (Wind Velocity of 90 km/hr) for normal wind load only are selected as CRITICAL conditions for bridge structure. i) Dead Load Multiplier Factors for Strength Limit State Design (USD) According to AASHTO-LRFD-3.4.1; Table 3.4.1-1&2 : a) Dead Load Multiplier Factor for Structural Components & Attachments-DC Applicable to All Components Except Wearing Course & Utilities (Max. value of Table 3.4.1-2)

gDC

1.250

b) Dead Load Multiplier Factor for Wearing Course & Utilities- DW , (Max. value of Table 3.4.1-2)

gDW

1.500

c) Multiplier Factor for Horizontal Active Earth Pressure on Substructure Components of Bridge-EH ; Applicable to Abutment & Wing Walls, (Max. value of Table 3.4.1-2)

gEH

1.500

d) Multiplier Factor for Vertical Earth Pressure on Substructure Components of Bridge-EV ; Applicable toAbutment & Wing Walls, (Max. value of Table 3.4.1-2)

gEV

1.350

e) Multiplier Factor for Surchage Pressure on Substructure Components of Bridge-ES ; Horizontal & Vertical Loads on Abutment & Wing Walls, (Max. value of Table 3.4.1-2)

gES

1.500

ii) Live Load Multiplier Factors for Strength Limit State Design (USD) According to AASHTO-LRFD-3.4.1; Table 3.4.1-1&2 : a) Multiplier Factor for Multiple Presence of Live Load ( No of Lane = 2)-m (ASSHTO LRFD-3.6.1.1.1)

m

1.000

gLL-Truck

1.750

IM

1.330

d) Multiplier Factor for Lane Loading-LL-Lane

gLL-Lane

1.750

e) Multiplier Factor for Pedestrian Loading-PL.

gLL-PL.

1.750

f) Multiplier Factor for Vehicular Centrifugal Force-CE

gLL-CE.

1.750

b) Multiplier Factor for Truck Loading (HS20 only)-LL-Truck . c) Multiplier Factor for Vhecular Dynamic Load Allowence-IM as per Provision of ASSHTO LRFD-3.6.2.1, Table 3.6.2.1-1; (Applicable only for Truck Loading & Tandem Loading)

Page 134

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

g) Multiplier Factor for Vhecular Breaking Force-BR .

gLL-BR.

1.750

h) Multiplier Factor for Live Load Surcharge-LS

gLL-LS.

1.750

gLL-WA.

1.000

i) Multiplier Factor for Water Load & Stream Pressure-WA j) Multiplier Factor for Wind Load on Structure-WS

STRENGTH - III

gLL-WS.

1.400

l) Multiplier Factor for Wind Load on Live Load-WL

STRENGTH - V

gLL-WL

1.000

gLL-FR.

1.000

gLL-TU.

1.000

gLL-CR.

1.000

n) Multiplier Factor for deformation due to Shrinkage of Concrete-SH (With Elastomeric Bearing).

gLL-SH.

1.000

o) Multiplier Factor for Temperature Gradient-TG (With Elastomeric Bearing).

gLL-TG.

1.000

p) Multiplier Factor for Settlement of Concrete-SE (With Elastomeric Bearing).

gLL-SE.

1.000

q) Multiplier Factor for Earthquake -EQ

gLL-EQ.

-

r) Multiplier Factor for Vehicular Collision Force-CT

gLL-CT.

-

t) Multiplier Factor for Vessel Collision Force-CV

gLL-CV.

1.000

k) Multiplier Factor for Water Load & Stream Pressure-FR l) Multiplier Factor for deformation due to Uniform Temperature Change -TU (With Elastomeric Bearing). m) Multiplier Factor for deformation due to Creep on Concrete-CR (With Elastomeric Bearing).

5 Load Calculations for Superstructural Components & Attachments (DL & LL) per meter Length of Girder: i) Dead Loads on 1 no. Exterior Girder from Different Components & Attachments : a) Dead Load on. Exterior Girder due to Self Wt.& Attachments (Without WC & Utilies) for per meter Length of Girder. b) Dead Load on Exterior Girder due to WC. & Utilities for per meter Length of Girder

DLExt-Gir-Self& Atta.

34.340

kN/m

DLExt-Gir-WC+ Utility.

3.203

kN/m

DLExt-Gir-X-Gir.

8.526

kN

DLExt.U-D

37.543

c) Concentrated Dead Load on Exterior Girder from to 1 no. Cross Girder d) Sumation of Uniformly Distributed Dead Loads on Exterior Girder (a + b) for per Meter Length of Girder.

Page 135

kN/m

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

ii) Dead Loads on 1 no. Interior Girder from Different Components & Attachments : a) Dead Load on.Interior Girder due to Self Wt.& Attachments (Without WC & Utilies) for per meter Length of Girder.

DLIntt-GirSelf & Atta.

25.260

kN/m

b) Dead Load on Interior Girder from WC. for per meter Length of Girder

DLInt-Gir-WC.

3.450

kN/m

c) Concentrated Dead Load on Interior Girder from to 1 no. Cross Girder

DLInt-Gir-X-Gir.

17.053

kN

DL-Int.UD

28.710

kN/m

d) Sumation of Uniformly Distributed Dead Loads on Interior Girder (a + b) for per Meter Length of Girder.

iii) Live Loads (LL) on 1 no. Exterior Girder due to Wheel Load, Lane Load & Pedestrian Load according Provisions of AASHTO-LRFD-3.6.1.2.2, 3.6.1.2.4 & 3.6.1.6 : a) Sketch Diagram For Distribution of Wheel Load, Lane Load & Pedestrian Load on Exterior Girders : Midd. & Rear Wheel Load = Front Wheel Load =

72.500 kN 17.500 kN 1.475 0.225 7.3

0.600

1.250 0.300

1.800

1.070 9.300kN/m Lane Load on

0.300 0.200 0.950

0.250 1.650

1.650

1.650

1.125

2.000

2.000

2.00

1.650

2.000

0.950

1.125

CL 10.250 b) LL on 1 no. Exterior Girder due to Wheel Load at distance 0.600m from Wheel Guard Face; i) From Front Wheel (Sketch Diagram) = 10.06 kN LLExt-Wheel-Front. ii) From Midd. & Rear Wheel (do) = 41.69 kN LLExt-Wheel-Mid& Rear. c) LL on 1 no. Exterior Girder due to Lane Load Uniformly Distributed over Full Bridge Length with Intensity of 3.100N/m/m-Wd. on 0.650m Width from Wheel Guard Face up to Middle point between Two Girders. (From Sketch Diagram) = 2.02 kN/m d) LL on 1 no. Exterior Girder due to Pedestrian Load Uniformly Distributed over Sidewalk on Full Bridge Length with Intensity of 4.000kN/m 2 on Sidewalk on each side (From Sketch Diagram) = 4.50 kN/m

10.063 41.688

LLExt-Lane.

2.015

kN/m

LLExt-Pedes.

4.500

kN/m

iv) Live Loads (LL) on 1 no. Interior Girder due to Wheel Load & Lane Load according to Provisions of

Page 136

kN kN

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

AASHTO-LRFD-3.6.1.2.2, 3.6.1.2.4 & 3.6.1.6 : a) Sketch Diagram For Distribution of Wheel Load & Lane Load on Interior Girders : Midd. & Rear Wheel Load = Front Wheel Load =

72.500 17.500

kN kN

72.500 17.500 1.475 7.300

0.200

1.800

1.200

0.225 1.250 0.300

0.800

1.070 9.300kN/m Lane Load on 9.300kN/m Lane Load on

0.300 0.200 0.950

0.25 1.650

1.125

2.000

1.650

1.650

2.000

2.000

1.650

0.950

2.000

1.125

CL 10.250 b) LL on 1 no.Interior Girder due to Wheel Load with One Line of Wheels LLInt-Wheel-Front. upon Girder & the other Line of Wheels at Axle Distance - 1.800m LLInt-Wheel-Mid& Rear. i) Load from Front Wheel (From Sketch Diagram) = 26.250 kN ii) Load from Midd. & Rear Wheel (From Sketch Diagram) = 108.750 kN

26.250 108.750

c) LL on 1 no. Interior Girder due to Uniformly Distributed Lane Load over LLInt-Lane. Full Bridge Length having Intensity of 9.300kN/m on 3.000m Width of Deck having Equally distance (1.500m) from Middle point of a Girder & action for Girder with 2.000m Width (From Sketch Diagram) = 6.200 kN/m

6.200

kN/m

FDLExt-Gir-Self & Atta. 42.925 kN/m

42.925

kN/m

b) Factored Dead Load on Exterior Girder due to WC. & Utilities for FDLExt-Gir-WC+ Utility. per Merter Length = gDW*DLExt.-Gir-WC+Utility = 4.804 kN/m

4.804

kN/m

kN kN

5 Factored Loads of Superstructure Components & Attachments (DL & LL) : i) Factored Dead Loads on 1 no. Exterior Girder from Different Components & Attachments : a) Factored Dead Load on Exterior Girder due to Self Wt.& Attachments (Without WC) for per Meter Length = gDC*DLExt-Gir-Self& Atta. =

c) Factored Concentrated Dead Load on Exterior Girder from to 1 no. Cross Girder = gDC*DLExt-Gir-X-Gir. =. 10.658 kN d) Sumation of Factored Uniformly Distributed Dead Loads on Exterior Girder (a + b) for per Meter Length of Girder.

Page 137

FDLExt-Gir-X-Gir.

10.658

kN

FDL-Ext.UD

47.729

kN/m

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

ii) Factored Dead Loads on 1 no. Interior Girder from Different Components & Attachments : a) Factored Dead Load on Interior Girder due to Self Wt.& Attachments (Without WC) for per Meter Length = gDC*DLInt-Gir-Self& Atta. = b) Factored Dead Load on Interior Girder due to WC. & Utilities for per Merter Length = gDW*DLInt.-Gir-WC = 5.175 kN/m

FDLIntt-GirSelf & Atta. 31.575 kN/m

31.575

kN/m

FDLInt-Gir-WC+ Utility.

5.175

kN/m

FDLInt-Gir-X-Gir.

21.316

kN

FDL-Int.UD

36.750

kN/m

FLLExt-Wheel-Front.

23.420

kN

FLLExt-Wheel-Mid& Rear.

97.028

kN

FLLExt-Lane.

3.526

kN/m

FLLExt-Pedes.

7.875

kN/m

FLL-Ext.

11.401

kN/m

FLLInt-Wheel-Front.

61.097

kN

FLLInt-Wheel-Mid& Rear.

253.116

kN

c) Factored Concentrated Dead Load on Interior Girder from to 1 no. Cross Girder = gDC*DLInt-Gir-X-Gir. =. 21.316 kN d) Sumation of Factored Uniformly Distributed Dead Loads on Interior Girder (a + b) for per Meter Length of Girder. iii) Factored Live Loads on Different Components for 1 no. Exterior Girder : i) From Front Wheel = mgLL-Truck*IM*LLExt-Wheel-Front = 23.420 kN ii) Load from Midd.& Rear Wheel=mgLL-Truck*IM*LLExt-Wheel-Mid&Rear. = 97.028 kN b) Factored LL on 1 no. Exterior Girder due to Lane Load = mgLL-Lane*LLExt-Lane. = 3.526 kN/m c) Factored LL on 1 no. Exterior Girder due to Pedestrian Load = mgLL-PL*LLExt-Pedes. = 7.875 kN/m d) Summation of Factored LL of Exterior Girder for per meter Length due to Lane Load & Pedestrian Loads iv) Factored Live Loads of Different Components for 1 no. Interior Girder : a) Factored LL on 1 no.Interior Girder due to Wheel Load i) Load from Front Wheel = mgLL-Truck*IM*LLInt-Wheel-Front = 61.097 kN ii) Load from Midd.& Rear Wheel=mgLL-Truck*IM*LLInt-Wheel-Mid&Rear. = 253.116 kN

b) Factored LL on 1 no. Interior Girder due to Lane Load for per meter Length = mgLL-Lane*LLInt-Lane. = 10.850 kN/m

FLLInt-Lane.

10.850

kN/m

6 Shear & Moments at different Positions of an Exterior Girder due to Factored Loads (DL& LL) from Superstructure Components & Attachments : i) Arrangement of Wheel Loads for Exteriod Girder & c.g Point : a) Sketch Diagram Showing Wheels Loads of Truck, c.g. of Wheels & Location of Mid-Wheel under the Provisions of Absulate Max. Moments:

Page 138

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

145.000

Rear

kN c.g. of Wheel 2.845 m

145.000

kN c.g. of Girder 0.728 m

Middle

35.000

kN

Front

4.300

4.300

b) Calculations for Center of Gravity (cg) Position of Truck with Wheel Load in Respect of Rear Wheel; c.g. Distance from Rear Wheel = (Wt.-Mid*4.300+Wt.-Fornt*(2*4.300))/(2*145.000+35.000)

c.g.Wheel

2.845 m

c) Calculation Mid Wheel Position in Respect of Girder c.g. under Absulate Max. Moment Provision = (Distance beteen 2-Wheel - Distance of c.g. of Wheels from Rear Wheel)/2 dMid-Wheel 0.728 m d) Sketch Diagram of Factored Wheel Loads for Exterior Girder : 97.028

kN

97.028 2.845

Rear

kN

23.420

kN

c.g.

Middle

Front

4.300

4.300

e) Sketch Diagram of Girder with Factored Uniformly Distributed & Concentrated DL & LL, Different Locations for Shear & Moments Including Max. Reactions at Supports due to Different DL, LL-Lane Load & LL-Wheel Load : X-Girder-1 X-Girder-2 X-Girder-3 X-Girder-4 X-Girder-5 10.658 kN 10.658 kN 10.658 kN 10.658 kN 10.658 kN 0.300 6.100 m 6.100 m 6.100 m 6.100 m 0.300 m Rear Wheel Positions under c.g Provisions. m CL of Girder CL of Bearing CL of Bearing L /2 12.200 m Midd. Wheel Positions under c.g Provisions. m 3L/8 0.728 m Front Wheel Positions under c.g Provisions. L /4 9.150 2.845 4.300 0.300 L /8 6.100 m m 0.300 m 3.050 m m  FDLExt-All = 47.729 kN/m  FLLExt-Lane-Ped. = 11.401kN/m

A

 FDLExt-All =  FLLExt-Lane-Ped =

0.375

B 47.729 kN/m 11.401 kN/m

0.375

m LSpan =

24.40 m

LTotal =

25.00 m

Page 139

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

RA-DL = 596.610 kN RA-DL-X-Gir.= 26.645 kN RA-LL-L = 142.516 kN RA-LL-Wh.= 115.224 (Max. Reaction due to Wheel Load at c.g. Position)

RB-DL = 596.610 kN RB-DL-X-Gir.= 26.645 kN RB-LL-L = 142.516 kN RB-LL-Wh.= 102.252 kN (Max. Reaction due to Wheel Load at c.g. Position)

ii) Calculation of Factored Shear Forces & Moments at Different Locations of Exterior Girder Against Applied Factored Loads : a) Table showing Factored Shear Forces & Moments at Different Location of Girder due to Uniformly Distributed Dead Loads from Sidewalk, Attachments, Utilities, WC, Slab, Self Weight of Girder & Concentrated Dead Loads of Cross Girders ( FDLExt-All & FDLExt-Gir-X-Gir.): Table-6-ii-a-1. Factored Shearing Forces due to all Uniformly Distributed Dead Loads on Exterior Girder. Location From Support-A Shearing Forces in kN

On Support 582.291

0.375m 564.393

L/8

L/4

3L/8

436.718

291.146

145.573

c.g.

L/2

-34.732

0.000

Table-6-ii-a-2. Factored Moments due to all Dead Loads (DL) on Exterior Girder. Location From Support-A Moments in kN-m

On Support

0.375m

L/8

L/4

3L/8

c.g.

L/2

0.000

220.373

1597.661

2751.326

3460.993

3724.446

3726.663

b) Table showing Factored Shear Forces & Moments at Different Location of Girder due to Concentrated Dead Load from Cross Girders (FDLExt-Gir-X-Gir.): Table-6-ii-b-1. Factored Shearing Forces due to Concentrated Dead Loads of X-Girder on Exterior Girder. Location From Support-A Shearing Forces in kN

On Support 15.987

0.375m

L/8

L/4

3L/8

c.g.

L/2

15.987

15.987

5.329

5.329

-5.329

-5.329

Table-6-ii-b-2. Factored Moments due to all Dead Loads (DL) on Exterior Girder. Location From Support-A Moments in kN-m

On Support

0.375m

L/8

L/4

3L/8

c.g.

L/2

0.000

5.995

48.760

97.520

113.774

126.149

130.027

c) Table showing Factored Shear Forces & Moments at Different Location of Girder due to Uniformly Distributed Dead Loads from Sidewalk, Attachments, Utilities, WC, Slab, Self Weight of Girder & Concentrated Dead Loads of Cross Girders ( FDLExt-All & FDLExt-Gir-X-Gir.): Table-6-ii-c-1. Factored Shearing Forces due to all Applied Dead Loads on Exterior Girder. Location From Support-A

On Support

0.375m

L/8

L/4

3L/8

c.g.

L/2

Uniformly Distributed Load in kN

582.291

564.393

436.718

291.146

145.573

-34.732

0.000

Concentrated Loads in kN Total Dead Load Shear in kN

15.987

15.987

15.987

5.329

5.329

-5.329

-5.329

598.278

580.380

452.705

296.475

150.902

-40.061

-5.329

c.g.

L/2

Table-6-ii-c-2. Factored Moments due to all Applied Dead Loads on Exterior Girder. Location From Support-A

On Support

0.375m

Page 140

L/8

L/4

3L/8

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

For Uniformly Distributed in kN-m

0.000

For Concentrated in kN-m Total Monents in kN

0.000

5.995

48.760

97.520

113.774

126.149

130.027

0.000

226.368

1646.421

2848.846

3574.767

3850.595

3856.690

220.373

1597.661

2751.326

3460.993

3724.446

3726.663

d) Table showing Factored Shear Forces & Moments at Different Location of Girder due to Uniformly Distributed Live Live Load & Pedestrian Loads (FLLExt-Lane-Ped) : Table-6-ii-d-1. Factored Shearing Forces on Exterior Girder due to Live Lane Load & Pedestrian Load (LL) . Location From Support-A Shearing Forces in kN

On Support

0.375m

L/8

L/4

3L/8

c.g.

L/2

139.095

134.820

104.321

69.548

34.774

-8.297

0.000

Table-6-ii-d-2. Factored Moments on Exterior Girder due to Live Lane Load & Pedestrian Load (LL) . Location From Support-A Moments in kN-m

On Support

0.375m

L/8

L/4

3L/8

c.g.

L/2

0.000

52.642

381.643

657.225

826.747

993.917

890.210

e) Table showing Factored Shear Forces & Moments at Different Locations of Girder due to Applied Live Wheel Loads (FLLExt-Wheel) : Table-6-ii-e-1. Factored Shearing Forces on Exterior Girder due to Live Wheel-Load (LL) . Locatio From Support-A Support Positon of Rear/Midd. & Direction Reaction Rear Wheel at Support, AB 192.122 Rear Wheel at 0.375m, AB 188.780 Rear Wheel at L/8, A B 164.937 Rear Wheel at L/4, A B 137.753 Rear Wheel at 3L/8, A B 110.568 Midd. Wheel on c.g. Poisition A B 115.224 Rear Wheel at L/2, A B 83.384 Midd. Wheel on c.g. Poisition B A 102.252 Rear Wheel at L/2, BA 134.092 Rear Wheel at 3L/8, B A 161.276 Rear Wheel at L/4, B A 162.641 Rear Wheel at L/8, B A 84.899 Rear Wheel at 0.375m, B A 95.536 Rear Wheel at Support, B A 97.028

On Support

0.375m

L/8

L/4

3L/8

L/2

95.094 91.752 67.910 40.725 13.541 -78.832 -13.644 -18.196 -83.384 -56.200 -31.415 -12.128 -1.491 0.000

Table-6-ii-e-2. Factored Moments on Exterior Girder due to Live Wheel-Load (LL) . Locatio From Support-A Support Positon of Rear/Midd. & Direction Reaction Rear Wheel at Support, A B 192.122 Rear Wheel at 0.375m, A B 188.780 Rear Wheel at L/8, A B 164.937 Rear Wheel at L/4, A B 137.753 Rear Wheel at 3L/8, A B 110.568 Midd. Wheel on c.g. Poisition A B 115.224 Rear Wheel at L/2, A B 83.384

On Support

0.375m

L/8

L/4

3L/8

L/2 c.g.

0.000 70.792 503.059 840.293 1011.702 1072.359 1017.285

Page 141

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Midd. Wheel on c.g. Poisition B A Rear Wheel at L/2, B A Rear Wheel at 3L/8, B A Rear Wheel at L/4, B A Rear Wheel at L/8, B A Rear Wheel at 0.375m, B A Rear Wheel at Support, B A

102.252

1072.359

134.092

1017.285

161.276

857.043

162.641

574.889

84.899

258.943

95.536

35.826

97.028

0.000

f) Table showing Max. Shear Forces at Different Locations of Exterior Girder due to respective Factored Dead Loads (DL), Live Loads (LL) for Lane Load & Wheel Load & their Summation for Each Point of Application :

Table-6-ii-f-1. Sum. of Factored Max. Shear Forces Against All Applied Loads (DL & LL) on Exterior Girder. Locations from Support-A Loading Type Unit a. Dead Load (FDLExt) b. Lane + Ped.(LL) (FLLExt) a. Wheel Live Load (WLLExt) Total Shears on Each Point

kN

0.375m kN

L/8 kN

L/4 kN

3L/8 kN

c.g. kN

L/2 kN

598.278

580.380

452.705

296.475

150.902

-40.061

-5.329

139.095

134.820

104.321

69.548

34.774

-8.297

0.000

On Support

95.094

91.752

67.910

40.725

13.541

1072.359

1017.285

832.468

806.951

624.936

406.747

199.216

1024.001

1011.956

e) Table showing the Max. Moments at Different Locations of Exterior Girder due to respective Factored Dead Loads (DL), Live Loads (LL) for Lane Load & Wheel Load & their Summation for Each Point of Application :

Table-6-ii-e-1. Sum. of Factored Max. Moments Against All Applied Loads (DL & LL) on Exterior Girder. Locations from Support-A Loading Type Unit a. Dead Load (FDLExt) b. Lane+Ped.(LL) (FL&PLExt) c. Wheel Live Load (FWLLExt) Total Moments on Each Point

kN-m

0.375m kN-m

L/8 kN-m

L/4 kN-m

3L/8 kN-m

c.g. kN-m

L/2 kN-m

0.000

226.368

1646.421

2848.846

3574.767

3850.595

3856.690

0.000

52.642

381.643

657.225

826.747

993.917

890.210

0.000

70.792

503.059

840.293

1011.702

1072.359

1017.285

0.000

106.618

2531.123

4346.364

5413.216

5916.871

5764.185

On Support

7 Factored Shear & Moments at different Positions of an Interior Girder due to Factored Loads (DL& LL) from Superstructure Components & Attachments : i) Arrangement of Wheel Loads for Interiod Girder & c.g Point : a) Sketch Diagram Showing Wheels Loads of Truck, c.g. of Wheels & Location of Mid-Wheel under the Provisions of Absulate Max. Moments: 145.000

Rear

kN c.g. of Wheel 2.845 m

145.000

kN c.g. of Girder 0.728 m

Middle

35.000

kN

Front

4.300

4.300

b) Calculations for Center of Gravity (cg) Position of Truck with Wheel Load in

Page 142

c.g.Wheel

2.845 m

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Respect of Rear Wheel; c.g. Distance from Rear Wheel = (Wt.-Mid*4.300+Wt.-Fornt*(2*4.300))/(2*145.000+35.000) c) Calculation Mid Wheel Position in Respect of Girder c.g. under Absulate Max. Moment Provision = (Distance beteen 2-Wheel - Distance of c.g. of Wheels from Rear Wheel)/2 dMid-Wheel 0.728 m d) Sketch Diagram Showing Factored Wheel Loads for Interior Girder : 253.116

kN

253.116 2.845

Rear

0.728 kN

61.097

kN

c.g.

Middle

Front

4.300

4.300

e) Sketch Diagram of Girder with Uniformly Distributed Factored DL & LL, Different Locations for Shear & Moments Including Max. Reactions at Supports due to DL, LL-Lane Load & LL-Wheel Load : X-Girder-1 21.316

X-Girder-2 kN

0.300

21.316 6.100

m

X-Girder-3 kN

21.316 6.100

X-Girder-4 kN

m

21.316 6.100

m

X-Girder-5 kN

21.316 6.100

kN

m

0.300

m Rear Wheel Positions under c.g Provisions.

m CL of Girder

CL of Bearing L /2 12.200 m

3L/8 L /4

0.300 m

L /8 3.050

9.150

6.100

m

c.g. of Wheels. m

Midd. Wheel Positions under c.g Provisions.

0.728 m

Front Wheel Positions under c.g Provisions.

2.845

4.300

m

0.300

m

m

 FDLInt-All = 36.750kN/m  FLLInt-Lane-Ped. = 10.850kN/m

A

CL of Bearing

0.375

B  FDLExt-All =

36.750 kN/m

 FLLExt-Lane-Ped =

10.850 kN/m

0.375

m LSpan =

24.400

m

LTotal =

25.000

m

RA-DL = 459.375 kN RA-DL-X-Gir.= 53.290 kN RA-LL-L = 135.625 kN RA-LL-Wh.= 300.584 (Max. Reaction due to Wheel Load at c.g. Position)

RB-DL = 459.375 kN RB-DL-X-Gir.= 53.290 kN RB-LL-L = 135.625 kN RB-LL-Wh.= 266.744 kN (Max. Reaction due to Wheel Load at c.g. Position)

ii) Calculation of Factored Shear Forces & Moments at Different Locations of Interior Girder Against Applied Factored Loads :

Page 143

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

a) Table showing Factored Shear Forces & Moments at Different Location of Girder due to Uniformly Distributed Dead Loads from Sidewalk, Attachments, Utilities, WC, Slab, Self Weight of Girder & Concentrated Dead Loads of Cross Girders ( FDLInt-All & FDLInt-Gir-X-Gir.): Table-7-ii-a-1. Factored Shearing Forces due to all Uniformly Distributed Dead Loads on Interior Girder. Location From Support-A Shearing Forces in kN

On Support 448.350

0.375m 434.569

L/8

L/4

3L/8

336.263

224.175

112.088

c.g.

L/2

-26.743

0.000

Table-7-ii-a-2. Factored Moments due to all Dead Loads (DL) on Interior Girder. Location From Support-A Moments in kN-m

On Support

0.375m

L/8

L/4

3L/8

c.g.

L/2

0.000

169.682

1230.160

2118.454

2664.880

2867.733

2869.440

b) Table showing Factored Shear Forces & Moments at Different Location of Girder due to Concentrated Dead Load from Cross Girders (FDLExt-Gir-X-Gir.): Table-7-ii-b-1. Factored Shearing Forces due to Concentrated Dead Loads of X-Girder on Interior Girder. Location From Support-A Shearing Forces in kN

On Support 31.974

0.375m

L/8

L/4

3L/8

c.g.

L/2

31.974

31.974

10.658

10.658

-10.658

-10.658

Table-7-ii-b-2. Factored Moments due to Concentrated Dead Loads of X-Girder on Interior Girder. Location From Support-A Moments in kN-m

On Support

0.375m

L/8

L/4

3L/8

c.g.

L/2

0.000

11.990

97.520

195.041

227.548

252.299

260.054

c) Table showing Factored Shear Forces & Moments at Different Location of Girder due to Uniformly Distributed Dead Loads from Sidewalk, Attachments, Utilities, WC, Slab, Self Weight of Girder & Concentrated Dead Loads of Cross Girders ( FDLExt-All & FDLExt-Gir-X-Gir.): Table-7-ii-c-1. Factored Shearing Forces due to all Applied Dead Loads on Interior Girder. Location From Support-A

On Support

0.375m

L/8

L/4

3L/8

c.g.

L/2

For Uniformly Distributed Loads

448.350

434.569

336.263

224.175

112.088

-26.743

0.000

For Concentrated Loads Total Dead Load Shear in kN

31.974

31.974

31.974

10.658

10.658

-10.658

-10.658

480.324

466.543

368.236

234.833

122.745

-37.401

-10.658

Table-7-ii-c-2. Factored Moments due to all Applied Dead Loads on Interior Girder. Location From Support-A

On Support

0.375m

L/8

L/4

3L/8

c.g.

L/2

For Uniformly Distributed Load

0.000

169.682

1230.160

2118.454

2664.880

2867.733

2869.440

For Concentrated Load Total Monents in kN-m

0.000

11.990

97.520

195.041

227.548

252.299

260.054

0.000

181.672

1327.681

2313.495

2892.428

3120.031

3129.494

d) Table showing Factored Shear Forces & Moments at Different Location of Girder due to Uniformly Distributed Live Live Load & Pedestrian Loads (FLLInt-Lane-Ped) : Table-7-ii-d-1. Factored Shearing Forces on Interior Girder due to Live Lane Load & Pedestrian Load (LL) .

Page 144

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Location From Support-A Shearing Forces in kN

On Support

0.375m

L/8

L/4

3L/8

c.g.

L/2

132.370

128.301

99.278

66.185

33.093

-7.895

0.000

Table-7-ii-d-2. Factored Moments on Interior Girder due to Live Lane Load & Pedestrian Load (LL) . Location From Support-A Moments in kN-m

On Support

0.375m

L/8

L/4

3L/8

c.g.

L/2

0.000

50.096

363.190

625.448

786.774

945.861

847.168

e) Table showing Factored Shear Forces & Moments at Different Locations of Girder due to Applied Live Wheel Loads (FLLInt-Wheel) : Table-7-ii-e-1. Factored Shearing Forces on Interior Girder due to Live Wheel-Load (LL) . Locatio From Support-A Support Positon of Rear/Midd. & Direction Reaction Rear Wheel at Support, AB 501.188 Rear Wheel at 0.375m, AB 492.468 Rear Wheel at L/8, A B 430.272 Rear Wheel at L/4, A B 359.356 Rear Wheel at 3L/8, A B 288.439 Midd. Wheel on c.g. Poisition A B 300.584 Rear Wheel at L/2, A B 217.523 Midd. Wheel on c.g. Poisition B A 266.744 Rear Wheel at L/2, BA 223.247 Rear Wheel at 3L/8, B A 420.721 Rear Wheel at L/4, B A 424.280 Rear Wheel at L/8, B A 221.476 Rear Wheel at 0.375m, B A 249.226 Rear Wheel at Support, B A 253.116

On Support

0.375m

L/8

L/4

3L/8

L/2

248.072 239.353 177.156 106.240 35.324 -205.648 -35.592 -47.468 -344.081 -146.607 -81.951 -31.639 -3.890 0.000

Table-7-ii-e-2. Factored Moments on Interior Girder due to Live Wheel-Load (LL) . Locatio From Support-A Support Positon of Rear/Midd. & Direction Reaction Rear Wheel at Support, A B 501.188 Rear Wheel at 0.375m, A B 492.468 Rear Wheel at L/8, A B 430.272 Rear Wheel at L/4, A B 359.356 Rear Wheel at 3L/8, A B 288.439 Midd. Wheel on c.g. Poisition A B 300.584 Rear Wheel at L/2, A B 217.523 Midd. Wheel on c.g. Poisition B A 266.744 Rear Wheel at L/2, B A 223.247 Rear Wheel at 3L/8, B A 420.721 Rear Wheel at L/4, B A 424.280 Rear Wheel at L/8, B A 221.476 Rear Wheel at 0.375m, B A 249.226 Rear Wheel at Support, B A 253.116

On Support

0.375m

L/8

L/4

3L/8

L/2 c.g.

0.000 184.676 1312.328 2192.069 2639.221 2797.457 2653.786 2797.457 1109.781 2588.380 2132.499 675.502 93.460 0.000

f) Table showing Max. Shear Forces at Different Locations of Interior Girder due to respective Factored Dead Loads

Page 145

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

(DL), Live Loads (LL) for Lane Load & Wheel Load & their Summation for Each Point of Application :

Table-7-ii-f-1. Sum. of Factored Max. Shear Forces Against All Applied Loads (DL & LL) on Interior Girder. Locations from Support-A Loading Type Unit a. Dead Load (FDLExt) b. Lane + Ped.(LL) (FLLExt) a. Wheel Live Load (WLLExt) Total Shears on Each Point

kN

0.375m kN

L/8 kN

L/4 kN

3L/8 kN

c.g. kN

L/2 kN

480.324

466.543

368.236

234.833

122.745

-37.401

-10.658

132.370

128.301

99.278

66.185

33.093

-7.895

0.000

248.072

239.353

177.156

106.240

35.324

-47.468

-35.592

860.766

834.197

644.670

407.258

191.162

-92.764

-46.250

On Support

e) Table showing the Max. Moments at Different Locations of Interior Girder due to respective Factored Dead Loads (DL), Live Loads (LL) for Lane Load & Wheel Load & their Summation for Each Point of Application :

Table-7-ii-e-1. Sum. of Factored Max. Moments Against All Applied Loads (DL & LL) on Interior Girder. Locations from Support-A Loading Type Unit a. Dead Load (FDLExt) b. Lane+Ped.(LL) (FL&PLExt) c. Wheel Live Load (FWLLExt) Total Moments on Each Point

kN-m

0.375m kN-m

L/8 kN-m

L/4 kN-m

3L/8 kN-m

c.g. kN-m

L/2 kN-m

0.000

181.672

1327.681

2313.495

2892.428

3120.031

3129.494

On Support

0.000

50.096

363.190

625.448

786.774

945.861

847.168

0.000

184.676

1312.328

2192.069

2639.221

2797.457

2653.786

0.000

278.135

3003.199

5131.011

6318.423

6863.350

6630.449

8 Factored Shear Forces at a Distance 2d from Face of Support for Interior Girder : a) d is Effective Depth of Neutral Axis of Tensial Reinforcement from the Extrm Compression Fiber of T-Girder for the Section. Here d = de = 1886.000 mm. c) Distance of 2d Loacation from Support Point (Bearing Point), L2d = 2de m

d

1.883 m

L2d

3.766

m

d) Shear Force due to Dead Load, FDL2d = RDL-A -  FDLInt*L2d -FDLInt-Gir-X-Gir.

FDL2d

e) Shear Force due to Live Lane Load, FLLL2d = RLLL-A -  FLLInt*L2d

FLLLdv

94.768

kN

f) Shering Force due to Live Wheel Load with Rear Wheel at a Distance from Support Point, FWLLInt. = RWLL-A - Wheel-LL-Rear

FWLL2d

160.517

kN

Vu-2d

608.249

kN

g) Total Factored Shear Force at a Distance 2*d from Support, FSF2d = FDL2d + FLLL2d + FWLL2d

352.96 kN

9 Factored Shear Forces & Moments at a Distance dv from Face of Support for Interior Girder : i) Factored Shear Forces at a Distance dv from Face of Support for Interior Girder : a) dv is Effective Shear Depth of T-Girder at a Section according to provision of AASHTO-LRFD-5.8.2.9 with a value dv = 1.697.000 mm for Interior Girder from Support Face.

Page 146

dv

1.712

m

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

b) Distance of Loacation from Support Point (Bearing Point), Ldv = (L0.375+ dv) m

Ldv

2.087

m

c) Shear Force due to Dead Load, FDLdv = RDL-A -  FDLInt*Ldv -FDLInt-Gir-X-Gir.

FDLdv

361.369

kN

d) Shear Force due to Live Lane Load, FLLLdv = RLLL-A -  FLLInt*Ldv

FLLLdv

112.983

kN

e) Shering Force due to Live Wheel Load with Rear Wheel at a Distance Ldv from Support Point, FWLLInt. = RWLL-A - Wheel-LL-Rear

FWLLdv

199.551

kN

Vu-dv

673.904

kN

f) Total Factored Shear Force at a Distance dv from Support Face, FSFdv = FDLdv + FLLLdv + FWLLdv

ii) Moments at a Distance dv from Face of Support for Interior Girder due to Factored Forces : a) Moment due to Dead Load, = RDL-All *Ldv - FDLInt*Ldv2/2-FDLInt-Gir-X-Gir.*Ldv

Mdv-DL

945.329

kN-m

b) Moment due to Live Lane Load, = RLLL-A *Ldv - FLLInt*Ldv2/2

Mdv-LLL

259.398

kN-m

c) Moment Wheel Loads having Rear Wheel on Critica Section

Mdv-LWL

774.875

kN-m

1,979.602

kN-m

d) Total Factored Moment at Critical Section due to Dead & Live Lodes.

Mdv-DL+LL

10 Moments at Different Locations of Exterior Girder due to Unfactored Dead Loads : a) Sketch Diagram showing required Locations of Exterior Girder for Moments including Unfactored Dead Load. X-Girder-1 X-Girder-2 8.526 kN 8.526 kN 0.300 6.100 m 6.100 m Rear Wheel Positions under c.g Provisions.

X-Girder-3 8.526 kN m 6.100 CL of Girder

CL of Bearing

L /2 3L /8 L /4 L /8 3.05

0.300

X-Girder-4 8.526 kN m 6.100

9.150

12.20 0.728

X-Girder-5 8.526 kN m

0.300 m

CL of Bearing

c.g. of Wheels. Midd. Wheel Positions under c.g Provisions. Front Wheel Positions under c.g Provisions.

2.845

4.300

6.100

0.300

 DLExt-UDL = 41.863kN/m

A

B  DLExt-UDL=

37.543 kN/m

0.375

RA-DL-UDL =

0.375

LSpan =

24.400 m

LTotal =

25.000 m

469.282 kN

RB-DL-UDL =

Page 147

469.282

kN

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

RA-DL-X-Gir =

21.316 kN

RB-DL-X-Gir =

21.316

kN

b) Moment at Different Section of Exterior Girder due to Uniformly Distributed & Concentrated Dead Load Table- 10-b-1. Moments due to Unfactored Uniformly Distribute & Concentrated Dead Loads : Locations from Support-A Loading Type Unit Uniformlu Distribute Load Concentrated Dead Load Total Unfactored Moment

kN-m

0.375m kN-m

L/8 kN-m

L/4 kN-m

3L/8 kN-m

c.g. kN-m

L/2 kN-m

0.000

173.341

1256.689

2164.139

2722.349

2929.576

2931.320

0.000

4.796

39.008

78.016

91.019

100.919

104.022

0.000

178.137

1295.697

2242.155

2813.368

3030.496

3035.342

On Support

11 Moments at Different Locations of Interior Girder due to Unfactored Dead Loads : a) Sketch Diagram showing required Locations of Interior Girder for Moments including Unfactored Dead Load. X-Girder-1 X-Girder-2 17.053 kN 17.053 kN 0.300 6.100 m 6.100 m Rear Wheel Positions under c.g Provisions.

X-Girder-3 17.053 kN m 6.100 CL of Girder

CL of Bearing

L /2 3L /8 L /4 L /8 3.050

0.300

X-Girder-4 17.053 kN m 6.100

9.150

X-Girder-5 17.053 kN m

0.300 m

CL of Bearing

c.g. of Wheels.

12.200 0.728

Midd. Wheel Positions under c.g Provisions. Front Wheel Positions under c.g Provisions.

2.845

4.300

6.100

0.300

 DLInt-UDL = 33.030kN/m

A

B  DLInt-UDL=

0.375

28.710 kN/m 0.375

RA-DL-UDL = RA-DL-Gir =

LSpan =

24.400 m

LTotal =

25.000 m

358.875 kN 42.632 kN

RB-DL-UDL = RB-DL-X-Gir =

358.875 42.632

kN kN

b) Moment at Different Section of Interior Girder due to Uniformly Distributed & Concentrated Dead Load Table- 11-b-1. Moments due to Unfactored Uniformly Distribute & Concentrated Dead Loads : Locations from Support-A Loading Type Unit Uniformlu Distribute Load Concentrated Dead Load Total Unfactored Moment

kN-m

0.375m kN-m

L/8 kN-m

L/4 kN-m

3L/8 kN-m

c.g. kN-m

L/2 kN-m

0.000

132.559

961.031

1654.988

2,081.870

2240.343

2241.677

0.000

9.592

78.016

156.033

182.038

226.657

208.044

0.000

142.152

1039.048

1811.021

2,263.908

2,467.000

2,449.720

On Support

Page 148

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 149

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

m-Wd.

Page 150

G. Calculations for Load, Shear & Moments of RCC Main Girders under Service Limit State of Design (WSD) : Description

Notation DImentions

Unit.

1 Structural Data : i) Dimentions of Superstructure : a) b) c) d) e) f) g) h) i) j) k) l) m) n) o) p) q) r) s) t) u) v) w) w-i) w-ii) x) y)

Span Length (Clear C/C distance between Bearings) Addl.Length of Girder beyond Bearing Center Line. Total Girder Length (a+2b) Carriageway Width Width of Side Walk on Each Side Width of Curb/Wheel Guard Width of Railing Curb/Post Guard Total Width of Bridge Deck Width & Depth of Railings Width & Breath of Railing Post Height of Railing Post Height of Wheel Guard/Curb Number of Railings on each Side C/C distance between Railing Posts Thickness of Deck Slab Thickness of Wearing Course Number of Main Girders Number of Cross Girders Depth of Main Girders (Including Deck Slab as Part of T-Girder) Depth of Cross Girders (Including Deck Slab) Width of Main Girders Width of Cross Girders C/C Distance between Main Girders & Flange Width C/C Distance between Cross Girders in Longitudinal Direction . Distance of Slab Outer Edge to Exterior Girder Center Clear Distance Between Main Interior Girders Filets : i) Main Girder in Vertical Direction ii) Main Girder in Horizontal Direction iii) X-Girder in Vertical Direction vi) X-Girder in Horizontal Direction z) Vertical Surface Area of Superstructure's Exposed Elements

SL SAddl. LGir. WCarr-Way. WS-Walk. WCurb. WR-Post. WB-Deck. RW&D. PW&B. hR-Post. hCurb. Rnos. C/CD-R-Post. tSlab. tWC NGirder. NX-Girder. hGirder. hX-Girder. bGirder. bX-Girder. C/CD-Girder. C/CD-X-Girder. CD-Ext.-Girder-Edg. ClD-Int.-Girder. FM-Girder-V. FM-Girder-H. FX-Girder-V. FX-Girder-H. ASup-Vert.

24.400 m 0.300 m 25.000 m 7.300 m 1.250 m 0.350 m 0.225 m 10.250 m 0.175 m 0.225 m 1.070 m 0.300 m 3.000 nos 2.000 m 0.200 m 0.075 m 5.000 nos 5.000 nos 2.000 m 1.900 m 0.350 m 0.250 m 2.000 m 6.100 m 1.125 m 1.650 m 0.150 m 0.150 m 0.075 m 0.075 m 2 87.108 m

ii) Number of Traffic Lane on Bridge Deck: a) Number of Design Traffic Lane = WCarr.-way/3600 = 7300/3600 Where WCarr.-way is Clear Carriageway Width in between Curbs in mm

NLane.

@

2.028

nos

2

nos

(ASSHTO LRFD-3.6.1.1.1) 2 Design Data : i) Design Criterion : a) AASHTO Load Resistance Factor Design (LRFD). b) Type of Loads : Combined Application of AASHTO HS20 Truck Loading & Lane Loading. ii) Design AASHTO HS20 Truck Loading : a) b) c) d) e) f) g) h)

Axle to Axle distance Wheel to Wheel distance Rear Wheel axle Load (Two Wheels) Rear Single Wheel Load Middle Wheel axle Load (Two Wheels) Middle Single Wheel Load Front Wheel axle Load (Two Wheels) Front Single Wheel Load

DAxel. DWheel. LLRW-Load LLRS-Load LLMW-Load LLMS-Load LLFW-Load LLFS-Load

1.800 4.300 145.000 72.500 145.000 72.500 35.000 17.500

m m kN kN kN kN kN kN

iii) Design AASHTO Lane Loading : a) Design Lane Loading is an Uniformly Distributed Load having Magnitude of 9.300N/mm through the Length of Bridge for 1 (One) Lane of Bridge & acting over a 3.000m Wide Dcak Strip in Transverse Direction. Thus Lane Load per meter Length of Bridge for 1 (One) Lane = (9.300*1000/1000)kN/m

LLLane

b) Design Lane Loading is an Uniformly Distributed Load having Magnitude of 9.300N/mm through the Length of Gridge for Single and acting over a 3.000m Wide Strip in Transverse Direction. Thus Intensity of Lane Load per meter Length & for per meter Width = 9.300/3.000kN/m/m-Wd.

LLLane-Int.

9.300 9.300

N/mm kN/m

3.100 kN/m/m-Wd. 0.00310 N/mm/mm-Wd.

iv) Design AASHTO Pedestrian Loading : a) Design Pedestrian Loading is an Uniformly Distributed Load having Magnitude of 3.600*10-3MPa through the Length of Sidewalk on both side and acting over the total Wide of Sidewalk. 3 vi) Unit Weight of Different Materials in kg/m : (Having value of Gravitional Acceleration, g =

a) b) c) d) e)

Unit weight of Normal Concrete Unit weight of Wearing Course Unit weight of Normal Water Unit weight of Saline Water Unit weight of Earth (Compected Clay/Sand/Silt)

LL-Pedest

2 0.00360 N/mm 2 3.600 kN/m

2 9.807 m/sec )

gc gWC gW-Nor. gW-Sali. gs

2,447.232 2,345.264 1,019.680 1,045.172 1,835.424

kg/m3 kg/m3 kg/m3 kg/m3 kg/m3

3 vii) Unit Weight of Materials in kN/m Related to Design Forces :

a) b) c) d) e)

Unit weight of Normal Concrete Unit weight of Wearing Course Unit weight of Normal Water Unit weight of Saline Water Unit weight of Earth (Compected Clay/Sand/Silt)

wc wWC wWater-Nor. wWater-Sali. wEatrh

24.000 23.000 10.000 10.250 18.000

kN/m3 kN/m3 kN/m3 kN/m3 kN/m3

viii) Strength Data related to Ultimate Strength Design( USD & AASHTO-LRFD-2004) : a) Concrete Ultimate Compressive Strength, f/c (Normal Concrete) b) Concrete Allowable Strength under Service Load Condition (SLC) = 0.40f/c c) Modulus of Elasticity of Concrete, Ec = 0.043gc1.50f/c = 0.043*24^(1.50)*21^(1/2) Mpa, (AASHTO LRFD-5.4.2.4). d) Poisson's Ration = 0.63f/c = 0.63*21^(1/2), subject to cracking and considered to be neglected (AASHTO LRFD-5.4.2.5). e) Modulus of Rupture of Concrete, fr = 0.63f/c Mpa (AASHTO LRFD-5.4.2.6). f) Steel Ultimate strength, fy (60 Grade Steel) g) Modulus of Elasticity of Reinforcement, Es for fy = 410 MPa

f/c fc Ec

21.000 8.400 23,855.620

MPa MPa MPa

2.887 fr fy ES

2.887

MPa

410.000 MPa 200000.000 MPa

ix) Other Design Related Data : a) Velocity of Wind Load in Normal Condition b) Velocity of Wind Load in Special Condition c) Velocity of Water/Stream Current Causing Water/Stream Load

VWL-Nor. VWL-Spe. VWA

90.000 260.000 4.200

3 Factors Applicable for Design of Different Structural Components : i) Formula for Load Factors & Selection of Load Combination : a) Formula for Load Factors Q = Σ ηigiQi  f Rn = Rr; (ASSHTO LRFD-1.3.2.1-1 & 3.4.1-1) Where, ηi is Load Modifier having values ηi = ηD ηR ηI  0.95 in which for Loads a Maximum value of gi Applicable; (ASSHTO LRFD-1.3.2.1-2), & ηi = 1/(ηD ηR ηI )  1.00 in which for Loads a Minimum value of gi Allpicable; (ASSHTO LRFD-1.3.2.1-3) Here: gi = Load Factor; a statistically based multiplier Applied to Force Effect, f = Resistance Factor; a statistically based multiplier Applied to Nominal Resitance, ηi = Load Modifier; a Factor related to Ductility, Redundancy and Operational Functions, For Strength Limit State; ηD ηi = ηD = 1.00 for Conventional Design related to Ductility, 1.000 ηR ηi = ηR = 1.00 for Conventional Levels of Redundancy , 1.000 ηi = ηI = 1.00 for Typical Bridges related to Operational Functions, Qi = Force Effect, Rn = Nominal Resitance,

ηl

1.000

km/hr km/hr m/s

Ri = Factored Resitance = fRn. 4 Different Load Multiplying Fatcors for Service Limit State Design (WSD) & Load Combination : a) The Bridge will have to face Cyclonic Storms with very high Intensity of Wind Load (Wind Velocity = 260km/hr), but those would be occasional. Thus the respective Multiplier Factors of Limit State SERVICE-I (Bridge used by Normal Vehicle with wind load having Wind Velocity of 90 km/hr) for normal operation & other respective Limit State SERVICE Groups are being Considered as CRITICAL conditions for Bridge Structure. i) Permanent & Dead Load Multiplier Factors for Service Limit State Design (WSD) According to AASHTOLRFD-3.4.1 ; Table 3.4.1-1&2 : a) Dead Load Multiplier Factor for Structural Components & Attachments-DC Applicable to All Components Except Wearing Course & Utilities (Max. value of Table 3.4.1-2)

gDC

1.000

b) Dead Load Multiplier Factor for Wearing Course & Utilities- DW , (Max. value of Table 3.4.1-2)

gDW

1.000

c) Multiplier Factor for Horizontal Active Earth Pressure on Substructure Components of Bridge-EH ; Applicable to Abutment & Wing Walls, (Max. value of Table 3.4.1-2)

gEH

1.000

d) Multiplier Factor for Vertical Earth Pressure on Substructure Components of Bridge-EV ; Applicable toAbutment & Wing Walls, (Max. value of Table 3.4.1-2)

gEV

1.000

e) Multiplier Factor for Surchage Pressure on Substructure Components of Bridge-ES ; Horizontal & Vertical Loads on Abutment & Wing Walls, (Max. value of Table 3.4.1-2)

gES

1.000

ii) Live Load Multiplier Factors for Service Limit State Design (WSD) According to AASHTO-LRFD-3.4.1; Table 3.4.1-1&2 : a) Multiplier Factor for Multiple Presence of Live Load ( No of Lane = 2)-m (ASSHTO LRFD-3.6.1.1.1)

m

1.000

gLL-Truck

1.000

IM

1.000

d) Multiplier Factor for Lane Loading-LL-Lane

gLL-Lane

1.000

e) Multiplier Factor for Pedestrian Loading-PL.

gLL-PL.

1.000

b) Multiplier Factor for Truck Loading (HS20 only)-LL-Truck . c) Multiplier Factor for Vhecular Dynamic Load Allowence-IM as per Provision of ASSHTO LRFD-3.6.2.1, Table 3.6.2.1-1(SERVICE - I); (Applicable only for Truck Loading & Tandem Loading)

f) Multiplier Factor for Vehicular Centrifugal Force-CE

SERVICE - II

gLL-CE.

1.300

g) Multiplier Factor for Vhecular Breaking Force-BR .

SERVICE - II

gLL-BR.

1.300

h) Multiplier Factor for Live Load Surcharge-LS i) Multiplier Factor for Water Load & Stream Pressure-WA

gLL-LS.

1.000

gLL-WA.

1.000

j) Multiplier Factor for Wind Load on Structure-WS

SERVICE - IV

gLL-WS.

0.700

l) Multiplier Factor for Wind Load on Live Load-WL

SERVICE - II

gLL-WL

1.300

gLL-FR.

1.000

gLL-TU.

1.000

gLL-CR.

1.000

n) Multiplier Factor for deformation due to Shrinkage of Concrete-SH (With Elastomeric Bearing).

gLL-SH.

1.000

o) Multiplier Factor for Temperature Gradient-TG (With Elastomeric Bearing).

gLL-TG.

1.000

p) Multiplier Factor for Settlement of Concrete-SE (With Elastomeric Bearing).

gLL-SE.

1.000

q) Multiplier Factor for Earthquake -EQ

gLL-EQ.

-

r) Multiplier Factor for Vehicular Collision Force-CT

gLL-CT.

-

t) Multiplier Factor for Vessel Collision Force-CV

gLL-CV.

1.000

k) Multiplier Factor for Water Load & Stream Pressure-FR l) Multiplier Factor for deformation due to Uniform Temperature Change -TU (With Elastomeric Bearing). m) Multiplier Factor for deformation due to Creep on Concrete-CR (With Elastomeric Bearing).

5 Load Calculations for Superstructural Components & Attachments (DL & LL) per meter Length of Girder: i) Dead Loads on 1 no. Exterior Girder from Different Components & Attachments : a) Dead Load on. Exterior Girder due to Self Wt.& Attachments (Without WC & Utilies) for per meter Length of Girder. b) Dead Load on Exterior Girder due to WC. & Utilities for per meter Length of Girder

DLExt-Gir-Self& Atta.

34.340

kN/m

DLExt-Gir-WC+ Utility.

3.203

kN/m

DLExt-Gir-X-Gir.

8.526

kN

DLExt.U-D

37.543

c) Concentrated Dead Load on Exterior Girder from to 1 no. Cross Girder d) Sumation of Uniformly Distributed Dead Loads on Exterior Girder (a + b) for per Meter Length of Girder.

ii) Dead Loads on 1 no. Interior Girder from Different Components & Attachments :

kN/m

a) Dead Load on.Interior Girder due to Self Wt.& Attachments (Without WC & Utilies) for per meter Length of Girder.

DLIntt-GirSelf & Atta.

25.260

kN/m

b) Dead Load on Interior Girder from WC. for per meter Length of Girder

DLInt-Gir-WC.

3.450

kN/m

c) Concentrated Dead Load on Interior Girder from to 1 no. Cross Girder

DLInt-Gir-X-Gir.

17.053

kN

DL-Int.UD

28.710

kN/m

d) Sumation of Uniformly Distributed Dead Loads on Interior Girder (a + b) for

iii) Live Loads (LL) on 1 no. Exterior Girder due to Wheel Load, Lane Load & Pedestrian Load according Provisions of AASHTO-LRFD-3.6.1.2.2, 3.6.1.2.4 & 3.6.1.6 : a) Sketch Diagram For Distribution of Wheel Load, Lane Load & Pedestrian Load on Exterior Girders : Midd. & Rear Wheel Load = Front Wheel Load =

72.500 kN 17.500 kN 1.475 0.225 7.300

0.600

1.250 0.300

1.800

1.070 9.300kN/m Lane Load on

0.300 0.200 0.950

0.250 1.650

1.650

1.125

2.000

2.000

1.650

2.000

1.650

2.000

0.950

1.125

CL 10.25 b) LL on 1 no. Exterior Girder due to Wheel Load at distance 0.600m from Wheel Guard Face; i) From Front Wheel (Sketch Diagram) = 10.063 kN LLExt-Wheel-Front. ii) From Midd. & Rear Wheel (do) = 41.688 kN LLExt-Wheel-Mid& Rear. c) LL on 1 no. Exterior Girder due to Lane Load Uniformly Distributed over Full Bridge Length with Intensity of 3.100N/m/m-Wd. on 0.650m Width from Wheel Guard Face up to Middle point between Two Girders. (From Sketch Diagram) = 2.015 kN/m d) LL on 1 no. Exterior Girder due to Pedestrian Load Uniformly Distributed over Sidewalk on Full Bridge Length with Intensity of 4.000kN/m 2 on Sidewalk on each side (From Sketch Diagram) = 4.500 kN/m

10.063 41.688

kN kN

LLExt-Lane.

2.015

kN/m

LLExt-Pedes.

4.500

kN/m

iv) Live Loads (LL) on 1 no. Interior Girder due to Wheel Load & Lane Load according to Provisions of AASHTO-LRFD-3.6.1.2.2, 3.6.1.2.4 & 3.6.1.6 :

a) Sketch Diagram For Distribution of Wheel Load & Lane Load on Interior Girders : Midd. & Rear Wheel Load = Front Wheel Load =

72.500 17.500

kN kN

72.500 kN 17.500 kN 1.475 7.300

0.200

1.800

1.200

0.225 1.250 0.300

0.800

1.070 9.300kN/m Lane Load on 9.300kN/m Lane Load on

0.300 0.200 0.950

1.125

0.250 1.650

2.000

1.650

1.650

2.000

2.000

1.650

0.950

2.000

1.125

CL 10.250 b) LL on 1 no.Interior Girder due to Wheel Load with One Line of Wheels LLInt-Wheel-Front. upon Girder & the other Line of Wheels at Axle Distance - 1.800m LLInt-Wheel-Mid& Rear. i) Load from Front Wheel (From Sketch Diagram) = 26.250 kN ii) Load from Midd. & Rear Wheel (From Sketch Diagram) = 108.750 kN

26.250 108.750

c) LL on 1 no. Interior Girder due to Lane Load Uniformly Distributed over LLInt-Lane. Full Bridge Length having Intensity of 9.300kN/m on 3.000m Width of Deck having Equally distance (1.500m) from Middle point of a Girder & action for Girder with 2.000m Width (From Sketch Diagram) = 6.200 kN/m

6.200

kN kN

kN/m

6 Factored Loads of Superstructure Components & Attachments (DL & LL) Service Limit State Design (WSD): i) Factored Dead Loads on 1 no. Exterior Girder from Different Components & Attachments : a) Factored Dead Load on Exterior Girder due to Self Wt.& Attachments (Without WC) for per Meter Length = gDC*DLExt-Gir-Self& Atta. =

FDLExt-Gir-Self & Atta. 34.340 kN/m

34.340

kN/m

b) Factored Dead Load on Exterior Girder due to WC. & Utilities for FDLExt-Gir-WC+ Utility. per Merter Length = gDW*DLExt.-Gir-WC+Utility = 3.203 kN/m

3.203

kN/m

c) Factored Concentrated Dead Load on Exterior Girder from to 1 no. Cross Girder = gDC*DLExt-Gir-X-Gir. =. 8.526 kN

FDLExt-Gir-X-Gir.

8.526

kN

FDL-Ext.UD

37.543

d) Sumation of Factored Uniformly Distributed Dead Loads on Exterior Girder (a + b) for per Meter Length of Girder.

ii) Factored Dead Loads on 1 no. Interior Girder from Different Components & Attachments :

kN/m

a) Factored Dead Load on Interior Girder due to Self Wt.& Attachments (Without WC) for per Meter Length = gDC*DLInt-Gir-Self& Atta. = b) Factored Dead Load on Interior Girder due to WC. & Utilities for per Merter Length = gDW*DLInt.-Gir-WC = 3.450 kN/m

FDLIntt-GirSelf & Atta. 25.260 kN/m

25.260

kN/m

FDLInt-Gir-WC+ Utility.

3.450

kN/m

FDLInt-Gir-X-Gir.

17.053

kN

FDL-Int.UD

28.710

kN/m

c) Factored Concentrated Dead Load on Interior Girder from to 1 no. Cross Girder = gDC*DLInt-Gir-X-Gir. =. 17.053 kN d) Sumation of Factored Uniformly Distributed Dead Loads on Interior Girder (a + b) for per Meter Length of Girder. iii) Factored Live Loads of Different Components for 1 no. Exterior Girder :

a) Factored LL on 1 no. Exterior Girder due to Wheel Load at distance 0.600m from Wheel Guard Face; i) From Front Wheel = mgLL-Truck*IM*LLExt-Wheel-Front FLLExt-Wheel-Front. 10.063 = 10.063 kN ii) Load from Midd.& Rear Wheel=mgLL-Truck*IM*LLExt-Wheel-Mid&Rear. FLLExt-Wheel-Mid& Rear. 41.688 = 41.688 kN b) Factored LL on 1 no. Exterior Girder due to Lane Load = mgLL-Lane*LLExt-Lane. = 2.015 kN/m c) Factored LL on 1 no. Exterior Girder due to Pedestrian Load = mgLL-PL*LLExt-Pedes. = 4.500 kN/m d) Summation of Factored LL of Exterior Girder for per meter Length due to Lane Load & Pedestrian Loads

kN kN

FLLExt-Lane.

2.015

kN/m

FLLExt-Pedes.

4.500

kN/m

FLL-Ext.

6.515

kN/m

iv) Factored Live Loads of Different Components for 1 no. Interior Girder : a) Factored LL on 1 no.Interior Girder due to Wheel Load i) Load from Front Wheel = mgLL-Truck*IM*LLInt-Wheel-Front = 26.250 kN ii) Load from Midd.& Rear Wheel=mgLL-Truck*IM*LLInt-Wheel-Mid&Rear. = 108.750 kN

FLLInt-Wheel-Front.

26.250

kN

FLLInt-Wheel-Mid& Rear.

108.750

kN

b) Factored LL on 1 no. Interior Girder due to Lane Load for per meter Length = mgLL-Lane*LLInt-Lane. = 6.20 kN/m

FLLInt-Lane.

6.200

kN/m

6 Shear & Moments at different Positions of an Exterior Girder due to Factored Loads (DL& LL) from Superstructure Components & Attachments : a) Sketch Diagram Showing Wheels Loads of Truck, c.g. of Wheels & Location of Mid-Wheel under the Provisions of Absulate Max. Moments: 145.000 kN 145.000 kN 35.000 kN c.g. of Wheel c.g. of Girder 2.845 m 0.728 m

Rear

Middle

Front

4.300

4.300

b) Calculations for Center of Gravity (cg) Position of Truck with Wheel Load in Respect of Rear Wheel; c.g. Distance from Rear Wheel = (Wt.-Mid*4.300+Wt.-Fornt*(2*4.300))/(2*145.000+35.000)

c.g.Wheel

2.845 m

c) Calculation Mid Wheel Position in Respect of Girder c.g. under Absulate Max. Moment Provision = (Distance beteen 2-Wheel - Distance of c.g. of Wheels from Rear Wheel)/2 dMid-Wheel 0.728 m d) Sketch Diagram of Factored Wheel Loads for Exterior Girder : 41.688

kN

41.688 2.845

Rear

kN

10.063

kN

c.g.

Middle

Front

4.300

4.300

e) Sketch Diagram of Girder with Factored Uniformly Distributed & Concentrated DL & LL, Different Locations for Shear & Moments Including Max. Reactions at Supports due to Different DL, LL-Lane Load & LL-Wheel Load : X-Girder-1 X-Girder-2 X-Girder-3 X-Girder-4 X-Girder-5 8.526 kN 8.526 kN 8.526 kN 8.526 kN 8.526 kN 0.300 6.100 m 6.100 m 6.100 m 6.100 m 0.300 m Rear Wheel Positions under c.g Provisions. m CL of Bearing CL of Girder CL of Bearing L /2 c.g. of Wheels. 12.200 m Midd. Wheel Positions under c.g Provisions. 3L/8 0.728 m Front Wheel Positions under c.g Provisions. L /4 9.150 2.845 4.300 0.300 L /8 6.100 m m 0.300 m 3.050 m m  FDLExt-All = 41863kN/m  FLLExt-Lane-Ped. = 65151kN/m

A 0.375

B

 FDLExt-All =  FLLExt-Lane-Ped =

m

37.543 kN/m 6.515 kN/m

0.375

m

RA-DL = RA-DL-X-Gir.=

469.282 kN 21.316 kN

LSpan =

24.400

m

LTotal =

25.000

m RB-DL = RB-DL-X-Gir.=

490.598 21.316

kN kN

RA-LL-L = 81.438 kN RA-LL-Wh.= 49.505 (Max. Reaction due to Wheel Load at c.g. Position)

RB-LL-L = 81.438 kN RB-LL-Wh.= 43.932 kN (Max. Reaction due to Wheel Load at c.g. Position)

ii) Calculation of Factored Shear Forces & Moments at Different Locations of Exterior Girder Against Applied Factored Loads : a) Table showing Factored Shear Forces & Moments at Different Location of Girder due to Uniformly Distributed Dead Loads from Sidewalk, Attachments, Utilities, WC, Slab, Self Weight of Girder & Concentrated Dead Loads of Cross Girders ( FDLExt-All & FDLExt-Gir-X-Gir.): Table-6-ii-a-1. Factored Shearing Forces due to all Uniformly Distributed Dead Loads on Exterior Girder. Location From Support-A Shearing Forces in kN

On Support 458.019

0.375m 443.940

L/8

L/4

3L/8

343.514

229.009

114.505

c.g.

L/2

-27.319

0.000

Table-6-ii-a-2. Factored Moments due to all Dead Loads (DL) on Exterior Girder. Location From Support-A Moments in kN-m

On Support

0.375m

L/8

L/4

3L/8

c.g.

L/2

0.000

173.341

1256.689

2164.139

2722.349

2929.576

2931.320

b) Table showing Factored Shear Forces & Moments at Different Location of Girder due to Concentrated Dead Load from Cross Girders (FDLExt-Gir-X-Gir.): Table-6-ii-b-1. Factored Shearing Forces due to Concentrated Dead Loads of X-Girder on Exterior Girder. Location From Support-A Shearing Forces in kN

On Support 12.790

0.375m

L/8

L/4

3L/8

c.g.

L/2

4.263

4.263

-4.263

-4.263

-12.790

-12.790

Table-6-ii-b-2. Factored Moments due to all Dead Loads (DL) on Exterior Girder. Location From Support-A Moments in kN-m

On Support

0.375m

L/8

L/4

3L/8

c.g.

L/2

0.000

4.796

39.008

78.016

91.019

100.919

104.022

c) Table showing Factored Shear Forces & Moments at Different Location of Girder due to Uniformly Distributed Dead Loads from Sidewalk, Attachments, Utilities, WC, Slab, Self Weight of Girder & Concentrated Dead Loads of Cross Girders ( FDLExt-All & FDLExt-Gir-X-Gir.): Table-6-ii-c-1. Factored Shearing Forces due to all Applied Dead Loads on Exterior Girder. Location From Support-A

On Support

0.375m

L/8

L/4

3L/8

c.g.

L/2

Uniformly Distributed Load in kN

458.019

443.940

343.514

229.009

114.505

-27.319

0.000

Concentrated Loads in kN Total Dead Load Shear in kN

12.790

4.263

4.263

-4.263

-4.263

-12.790

-12.790

470.808

448.204

347.777

224.746

110.242

-40.109

-12.790

Table-6-ii-c-2. Factored Moments due to all Applied Dead Loads on Exterior Girder. Location From Support-A

On Support

0.375m

L/8

L/4

3L/8

c.g.

L/2

For Uniformly Distributed in kN-m

0.000

173.341

1256.689

2164.139

2722.349

2929.576

2931.320

For Concentrated in kN-m

0.000

4.796

39.008

78.016

91.019

100.919

104.022

Total Monents in kN

0.000

178.137

1295.697

2242.155

2813.368

3030.496

3035.342

d) Table showing Factored Shear Forces & Moments at Different Location of Girder due to Uniformly Distributed Live Live Load & Pedestrian Loads (FLLExt-Lane-Ped) : Table-6-ii-d-1. Factored Shearing Forces on Exterior Girder due to Live Lane Load & Pedestrian Load (LL) . Location From Support-A Shearing Forces in kN

On Support

0.375m

L/8

L/4

3L/8

c.g.

L/2

79.483

77.040

59.612

39.742

19.871

-4.741

0.000

Table-6-ii-d-2. Factored Moments on Exterior Girder due to Live Lane Load & Pedestrian Load (LL) . Location From Support-A Moments in kN-m

On Support

0.375m

L/8

L/4

3L/8

c.g.

L/2

0.000

30.081

218.081

375.557

472.427

508.389

508.691

e) Table showing Factored Shear Forces & Moments at Different Locations of Girder due to Applied Live Wheel Loads (FLLExt-Wheel) : Table-6-ii-e-1. Factored Shearing Forces on Exterior Girder due to Live Wheel-Load (LL) . Locatio From Support-A Support Positon of Rear/Midd. & Direction Reaction Rear Wheel at Support, AB 82.544 Rear Wheel at 0.375m, AB 81.108 Rear Wheel at L/8, A B 70.865 Rear Wheel at L/4, A B 59.185 Rear Wheel at 3L/8, A B 47.505 Midd. Wheel on c.g. Poisition A B 49.505 Rear Wheel at L/2, A B 35.826 Midd. Wheel on c.g. Poisition B A 43.932 Rear Wheel at L/2, BA 36.768 Rear Wheel at 3L/8, B A 69.292 Rear Wheel at L/4, B A 69.878 Rear Wheel at L/8, B A 36.477 Rear Wheel at 0.375m, B A 41.047 Rear Wheel at Support, B A 41.688

On Support

0.375m

L/8

L/4

3L/8

L/2

40.857 39.421 29.177 17.497 5.818 -33.870 -5.862 -7.818 -56.669 -24.146 -13.497 -5.211 -0.641 0.000

Table-6-ii-e-2. Factored Moments on Exterior Girder due to Live Wheel-Load (LL) . Locatio From Support-A Support Positon of Rear/Midd. & Direction Reaction Rear Wheel at Support, A B 82.544 Rear Wheel at 0.375m, A B 81.108 Rear Wheel at L/8, A B 70.865 Rear Wheel at L/4, A B 59.185 Rear Wheel at 3L/8, A B 47.505 Midd. Wheel on c.g. Poisition A B 49.505 Rear Wheel at L/2, A B 35.826 Midd. Wheel on c.g. Poisition B A 43.932 Rear Wheel at L/2, B A 36.768

On Support

0.375m

L/8

L/4

3L/8

L/2 c.g.

0.000 30.416 216.137 361.028 434.673 460.734 437.072 460.734 182.778

Rear Wheel at 3L/8, B A Rear Wheel at L/4, B A Rear Wheel at L/8, B A Rear Wheel at 0.375m, B A Rear Wheel at Support, B A

69.292

368.225

69.878

246.998

36.477

111.254

41.047

15.393

41.688

0.000

f) Table showing Max. Shear Forces at Different Locations of Exterior Girder due to respective Factored Dead Loads (DL), Live Loads (LL) for Lane Load & Wheel Load & their Summation for Each Point of Application :

Table-6-ii-f-1. Sum. of Factored Max. Shear Forces Against All Applied Loads (DL & LL) on Exterior Girder. Locations from Support-A Loading Type Unit a. Dead Load (FDLExt) b. Lane + Ped.(LL) (FLLExt) a. Wheel Live Load (WLLExt) Total Shears on Each Point

kN

0.375m kN

L/8 kN

L/4 kN

3L/8 kN

c.g. kN

L/2 kN

470.808

448.204

347.777

224.746

110.242

-40.109

-12.790

79.483

77.040

59.612

39.742

19.871

-4.741

0.000

On Support

40.857

39.421

29.177

17.497

5.818

-7.818

-5.862

591.148

564.664

436.567

281.985

135.930

-52.668

-18.651

e) Table showing the Max. Moments at Different Locations of Exterior Girder due to respective Factored Dead Loads (DL), Live Loads (LL) for Lane Load & Wheel Load & their Summation for Each Point of Application :

Table-6-ii-e-1. Sum. of Factored Max. Moments Against All Applied Loads (DL & LL) on Exterior Girder. Locations from Support-A Loading Type Unit a. Dead Load (FDLExt) b. Lane+Ped.(LL) (FL&PLExt) c. Wheel Live Load (FWLLExt) Total Moments on Each Point

kN-m

0.375m kN-m

L/8 kN-m

L/4 kN-m

3L/8 kN-m

c.g. kN-m

L/2 kN-m

0.000

178.137

1295.697

2242.155

2813.368

3030.496

3035.342

0.000

30.081

218.081

375.557

472.427

508.389

508.691

0.000

30.416

216.137

361.028

434.673

460.734

437.072

0.000

45.808

1729.916

2978.740

3720.468

3999.618

3981.105

On Support

7 Factored Shear & Moments at different Positions of an Interior Girder due to Factored Loads (DL& LL) from Superstructure Components & Attachments : i) Arrangement of Wheel Loads for Interiod Girder & c.g Point : a) Sketch Diagram Showing Wheels Loads of Truck, c.g. of Wheels & Location of Mid-Wheel under the Provisions of Absulate Max. Moments: 145.000

Rear

kN c.g. of Wheel 2.845 m Middle

4.300

145.000

kN c.g. of Girder 0.728 m

35.000

kN

Front

4.300

b) Calculations for Center of Gravity (cg) Position of Truck with Wheel Load in Respect of Rear Wheel; c.g. Distance from Rear Wheel

c.g.Wheel

2.845 m

= (Wt.-Mid*4.300+Wt.-Fornt*(2*4.300))/(2*145.000+35.000) c) Calculation Mid Wheel Position in Respect of Girder c.g. under Absulate Max. Moment Provision = (Distance beteen 2-Wheel - Distance of c.g. of Wheels from Rear Wheel)/2 dMid-Wheel 0.728 m d) Sketch Diagram Showing Factored Wheel Loads for Interior Girder : 108.750

kN

108.750 2.845

Rear

0.728 kN

26.250

kN

c.g.

Middle

Front

4.300

4.300

e) Sketch Diagram of Girder with Uniformly Distributed Factored DL & LL, Different Locations for Shear & Moments Including Max. Reactions at Supports due to DL, LL-Lane Load & LL-Wheel Load : X-Girder-1 X-Girder-2 X-Girder-3 X-Girder-4 X-Girder-5 17.053 kN 17.053 kN 17.053 kN 17.053 kN 17.053 kN 0.300 6.100 m 6.100 m 6.100 m 6.100 m 0.300 m Rear Wheel Positions under c.g Provisions. m CL of Bearing CL of Girder CL of Bearing L /2 c.g. of Wheels. Midd. Wheel Positions under c.g Provisions. 12.200 m Front Wheel Positions under c.g Provisions. 3L/8 0.728 m L /4 9.150 1.455 4.300 0.300 L /8 6.100 m 0.300 m 3.050 m m  FDLInt-All = 28.710kN/m  FLLInt-Lane-Ped. = 6.200kN/m

A 0.375

B

 FDLInt-All =  FLLInt-Lane-Ped =

m

28.710 kN/m 6.200 kN/m

0.375

m LSpan =

24.400

m

LTotal = 25.000 RA-DL = 358.875 kN RA-DL-X-Gir.= 42.632 kN RA-LL-L = 77.500 kN RA-LL-Wh.= 129.144 (Max. Reaction due to Wheel Load at c.g. Position)

m RB-DL = 358.875 kN RB-DL-X-Gir.= 42.632 kN RB-LL-L = 77.500 kN RB-LL-Wh.= 114.606 kN (Max. Reaction due to Wheel Load at c.g. Position)

ii) Calculation of Factored Shear Forces & Moments at Different Locations of Interior Girder Against Applied Factored Loads : a) Table showing Factored Shear Forces & Moments at Different Location of Girder due to Uniformly Distributed Dead

Loads from Sidewalk, Attachments, Utilities, WC, Slab, Self Weight of Girder & Concentrated Dead Loads of Cross Girders ( FDLInt-All & FDLInt-Gir-X-Gir.): Table-7-ii-a-1. Factored Shearing Forces due to all Uniformly Distributed Dead Loads on Interior Girder. Location From Support-A Shearing Forces in kN

On Support

0.375m

L/8

L/4

3L/8

c.g.

L/2

350.262

339.496

262.697

175.131

87.566

-20.892

0.000

Table-7-ii-a-2. Factored Moments due to all Dead Loads (DL) on Interior Girder. Location From Support-A Moments in kN-m

On Support

0.375m

L/8

L/4

3L/8

c.g.

L/2

0.000

132.559

961.031

1654.988

2081.870

2240.343

2241.677

b) Table showing Factored Shear Forces & Moments at Different Location of Girder due to Concentrated Dead Load from Cross Girders (FDLExt-Gir-X-Gir.): Table-7-ii-b-1. Factored Shearing Forces due to Concentrated Dead Loads of X-Girder on Interior Girder. Location From Support-A Shearing Forces in kN

On Support

0.375m

L/8

L/4

3L/8

c.g.

L/2

25.579

25.579

25.579

8.526

8.526

-8.526

-8.526

Table-7-ii-b-2. Factored Moments due to all Dead Loads (DL) on Interior Girder. Location From Support-A Moments in kN-m

On Support

0.375m

L/8

L/4

3L/8

c.g.

L/2

0.000

9.592

78.016

156.033

182.038

201.839

208.044

c) Table showing Factored Shear Forces & Moments at Different Location of Girder due to Uniformly Distributed Dead Loads from Sidewalk, Attachments, Utilities, WC, Slab, Self Weight of Girder & Concentrated Dead Loads of Cross Girders ( FDLExt-All & FDLExt-Gir-X-Gir.): Table-7-ii-c-1. Factored Shearing Forces due to all Applied Dead Loads on Interior Girder. Location From Support-A

On Support

0.375m

L/8

L/4

3L/8

c.g.

L/2

Uniformly Distributed Load in kN

350.262

339.496

262.697

175.131

87.566

-20.892

0.000

Concentrated Loads in kN Total Dead Load Shear in kN

25.579

25.579

25.579

8.526

8.526

-8.526

-8.526

375.841

365.075

288.276

183.657

96.092

-29.418

-8.526

Table-7-ii-c-2. Factored Moments due to all Applied Dead Loads on Interior Girder. Location From Support-A

On Support

0.375m

L/8

L/4

3L/8

c.g.

L/2

For Uniformly Distributed in kN-m

0.000

132.559

961.031

1654.988

2081.870

2240.343

2241.677

For Concentrated in kN-m Total Monents in kN

0.000

9.592

78.016

156.033

182.038

201.839

208.044

0.000

142.152

1039.048

1811.021

2263.908

2442.182

2449.720

d) Table showing Factored Shear Forces & Moments at Different Location of Girder due to Uniformly Distributed Live Live Load & Pedestrian Loads (FLLInt-Lane-Ped) : Table-7-ii-d-1. Factored Shearing Forces on Interior Girder due to Live Lane Load & Pedestrian Load (LL) . Location From Support-A

On Support

0.375m

L/8

L/4

3L/8

c.g.

L/2

Shearing Forces in kN

75.640

73.315

56.730

37.820

18.910

-4.512

0.000

Table-7-ii-d-2. Factored Moments on Interior Girder due to Live Lane Load & Pedestrian Load (LL) . Location From Support-A Moments in kN-m

On Support

0.375m

L/8

L/4

3L/8

c.g.

L/2

0.000

28.627

207.537

357.399

449.585

483.808

484.096

e) Table showing Factored Shear Forces & Moments at Different Locations of Girder due to Applied Live Wheel Loads (FLLInt-Wheel) : Table-7-ii-e-1. Factored Shearing Forces on Interior Girder due to Live Wheel-Load (LL) . Locatio From Support-A Support Positon of Rear/Midd. & Direction Reaction Rear Wheel at Support, AB 215.333 Rear Wheel at 0.375m, AB 211.587 Rear Wheel at L/8, A B 184.864 Rear Wheel at L/4, A B 154.395 Rear Wheel at 3L/8, A B 123.927 Midd. Wheel on c.g. Poisition A B 129.144 Rear Wheel at L/2, A B 93.458 Midd. Wheel on c.g. Poisition B A 114.606 Rear Wheel at L/2, BA 150.292 Rear Wheel at 3L/8, B A 180.761 Rear Wheel at L/4, B A 182.290 Rear Wheel at L/8, B A 95.156 Rear Wheel at 0.375m, B A 107.079 Rear Wheel at Support, B A 108.750

On Support

0.375m

L/8

L/4

3L/8

L/2

106.583 102.837 76.114 45.645 15.177 -88.356 -15.292 -20.394 -93.458 -62.989 -35.210 -13.594 -1.671 0.000

Table-7-ii-e-2. Factored Moments on Interior Girder due to Live Wheel-Load (LL) . Locatio From Support-A Support Positon of Rear/Midd. & Direction Reaction Rear Wheel at Support, A B 215.333 Rear Wheel at 0.375m, A B 211.587 Rear Wheel at L/8, A B 184.864 Rear Wheel at L/4, A B 154.395 Rear Wheel at 3L/8, A B 123.927 Midd. Wheel on c.g. Poisition A B 129.144 Rear Wheel at L/2, A B 93.458 Midd. Wheel on c.g. Poisition B A 114.606 Rear Wheel at L/2, B A 150.292 Rear Wheel at 3L/8, B A 180.761 Rear Wheel at L/4, B A 182.290 Rear Wheel at L/8, B A 95.156 Rear Wheel at 0.375m, B A 107.079 Rear Wheel at Support, B A 108.750

On Support

0.375m

L/8

L/4

3L/8

L/2 c.g.

0.000 79.345 563.836 941.813 1133.930 1201.915 1140.188 1201.915 1140.188 960.586 644.344 290.227 40.154 0.000

f) Table showing Max. Shear Forces at Different Locations of Interior Girder due to respective Factored Dead Loads (DL), Live Loads (LL) for Lane Load & Wheel Load & their Summation for Each Point of Application :

Table-7-ii-f-1. Sum. of Factored Max. Shear Forces Against All Applied Loads (DL & LL) on Interior Girder. Locations from Support-A Loading Type Unit a. Dead Load (FDLExt) b. Lane + Ped.(LL) (FLLExt) a. Wheel Live Load (WLLExt) Total Shears on Each Point

kN

0.375m kN

L/8 kN

L/4 kN

3L/8 kN

c.g. kN

L/2 kN

375.841

365.075

288.276

183.657

96.092

-29.418

-8.526

On Support

75.640

73.315

56.730

37.820

18.910

-4.512

0.000

106.583

102.837

76.114

45.645

15.177

-20.394

-15.292

558.064

541.227

421.120

267.123

130.179

-54.325

-23.818

e) Table showing the Max. Moments at Different Locations of Interior Girder due to respective Factored Dead Loads (DL), Live Loads (LL) for Lane Load & Wheel Load & their Summation for Each Point of Application :

Table-7-ii-e-1. Sum. of Factored Max. Moments Against All Applied Loads (DL & LL) on Interior Girder. Locations from Support-A Loading Type Unit a. Dead Load (FDLExt) b. Lane+Ped.(LL) (FL&PLExt) c. Wheel Live Load (FWLLExt) Total Moments on Each Point

kN-m

0.375m kN-m

L/8 kN-m

L/4 kN-m

3L/8 kN-m

c.g. kN-m

L/2 kN-m

0.000

142.152

1039.048

1811.021

2263.908

2442.182

2449.720

0.000

28.627

207.537

357.399

449.585

483.808

484.096

0.000

79.345

563.836

941.813

1133.930

1201.915

1140.188

0.000

119.500

1810.421

3110.232

3847.423

4127.905

4074.004

On Support

m-Wd.

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

H. Strength Limit State Design (USD) of Main Girder & Cross Girders Against Applied Forces : 1 Data for Flexural Design : Description

Notation Dimensions

Unit.

i) Dimensional Data of Superstructure : a) b) c) d) e) f) g) h) i) j) k) l) m) n) o) p)

Span Length (Clear C/C distance between Bearings) Addl.Length of Girder beyond Bearing Center Line. Total Girder Length (a+2b) Thickness of Deck Slab Thickness of Wearing Course Number of Main Girders Number of Cross Girders Depth of Main Girders (Including Slab as T-Girder) Depth of Cross Girders (Including Slab as T-Girder) Width of Web for Main Girders Width of Web for Cross Girders C/C Distance Between Main Girders Distance of Slab Outer Edge to Exterior Girder Center Clear Distance Between Main Interior Girders Filets : i) Main Girder in Vertical Direction ii) Main Girder in Horizontal Direction iii) X-Girder in Vertical Direction vi) X-Girder in Horizontal Direction

SL SAddl. LGir. hSlab. hWC NGir. NX-Gir. hGir. hX-Gir. bWeb-Gir.

24.400 0.300 25.000 0.200 0.075 5 5 2.000 1.900 0.350 0.250 2.000 1.125 1.650 0.150 0.150 0.075 0.075

m m m m m nos nos m m m m m m m m m m m

1.800 4.300 145.000 72.500 145.000 72.500 35.000 17.500

m m kN kN kN kN kN kN

bWeb-X-Gir. C/CD-Gir. CD-Ext.-Gir-Edg. ClD-Int.-Gir. FM-Girder-V. FM-Girder-H. FX-Girder-V. FX-Girder-H.

2 Design Criterion, Loadings, Design Data (Materials) & Different Factors : i) Design Criterion : AASHTO Load Resistance Factor Design (LRFD-USD). ii) Type of Loads : Combined Application of AASHTO HS20 Truck, Lane & Pedestrian Loadings. iii) Design AASHTO HS20 Truck Loading : a) b) c) d) e) f) g) h)

Axle to Axle distance Wheel to Wheel distance Rear Wheel axle Load (Two Wheels) Rear Single Wheel Load Middle Wheel axle Load (Two Wheels) Middle Single Wheel Load Front Wheel axle Load (Two Wheels) Front Single Wheel Load

DAxel. DWheel. LLRW-Load LLRSW-Load LLMW-Load LLMSW-Load LLFW-Load LLFSW-Load

iv) Design AASHTO Lane Loading : a) Design Lane Loading is an Uniformly Distributed Load having Magnitude of

Page 169

LL-Lane

9.300

N/mm

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

9.300N/mm through the Length of Gridge for Single and acting over a 3.000m Wide Strip in Transverse Direction.

9.300

kN/m

v) Design AASHTO Pedestrian Loading : a) Design Pedestrian Loading is an Uniformly Distributed Load having Magnitude of 3.600*10-3MPa through the Length of Sidewalk on both side and acting over the total Wide of Sidewalk. 3 vi) Unit Weight of Different Materials in kg/m : (Having value of Gravitional Acceleration, g =

a) b) c) d) e)

LL-Pedest

0.003600 3.600

gc gWC

2,447.232 2,345.264 1,019.680 1,045.172 1,835.424

N/mm^2 kN/m^2

2 9.807 m/sec )

Unit weight of Normal Concrete Unit weight of Wearing Course Unit weight of Normal Water Unit weight of Saline Water Unit weight of Earth (Compected Clay/Sand/Silt)

gW-Nor. gW-Sali. gs

kg/m3 kg/m3 kg/m3 kg/m3 kg/m3

3 vii) Unit Weight of Materials in kN/m Related to Design Forces :

a) b) c) d) e)

Unit weight of Normal Concrete Unit weight of Wearing Course Unit weight of Normal Water Unit weight of Saline Water Unit weight of Earth (Compected Clay/Sand/Silt)

wc wWC wWater-Nor. wWater-Sali. wEatrh

24.000 23.000 10.000 10.250 18.000

kN/m^3 kN/m^3 kN/m^3 kN/m^3 kN/m^3

viii) Strength Data related to Ultimate Strength Design( USD & AASHTO-LRFD-2004) : a) Concrete Ultimate Compressive Strength, f/c (Normal Concrete) b) Concrete Allowable Strength under Service Limit State (WSD) = 0.40f/c c) Modulus of Elasticity of Concrete, Ec = 0.043gc1.50f/c = 0.043*24^(1.50)*21^(1/2) Mpa, (AASHTO LRFD-5.4.2.4). d) Poisson's Ration = 0.200, subject to cracking and considered to be neglected (AASHTO LRFD-5.4.2.5). e) Modulus of Rupture of Concrete, fr = 0.63f/c Mpa (AASHTO LRFD-5.4.2.6). f) Steel Ultimate strength, fy (60 Grade Steel) g) Steel Allowable Strength under Service Limit State (WSD) = 0.40fy h) Modulus of Elasticity of Reinforcement, Es for fy = 410 MPa

f/c fc Ec

21.000 8.400 23,855.620

MPa MPa MPa

0.200 fr fy fs ES

2.887

MPa

410.000 MPa 164.00 MPa 200000 MPa

ix) Conventional Resistance Factors for Ultimate Stressed Design & Construction (AASHTO LRFD-5.5.4.2.1) : (Respective Resistance Factors are mentioned as f or b value) a) b) c) d)

For Flexural & Tension in Reinforced Concrete For Flexural & Tension in Prestressed Concrete For Shear & Torsion of Normal Concrete For Axil Comression with Spirals or Ties & Seismic Zones at Extreme Limit

Page 170

fFlx-Rin. fFlx-Pres. fShear/Torsion. fSpir/Tie/Seim.

0.90 1.00 0.90 0.75

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

e) f) g) h) i) j) h)

State (Zone 3 & 4). For Bearing on Concrete For Compression in Strut-and-Tie Modeis For Compression in Anchorage Zones with Normal Concrete For Tension in Steel in Anchorage Zones For resistance during Pile Driving Value of b1 for Flexural Compression in Reinforced Concrete (AASHTO LRFD-5.7.2..2.) Value of b for Flexural Tension of Reinforcement in Concrete

fBearig. fStrut&Tie. fAnc-Copm-Conc. fAnc-Ten-Steel. fPile-Resistanc. b1 b

0.70 0.70 0.80 1.00 1.00 0.85 0.85

viii) Dead Load Multiplier Factors for Strength Limit State Design (USD) According to AASHTO-LRFD-3.4.1; Table 3.4.1-1&2 : a) Dead Load Multiplier Factor for Structural Components & Attachments-DC Applicable to All Components Except Wearing Course & Utilities (Max. value of Table 3.4.1-2)

gDC

1.250

b) Dead Load Multiplier Factor for Wearing Course & Utilities- DW , (Max. value of Table 3.4.1-2)

gDW

1.500

c) Multiplier Factor for Horizontal Active Earth Pressure on Substructure Components of Bridge-EH ; Applicable to Abutment & Wing Walls, (Max. value of Table 3.4.1-2)

gEH

1.500

d) Multiplier Factor for Vertical Earth Pressure on Substructure Components of Bridge-EV ; Applicable toAbutment & Wing Walls, (Max. value of Table 3.4.1-2)

gEV

1.350

e) Multiplier Factor for Surchage Pressure on Substructure Components of Bridge-ES ; Horizontal & Vertical Loads on Abutment & Wing Walls, (Max. value of Table 3.4.1-2)

gES

1.500

ix) Live Load Multiplier Factors for Strength Limit State Design (USD) According to AASHTO-LRFD-3.4.1; Table 3.4.1-1&2 : a) Multiplier Factor for Multiple Presence of Live Load ( No of Lane = 2)-m (ASSHTO LRFD-3.6.1.1.1)

m

1.000

gLL-Truck

1.750

IM

1.330

d) Multiplier Factor for Lane Loading-LL-Lane

gLL-Lane

1.750

e) Multiplier Factor for Pedestrian Loading-PL.

gLL-PL.

1.750

f) Multiplier Factor for Vehicular Centrifugal Force-CE

gLL-CE.

1.750

b) Multiplier Factor for Truck Loading (HS20 only)-LL-Truck . c) Multiplier Factor for Vhecular Dynamic Load Allowence-IM as per Provision of ASSHTO LRFD-3.6.2.1, Table 3.6.2.1-1; (Applicable only for Truck Loading & Tandem Loading)

Page 171

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

g) Multiplier Factor for Vhecular Breaking Force-BR .

gLL-BR.

1.750

h) Multiplier Factor for Live Load Surcharge-LS

gLL-LS.

1.750

gLL-WA.

1.000

i) Multiplier Factor for Water Load & Stream Pressure-WA j) Multiplier Factor for Wind Load on Structure-WS

STRENGTH - III

gLL-WS.

1.400

l) Multiplier Factor for Wind Load on Live Load-WL

STRENGTH - V

gLL-WL

1.000

gLL-FR.

1.000

gLL-TU.

1.000

gLL-CR.

1.000

n) Multiplier Factor for deformation due to Shrinkage of Concrete-SH (With Elastomeric Bearing).

gLL-SH.

1.000

o) Multiplier Factor for Temperature Gradient-TG (With Elastomeric Bearing).

gLL-TG.

1.000

p) Multiplier Factor for Settlement of Concrete-SE (With Elastomeric Bearing).

gLL-SE.

1.000

q) Multiplier Factor for Earthquake -EQ

gLL-EQ.

-

r) Multiplier Factor for Vehicular Collision Force-CT

gLL-CT.

-

t) Multiplier Factor for Vessel Collision Force-CV

gLL-CV.

k) Multiplier Factor for Water Load & Stream Pressure-FR l) Multiplier Factor for deformation due to Uniform Temperature Change -TU (With Elastomeric Bearing). m) Multiplier Factor for deformation due to Creep on Concrete-CR (With Elastomeric Bearing).

1.000

x) Design Data for Site Conditions : a) Velocity of Wind Load in Normal Condition b) Velocity of Wind Load in Cyclonic Storm Condition c) Velocity of Water/Stream Current Causing Water/Stream Load

VWL-Nor. VWL-Spe. VWA

90.000 260.000 4.200

km/hr km/hr m/s

3 Design Phenomena, Selection of T-Girder Flange Width, Girder Depth & Calculations for Monent & Shear : i) Design Phenomena : a) The Flexural of Girders will be according to AASHTO LRFD or Ultimate Strength Design (USD) Procedures. b) Since the Interior Girders of the Bridge have the Max. Moments & Shearing Forces caused by Applied Loads (DL & LL), thus it is require to conduct the Flexural Design for Reinforcements of Bridge Girders Based on Calculated

Page 172

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

respective Moments & Shears. Since the Bridge Deck Slab is integral Part of Girders, thus the Design of Girders will be under T-Beam if the Provisions in these Respect Satisfy, otherwise Designee will be under Provisions for the Rectangular Beam. c) The T-Girder will have to Provide Longitudinal Shrinkage & Temperature Reinforcement on Compression Face with a reasonable Steel Area, thus an Equivalent Additional Steel Area can also Provide on Tension Face against those Shrinkage & Temperature Reinforcement. These arrangement will provide a Higher Stiffness for the Structure within Flexural provisions. ii) Cross Sectional Sketch Diagram of Bridge Girders & Dack Slab : 1.475 0.225 7.300

1.250 0.300 1.070 0.300 0.200

0.950

0.250 1.650

1.650

1.650

1.650

0.950

1.125

2.000

2.000

2.000

2.000

1.125

CL 10.250 iii) Selection of T-Girder Effective Flange Width under Provisions of AASHTO-LRFD-4.6.2.6 (4.6.2.6.1) : a) Since the Bridge is a Simple Supported T-Girder Structure, thus Falnge Width will be the least Dimention of : i) One-quarter of Effective Span Length = 1/4*SL = 6.100 m ii) 12.0 times average Depth of Slab + Greater Thickness of Web = 12*hSlab + bGir. = 2.750 m iii) One-half the Width of Girder Top Flange (It is not req. as there is no Addl. Top Flange) iv) The average Spacing of Adjacent Beams/Girders = C/CD-Gir. = 2.000 m b) From Calculations, Average Spacing of Adjacent Beams/Girders is the Least one, thus the Flange Width of Interior Girders, bFla-Gir = 2.000m

bFl-Gir.

2.000 m

iv) Selection of Depth (Including Slab Depth) for T-Girder under Provisions of AASHTO-LRFD-2.5.2.6.3 & Table 2.5.2.6.3-1 : a) Since the Bridge is a Simple Supported T-Girder Structure, thus According to Table-2.5.2.6.3-1; the Min. Required Girder Depth Including Salb Thickness is = 0.0708L; where b) L is the Span Length, the Clear Distance between Bearing Centers of Supports = SL c) Thus required Minimum Depth of T-Girder Including Salb = 0.070*SL

Page 173

L

24.400 m

hT-Girder.

1.732 m

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

d) Considering the Clear Covering both on Top & Bottom, Let Provide a Depth for the T-Girder = 2.000m.

hGir-pro.

2.000 m

v) Calculations for Monent at Different Location of Girder : a) From Load, Shear & Moment Calcutation Tables it appares that, the Interior Girders are facing the Max. Resultant Forces (DL & LL) causing Max. Shears & Moments, thus One of Interior Girders is considered as Typical one for the Flexural Design in respect of All Applied Loads (DL & LL) and Corresponding Moments & Shears. b) Table for Max. Moments at Different Locations of Interior Girder due to Factored DL, Lane-LL & Wheel-LL : Table-1. Sum. of Max. Moments Against All Applied Loads (DL & LL) on Interior Girder. Locations from Support-A Loading Type Unit a. Dead Load (FDLInt) b. Lane Live Load (FLLInt) c. Wheel Live Load (WLLInt) Total Moments on Each Point

kN-m

0.375m kN-m

L/8 kN-m

L/4 kN-m

3L/8 kN-m

c.g. kN-m

L/2 kN-m

0.000

181.672

1,327.681

2,313.495

2,892.428

3,120.031

3,129.494

On Support

0.000

50.096

363.190

625.448

786.774

945.861

847.168

0.000

184.676

1,312.328

2,192.069

2,639.221

2,797.457

2,653.786

0.000

278.135

3,003.199

5,131.011

6,318.423

6,863.350

6,630.449

c) Moment at Sopport Position of Girder

Mu-Support.

0.000 kN-m

d) Moment at a Distance 0.375m from Sopport of Girder

Mu-0.375m.

278.135 kN-m

e) Moment at a Distance L/8 from Sopport of Girder

Mu-L/8.

3,003.199 kN-m

f) Moment at a Distance L/4 from Sopport of Girder

Mu-L/4.

5,131.011 kN-m

g) Moment at a Distance 3L/8 from Sopport of Girder

Mu-3L/4.

6,318.423 kN-m

h) Moment at Absolute Max. Moment Loaction (c.g. Position) of Girder

Mu-c.g.

6,863.350 kN-m

i) Moment at a Distance L/2 (Middle of Span) from Sopport of Girder

Mu-L/2.

6,630.449 kN-m

j) Sketch Diagram of Main Girder T-Beam : b 2.000 hf =

0.200

m

d=

bWeb =

0.350

vi) Limits For Maximum Reinforcement, (AASHTO-LRFD-5.7.3.3.1) : .

Page 174

1.808

m

hGir. = m

2.000

m

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

a) With Maximum Amount of Prestressed & Nonprestressed Reinforcement for a Section c/de  0.42 in which;

c/de-Max.

0.420

b) c is the distance from extreme Compression Fiber to the Neutral Axis in mm

c

Variable

c) de is the corresponding Effective Depth from extreme Compression Fiber to the Centroid of Tensial Forces in Tensial Reinforcements in mm. Here; i) de = (Apsfpsdp + Asfyds)/(Apsfps + Asfy), where ; ii) As = Steel Area of Nonprestressing Tinsion Reinforcement in mm2 iii) Aps = Area of Prestressing Steel in mm2 iv) fy = Yeiled Strength of Nonprestressing Tension Bar in MPa. vi) fps = Average Strength of Prestressing Steel in MPa. xi) dp = Distance of Extreme Compression Fiber from Prestressing Tendon Centroid in mm. xii) ds = Distance of Centroid of Nonprestressed Tensial Reinforcement from the Extreme Compression Fiber in mm.

de

Variable

As Aps fy fps dp

Variable Variable Variable Variable

mm2 mm2 N/mm2 N/mm2 mm

ds

Variable

mm

d) For a Structure having only Nonprestressed Tensial Reinforcement the values of Aps, fps & dp are = 0. Thus Equation for value of de stands to de = Asfyds/Asfy & thus de = ds . vii) Limits For Manimum Reinforcement, (AASHTO-LRFD-5.7.3.3.2) : a) For Section of a Flexural Component having both Prestressed & Nonprestressed Tensile Reinforcements should have Minimum Resisting Moment Mr  1.2*Mcr or 1.33 Times the Calculated Factored Moment for the Section Based on AASHTO-LRFD-3.4.1-Table-3.4.1-1, which one is less.For Compnents having Nonprestressed Tensile Reinforcements only Mr = 1.2Mcr. b) The Cracking Moment of a Section Mcr = Sc(fr + fcpe) - Mdnc(Sc/Snc - 1)  Scfr where; i) fcpe = Compressive Stress in Concrete due to effective Prestress Forces only at Extreme Fiber where Tensile Stress is caused by Externally Applied Forces after allowance for all Prestressing Losses in MPa. For Nonprestressing RCC Components value of fcpe = 0. ii) Mdnc = Total Unfactored Dead Load Moment acting on the Monolithic or Noncomposite Section in N-mm.

Mcr

Variable

fcpe

-

Mdnc

N-mm N/mm2

2,449.720 N-mm

iii) Sc = Section Modulus for the Extreme Fiber of the Composite Section where Tensile Stress Caused by Externally Applied Loads in mm3.

Sc

Variable

mm3

iv) Snc = Section Modulus of Extreme Fiber of the Monolithic or Noncomposite Section where Tensile Stress Caused by Externally Applied Loads in mm3. For the Rectangular RCC Girder Section value of Snc = (bWebhGir3/12)/(hGit/2) v) fr = Modulus of Rupture of Concrete in RCC in Mpa,(AASHTO LRFD-5.4.2.6).

Snc

233333333 0.233333 233.333/10^3 2.887

mm3

c) For Nonprestressing & Monolithic or Noncomposite Beam or Elements,

Page 175

fr Mcr

673638627.159

m3 m3 N/mm2 N-mm

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Sc = Snc & fcpe = 0, thus Equation for Cracking Moment Stands to Mcr = Sncfr

673.639 kN-m

d) Thus Calculated value of Mcr according to respective values of Equation

Mcr-1

Variable

N-mm

e) The value of Mcr = Scfr

Mcr-2

Variable

N-mm

f) Cpoputed value of Mcr = 1.33*MExt Factored Moment due to External Forces

Mcr-3

Variable

N-mm

g) Table-3 Showing Allowable Resistance Moment M r for requirment of Minimum Reinforcement at Different Sections Location of Value of Value of Actuat Acceptable 1.2 Times Section Unfactored Mcr-1 Cracking Mcr of Mcr from Dead Load As per Moment Cracking Cracking Support Moment Equation Value Moment Moment MDL-UF 5.7.3.3.2-1 Sncfr (Mcr-1Sncfr) (1.2*Mcr) kN-m kN-m kN-m kN-m kN-m At Support 0.000 673.639 673.639 673.639 808.366 At L0.375m 142.152 673.639 673.639 673.639 808.366 At L/8 1039.048 673.639 673.639 673.639 808.366 At L/4 1811.021 673.639 673.639 673.639 808.366 At 3L/8 2263.908 673.639 673.639 673.639 808.366 At c.g/L/2 2449.720 673.639 673.639 673.639 808.366

1.33 Times M of M, Factored Moment of Section

Factored Moment

Mr Allowable Min. Moment for RCC

M kN-m

(1.33*M) kN-m

kN-m

Mu (M  Mr) kN-m

1.2Mcr

Maximum Flexural Moment

0.000

0.000

808.366

808.366

278.135

369.920

808.366

808.366

3003.199

3994.255

808.366

3003.199

5131.011

6824.245

808.366

5131.011

6318.423

8403.503

808.366

6318.423

6863.350

9128.255

808.366

6863.350

viii) Flexural Design of Main Girder with Max, Moment value (At c.g. Position) : a) The Absolute Max. Moments on Interior Girder is at c.g. Point. Since it is very close to Middle Position of Span having value MU.= 6863.350*10^6 N-mm, thus this value is Considerd as the Moment at Middle Position of Span. b) Let the Clear Cover at Bottom Surface of Girder, C-Cov.Bot. = 50mm, Let the Clear Cover at Top of Girder, C-Cov.Top = 50mm, Let the Clear Cover at Vertical Faces of Girder, C-Cov.Vert. =38mm,

MU

6,863.350 kN-M 6863.350*10^6 N-mm

C-Cov-Bot. C-Cov-Top. C-Cov-Side.

50 mm 50 mm 38 mm

c) Let the Main Reinforcements are 32f Bars in 4 Layers,

DBar

32 mm

2 2 d) X-Sectional Area of Main Reinforcements Af = p*DBar /4mm

Af-32

e) The Vertical Spacing between Reinforcement Bars, sVer. = 32 mm

sVer.

32 mm

f) Let the Transverse/Shear Reinforcements (Stirrups) are of 12f Bars,

DStir.

12 mm

g) Let Assume Main Tensile Reinforcements are being placed in 4 Layers each having Equal nos. of Bars, thus the Effective Depth of Reinforcements from Top of Girder up to the Centroid of Assumed Group of Reinforcements = (hGir - C-Cov-Bot -DStri -2*DBar - 1.5*sVer.) h) Balanced Steel Ratio for Grider Section according to AASHTO-1996-8.16.2.2

Page 176

2 804.248 mm

dasu-L/2

1,826.000 mm

rb.

0.022

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

rb. = (0.85*0.85*(f/c/fy)*(599.843/(599.843+fy)) i) Max. Steel Ratio, rMax = 0.75*rb. (AASHTO-1996-8.16.2.1)

rMax

0.0165

ix) Checking's Whether the Bridge Girder would Designed as T-Beam or Rectangular Beam Provisions : a) According to Ultimate Stressed Design Provisions a Rectangular having Flange with Reasonable Thickness on its Top should be Designed as T-Beam if Depth of Equivalent Compression Block 'a' is Less than Flange Thickness b) Let Consider the T-Girder will behave as Rectangular Beam for which the Total Flange Width-'b' will be the Width of Rectangular Beam. c) For a Rectangular Section having Assumed Effective Depth dacu; Beam Width b and the Calculated Max. Factored Ultimate Moment (Absolute Moment) MU; the value Equivalent Compression Block a = de(1 - (1 - 2MU/0.85f/cbde2)1/2)

a

108.509 mm aMu Satisfied

ix) Checking in respect of Control of Cracking By Distribution of Reinforcement, (AASHTO-LRFD-5.7.3.4) : a) Under Service Limit State Load Condition, Developed Tensile Stress of Reinforcement fs-Dev. of a Concrete Elements, should not exceed fsa the Computed Tensile Stress of Reinforcement under provision of AASHTO-LRFD-5.7.3.4. Where; 2 157.694 N/mm

b) fs-Dev. is Developed Tinsel Stress in Provided Reinforcements of Section under the Service Limit State of Loads = M/As-prode in which,

fs-Dev.

i) M is Calculated Moment for the Section under Service Limit State of Loads

MWSD.

ii) As-pro is the Steel Area for the Section under USD Design Calculation.

As-pro

2 14,476.459 mm

de

1,808.222 mm

iii) de is Effective Depth between Extreme Compression Fiber to Centroid of the Tensile Reinforcement for the Section. c) fsa is Computed Tensile Stress of Reinforcement having its value = Z/(dcA)1/3  0.6fy, in Which; i) dc = Depth of Concrete Extreme Tension Face from the Center of the Closest Tension Bar. The Depth is Summation Bottom/Top Clear Cover & Radius of the

Page 183

fsa

dc

4,127.905 kN-m 4127.905*10^6 N-mm

2 291.299 N/mm

66.000 mm

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Closest Bar to Tension Face. The Max. Clear Cover = 50mm. For a Section of T-Girder Component, dc = DBar/2 + CCov-Bot. Since Clear Cover at Bottom of T-Girder, CCover-Bot = 50mm & Bar Dia, DBar = 32f ; thus dc = (32/2 + 50)mm ii) A = Area of Concrete Surrounding a Single Tension Bar, which is Calculated A by Dividing the Total Concrete Area bounded in between Extreme Tension Face & a Straight Line parallel to Neutral Axis of Component having equal distance from the Centrioed of Main Tension Reinforcement Bars on both side & Diving the Area by the total Number of Main Bars as Tensile Reinforcement having 50mm.Max. Clear Cover. The Girder is being Provided with 50mm Clear Cover at Bottom, 18nos. 32f Bars Tension Bar in 5 Layers on Mid Span having 4 nos. Bars on Botton 4 Layers & 2nos. on Top Layer. Though the Vertical Spacing among the Layers of Tension Reinforcement are 32mm but due to dissimilarity of Bar arrangement the Centroid of Bars does not Coincide with the Center of Vertical Spacings. Thus, based on actual Cintroid of Bars value of A = bWeb{2*(hGir. - de-pro)}/NBar-pro. iii) Z = Crack Width Parameter for Cast In Place Components in N/mm. For a) Structure with Moderate Exposure Components the Max. value of Z = 30000 b) Structure with Severe Exposure Components the Max. value of Z = 23000 c) Structure with Buried Components the Max. value of Z = 17000 Since the Structure is very close to Sea, thus it’s Components are of Severe Exposure Category having Allowable Max. value of ZMax. = 23000N/mm

ZMax.

iv) The Computed value of 0.6*fy for the Concrete Element.

0.6*fy

2 7,458.025 mm

23,000.000 N/mm

2 246.000 N/mm

d) Since the Calculated value of fs-Dev. is responsible for Controlling the formation of Cracks under Applied Loads to the T-Girder Structure, thus value of the Crack Width Parameter Z should calculate based the value of fs-Dve. e) Based on fs-Dve. the value of Crack Width Parameter ZDev. = fs-Dev.*(dcA)1/3

ZDev.

f) Relation between of Developed Tensile Stress fs-Dev. & Allowable Tensile Stress fs g) Relation between Computed Tensile Stress fsa & Calculated value of 0.6fy h) Relation between Allowable Max. value of ZMax. & Developed value ZDev.

12,451.016 N/mm fs-Dev.< fsa

fsa > 0.6fy

Satisfied

Not Satisfied Zdev.< Zmax.

Satisfy

i) Since the Developed Tensile Stress of Tension Reinforcement of T-Girder fs-Dev.< fsa the Computed Tensile Stress with Alloable Max. Crack Width Parimeter ZMax.; the Developed Crack Width Parimeter ZDev. < ZMax. thus Provision of Main Tensial Reinforcement for T-Girder in respect of Control of Cracking by Distribution of Reinforcement are OK j) More over though the Structure is a Nonprestrssed one, but value of dc have not Exceeds 900 mm, thus Component does require any additional Longitudinal Skein Reinforcement. x) Since, i) The Value of Resisting Moment > Design Moment; ii) The Calculated value of c/de  0.42; iii) The Provided Stee Ratio for Rectangular Section of T-Girder, rRec-pro < rMax. Balance Steel Ratio; iv) The Computed Factored Flexural Resistance M r > Mu the Actual Factored Moment at Mid Span (Absulate Max. Moment at c.g. Point);

Page 184

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

v) The Provided Main Reinforcements are anough in respect of Control of Cracking by Distribution of Reinforcement; Thus Flexural Design of Reinforcements for the T-Girder Span is OK. 5 Design of Longitudinal Reinforcement on Top & Vertical Surfaces of Girder : i) Shrinkage & Temperature Reinforcement in Longitudinal Direction on Top Surface of Girder : a) Since the Girders are Simply Supported Structure & at Middle Location the Moments are with (+) ve. value, thus the Top Surface of Girder will be under Compression. Under Single Reinforced Flexural Design Provision Top Surface of Girder does not require any Longitudinal Reinforcement. Yet for Safe Guard & provide the Web/Shear Reinforcements in the form of Stirrups, this Surface is also require Longitudinal Reinforcement, which can arrange under the Provision of Shrinkage & Temperature Reinforcement according to AASHTO-LRFD-5.10.8. b) Let consider 1 (One) meter Strip Length of Girder for Calculation of Shrinkage & Temperature Reinforcement in Longitudinal Direction on Top Surface of Girder,

LGirder.

c) Let consider the Width of Girder is the Web Width of T-Girder = 0.450m

bWeb.

d) According to AASHTO-LRFD-5.10.8.1. Steel Area required as Shrinkage & Temperature Reinforcement for Structural Components with Thickness Less than 1200mm; As  0.11Ag/fy . (Width of Girder is its thicknes, b = 4500mm < 1200mm).

As-req-Top.

1.000 m 1,000.000 mm 0.350 m 350.000 mm 2 93.902 mm

2 350000.000 mm

e) Here Ag is Gross Area of Girder Top Surface = LGirder*bWeb

Ag-Top

f) Let provide 32f bars as Longitudinal Shrinkage & Temperature on Top Girder.

DBar.

32.000 mm

g) X-Sectional Area of 32f bar = pDBar2/4

Af-32

2 804.248 mm

h) Let provide 2 nos. 32f bars as Longitudinal Shrinkage & Temperature on Top Surface of Girder. i) Provide Steel Area for Longitudinal Shrinkage & Temperature on Top Surface of Girder = NBar-S&T-Top*Af-32

NBar-S&T-Top

2.000 nos.

As-pro-S&T.

2 1,608.495 mm

j) Spacing of Shrinkage & Temperature Reinforcements will less of 3-times the Component thickness = 4*bWeb = 1,400.00 mm or = 450 mm

s-req-Top.

450 mm

k) Spacing in between 2 nos. 32f Longitudinal bars on Top Surface = (b - 2.*CCover-Side - 2*DStir. - 2*DBar)

s-pro-Top.

186 mm

l) Whether Provision of Longitudinal Shrinkage & Temperature Reinforcement have Satisfied or not. m) Whether Provision of Spacing have Satisfied or not.

Page 185

As-pro-S&T>As-req.Top Satisfied s-pro-Top < s-req.Top Satisfied

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

n) Since As-pro-Top. > As-req-Top & spro-Top < s-req-Top, thus the provision of Longitudinal Shrinkage & Temperature on Top Surface of Girde is OK. ii) Shrinkage & Temperature Reinforcement in Longitudinal Direction on Vertical Faces of Girder : a) Girders are Simply Supported Structure having the Longitudinal Flexural Reinforcements due to Moments on Bottom Surface & also on Top Surface (In case of Doubly Reinforced or under Shrinkage & Temperature Provision). There will be also Lateral & Vertical Reinforcements on Bottom, Top & Vertiocal Surfaces under the provisiona of Shear & Web Reinforcement. It also requires Longitudinal Reinforcement on its Vertical Faces, those can provide under Shrinkage & Temperature Reinforcement Provisions according to AASHTO-LRFD-5.10.8. b) Let consider 1 (One) meter Strip Length of Girder for Calculation of Shrinkage LGirder. & Temperature Reinforcement in Longitudinal Direction on Vertical Faces of Girder.

1.000 m 1,000.000 mm

c) Let consider the Depth of T-Girder as Height of Girder, h = 2.00m

2.000 m 2,000.000 mm

hGirder.

d) According to AASHTO-LRFD-5.10.8.1. Steel Area required as Shrinkage As-req-S&T.-Hori. & Temperature Reinforcement for Structural Components with Thickness Less than 1200mm; As  0.11Ag/fy . e) Here Ag is Gross Area of Girder's Each Vertical Face = LGirder*hGirder

Ag-Vert.

f) Let provide 16f bars as Longitudinal Shrinkage & Temperature on Vertical Faces of Girder.

DBar.

g) X-Sectional Area of 16f bar = pDBar2/4

Af-16

h) Spacing of Shrinkage & Temperature Reinforcements is less of 3-times the Component thickness = 3*bWeb = 1,050 mm or = 450 mm

2 536.585 mm

2 2000000.000 mm

16 mm

2 201.062 mm

s-req-S&T.-Hori.

450 mm

NBar-req-S&T-Hori.

2.669 nos.

j) Spacing of 16f bars at Support Position as Horizontal Shrinkage & sCal-req-S&T-Hori. Temperature Reinforcementon Vertical Faces of Girder for Calculated Steel Area = (hGir -2*Ccov -2.669*DBar-32 - sVer- 2*DStri)/NBar-req-S&T-Hor.

374.096 mm

i) Number of 16f bars required against Calculated Steel Area as Horizontal Shrinkage & Temperature Reinforcements on Vertical Surface of Girder = As-req-Long./Af-16

k) Let Provide 5 nos. 16f as Longitudinal bars as Shrinkage & Temperature Reinforcement.

NBar-pro-S&T-Hori.

5 nos

l) Spacing of 16f bars at Support Position as Horizontal Shrinkage & spro-S&T-Hori. Temperature Reinforcementon Vertical Faces of Girder for Calculated Steel Area = (hGir -2*Ccov -5*DBar-32 - sVer- 2*DStri)/NBar-req-S&T-Hor.

232.857 mm

m) Steel Area against Provided Longitudinal Shrinkage & Temperature Reinforcement on Vertical Surfaces of Girder = Af-16*Barpro-S&T-Hori.

Page 186

As-pro-S&T-Hori.

2 1,005.310 mm

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

n) Whether Provision of Longitudinal Shrinkage & Temperature Reinforcement have Satisfied or not.

As-pro-S&T-Hori. > As-req-S&T.-Hori.

o) Whether Provision of Spacing have Satisfied or not.

Satisfied spro-S&T-Hori.. As-req-Long & spro-S&T-Hori.< s-req-S&T-Hori. thus the provisions of Longitudinal Reinforcement as Shrinkage & Temperature on Vertical Faces of Girder is OK. 4 Checking for Development Length & Splices of Reinforcements under Provisions of AASHTO-LRFD-5.11 : i) Provisions Article 5.11.1.1.1 : a) The Calculated Force effects in Reinforcement at each Section shall be Developed on each side of that Section by Embedment of Length of Reinforcement, Hooks or any Mechanical Device or a Combination of all together. These are especially required for Tension Zones. ii) Provisions Flexural Reinforcement (Article 5.11.1.2.1) : a) In Flexural Members the Critical Sections are, i) The Points of Maximum Stress; ii) The Points within the Span where Adjacent Reinforcement Terminates or Bands. b) Except at Supports of Simple Spans and at the Free Ends of Cantilevers, Reinforcements shall be extended further beyond the Point where they are no longer requred to resist the Flexural for a Distance as mentioned below: i) Not less than the Effective Depth of Component; ii) Not Less than the Nominal Diameter of Bar proposed, and iii) Not Less than 1/20 of Clear Span. c) In Continuing Reinforcements the Extended Length shall not be Less than the Development Length ld, beyond the Point of Bent or Tarminated Tension Reinforcenenta are no longer requred. The value of Development Length Id will be according to Provisions as mentioned in Article 5.11.2. d) In no case Termination of more than 50% of Reinforcement at any Section is permitted & Termination of adjusecent Bars on the same Section is restricted. f) For Bent of Tension Reinforcements Across the Web to the Compression Face, in that case a Development Length ld should Provide on Compression Face for Termination of Bars. Otherwise Continuity of Bended Bars would remain on the Compression Face of the Component. g) Components of i) Sloped, Stepped or Tapered Footings; ii) Brackets; iii) Deep Flexural Members; & iv) Unparallel Tension & Compression Reinforcements and the Reinfocement Forces are not Directly Proportional to the Factored Moments, those Provide with Supplementary Ancorages for Flexural Tension Reinforcements. iii) Provisins of Development Length le under Article 5.11.2 : a) According to Article 5.11.2.1.1 the Tension Development Length le should not be less than the product of the Basic Development Length ldb & the Modification Factors as Specified in Articles 5.11.2.1.2 & 5.11.2.1.3. Whereas the Basic Tension Development Length in mm for Different Size of Deformed Bars & Wires are;

Page 187

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

b) For bar No-36 & below, ldb = 0.02Abfy/f/c  0.06dbfy; c) For bar No-43 & below, ldb = 25fy/f/c; d) For bar No-57, ldb = 34fy/f/c; e) For Deformed Wire, ldb = 0.36dbfy/f/c. Where f) Ab is Cross-sectional Area of Deform Ber/Wire in mm2. g) fy is Yield Strength of deform Ber/Wire in MPa. h) Abfy/f/c is the Specified Compressive Strength of Concrete in MPa. i) db is Diameter of Bar/Wire in mm. iv) Provisins of Article 5.11.2.2 in respect of Positive Moment Reinforcement & the Provided Reinforcement: a) In Simple Supported Span at-least One-third or 33% of Positive Moment Reinforcement should be Extended beyond the Centerline of Support and would continue not Less than 150mm. Whereas in Continuous Spans that will be at least One-fourth or 25% of Positive Moment Reinforcement on the same Face. b) Provided Steel (Reinforcement) Area against Maximum Positive moment for the T-Girder Span = As-pro-L/2

As-pro-L/2

c) Provided Steel (Reinforcement) Area on Support Position of T-Girder Span both on Bottom & Top Surface = As-pro-Supp

As-pro-Supp

d) Percentage of Provided Reinforcement on Support of T-Girder in respect of the Maximum Positive Moment Reinforcement = 100*As-pro-Supp/As-pro-L/2

%As-pro-Supp

2 14,476.459 mm

2 6,433.982 mm

44.444 %

e) Since the Provided Reinforcement on Support is 44.444% of the Provided at Max. Positive Moment Reinforcement, thus According Article 5.11.2.2 in respect of Positive Moment Reinforcement the Design is OK. v) Computed value of Development Length le & Basic Development Length ldb for T-Girder Beam : a) Provided bar Diameter for Main T-Girder of Simple Supported Bridge

DBar

b) Maximum Number of Main Bars on Each Layer = NBar

NBar

32 mm 4

c) Clear Cover at Bottom of Main Girder = C-Cov-Bot

C-Cov-Bot

50 mm

e) Clear Cover at Top of Main Girder = C-Cov-Top

C-Cov-Top

50 mm

f) Clear Cover on both Sides of Main Girder = C-Cov-Side

C-Cov-Side

38 mm

Page 188

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

g) Provided bar Diameter for Transverse/Shear Reinforcements (Stirrups)

DStir.

h) Lateral Spacing of Main Bars = (bWeb-2*C-Cov-Side.-2*DStri-NBar*DBar)/(NBar-1) i) Cross-sectional Area of Provided Main Deform Ber = pDBar2/4

12 mm

sLateral

40.667 mm

Af-32

2 804.248 mm

j) Depth of Concrete below the Top Horizontal Bar = hGir- C-Cov-Top.-DStri-DBar

hTop-Bar

1,906.000 mm

k) Modification Factor for Basic Development Length ldb (Since Depth below the Top Horizontal Bars is greater than 300mm, thus Factor is for Increase of ldb).

MFactort

1.400

l) Calculated Basic Development Length ldb for 32 No. Main Longitudinal Bar of T-Girder = MFactor*0.02Af-32fy/f/c

ldb-Cal

2,014.754 mm

m) Calculated value of 0.06DBarfy;

0.06DBarfy

787.200 mm

/ n) Computed value of Development Length, lb = 0.02Af-32fy/f c  0.06DBarfy;

lb-req

2,014.754 mm

o) Let Provide the Development Length for 32 No. Main Bars = 2025mm

lb-pro

2,025.000 mm

p) Since the Provided Development Length for Main Reinforcement is greater than the required Development Length, thus the Design is OK in respect of Development Length for Main Reinforcement of Girder. 5 Design of Shear Reinforcement & Checking of RCC Girder against Shearing Forces at Different Locations : i) Calculated Factored Shearing Forces (Vu) at Different Locations due to Applied Loads (DL & LL): a) Table for Max. Shear Forces at Different Locations of Interior Girder due to Factored DL, Lane-LL & Wheel-LL : Table-2. Sum. of Max. Shear Forces Against All Applied Loads (DL & LL) on Interior Girder. Locations from Support-A Loading Type Unit a. Dead Load (FDLInt) b. Lane Live Load (FLLInt) a. Wheel Live Load (WLLInt) Total Shears on Each Point

kN

0.375m kN

L/8 kN

L/4 kN

3L/8 kN

c.g. kN

L/2 kN

480.324

466.543

368.236

234.833

122.745

-37.401

-10.658

132.370

128.301

99.278

66.185

33.093

-7.895

0.000

248.072

239.353

177.156

106.240

35.324

-47.468

-35.592

860.766

834.197

644.670

407.258

191.162

-92.764

-46.250

On Support

b) Shearing Forces at Sopport Position of Girder

Vu-Supp.

860.766 kN

c) Shearing Forces at Loaction 0.375m from Sopport of Girder

Vu-0.375m.

834.197 kN

d) Shearing Forces at Loaction L/8 from Sopport of Girder

Vu-L/8.

644.670 kN

e) Shearing Forces at Loaction L/4 from Sopport of Girder

Vu-L/4.

407.258 kN

f) Shearing Forces at Loaction 3L/8 from Sopport of Girder

Vu-3L/4.

191.162 kN

Page 189

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

g) Shearing Forces at Absolute Max. Moment Loaction (c.g. Position) of Girder

Vu-c.g.

(92.764) kN

h) Shearing Forces at Loaction L/2 (Middle of Span) from Sopport of Girder

Vu-L/2.

(46.250) kN

ii) Factored Shearing Stress & Shearing Depth at Different Locations : a) The Shearing Steress on Concrete due to Applied Shear Force. vu = (Vu - fVp)/fbvdv, = Vu/fbvdv ; Since Vp = 0; (AASSHTO-LRFD-5.8.2.9).Here, b) Vp is Component of Prestressing applied Forces. For Nonprestressing RCC Structural Component the value of Vp = 0

Vp

-

c) bv is Width of T-Girder Web = bWeb. mm,

bv

350 mm

d) dv is Effective Shear Depth taken as the distance measured perpendicular to the neutral axis between Resultants of the Tensile & Compressive Forces due to Flexural having the greater value of either of 0.9de or 0.72h in mm. Here,

dv 0.9de 0.72h

i) de is Effective Depth of Tensile Reinforcement for the Section in mm

de

ii) h is Depth of T-Girder, hGir = 2000 mm,

h

e) f is Resistance Factor for Shear = 0.90 (AASHTO-LRFD-5.5.4.2).

Mpa

Variable mm Variable mm 1,440.000 mm Variable

mm

2,000 mm

f

0.90

f) Table for Computation of values of vu, de, bv, 0.9de , 0.72h & dv at different Section of Girder. Table-3 Values of vu, de, bv, 0.9de , 0.72h & dv at different Section of Girder. Location

Length of

Width of

of Section

Segment

T-Girder

from

from the

Web

Support

Depth of T-Girder

Earlier Section

(bv)

mm

(h) mm

Effective

Calculated

Calculated

Calculated

Depth of

value of

value of

value of

Calculated value of

Section for

0.9de

0.72h

Effective

Shearing

Tensial

Shear Depth

Stress

(de)

(dv)

(vu)

2000.000 2000.000

mm 1902.000 1902.000

mm 1711.800 1711.800

mm 1440.000 1440.000

mm 1711.800 1711.800

N/mm2 1.596 1.547

At Support

0.000

L0.375m L1/8 L1/4 L3/8 L1/2

375.000

mm 350.000 350.000

3050.000

350.000

2000.000

1882.800

1694.520

1440.000

1694.520

1.208

3050.000

350.000

2000.000

1851.714

1666.543

1440.000

1666.543

0.776

3050.000

350.000

2000.000

1794.000

1614.600

1440.000

1614.600

0.376

3050.000

350.000

2000.000

1808.222

1627.400

1440.000

1627.400

-0.090

g) Shearing Stress due to Applied Factored Shearing Forces at Different Sections of Girder : i) Shearing Stress due to Applied Shearing Force at Support Position of Girder = Vu-Supp/fbvdv N/mm2

vu-Supp.

2 1.596 N/mm

ii) Shearing Stress due to Applied Shearing Force at a distance 0.375m from

vu-0.375m.

2 1.547 N/mm

Page 190

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Support = Vu-0.375/fbvdv N/mm2 iii) Shearing Stress due to Applied Shearing Force at a distance L/8 from

vu-L/8.

2 1.208 N/mm

vu-L/4.

2 0.776 N/mm

vC-3L/8.

2 0.376 N/mm

vu-L/2.

2 (0.090) N/mm

Support = Vu-L/8/fbvdv N/mm2 iv) Shearing Stress due to Applied Shearing Force at a distance L/4 from Support = Vu-L/4/fbvdv N/mm2 v) Shearing Stress due to Applied Shearing Force at a distance 3L/8 from Support = Vu-3L/8/fbvdv N/mm2 vi) Shearing Stress due to Applied Shearing Force at a distance L/2 from Support = Vu-L/2/fbvdv N/mm2 . (The (-) ve. velue is not applicable.)

iii) Factored Shearing Resistance for a Section under provision of AASHTO-LRFD-5.8.2.1-(Equ-5.8.2.1-2) : a) The Factored Shear Resitance at any Section of Component is Expressed by the Equation-5.8.2.1-2. Having the value, Vr = fVn in which; b) Vr is the Factored Shear Resitance at a Section in N

Vr.

N

c) Vn is Nominal Shear Resitance in N according to AASHTO-LRFD-5.8.3.3.

Vn.

N

d) f is Resistance Factor according to AASHTO-LRFD-5.5.4.2.

f

0.90

iv) Computation of values of q & b to Calculate the Nominal Shear Resistance (Vn) at Different Locations due to Factored Shear Forces under Provisions of AASHTO-LRFD-5.8.2.4 : a) The Nominal Shear Resistance Vn at any Section of Girder is the Lesser value Computed by the Equations i) Vn = Vc + Vs + Vp (Equ. 5.8.3.3-1) & ii) Vn = 0.25f/cbvdv + Vp, (Equ. 5.8.3.3-2) in which, b) Vc is Nominal Shear Resistance of Conrete in N having value = 0.083bf/cbvdv, (Equ. 5.8.3.3-1); c) Vs is Shear Resistance Provided by Shear Reinforcement in N having value = Avfydv(cotq + cota)sina /s (Equ. 5.8.3.3-3) in which, d) s is Spacing of Stirrups in mm; e) b a is Factor for the Diagonally Cracked Concrete to transmit Tension as per AASHTO-LRFD-5.8.3.4; 0 f) q is Angle of Inclenation of Digonal Compressive Stress in ( ) as per AASHTO-LRFD-5.8.3.4; 0 g) a is Angle of Inclenation of Transverse/Shear Reinforcement to Longitudinal Bars in ( ); AASHTO-LRFD-5.8.3.4. For Vertical Transverse/Shear Reinforcement the Angle of Inclenation, a = 900 a 90 0

h) Av is Area of Shear Reinforcement within a distance s in mm;

Page 191

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

i) Vp is component of Prestressing Force in direction of Shear Force in N; For Nonprestressing RCC Structural Component, the value of Vp = 0.

Vp.

-

N

v) Computation of Value b & q at different Locations of Girder as per AASHTO-LRFD-5.8.3.4: a) Calculation of Longitudinal Strain in Web Reinforcement εs in mm/mm on the Flexural Tension side of Girder with Equations ; b) ex = (Mu/dv+0.5Nu + 0.5(Vu -Vp)cotq - Apsfpo)/2(EsAs + EpAps); (Equ-5.8.3.4.2-1 for the Case with at Least the Min.Shear Reinforcement). c) ex = (Mu/dv+0.5Nu + 0.5(Vu -Vp)cotq - Apsfpo)/(EsAs + EpAps); (Equ-5.8.3.4.2-2 for the Case with Less then the Min.Shear Reinforcement); d) ex= (Mu/dv+0.5Nu + 0.5(Vu -Vp)cotq - Apsfpo)/(2(EsAs + EpAps); (Equ-5.8.3.4.2-3 for the Cases when value of es is (-) ve.in Equ.5.8.3.4.2-1& Equ.5.8.3.4.2-2). Where, e) Ac is Area of Concerte on Flexural Tention side of Girder in mm2 having value Ac = bWeb* hGir,/2 mm2

Ac

f) Aps is Area of Prestressing Steel on Flexural Tention side of Girder in mm2. For RCC Structure, the value of Aps = 0

Aps

g) As is Area of Non-Prestressing Steel on Flexural Tention side of Girder for the in mm2 under Consideration having respective values of Steel Area. i) On Support Position value of Provided Steel Area in mm2 ii) At Distance 0.375m from Support, Provided Steel Area in mm2 iii) At Distance L/8 from Support, Provided Steel Area in mm2 iv) At Distance L/4 from Support, Provided Steel Area in mm2 v) At Distance 3L/8 from Support, Provided Steel Area in mm2 vi) At Distance L/2 from Support, Provided Steel Area in mm2

As-Sup. As-0.375m. As-L/8. As-L/4. As-3L/8. As-L/2.

h) fpo is a Parameter for Modulus of Elasticity of Prestressing Tendons which is multiplied by Locked-in differencein Strain between the Prestressing Tendons and Surrounding Concrete (Mpa). For the usal level of Prestressing, the value recommended = 0.7fpu for both Pretensioned & Post-tensioned Case. For Nonprestressed RCC Structural Component, the value of fpo = 0. i) Nu is Factored Axil Force in N, Value will be (+) ve for the case of Tensile & (-) for the case of Compressive due to Prestressing. For Nonprestressing RCC Structural Component, the value of Nu = 0. j) Mu is Factored (+) ve Moment quantity of the Section in N-mm but not less then Vudv. k) Vu is Factored Shear Force (Only (+) ve values are applicable) for the Section in N.

Page 192

2 350,000 mm

-

6,433.982 6,433.982 8,042.477 11,259.468 16,084.954 14,476.459

mm2

mm2 mm2 mm2 mm2 mm2 mm2

fpo.

-

MPa.

Nu

-

N

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

I) Table Showing the values of Mu, Vu, Computed value of Vudv & Effective value of Vudv. Table-4. Showing the values of M u, Vu, Computed value of Vudv & Effective value of M u-Eff  Vudv. Location

Length of

Factored

Factored

Calculated

Calculated

Effective

of Section

Segment

Moment

Shear

value of

value of

Moment

from

from the

for the

for the

Effective

Vudv

value

Support

Earlier

Section.

Section.

Shear Depth

Section

(Mu)

(dv)

(Vudv)

(MuEff)

MuEff

mm

kN-m

(Vu) kN

mm

kN

kN-m

At Support

0.000

0.00

860.766

1711.800

1473.459

1473.459

L0.375m L1/8 L1/4 L3/8 L1/2

375.000

278.14

834.197

1711.800

1427.978

1427.978

2675.000

3,003.20

644.670

1694.520

1092.406

3003.199

3050.000

5,131.01

407.258

1666.543

678.713

5131.011

3050.000

6,318.42

191.162

1614.600

308.650

6318.423

3050.000

6,630.45

-46.250

1627.400

-75.267

6630.449

vi) Value of vc/f/c (Ratio of Shearing Stress & Concrete Compressive Strength) at Different Section of Girder : / / a) Value of vc/f c at Support Pisition of Girder = vc-Sup/f c

vc-Supp/f/c

0.076

/ / b) Value of vc/f c at a distance 0.375m from Support = vc-0.375/f c

vc-0.375/f/c

0.076

/ / c) Value of vc/f c at a distance L/8 from Support = vc-L/8/f c

vc-L/8/f/c

0.058

/ / d) Value of vc/f c at a distance L/4 from Support = vc-L/4/f c

vc-L/4/f/c

0.037

/ / e) Value of vc/f c at a distance 3L/8 from Support = vc-3L/8/f c

vc-3L/8/f/c

0.018

vc-L/2/f/c

(0.004)

/ / f) Value of vc/f c at a distance L/2 from Support = vc-L/2/f c

vii) Values of esx1000 with at Least the Min. Transverse/Shear Reinforcement under AASHTO-LRFD-5.8.2.5 & provisions of Equation 5.8.3.4.2-1 : a) Since for RCC Girder values of Prestressing Components Nu, Vp, Asp, fpo, Ep etc. are = 0, thus equation ex = (Mu/dv+0.5Nu + 0.5(Vu -Vp)cotq - Apsfpo)/2(EsAs + EpAps) stands to ex = (Mu/dv + 0.5Vucotq )/2EsAs b) Considering the Initial value of ex = 0.001at Support Position & the Effective Moment Mu-Eff. From the Equation Cotq = (ex2EsAs - Mu/dv)/0.5Vu

cotq

3.980

c) Having the value of cotq = 2.241, the values of exx1000 at Different Locations are ; d) At Support (Bearing Center) Position = ((Mu/dv + 0.5Vucotq )/(2EsAs))*1000 d) At 0.375m from Support = ((Mu/dv + 0.5Vucotq )/(2EsAs))*1000

Page 193

ex-Suport*1000

1.000

ex-0.375*1000

0.969

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

e) At a Distance L/8 from Support = ((Mu/dv + 0.5Vucotq )/(2EsAs))*1000

ex-L/8*1000

0.950

f) At a Distance L/4 from Support = ((Mu/dv + 0.5Vucotq )/(2EsAs))*1000

ex-L/4*1000

0.864

g) At a Distance 3L/8 from Support = ((Mu/dv + 0.5Vucotq )/(2EsAs))*1000

ex-3L/8*1000

0.667

h) At a Distance L/2 from Support = ((Mu/dv + 0.5Vucotq )/(2EsAs))*1000

ex-L/2*1000

0.688

i) Since at Absolute Max. Moment Position & at L/2 Distance from Support the Shear Forces are of (-) ve value, thus calculations for the values of ex-x1000 these Locations are not essential. j) Since in all Sections from Support to L/2 the values of es-x1000 ≤ 1.00, thus values of q & b for the Sections can be obtain from Table-5.8.3.4.2-1 in respect of values of vc/f/c. For Sections having the es-x1000>1.00, for those Cases values of q & b can obtain in respect of value of Crack Spacing Parameter sxe, using the Equation .No.5.8.3.4.2-2, Equation No. 5.8.3.4.2-4 & Table -5.8.3.4.2-2. viii) Values of esx1000 with Less than Min. Transverse/Shear Reinforcement under AASHTO-LRFD-5.8.2.5 & the provisions of Equation 5.8.3.4.2-2 : a) Since in RCC Girder the values for Prestressing Components Nu, Vp, Asp, fpo, Ep etc. are = 0, thus equation ex= (Mu/dv+0.5Nu + 0.5(Vu -Vp)cotq - Apsfpo)/(EsAs + EpAps) stands to ex = (Mu/dv + 0.5Vucotq )/EsAs b) Considering the Initial value of ex = 0.002 at Support Position & the Effective Moment Mu-Eff. From the Equation Cotq = (exEsAs - Mu/dv)/0.5Vu c) Values of exx1000 at Location = (Mu/dv + 0.5Vucotq )/EsAs

cotq

ex-*1000

3.980

0.002

ix) Computation of values of Crack Spacing Parameter, sxe for Sectiona are : a) The Crack Spacing Parameter of a Section, sxe = sx(35/(ag+16))  2000mm, In which; b) sx = the Lesser value of either dv or the Spacing of Longitudinal Crack Control Reinforcements on Vertical Faces (as Shrinkage & Tempeture Reinforcement) having Steel Area in a Horizontal Reinforcement Layer if As > 0.003bvs. Here;

sx

i) As is Steel Area of 2nos Shrinkage & Tempeture Reinforcement Bars on Opposite Vertical Faces of T-Girder in same Horizontal Layer, = As-S&T-Hori. = 2*pDBar2/4 = 2*Af-16

As

ii) dv is Effective Shear Depth of Tensil Reinforcement for the Section

dv

iii) s is Spacing of Longitudinal Bars as Shrinkage & Tempeture Reinforcement on Vertical Faces of T-Girder.

s

iv) Thus Computed value of 0.003dvs for a Section

Page 194

0.003dvs

-

mm

2 402.124 mm

-

mm

232.857 mm

-

mm2

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

v) For Computed value of 0.003bvs at Section > As, the value of sx = dv

0.003dvs 1.00 & the value of sxe at a Sections should Computed from the Respective Tablel. x) Computation of Values of q & b from AASHTO-LRFD'sTable -5.8.3.4.2-1. & Table -5.8.3.4.2-2. against the Respective Calculated values of esx1000, Ratio vc/f/c & sxe.: a)

Table for Values of q & b at Different Location of Girder. Location of Section From Support

Referece of Table

vc/f/c

exx1000

sxe

q

b

a) At Support Position b) At L0.375mDistance of Support c) At L/8 Distance of Support d) At L/4 Distance of Support e) At 3L/8 Distance of Support f) At L/2 Distance of Support

5.8.3.4.2.-1

0.076

1.000

NA

36.40

2.23

5.8.3.4.2.-1

0.076

0.969

NA

36.40

2.23

5.8.3.4.2.-1

0.058

0.950

NA

36.40

2.23

5.8.3.4.2.-1

0.037

0.864

NA

36.40

2.23

5.8.3.4.2.-1

0.018

0.667

NA

33.70

2.38

5.8.3.4.2.-1

-0.004

0.688

NA

33.70

2.38

Value of

b) Value of Cotq at different Locaion of Girder : i) At Support (Bearing Center) Position value of Cotq

Cotq

1.356

ii) At a Distance 0.375m from Support value of Cotq

Cotq

1.356

iii) At a DistanceL/8 from Support value of Cotq

Cotq

1.356

iv) At a Distance L/4 from Support value of Cotq

Cotq

1.356

v) At a Distance 3L/8 from Support value of Cotq

Cotq

1.499

vi) At a Distance L/2m from Support value of Cotq

Cotq

1.499

xi) Computation of Value for Nominal Shearing Strength of Concrete (Vc) using the Values of q & b : a) Since the Location of L/8 is next to the Critical Section at a Distance 0.375m from Support, thus Values of q & b of Section L/8 are the Governing Values for Computation of Nominal Shearing Strength of Concrete (Vc) for the Girder. b) Nominal Shear Resistance of Conrete of Girder Vc = 0.083bf/cbvdv, AASHTO-LRFD-5.8.3.3-(Equ. 5.8.3.3-1);

Vc

18,452.293 kN 18452.293*10^3 N

xii) Regions Requiring Transverse or Shear/Web Reinforcements under AASHTO-LRFD-5.8.2.4 : a) The Transverse or Shear Reinforcements are required for those Sections where the Factored Shearing Force due to the Applied Loads (DL & LL), Vu > 0.5f (Vc + Vp); AASHTO-LRFD-5.8.2.4; Equ-5.8.2.4-1; Here,

Page 195

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

b) Vu is Factored Shearing Force due to the Applied Loads for the Selected Section in N, c) Vc is Nominal Shear Resistance for the Section having value = 0.083bf/cbvdv according to AASHTO-LRFD-5.8.3.3. Equation-5.8.3.3-4. d) Vp is component of Prestressing Force in direction of Shear Force in N; For Nonprestressing RCC Structural Component, the value of Vp = 0.

Vp.

-

N

e) b a is Factor for the Diagonally Cracked Concrete to transmit Tension according to AASHTO-LRFD-5.8.3.4; f) f is Resistance Factor according to AASHTO-LRFD-5.5.4.2. having value = 90

f

0.90

g) Thus for Nonprestressing Structure the Eqution-5.8.2.4-1 Stands to Vu > 0.5Vc h) Table showing the values of b, Vu, Vc, 0.5Vc & Relation between Vu & 0.5Vc at Different Location of Girder. Location from Girder's Bearing Center.

Values of

b

Vu N

Vc N

0.5fVc N

Relation Equation Between Satisfied/ Vu & Vc Not Satisfied

a) At Support (Bearing Center) Position

2.230

860765.82

48903800.52

22,006,710

Vu 0.125f/c ; smax. = 0.4dv ≤ 300mm, (AASHTO-LRFD-Equ.5.8.2.7-2). xix) Chacking for Transverse/Shear/Web Reinforcements as Deep Beam Component (AASHTO-LRFD-5.8.1.1) : a) The Component in which a Load causing more than 1/2 of the Shear at a Distance closer than 2d from the Face of Support is Considered as a Deep Component. Deep Beam Components the Shear Reinforcements are being Provide according to Provisions of AASHTO-LRFD-5.6.3 (Provisions of Strut-and-Tied Model) & AASHTO-LRFD-5.13.2.3. b) Factored Shear Force at Support of Girder, = Vu-Supp. kN.

Vu-Supp.

860.766 kN

c) 1/2 of Factored Shear Force at Support of Girder, = 1/2Vu-Supp. kN.

1/2Vu-Supp.

430.383 kN

d) Factored Shear Force at a Distance 2d from Support, = Vu-2d. kN.

Vu-2d.

608.249 kN

e) Status of 1/2Vu-Supp. & Vu-2d

Vu-2d>Vu-Supp.

f) Since the Factored Shear Force at a Distance 2d, Vu-2d > 1/2Vu-Supp. the Max. Shear Force at Support, thus the Girder is Deep Beam Component & under Article 5.13.2.3. Of AASHTO-LRFD its Transverse/Shear Reinforcement can Provide. xx) Detaling of Requirments for Deep Beam Component to Provide Transverse/Shear/Web Reinforcements for Girder under provision of AASHTO-LRFD-5.13.2.3 : a) To provide Transverse/Shear/Web Reinforcements at Different Section of Girder, it should Satisfy the Equation, Ng = f fyAs  0.83bvs (AASHTO-LRFD-5.13.2.3). Here, b) Ng is Factored Tensial Resitance of Transverse Reinforcement (Each Pair) in N.

Ng.

c) bv is Width of Girder Web in mm.

bv.

d) fy is Yield Strength of Reinforceing Steel as Transverse/Shear Reinforcement

fy.

Page 197

N 350 mm 410.000 MPa

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

e) As is Steel Area of Transverse/Shear Reinforcement in mm2 having Spacing s .

AS

f) s is Spacing of Transverse /Shear Reinforcement in mm. The value of s should not excide eithe of d/4 or 300mm

s-Max

mm2 300 mm

g) The Vertical Spacing, sVetrt. for Crack Control Longitudinal Reinforcement on both sVert.-Max Vertical Faces of Girder should not Excide either d/3 or 300 mm.

300 mm

xxi) Computation of Spacing for Transverse/Shear Reinforcement at Different Section of Girder : a) Value of d/4 for the Section under cosideration having d = hGir. (Girder Depth).

d/4

500 mm

b) Allowable Max. Spacing for Transverse/Shear Reinforcement

s-Max

300 mm

c) Let Provide 2-Leged 12f bars as Transverse/Shear Reinforcement in the form of Vertical Stirrups.

DStir.

12 mm

d) X-Sectional Area of 2-Leged 12f Bars as Transverse/Shear Reinforcement; = 2*pDStir.2/4 mm2

Av

2 226.195 mm

d) Let Provide the 175mm Spacing for Transvers/Shear Reinforcement from Outer Face of Girder up to Support Face at Section at L0.375m Distance.

s-0.375m.

175 mm

e) Let Provide the 175mm Spacing for Transvers/Shear Reinforcement in between Support Face Section at L0.375m & Section at L/8 Distance

s-L/8

175 mm

i) Let Provide the 200mm Spacing for Transvers/Shear Reinforcement in between Section at L/8 & Section at L/4 Distance

s-L/4

200 mm

j) Let Provide the 200mm Spacing for Transvers/Shear Reinforcement in between Section at L/4 & Section at 3L/4 Distance

s-3L/8

200 mm

j) Let Provide the 200mm Spacing for Transvers/Shear Reinforcement in between Section at 3L/4 & Section at L/2 Distance

sL/2

200 mm

xxi) Checking for Requirements of Minimum Transverse Reinforcement for Different Section of Girder: a) Minimum Transverse/Shear Reinforcement at a Section, Av  0.083f/c(bvs/fy), AASHTO-LRFD-5.8.2.5. Where, s is Length of Girder Segment under consideration for Transverse/Shear Reinforcement. b)

Table for Minimum Transverse/Shear Reinforcement at Different Section of Girder. Location from Bearing Center of Girder.

Length of Segment mm

bv' Web Width mm

s' Web Bar Spacing mm

Min. Av Required mm2

Av-pro

Status of

Provided Provided & mm2 Required Av

a)Between outer Face to Support Face b)From Support Face to L/8 of Girder

300.000

350.000

175.000

56.821

226.195

Av-pro> Av

3050.000

350.000

175.000

56.821

226.195

Av-pro> Av

c) From L/8 to L/4 of Girder Length

3050.000

350.000

200.000

64.938

226.195

Av-pro> Av

Page 198

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

d) From L/4 to 3L/4 of Girder Length

3050.000

350.000

200.000

64.938

226.195

Av-pro> Av

e) From 3L/4 to L/2 of Girder Length

3050.000

350.000

200.000

64.938

226.195

Av-pro> Av

xxii) Computation of Values of Vs,the Shear Resistance against Provided Shear Reinforcement & Spacings at Different Sections according to Vs = Avfydv(cotq + cota)sina /s (AASHTO-LRFD-Equ. 5.8.3.3-3) : a) With Vertical Shear Reinforcement the value of a = 900 & the Equation Vs = Avfydv(cotq + cota)sina /s stands to Vs = Avfydvcotq /s, b) At Support Position (Bearing Center) of Girder Vs= Avfydv-Supp.Cotq/sL0.375m

VS-Supp.

1,230.434 kN 1230.434*10^3 N

c) At distance 0.375m from the Support of Girder Vs=Avfydv-L0.375mCotq/sL0.375m

VS-L0.375m

1,230.434 kN 1230.434*10^3 N

d) At a distance L/8 from the Support of Girder Vs = Avfydv-L/8Cotq/sL/8

VS-L/8

1,230.434 kN 1230.434*10^3 N

e) At a distance L/4 from the Support of Girder Vs = Avfydv-L/4Cotq/sL/4

VS-L/4

1,065.762 kN 1065.762*10^3 N

f) At a distance 3L/8 from the Support of Girder Vs = Avfydv-3L/8Cotq/s3L/8

VS-3L/8

1,158.726 kN 1158.726*10^3 N

g) At a distance L/2 from the Support of Girder Vs = Avfydv-L/8&L/2Cotq/s 3L/8&L/2

VS-L/2

1,122.611 kN 1122.611*10^3 N

xxii) Computation of values for Nominal Shear Resistance (Vn) at Different Section of Girder under Provisions of AASHTO-LRFD-5.8.3.3 against Equation Vn = Vc + Vs + Vp (Equ. 5.8.3.3-2) : a) The Nominal Shear Resistanceat any Section of Girder is Vn = Vc + Vs + Vp (Equ. 5.8.3.3-1) b) For RCC Girder the value of Vp = 0, thus Equation stands to Vn-1 = Vc + Vs c) At Support Position (Bearing Center) of Girder Vn= Vc-Supp + Vs-Supp.

d) At distance 0.375m from the Support of Girder Vn = Vc-L0.375m + Vs-L0.375m

Vn-Supp.-1 50,134.235 kN 50134.235*10^3 N Vn-L0.375m-1 50,134.235 kN 50134.235*10^3 N

e) At distance L/8 from the Support of Girder Vn = Vc-L/8 + Vs-L/8

Vn-L/8-1

49,640.569 kN 49640.569*10^3 N

f) At distance L/4 from the Support of Girder Vn = Vc-L/4 + Vs-L/4

Vn-L/4-1

48,676.627 kN 48676.627*10^3 N

g) At distance 3L/8from the Support of Girder Vn = Vc-3L/8 + Vs-3L/8

Vn-3L/8-1

50,388.363 kN 50778.639*10^3 N

Page 199

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

h) At distance L/2 from the Support of Girder Vn = Vc-L/2 + Vs-L/2

Vn-L/2-1

50,742.524 kN 50742.524*10^3 N

xxiii) Computation of values for Nominal Shear Resistance (Vn) at Different Section of Girder under Provisions of AASHTO-LRFD-5.8.3.3 against Equation Vn = 0.25f/cbvdv + Vp (Equ. 5.8.3.3-2) : a) According to Equ. 5.8.3.3-1 the Nominal Shear Resistanceat any Section of Girder is Vn = 0.25f/cbvdv + Vp b) For RCC Girder the value of Vp = 0, thus Equation stands to Vn = 0.25f/cbvdv c) At Support Position (Bearing Center) of Girder Vn= 0.25f/c-bv-Suppdv-Supp.

Vn-Sup.

3,145.433 kN 3145.433*10^3 N

Vn-L0.375m-2

3,145.433 kN 3145.433*10^3 N

e) At distance L/8 m from the Support of Girder Vn= 0.25f/c-bv-L/8dv-L/8

Vn-L/8-2

3,145.433 kN 3145.433*10^3 N

f) At distance L/4 m from the Support of Girder Vn= 0.25f/c-bv-L/4dv-L/4

Vn-L/4-2

3,113.681 kN 3113.681*10^6 N

g) At distance 3L/4 m from the Support of Girder Vn= 0.25f/c-bv-3L/4dv-3L/4

Vn-3L/8-2

3,062.273 kN 3062.273*10^3 N

h) At distance L/2 m from the Support of Girder Vn= 0.25f/c-bv-L/2dv-L/2

Vn-L/2-2

2,966.828 kN 2966.828*10^3 N

d) At distance 0.375m from the Support of Girder Vn= 0.25f/c-bv-L0.375mdv-L0.375m.

xxix) Accepted Nominal Shear Resistance-Vn & Factored Shearing Resistance-Vr at Different Section of Girder Computed accordting Provisions of AASHTO-LRFD-5.8.3.3 & AASHTO-LRFD-5.8.2.1 : a) Nominal Shear Resistance, Vn at any Section of Component is the Lesser value of of the Equqtions as mentioned below ; b) Vn = Vc + Vs + Vp (Equ. 5.8.3.3-1; AASHTO-LRFD-5.8.3.3) c) Vn = 0.25f/cbvdv + Vp (Equ. 5.8.3.3-2; AASHTO-LRFD-5.8.3.3) : d) For RCC Girder, Vp = 0. e) The Factored Shear Resitance at any Section of Component is Expressed by the Equation-5.8.2.1-2. Having the value, Vr = fVn in which; f) Vr is the Factored Shear Resitance at a Section in N g) f is Resistance Factor according to AASHTO-LRFD-5.5.4.2.

Page 200

Vr. f

N 0.90

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

h) The Acceptable Nominal Shear Resistance, Vn, Respective Factored Shear Resitance-Vr at Different Section of T-Girder, the Staus between the vaues of Vn Computed under Equ. 5.8.3.3-1 & Equ. 5.8.3.3-2 are shown in Table below :. i) Table-; Accepted Nominal Shear Resistance-Vn & Factored Shear Resitance-Vr at Different Section : Section

Calculated

Vn-1

Vn-2

Relation

Accepted

Factored

Relation

Location

Factored

As per

As per Equ.

between

Value of

Shear

between

from Center

Shear

Equation.

5.8.3.3-2

Values of

Vn

Resitance

Values of

of Bearing.

Force-Vu

5.8.3.3-1

kN

kN

kN

At Support

860.766

50134.235

3145.433

Vn-1> Vn-2

3145.433

2,830.889

At L0.375m

834.197

50134.235

3145.433

Vn-1> Vn-2

3145.433

2,830.889

At L/8

644.670

49640.569

3145.433

Vn-1> Vn-2

3145.433

2,830.889

At L/4

407.258

48676.627

3113.681

Vn-1> Vn-2

3113.681

2,802.312

At 3L/4

191.162

50388.363

3062.273

Vn-1> Vn-2

3062.273

2,756.045

At L/2

-46.250

50742.524

2966.828

Vn-1> Vn-2

2966.828

2,670.145

Vr

Vn-1 & Vn-2 Vn-1 > Vn-2

kN

kN

Status If Vr > Vu, the Structure is

Vr& VU Safe otherwise Vr> VU No Safe. Vr> Vu Structure Safe Vr> Vu Structure Safe Vr> Vu Structure Safe Vr> Vu Structure Safe Vr> Vu Structure Safe Vr> Vu Structure Safe

xxx) Relation between Factored Shearing Force (Vu) & the Nominal Shear Resistance (Vn) at Different Section of Girder, Computed under Provisions of AASHTO-LRFD-5.8.3.3 : a) The Relation between Factored Shearing Force, Vu & the Nominal Shear Resistance Vn at Different Section of Girder are shown in the Table blow : Table-; Showing between Factored Shearing Force, Vu & the Nominal Shear Resistance Vn : Location of Section from Bearing Center of Girder.

a) At Support (Bearing Point) Position b) At Distance L0.375m from Support. c) At Distance L/8 from Support. d) At Distance L/4 from Support. e) At Distance 3L/4 from Support. f) At Distance L/2from Support.

Calculated Computed Status value of value of between Vu Vn Values of kN 860.766 834.197 644.670 407.258 191.162 -92.764

kN 3145.433 3145.433 3145.433 3113.681 3062.273 2966.828

Vu & Vn Vu< Vn Vu< Vn Vu< Vn Vu< Vn Vu< Vn Vu< Vn

b) Since the Factored Shearing Forces Vu < Vn < Vr, the Computed Nominal Shear Resistance, thus the Girder is Safe in respect of Applied Shearing Forces caused by Dead Load & Live Loads to the Bridge Structure. xxxi) Checking of T-Girder Web Width (bWeb) in respect of Nominal Shearing Resistance (Vn) at Critical Section : a) According to AASHTO-LRFD-5.8.3.2 the Critical Section for Shearing Forces Prevails at a Distance dv from Face of Support. b) Since In-between Support & the Section at L/4 the value of dv is same, thus on Critial Section value of dv = 1697.400mm c) Distance of Critical Section from Support/Bearing Point, LCrit = (0.375 + dv )

Page 201

dv

LCrit.

1,711.800 mm

2.087 m

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

e) Since the Nominal Shearing Resistance Vn for Girder In-between Support & the Section at L/4 have same values, thus at Critical Section Vn will have same value.

Vn-Crit.

3,145.433 kN 3145.433*10^3 N

f) Since the T-Girders are being provided equal Web Width through the Length, thus Web Width for Critical Section, bWeb = 350 mm which is the Effective Web Width bv for the Section.

bv-Crit.

350 mm

g) According to Equ. 5.8.3.3-2, at any Section of Girder the Effective Web Width, bv = (Vn - Vp)/0.25*f/cdv. In a RCC Girder the value of Vp = 0. and the Equation Stands to, bv = Vn/0.25*f/cdv. from which value of bv-Crit can Calculate.

bv-Crit-Cal.

350 mm

h) Since the Calculated value of Effective Web Width for Critical Section bv-Crit = bWeb the Provided Web Width, thus Design of Critical Section is OK. xxxii) Checking in respect of Longitudinal Reinforcements (Tensile Reinforcements) Provided for Girder under Provision of AASHTO-LRFD-5.8.3.5 : a) At each Section the Tensial Capacity of Longitudinal Reinforcement on Flexural Tension side of the Member shall be proportationed to Satisfy Equation, Asfy + Apsfps  Mu/dvff + 0.5Nu/fc + (Vu/fv - 0.5Vs -Vp)Cotq. (Equ-5.8.3.5-1). Where; b) As is Area of Nonprestressing Steel on Flexural Tention side of Girder in mm2

As

c) fy is Yield Strength of Nonprestressing Reinforceing Steel in MPa.

fy

Variable

mm2

410.000 MPa

d) Aps is Area of Prestressing Steel on Flexural Tention side of Girder in mm2. For Nonprestressing RCC Structure, the value of Aps = 0

Aps

-

mm2

e) fps is Yield Strength of Prestressing Steel in MPa. For Nonprestressing RCC Structure, the value of fps = 0

fps

-

MPa

f) Mu is Factored Moment of the Section due to Dead & Live Loads Loads on Structure. in N-mm but not less then Vudv.

Mu

Variable

g) Nu is Factored Axil Force in N, Value will be (+) ve for the case of Tensile & (-) for the case of Compressive due to Prestressing. For Nonprestressing RCC Structural Component, the value of Nu = 0.

Nu

-

h) dv is Effective Shear Depth of Tensil Reinforcement for the Section in mm.

dv

Variable

mm

i) Vu is Factored Shear Force for the Section in N.

Vu

Variable

N

j) Vs is Shear Resistance Provided by Shear Reinforcement in N for the Section.

Vs

Variable

N

k) Vp is component of Prestressing Force in direction of Shear Force in N; For Nonprestressing RCC Structural Component, the value of Vp = 0.

Vp.

-

N

Page 202

N-mm

N

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

0 l) q is Angle of Inclenation of Digonal Compressive Stress in ( ) according to AASHTO-LRFD-5.8.3.4;

q

Variable

m) ff is Resistance Factor for Flexural Tension of Reinforced Concrete according to AASHTO-LRFD-5.5.4.2.

ff

0.90

n) fv is Resistance Factor for Shearing Force of Reinforced Concrete according to AASHTO-LRFD-5.5.4.2,

fv

0.90

o) fc is Resistance Factor for Compression due to Prestressing according to AASHTO-LRFD-5.5.4.2.

fc

0.80

O

p) Since for Nonprestressing RCC Structural Components the Items Aps, fps, Nu & Vp have Values = 0, thus mentioned Equ-5.8.3.5-1. Stands to, Asfy  Mu/dvff + (Vu/fv - 0.5Vs)Cotq. q) Table- Showing Evalution of Equation-5.8.3.5-1 at Different Section of Girder & Status of Results.

Location of Section from Bearing Center of Girder.

a)At Support b) At L0.375m. c) At L/8. d) At L/4. e) At 3L/4. f) At L/2.

As.

Mu

Vu

Vs

Calculted Calculted R/H Part of the

Provided Factored Factored Shearing Value of Tensile Moment Shearing Resistance Asfy Steel Area Force of Stirrups (L/H Part) mm2 kN-mm kN kN kN

Equation kN

6433.982

1473.459

860.766 1230.434261

2637.933

1,237.467

6433.982

1427.978

834.197 1230.434261

2637.933

1,173.513

8042.477

3003.199

644.670 1230.434261

3297.416

1,732.176

11259.468

5131.011

407.258 1065.761789

4616.382

2,616.188

16084.954

6318.423

191.162 1158.726304

6594.831

2,861.967

14476.459

6630.449

-92.764 1122.611089

5935.348

2,699.711

Status

of the Equation Satisfied Not Satisfied Satisfied Satisfied Satisfied Satisfied Satisfied Satisfied

j) Since at all Section the requirments of Equation are being Satisfied, thus provision of Transverse/Shear Reinforcements for Girder is OK. xxxiii) Checking for Factored Tensile Resistance of Transverse/Shear Reinforcements Provided for Girder: a) The provided Transverse/Shear/Web Reinforcements at Different Section of Girder under the Provision of Deep Beam should Satisfy the Equation, Ng = f fyAs  0.83bvs (AASHTO-LRFD-5.13.2.3; Equ-5.13.2.3-1). Here, b) Ng is Factored Tensial Resitance of Transverse Reinforcement (Each Pair) in N.

Ng.

c) bv is Width of Girder Web in mm.

bv.

350 mm

d) fy is Yield Strength of Reinforceing Steel as Transverse/Shear Reinforcement

fy.

410.000 Mpa

e) As is Steel Area of Transverse/Shear Reinforcement in mm2 having the Spacing AS s mm. Here As = Av, the X-Sectional Area of 2-Leged the 12f Dia. Vertical Stirrups.

2 226.195 mm

Page 203

Variable

N

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

f) s is Spacing of Transverse /Shear Reinforcement in mm. The value s should not Excide eithe d/4 or 300mm

s

Variable

mm

g) The Girders are being provided with Transverse/Shear Reinforcements in the form of Vertical Stirrups against Shear Forces caused by the Dead Load & Live Loads applied to the Bridge Structure. Due to Vertical Positioning of those Transverse/Shear Reinforcements they will also under Tensile Stress caused by the same Shearing Forces whose actions are in some extent in Vertical Direction. On these back drop mentioned Shearing Forces at different Section of Girder may be considered as Tensile Forces for Vertical Stirrups. Thus the Factored Shearing Forces at Each Section, Vu = Ng, the Factored Tensile Resistance Carried by the Pair of Transverse Reinforcement. h) The Checking for Factored Tensile Resistance of Transverse/Shear Reinforcements at Different Section of Girder are shown in the under mention Table: i) Table- Showing Minimum Transverse/Shear Reinforcement at Different Section of Girder. Location of Section from Bearing Center of Girder.

a) At Support (Bearing Point) Position b) At Distance L0.375m from Support. c) At Distance L/8 from Support. d) At Distance L/4 from Support. e) At Distance 3L/4 from Support. f) At Distance L/2from Support.

s'-Spacing As of Shear Provided Bars Steel Area mm2 mm 175.000 226.195 175.000 226.195 175.000 226.195 200.000 226.195 200.000 226.195 200.000 226.195

Calculted Calculted Value of Value of ffyAs 0.83bvs 83465.834 83465.834 83465.834 83465.834 83465.834 83465.834

Status of

Equation Satisfied Not Satisfied 50837.50 Satisfied 50837.50 Satisfied 50837.50 Satisfied 58100.00 Satisfied 58100.00 Satisfied 58100.00 Satisfied

j) Since in all Section the requirments of Equation Equ-5.13.2.3-1, Ng = ffyAs > 0.83bvs are being Satisfyed, thus Provision of Transverse/Shear Reinforcements for Girder is OK. xxxiv) Checking the Critical Section Near Support in respect of M n the Nominal Flexural Resistance under the Provision of AASHTO-LRFD-5.8.3.2 : a) According to AASHTO-LRFD-5.8.3.2 the Critical Section for Shearing Forces Prevails at a Distance dv from Face of Support & the Area In-between this Section & Support Face should be Designed for Shear accordingly. b) According to AASHTO-LRFD-5.8.3.2 at Critical Section will have Nominal Flexural Resistance Mn= dv*(Apsfps + Asfy) in N-mm both for Top & Bottom Tension Reinforcement Bars. c) Since the position of Critical Section at a Distance dv from Support is related to Distance of the Sections fron Support to 0.375m & L/8. The Calculated Value of dv for Section at Support, at 0.375m, L/8 & L/4 are same. Thus for Critical Section the value of dv within mentioned Sections are Applicable.

dv-Crit

d) Distance of Critical Section from Support/Bearing Point, LCrit = (0.375+ dv )

LCrit.

2.087 m

Mn-Crit-1.

4,515.613 kN-m

e) For Nonprestrssed RCC Structure value of Aps = 0 & also fps = 0; thus for the Critical Section Equation Mn = dv(Apsfps + Asfy) stands to Mn= dvAsfy.

Page 204

1,711.800 mm

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

f) For a Nonprestressing Structural Component having Either of I or T Section with Flenge & Web Elements, at any Section the Nominal Resistance, Mn = Asfy(ds-a/2) + 0.85f/c(b-bw)b1hf(a/2-hf/2) in which, g) The provided Steel Area as Tension Reinforcemen on bottom surface of Critical Section have same value that for the Sections In-between Support Point & L/8. Section. The Critical Section is being also provised same Steel Area on its Top Surface.

As-Crit.

2 6,433.982 mm

h) The Effective Depth for Tension Reinforcement of Critical Section, de = ds is same that for the Sections In-between Support Point & L/8.

ds-Crit.

1,882.800 mm

i) Accordingly the Depth of Compressin Block 'a' for Critical Section have same value that for the Sections In-between Support Point & L/8.

aCrit.

j) For Simple Supported & Single Reinforced T-Girder Beam the with Provided Steel Area against Factored Max. Moments at its Critical Section will have the Nominal Resistance, Mn = Asfy(ds-a/2) + 0.85f/c(b-bw)b1hf(a/2-hf/2)

Mn-Crit-2.

21.266 mm

4,491.197 kN-m 4491.197*10^6 N-mm

k) Since the Calculated value of Nominal Resistance based on provided Effective Shear Depth, Mn-Crit.-1 < Mn-Crit-2 the Calculated value of Nominal Resistance based on provided Effective for Tensial Reinforcement for Critical Section thus the Design of Critical Section is OK. xxxv) Checking the Critical Section Near Support in respect of Provided Shear & Tensial Reinforcements for the Section according to Provisions of AASHTO-LRFD-5.8.3.2 : a) The Shearing Resistance for the provided Shearing Reinforcement In-between Support Face & Critical Section should have the value Vs = AvfydvCotq/s in N/mm2. b) The Calculated Shearing Forces at Critical Section due Factored Loads

VU-Crit.

c) The Calculated Moment at Critical Section due Factored Loads (DL & LL).

MU-Crit.

d) Calculated value of VU*dv for Critical Section

VU*dv

e) The Effcetive Moment for Critical Section is Greater One of MU-Crit & VU*dv

MEff.

f) The Shearing Stress at Critical Section vu = VU/fbvdv N/mm2 g) Value of vu/f/c for Critical Section

vu

673.904 kN 673.904*10^3 N 1,979.602 kN-m 1979.602*10^3 N-mm 1,153.589 kN-m 1,979.602 kN-m 1979.602*10^3 N-mm 2 1.250 N/mm

vu/f/c

0.060

h) Based on the Initial Longitudinal Straion of Tensial Reinforcement ex = 0.001, Effcetive Moment for Critical Section MEff,Effective Depth dv & value of Cotq the Computed value of ex*1000 = (MU/dv + 0.5VUcot q )/EsAs

ex*1000

0.001

i) Based on values of ex*1000 & vu/f/c from respective Table LRFD-5.8.3.4.2-1

q

24.300

Page 205

O

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

j) Value of Cotq for Critical Section

Cotq

k) Provided Spacing of 2-Legged 12f Vertical Stirrups between Support & Critical Section. l) Steel Area of 2-Legged 12f Vertical Stirrups between Support & Critical Section m) Computed value of Vs = AvfydvCotq/s for the Critical Section

n) Computation of values of Equation Asfy  Mu/dvff + (Vu/fv - 0.5Vs)Cotq. for the Critical Section as LHP (Left hand Part) & RHP (Right hand Part) in respect of whether those Satisfy the Provision of Equation or Not.

2.215

s

175.000 mm

Av

2 226.195 mm

Vs-Crit.

LHP RHP

2,009.124 kN 2009.124*10^3 N 2,637.933 kN 474.310 kN LHP>RHP Satisfy

o) Since the Provisions of Equation Asfy  Mu/dvff + (Vu/fv - 0.5Vs)Cotq. are being Satisfied by the arramgement of Shear Reinforcements as well as by the Tensial Reinforcements provided In-between Support Face & the Critical Section, thus the Flexural Design of Critical Section is OK. 6 Design of Reinforcement for Torsion & Checking against Forces due to Torsion at Different Locations : i) Design Phenomenon for Tensional Effect upon Girder & Checking in these respect : a) The Bridge Girders are being considered as T-Beam having Dead Loads due to Self Weight & Superimposed Loads from Deck Slab, W/C, Sidewalk, Curb/Wheel Guard, Railing, Rail Posts etc. whereas Live Loads from Wheel Loads of Truck, Lane Loads, Pedestrian etc. Thus the Torsional Forces at Section is the Total Shearing Forces acting on that Section. b) Bridge Interior T-Girders has a Flange Width, b = 2.000m, & Web bWeb = 0.450m. Girders are being effect by the Tensional Forces due to Eccentric Loading of both Dead Loads & Live Loads. Dead Loads of Structure & Live Lane Loads have almost equilibrium actions. Whereas Truck Live Loads have a significant effect in these respect. Wheel Position of a moving Truck may change over Bridge Deck & will have effect up to a distance of b/2 from the Center Line of Girder of each side of Interior Girders. Thus Location or Eccentricity of Torsional Force action will be consider at a distance b/4 from Girder Center Line. c) Based on the assumption-a the Factored Torsional Forces (DL + LL) will be the Factored Shearing Forces at a Section. Thus FTor. = FShear

FTor.

d) Based on the assumption-b of Torsional Forces (DL & LL) action Positions, the Eccentricity eTor. = b/4 from Center of Girder.

eTor.

d) Accordingly Factored Torsional Moment at any Section will be Tu = FTor.*eTor.

Tu.

860.765820 kN 860765.820 N 500 mm

430.383 kN-m 430.383*10^6 N-mm

ii) Computation of Factored Torsional Forces (T Forces) &Torsional Moments (Tu) under assumed Provisions : a) According to assumption the Factored Forces for Torsion, FTor. due to Dead Load & Live Loads at Different Section of Girder are the respective Factored Shearing Forces FShear. Whereas the Torsional Moments, Tu are due to the

Page 206

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Eccentric action of Torsional Forces FTor. The Factored Shear Forces FShear, Factored Torsional Forces, Fu & the respective Torsional Moments, Tu at different Sections of Girder are shown in under mentioned Table. b) Table-2. Factored Shear Forces, Torsional Forces & Moments at Different Sections on Interior Girder. Locations from Support Shearing Forces, FTor. (kN) Torsional Forces, FTor. (kN) Torsional Monent, Tu (kN-m)

0.375m

L/8

L/4

3L/8

L/2

248.07

239.353

177.156

106.240

35.324

-47.468

860.77

834.197

644.670

407.258

191.162

-92.764

430.383

417.098

322.335

203.629

95.581

-46.382

On Support

c) From Table - 2, it appears that, magnitude of Torsional Forces & Moments are highest at Support Positions & those gradually reduced to zero or (-) ve value towards the Center of Span. b) Since opposite direction Torsional Forces & Moments at two Support Positions with highest magnitude causes the Torsional affect on T-Girders, thus those are considered as the Governing Torsional Forces & Moments for Design. iii) Checking of Design in respect of Factored Torsional Moment (T u) at Support Position under Provisions of AASHTO-LRFD-5.8.2.1 : a) In Normal density Concrete the Factored Torsonal Moment, Tu > 0.25fTcr (Equ.-5.8.52.1-3), in which; b) Tu is Calculated Factored Torsional Moment at Support Position in N-mm.

Tu

430.383 kN-m 430.383*106 N-mm

c) Tcr is Torsional Cracking Moment of Component in N-mm. having the value, Tcr = 0.328f/c*(Acp2/Pc)(1 + fpc/0.328f/c) N-mm. where,

Tcr

607.707 kN-m 607.707*10^6 N-mm

d) Acp is Total Area Enclosed by the Outside Perimeter of the Concrete Section in mm2; Here for T-Girder Section Acp = b*hf +bWeb*(hGir. - hf) mm2

Acp

e) Pc is Length of Outside Parameter of Concrete Section in mm. Here for T-Girder Section Pc = 2*(b + hf) - bWeb + 2*(hGir - hf) + bWeb mm

Pc

8,000.000 mm

f) fpc is Compressive Stress in Concrete Section for Prestressing after occurrence of Prestress Losses either at the Centroid of Cross-section Resisting Transient Loads or at the Junction of Web & Flange when the Centroid Lies within Flange having unit of value in Mpa. For Nonprestressing RCC Structural Components the value of fcp = 0.

fpc

-

g) f is Resistance Factor for Torsion according to AASHT-LRFD-5.5.4.2.

f

h) Calculated value of 0.25f Tcr for T-Girder

0.25fTcr

2 1030000.000 mm

Mpa

0.90 136.734 kN-m 136.734*10^6 N-mm

i) Table-2. Status of Factored Moments (T u) in respect of Torsional Cracking Moment (T cr)at Different Section. Locations from Support Unit of Moments

On Support kN-m

0.375m kN-m

Page 207

L/8 kN-m

L/4 kN-m

3L/8 kN-m

L/2 kN-m

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Value of Torsional Monent, Tu Value of 0.25fTcr Statu between Tu & 0.25fTcr

430.383

417.098

322.335

203.629

95.581

-46.382

136.734

136.734

136.734

136.734

136.734

136.734

Tu>0.25fTcr Tu>0.25fTcr

Tu>0.25fTcr

Tu>0.25fTcr Tu1.00, for those Cases values of q & b can obtain in respect of value of Crack Spacing Parameter sxe, using the Equation .No.5.8.3.4.2-2, Equation No. 5.8.3.4.2-4 & Table -5.8.3.4.2-2. viii) Values of esx1000 with Less than Min. Transverse/Shear Reinforcement under AASHTO-LRFD-5.8.2.5 & the provisions of Equation 5.8.3.4.2-2 : a) Since in RCC Girder the values for Prestressing Components Nu, Vp, Asp, fpo, Ep etc. are = 0, thus equation ex= (Mu/dv+0.5Nu + 0.5(Vu -Vp)cotq - Apsfpo)/(EsAs + EpAps) stands to ex = (Mu/dv + 0.5Vucotq )/EsAs b) Considering the Initial value of ex = 0.002 at Support Position & the Effective Moment Mu-Eff. From the Equation Cotq = (exEsAs - Mu/dv)/0.5Vu

cotq

c) Values of exx1000 at Location = (Mu/dv + 0.5Vucotq )/EsAs

ex-*1000

2.901

-

ix) Computation of values of Crack Spacing Parameter, sxe for Section at L/8 : a) The Crack Spacing Parameter of a Section, sxe = sx(35/(ag+16))  2000mm, In which; b) sx = the Lesser value of either dv or the Spacing of Longitudinal Crack Control Reinforcements on Vertical Faces (as Shrinkage & Tempeture Reinforcement) having Steel Area in a Horizontal Reinforcement Layer if As > 0.003bvs. Here;

sx

i) As is Steel Area of 2nos Shrinkage & Tempeture Reinforcement Bars on Opposite Vertical Faces of T-Girder in same Horizontal Layer, = As-S&T-Hori. = 2*pDBar2/4 = 2*Af-16

As

ii) dv is Effective Shear Depth of Tensil Reinforcement for the Section

dv

iii) s is Spacing of Longitudinal Bars as Shrinkage & Tempeture Reinforcement on Vertical Faces of T-Girder.

s

iv) Thus Computed value of 0.003bvs for a Section

-

mm

2 201.062 mm

-

mm

232.857 mm

mm2 0.003dvs 0.003dvs>As s-Applicable

v) For Computed value of 0.003bvs at Section > As, the value of sx = dv c) ag is Max. Aggragate size for Concrete = 20mm

ag

d) Thus Computed value of sxe = sx(35/(ag+16)) for a Section

sxe

20 mm -

f) For value of ex-*1000 > 1.00 & the value of sxe at a Sections should Computed from the Respective Tablel.

Page 210

mm

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

x) Computation of Values of q from AASHTO-LRFD'sTable -5.8.3.4.2-1. & Table -5.8.3.4.2-2. against the Respective Calculated values of esx1000, Ratio vc/f/c & sxe.: Table-7 for Values of q & Cotq at Different Location of Girder.

a)

Location of Section From Support a) At Support Position b) At L0.375mDistance of Support c) At L/8 Distance of Support d) At L/4 Distance of Support e) At 3L/8 Distance of Support f) At L/2 Distance of Support

Referece of Table

vu/f/c

exx1000

sxe

Value of q

5.8.3.4.2.-1

0.198

1.000

NA

36.400

1.356

5.8.3.4.2.-1

0.192

0.969

NA

36.400

1.356

5.8.3.4.2.-1 5.8.3.4.2.-1 5.8.3.4.2.-1 5.8.3.4.2.-2

0.148 0.094 0.044 0.021

0.950 0.864 0.667 0.728

NA NA NA NA

36.400 36.400 33.700 33.700

1.356 1.356 1.499 1.499

Value of Cotq

xi) Computation of Nominal Torsional Resistance (T n) Subject to Combined Shear & Torsion under Provisions of AASHTO-LRFD-5.8.3.6 a) According to AASHTO-LRFD-5.8.2.1 the Factored Torsional Resistance of a Section, Tr = fTn in N-mm. b) According to AASHTO-LRFD-5.8.3.6 the Nominal Torsional Resistance of a Section, Tn = 2AoAtfycotq/s in N-mm. c) The Computed values for Factored Torsional Moment Tu, Factored Torsional Resistance Tr & the Nominal Torsional Resistance Tn in respect of provided Steel Area for Torsional Reinforcement Combined with Shear Reinforcement At, Spacing of Combined with Shear & Torsional Reinforcement s, Computed values of Ao the Area enclosed by Shear Flow Path & Cotq at different Section along with respective Status are shown in the under mentioned Table-8. d) Table-8. Showing the values of T u, Tr,Tn, At, Ao, Cotq , s & Status of different events related to Torsion. Location

Calculated

Calculated

Factored

Calculated

Calculated

Provided

Provided

Status

Status

of Section

value of

Factored

Torsional

Nominal

value of

Steel Area

Spacing of

between

between

from

Cotq

Torsional

Resistance

Torsional

Ao

of Torsional

Torsional

Tu &Tr

Tu &Tn

Bars

Bars

(At)

(s)

Support

Moment

(Tu)

Resistance

kN-m

(Tr) kN

(Tn) kN

mm

At Support

1.356

430.383

666.3235

740.359

1030000.000

113.097

175.000

Tu0.5Vc

Satisfied

i) The Table indicates that all the Sections of RCC Girder have satisfied the required provisions for Transverse/Shear Reinforcements under Equation Vu > 0.5f (Vc + Vp). AASHTO-LRFD-Equation-5.8.2.4-1. xi) Checking of Required Max. Spacing for Transvers/Shear Reinforcement due to Applied Shearing Stress on Girder under provision of AASHTO-LRFD-5.8.2.7 : a) Due to applied Shearing Stress, vu < 0.125f/c, the Max. Spacing of Transverse/Shear Reinforcement at a Section is smax.-1 = 0.8dv ≤ 600mm, (AASHTO-LRFD-Equ. 5.8.2.7-1). b) Due to applied Shearing Stress, vu > 0.125f/c, the Max. Spacing of Transverse/Shear Reinforcement at a Section is smax.-2 = 0.4dv ≤ 300mm (AASHTO-LRFD-Equ. 5.8.2.7-2) c) Value of 0.125f/c in respect of Max. Spacing of Transvers/Shear Reinforcement due to Applied Shearing Stress at Defferent Section of Girder.

0.125f/c

2 2.625 N/mm

d) Table Showing values of vu, 0.8dv, 0.4dv againest the respective values of 0.125f/c : Table- ; Showing Spacing of Transverse/Shear Reinforcements in respect of Max. Spacing & Status : Segment. Value of

Value of

Value of

Relation

Value of

Page 230

Value of

Relation

Relation

Formula

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Location dv (Between for the 2-Section) Section mm Section at 1647.00 Faces Section at 1,647.00 Middle

vu

0.125f/c

between vu & 0.125f/c

Maximum

N/mm2

N/mm2 vu0.125f/c

0.8dv for the Section mm

0.4dv for the Section mm

between 0.8dv & sMax-1300

Not Satisfy

e) The Table indicates that non of the Sections of Cross-Girder have satisfied the required provisions for Spacings of the Transverse/Shear Reinforcement under Equations, For vu < 0.125f/c ; smax. = 0.8dv ≤ 600mm, (AASHTO-LRFD-Equ. 5.8.2.7-1). & For vu > 0.125f/c ; smax. = 0.4dv ≤ 300mm, (AASHTO-LRFD-Equ.5.8.2.7-2). xii) Chacking for Transverse/Shear/Web Reinforcements as Deep Beam Component (AASHTO-LRFD-5.8.1.1) : a) The Component in which a Load causing more than 1/2 of the Shear at a Distance closer than 2d from the Face of Support is Considered as a Deep Component. Deep Beam Components the Shear Reinforcements are being Provide according to Provisions of AASHTO-LRFD-5.6.3 (Provisions of Strut-and-Tied Model) & AASHTO-LRFD-5.13.2.3. b) Factored Shear Force at Face of Main Girder, Vu-Face.= c) Value of 1/2 of Factored Shear Force at Face

268.3508 kN.

Vu-Face.

268.351 kN

134.18 kN

1/2Vu-Face.

134.175 kN

168.744 kN.

Vu-Mid

168.744 kN

=

d) Factored Shear Force at Middle of Cros-Girder Vu-Mid = e) Status in between the values of 1/2Vu-Supp. & Vu-Mid

Vu-Mid >1/2Vu-Face.

f) Since the Distance 2d from Face of Main Girder is beyond the Cross-Girder Span & value of Shearing Force at Mid Span is greater than 1/2Vu-Face, thus the Cross-Girder can consider as a Deep Beam Component. Accordingly its Transverse/Shear Reinforcementsb can provide under Article 5.13.2.3. Of AASHTO-LRFD. xiii) Detaling of Requirments for Deep Beam Component to Provide Transverse/Shear/Web Reinforcements for Girder under provision of AASHTO-LRFD-5.13.2.3 : a) To provide Transverse/Shear/Web Reinforcements at Different Section of Girder, it should Satisfy the Equation, Ng = f fyAs  0.83bvs (AASHTO-LRFD-5.13.2.3). Here, b) Ng is Factored Tensial Resitance of Transverse Reinforcement (Each Pair) in N.

Ng.

c) bv is Width of Girder Web in mm.

bv.

d) fy is Yield Strength of Reinforceing Steel as Transverse/Shear Reinforcement

fy.

410.00 MPa

e) As is Steel Area of Transverse/Shear Reinforcement in mm2 having Spacing s .

AS

mm2

f) s is Spacing of Transverse /Shear Reinforcement in mm. The value of s should not excide eithe of d/4 or 300mm

s-Max

Page 231

N 250 mm

300 mm

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

g) The Vertical Spacing, sVetrt. for Crack Control Longitudinal Reinforcement on both Vertical Faces of Girder should not Excide either d/3 or 300 mm.

sVert.-Max

300 mm

xxi) Computation of Spacing for Transverse/Shear Reinforcement at Different Section of Girder : a) Value of d/4 for the Section under cosideration having d = hGir. (Girder Depth).

d/4

475 mm

b) Allowable Max. Spacing for Transverse/Shear Reinforcement

s-Max

300 mm

c) Let Provide 2-Leged 10f bars as Transverse/Shear Reinforcement in the form of Vertical Stirrups.

DStir.

10 mm

d) X-Sectional Area of 2-Leged 10f Bars as Transverse/Shear Reinforcement; = 2*pDStir.2/4 mm2

Av

d) Let Provide the 175mm Spacing for Transvers/Shear Reinforcements for total Length of Cross-Girder.

s-X-Gir.

2 157.080 mm

175 mm

xxi) Checking for Requirements of Minimum Transverse Reinforcements for Cross-Girder: a) Minimum Transverse/Shear Reinforcement at a Section, Av  0.083f/c(bvs/fy), AASHTO-LRFD-5.8.2.5. Where, s is Length of Girder Segment under consideration for Transverse/Shear Reinforcement. b)

Table for Minimum Transverse/Shear Reinforcement at Different Section of Girder. Location from Bearing Center of Girder. Total Length of Cross-Girder.

Length of Segment mm

bv' Web Width mm

s-Web-Bar Spacing mm

Min. Av Required mm2

1650.000

250.000

175.000

40.587

Av-pro

Status of

Provided Provided & mm2 Required Av 157.080

Av-pro> Av

xxii) Computation of Values of Vs,the Shear Resistance against Provided Shear Reinforcement & Spacings at Different Sections according to Vs = Avfydv(cotq + cota)sina /s (AASHTO-LRFD-Equ. 5.8.3.3-3) : a) With Vertical Shear Reinforcement the value of a = 900 & the Equation Vs = Avfydv(cotq + cota)sina /s stands to Vs = Avfydvcotq /s, b) At Faces of Main Girder Vs= Avfydv-Face.Cotq/sX-Gir.

VS-Face

822.122 kN 822.122*10^3 N

c) At Middle of Cross-Girder Span Vs=AvfydvMidCotq/sX-Gir.

VSMid.

908.840 kN 913.806*10^3 N

xxiii) Computation of values for Nominal Shear Resistance (Vn) at Different Section of Girder under Provisions of AASHTO-LRFD-5.8.3.3 against Equation Vn = Vc + Vs + Vp (Equ. 5.8.3.3-2) : a) The Nominal Shear Resistanceat any Section of Girder is Vn = Vc + Vs + Vp (Equ. 5.8.3.3-1) b) For RCC Girder the value of Vp = 0, thus Equation stands to Vn-1 = Vc + Vs

Page 232

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

c) At Faces of Main Girder Vn= Vc-Face + Vs-Face.

Vn-Vace-1

855.731 kN 855.731*10^3 N

d) At Middle of Cross-Girder Vn = Vc-Mid. + Vs-Mid.

Vn-Mid-1

914.579 kN 914.579*10^3 N

xxiv) Computation of values for Nominal Shear Resistance (Vn) at Different Section of Girder under Provisions of AASHTO-LRFD-5.8.3.3 against Equation Vn = 0.25f/cbvdv + Vp (Equ. 5.8.3.3-2) : a) According to Equ. 5.8.3.3-1 the Nominal Shear Resistanceat any Section of Girder is Vn = 0.25f/cbvdv + Vp b) For RCC Girder the value of Vp = 0, thus Equation stands to Vn = 0.25f/cbvdv c) At Faces of Main Girderr Vn= 0.25f/c-bv-Facedv-Face.

Vn-Face.-2

d) At Middle of Cross-Girder Vn= 0.25f/c-bvMiddv-Mid.

Vn-Mid-2

2,161.688 kN 2161.688*10^3 N 2,161.688 kN 2161.688*10^3 N

xxv) Accepted Nominal Shear Resistance-Vn & Factored Shearing Resistance-Vr at Different Section of Girder Computed accordting Provisions of AASHTO-LRFD-5.8.3.3 & AASHTO-LRFD-5.8.2.1 : a) Nominal Shear Resistance, Vn at any Section of Component is the Lesser value of of the Equqtions as mentioned below ; b) Vn = Vc + Vs + Vp (Equ. 5.8.3.3-1; AASHTO-LRFD-5.8.3.3) c) Vn = 0.25f/cbvdv + Vp (Equ. 5.8.3.3-2; AASHTO-LRFD-5.8.3.3) : d) For RCC Girder, Vp = 0. e) The Factored Shear Resitance at any Section of Component is Expressed by the Equation-5.8.2.1-2. Having the value, Vr = fVn in which; f) Vr is the Factored Shear Resitance at a Section in N

Vr.

N

f

g) f is Resistance Factor according to AASHTO-LRFD-5.5.4.2.

0.90

h) The Acceptable Nominal Shear Resistance, Vn, Respective Factored Shear Resitance-Vr at Different Section of T-Girder, the Staus between the vaues of Vn Computed under Equ. 5.8.3.3-1 & Equ. 5.8.3.3-2 are shown in Table below :. i) Table-; Accepted Nominal Shear Resistance-Vn & Factored Shear Resitance-Vr at Different Section : Section

Calculated

Vn-1

Vn-2

Relation

Accepted

Factored

Relation

Location

Factored

As per

As per Equ.

between

Value of

Shear

between

from Center

Shear

Equation.

5.8.3.3-2

Values of

Vn

Resitance

Values of

Structure is

of Bearing.

Force-Vu

5.8.3.3-1

Vr

Vr& VU

Safe otherwise

Vn-1 & Vn-2

Page 233

Status If Vr > Vu, the

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Vn-1 > Vn-2

kN

kN

kN

At Faces

268.351

855.731

2161.688

Vn-1< Vn-2

855.731

kN

kN 770.16

At Mid Span

168.744

914.579

2161.688

Vn-1< Vn-2

914.579

823.12

Vr> VU Vr> Vu Vr> Vu

No Safe. Structure Safe Structure Safe

xxx) Relation between Factored Shearing Force (Vu) & the Nominal Shear Resistance (Vn) at Different Section of Girder, Computed under Provisions of AASHTO-LRFD-5.8.3.3 : a) The Relation between Factored Shearing Force, Vu & the Nominal Shear Resistance Vn at Different Section of Girder are shown in the Table blow : Table-; Showing between Factored Shearing Force, Vu & the Nominal Shear Resistance Vn : Location of Section from Bearing Center of Girder.

a) At Faces of Main Girder b) At Middle of Cross-Girder

Calculated Computed Status value of value of between Vu Vn Values of kN 268.351 168.744

kN 855.731 914.579

Vu & Vn Vu< Vn Vu< Vn

b) Since the Factored Shearing Forces Vu < Vn < Vr, the Computed Nominal Shear Resistance, thus the Girder is Safe in respect of Applied Shearing Forces caused by Dead Load & Live Loads to the Bridge Structure. xxxi) Checking of T-Girder Web Width (bWeb) in respect of Nominal Shearing Resistance (Vn) at Critical Section : a) Against Applied Loads (DL & LL) the Critical Section for Shearing Forces Prevails at the Face of Support, which is at a Distance 0.150m from Girder's Bearing Center (AASHTO-LRFD-5.8.3.2). b) Calculated Nominal Shearing Resistance for Girder on Face of Main Girder, Vn = 860.408*10^3 N.

Vn

855.731 kN 855.731*10^3 N

c) Provided Girder Width (Web Width of T-Girder) = bX-Web mm.

bX-Web

250 mm

e) In RCC Girder the value of Vp = 0, thus according to Equ. 5.8.3.3-2, the Width of cross-Girder, bv = Vn/0.25*f/cdv, where dv is Calculated Effective Shear Depth for the Critical Section.

bv-Cal.

105.771 mm

f) Since the Calculated value of Girder width bv-Cal = bv the Provided Girder Width, thus Design Critical Section is OK. xxxii) Checking in respect of Longitudinal Reinforcements (Tensile Reinforcements) Provided for Girder under Provision of AASHTO-LRFD-5.8.3.5 : a) At each Section the Tensial Capacity of Longitudinal Reinforcement on Flexural Tension side of the Member shall be proportationed to Satisfy Equation, Asfy + Apsfps  Mu/dvff + 0.5Nu/fc + (Vu/fv - 0.5Vs -Vp)Cotq. (Equ-5.8.3.5-1). Where; b) As is Area of Nonprestressing Steel on Flexural Tention side of Girder in mm2

As

c) fy is Yield Strength of Nonprestressing Reinforceing Steel in MPa.

fy

Page 234

Variable

mm2

410.00 MPa

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

d) Aps is Area of Prestressing Steel on Flexural Tention side of Girder in mm2. For Nonprestressing RCC Structure, the value of Aps = 0

Aps

-

mm2

e) fps is Yield Strength of Prestressing Steel in MPa. For Nonprestressing RCC Structure, the value of fps = 0

fps

-

MPa

f) Mu is Factored Moment of the Section due to Dead & Live Loads Loads on Structure. in N-mm but not less then Vudv.

Mu

Variable

g) Nu is Factored Axil Force in N, Value will be (+) ve for the case of Tensile & (-) for the case of Compressive due to Prestressing. For Nonprestressing RCC Structural Component, the value of Nu = 0.

Nu

-

h) dv is Effective Shear Depth of Tensil Reinforcement for the Section in mm.

dv

Variable

mm

i) Vu is Factored Shear Force for the Section in N.

Vu

Variable

N

j) Vs is Shear Resistance Provided by Shear Reinforcement in N for the Section.

Vs

Variable

N

k) Vp is component of Prestressing Force in direction of Shear Force in N; For Nonprestressing RCC Structural Component, the value of Vp = 0.

Vp.

-

N

0 l) q is Angle of Inclenation of Digonal Compressive Stress in ( ) according to AASHTO-LRFD-5.8.3.4;

q

Variable

m) ff is Resistance Factor for Flexural Tension of Reinforced Concrete according to AASHTO-LRFD-5.5.4.2.

ff

0.90

n) fv is Resistance Factor for Shearing Force of Reinforced Concrete according to AASHTO-LRFD-5.5.4.2,

fv

0.90

o) fc is Resistance Factor for Compression due to Prestressing according to AASHTO-LRFD-5.5.4.2.

fc

1.00

N-mm

N

O

p) Since for Nonprestressing RCC Structural Components the Items Aps, fps, Nu & Vp have Values = 0, thus mentioned Equ-5.8.3.5-1. Stands to, Asfy  Mu/dvff + (Vu/fv - 0.5Vs)Cotq. q) Table- Showing Evalution of Equation-5.8.3.5-1 at Different Section of Girder & Status of Results.

Location of Section from Bearing Center of Girder.

a)At Faces b) At Middle

As.

Mu Vu Provided Factored Factored

Vs Shearing

Calculted Calculted Status Value of R/H Part of the Shearing Resistance Asfy of the Equation Force of Stirrups (L/H Part) Equation Satisfied kN kN kN kN Not Satisfied

Tensile Steel Area mm2

Moment

1256.637

441.974

268.351 822.1224362

515.221

88.390

1256.637

277.921

168.744 908.8400011

515.221

(248.371)

kN-mm

Page 235

Satisfied Satisfied

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

j) Since at all Section the requirments of Equation are being Satisfied, thus provision of Transverse/Shear Reinforcements for Girder is OK. xxxiii) Checking for Factored Tensile Resistance of Transverse/Shear Reinforcements Provided for Girder: a) The provided Transverse/Shear/Web Reinforcements at Different Section of Girder under the Provision of Deep Beam should Satisfy the Equation, Ng = f fyAs  0.83bvs (AASHTO-LRFD-5.13.2.3; Equ-5.13.2.3-1). Here, b) Ng is Factored Tensial Resitance of Transverse Reinforcement (Each Pair) in N.

Ng.

c) bv is Width of Girder Web in mm.

bv.

250 mm

d) fy is Yield Strength of Reinforceing Steel as Transverse/Shear Reinforcement

fy.

410.00 Mpa

e) As is Steel Area of Transverse/Shear Reinforcement in mm2 having the Spacing AS s mm. Here As = Av, the X-Sectional Area of 2-Leged the 10f Dia. Vertical Stirrups.

2 157.080 mm

f) s is Spacing of Transverse /Shear Reinforcement in mm. The value s should not Excide eithe d/4 or 300mm

s

Variable

Variable

N

mm

g) The Girders are being provided with Transverse/Shear Reinforcements in the form of Vertical Stirrups against Shear Forces caused by the Dead Load & Live Loads applied to the Bridge Structure. Due to Vertical Positioning of those Transverse/Shear Reinforcements they will also under Tensile Stress caused by the same Shearing Forces whose actions are in some extent in Vertical Direction. On these back drop mentioned Shearing Forces at different Section of Girder may be considered as Tensile Forces for Vertical Stirrups. Thus the Factored Shearing Forces at Each Section, Vu = Ng, the Factored Tensile Resistance Carried by the Pair of Transverse Reinforcement. h) The Checking for Factored Tensile Resistance of Transverse/Shear Reinforcements at Different Section of Girder are shown in the under mention Table: i) Table- Showing Minimum Transverse/Shear Reinforcement at Different Section of Cross-Girder. Location of Section from Bearing Center of Girder.

a) At Faces of main Girder b) Middle of Cross-Girder

s'-Spacing As of Shear Provided Bars Steel Area mm2 mm 175.000 157.080 175.000 157.080

Calculted Calculted Value of Value of ffyAs 0.83bvs 57962.384 57962.384

Status of

Equation Satisfied Not Satisfied 36312.500 Satisfied 36312.500 Satisfied

j) Since in all Section the requirments of Equation Equ-5.13.2.3-1, Ng = ffyAs > 0.83bvs are being Satisfyed, thus Provision of Transverse/Shear Reinforcements for Cross-Girders are OK. 11 Design of Bridge Girder & Cross-Girder against Earthquake Forces including Checking: i) According to AASHTO-LRFD-4.7.4.2 for Single-Span Bridges no Seismic analysis is required regardless of Location Seismic Zone. ii) In Single-Span Bridges the Connections between Superstructure & Substructure on Abutment Cap/Seat

Page 236

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

& Bridge Bearings should be Designed according to provisions of AASHTO-LRFD-3.10.9 & 4.7.4.4. iii) Design of Abutment Cap/Seat & Bridge Bearings are being done in Respective Design Sheets.

Page 237

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 238

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 239

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 240

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 241

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 242

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 243

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 244

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 245

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 246

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 247

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 248

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 249

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 250

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 251

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 252

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

isfied

Page 253

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 254

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 255

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 256

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 257

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 258

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 259

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 260

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 261

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 262

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 263

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 264

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 265

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Satisfy

Satisfy

Satisfy

Satisfy

Satisfy

Satisfy

Page 266

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 267

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 268

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 269

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

below :.

Page 270

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 271

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 272

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 273

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 274

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 275

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 276

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 277

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 278

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 279

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 280

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 281

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 282

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 283

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 284

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 285

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 286

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 287

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 288

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 289

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 290

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 291

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 292

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 293

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 294

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 295

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 296

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 297

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 298

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 299

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Satisfy

Satisfy

Satisfy

Page 300

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

Page 301

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

below :.

Page 302

I. Service Limit State Design (WSD) of Main Girder & Cross Girders Against Applied Forces : 1 Data for Flexural Design : Description

Notation Dimensions

Unit.

i) Dimensional Data of Superstructure : a) b) c) d) e) f) g) h) i) j) k) l) m) n) o) p)

Span Length (Clear C/C distance between Bearings) Addl.Length of Girder beyond Bearing Center Line. Total Girder Length (a+2b) Thickness of Deck Slab Thickness of Wearing Course Number of Main Girders Number of Cross Girders Depth of Main Girders (Including Slab as T-Girder) Depth of Cross Girders (Excluding Slab) Width of Main Girders Width of Cross Girders C/C Distance Between Main Girders Distance of Slab Outer Edge to Exterior Girder Center Clear Distance Between Main Interior Girders Filets : i) Main Girder in Vertical Direction ii) Main Girder in Horizontal Direction iii) X-Girder in Vertical Direction vi) X-Girder in Horizontal Direction

SL SAddl. LGir. hSlab. hWC NGir. NX-Gir. hGir. hX-Gir. bGir. bX-Gir. C/CD-Gir. CD-Ext.-Gir-Edg. ClD-Int.-Gir. FM-Girder-V. FM-Girder-H. FX-Girder-V. FX-Girder-H.

24.40 0.30 25.00 0.20 0.08 5 5 2.00 1.70 0.35 0.25 2.00 1.13 1.65 0.15 0.15 0.08 0.075

m m m m m nos nos m m m m m m m m m m m

ii) Design Data related to Live Loading: a) Design Criterion : AASHTO Load Resistance Factor Design (LRFD). b) Type of Loads : Combined Application of AASHTO HS20 Truck Loading & Lane Loading. iii) Design AASHTO HS20 Truck Loading : a) b) c) d) e) f) g) h)

Axle to Axle distance Wheel to Wheel distance Rear Wheel axle Load (Two Wheels) Rear Single Wheel Load Middle Wheel axle Load (Two Wheels) Middle Single Wheel Load Front Wheel axle Load (Two Wheels) Front Single Wheel Load

DAxel. DWheel. LLRW-Load LLRS-Load LLMW-Load LLMS-Load LLFW-Load LLFS-Load

1.80 4.30 145.00 72.50 145.00 72.50 35.00 17.50

m m kN kN kN kN kN kN

iv) Design AASHTO Lane Loading : a) Design Lane Loading is an Uniformly Distributed Load having Magnitude of

LL-Lane

9.30

N/mm

9.300N/mm through the Length of Gridge for Single and acting over a 3.000m Wide Strip in Transverse Direction.

9.30

kN/m

v) Design AASHTO Pedestrian Loading : a) Design Pedestrian Loading is an Uniformly Distributed Load having Magnitude of 3.600*10-3MPa through the Length of Sidewalk on both side and acting over the total Wide of Sidewalk. 3 vi) Unit Weight of Different Materials in kg/m : (Having value of Gravitional Acceleration, g =

LL-Pedest

2 0.00 N/mm 2 4.00 kN/m

2 9.807 m/sec )

Unit weight of Normal Concrete Unit weight of Wearing Course Unit weight of Normal Water Unit weight of Saline Water Unit weight of Earth (Compected Clay/Sand/Silt)

gc gWC gW-Nor. gW-Sali. gs

2,447.23 2,345.26 1,019.68 1,045.17 1,835.42

kg/m3 kg/m3 kg/m3 kg/m3 kg/m3

24.00 23.00 10.00 10.25 18.00

kN/m3 kN/m3 kN/m3 kN/m3 kN/m3

3 vii) Unit Weight of Materials in kN/m Related to Design Forces :

a) b) c) d) e)

Unit weight of Normal Concrete Unit weight of Wearing Course Unit weight of Normal Water Unit weight of Saline Water Unit weight of Earth (Compected Clay/Sand/Silt)

wc wWC wWater-Nor. wWater-Sali. wEatrh

viii) Strength Data related to Ultimate Strength Design( USD & AASHTO-LRFD-2004) : a) Concrete Ultimate Compressive Strength, f/c (Normal Concrete) b) Concrete Allowable Strength under Service Limit State (WSD) = 0.40f/c c) Modulus of Elasticity of Concrete, Ec = 0.043gc1.50f/c (AASHTO LRFD-5.4.2.4). c) Poisson's Ration = 0.63f/c = 0.63*21^(1/2), subject to cracking and considered to be neglected (AASHTO LRFD-5.4.2.5). d) Modulus of Rupture of Concrete, fr = 0.63f/c Mpa (AASHTO LRFD-5.4.2.6). e) Steel Ultimate strength, fy (60 Grade Steel) f) Modulus of Elasticity of Reinforcement, Es for fy = 410 MPa

f/c fc Ec

21.00 MPa 8.40 MPa 23,855.62 MPa 2.89

fr

2.89 MPa

fy ES

410.00 MPa 200000 MPa

ix) Strength Data related to Working Stress Design (WSD) under Service Limit State ( SLS ) According to AASHTO-LRFD-5.7.1: a) Concrete Allowable Strength under Service Limit State (WSD) = 0.40f/c fc 8.40 MPa b) Steel Allowable Strength under Service Limit State (WSD) = 0.40fy fs 164.00 MPa c) Modular Ratio, n = Es/Ec  6 n 8 d) Value of Ratio of Steel & Concrete Flexural Strength, r = fs/fc r 20 e) Value of k = n/(n + r) k 0.30

f) Value of j = 1 - k/3 g) Value of R = 0.5*(fckj)

j R

0.90 1.14

x) Design Data for Site Conditions : a) Velocity of Wind Load in Normal Condition b) Velocity of Wind Load in Cyclonic Storm Condition c) Velocity of Water/Stream Current Causing Water/Stream Load

VWL-Nor. VWL-Spe. VWA

90.00 km/hr 260.00 km/hr 4.20 m/s

2 Design Phenomena & Calculations for Monent & Shear : i) Design Phenomena under Service Limit State (WSD) : a) The Flexural of Girders will be according to AASHTO LRFD or Ultimate Strength Design (USD) Procedures but for Checking in respective Issues, Designing under Service Limit State (WSD) up to Certain Level would be done. b) Since the Interior Girders of the Bridge have the Max. Moments & Shearing Forces caused by Applied Loads (DL & LL), thus it is require to conduct the Flexural Design for Reinforcements of Bridge Girders Based on Calculated respective Moments & Shears. Since the Bridge Deck Slab is integral Part of Girders, thus the Design of Girders will be under T-Beam if the Provisions in these Respect Satisfy, otherwise Designee will be under Provisions for the Rectangular Beam. ii) Calculation of Flange Width for Girders : a) Cross Sectional Sketch Diagram of Bridge Girders & Dack Slab : 1.475 0.23 7.30

1.25 0.30 1.070 0.300 0.200

0.950

1.13

0.25 1.65

1.650

1.65

1.650

0.95

2.00

2.000

2.00

2.000

1.125

CL 10.25 b) Calculation of Effective Flange Width of T-Girder under AASHTO LRFD-4.6.2.6 (4.6.2.6.1) as least Dinention of : * One-quarter of Effective Span Length = 1/4*SL * 12.0 times average Depth of Slab + Greater Thickness of Web = 12*hSlab + WGir. = * One-half the Width of Girder Top Flange (It is not req. as there is no Addl. Top Flange) * The average Spacing of Adjacent Beams/Girders = C/CD-Gir. Since Average Spacing of Adjacent Beams/Girders is the Least one,

=

6.10 m 2.75 m

=

2m

thus the Flange Width of Interior Girders, WFlang = 2.000m

bFlan.

2.00 m

c) From Load, Shear & Moment Calcutation Tables it appares that, the Interior Girders are facing the Max. Resultant Forces (DL & LL) causing Max. Shears & Moments, thus One of Interior Girders is considered for as Typical one for Flexural Design in respect of All Applied Loads (DL + LL) and Corresponding Moments & Shears. iii) Calculations for Monent at Different Location of Girder : a) Table for Max. Moments at Different Locations of Interior Girder due to Factored DL, Lane-LL & Wheel-LL : Table-1. Sum. of Max. Moments Against All Applied Loads (DL & LL) on Interior Girder. Locations from Support-A Loading Type Unit a. Dead Load (FDLInt) b. Lane Live Load (FLLInt) c. Wheel Live Load (WLLInt) Total Moments on Each Point

kN-m

0.375m kN-m

L/8 kN-m

L/4 kN-m

3L/8 kN-m

c.g. kN-m

L/2 kN-m

0.000

142.152

1039.048

1811.021

2263.908

2442.182

2449.720

0.000

28.627

207.537

357.399

449.585

483.808

484.096

0.000

79.345

563.836

941.813

1133.930

1201.915

1140.188

0.000

119.500

1810.421

3110.232

3847.423

4127.905

4074.004

On Support

b) Moment at Sopport Position of Girder

Mu-Support.

0 kN-m

c) Moment at a Distance 0.150m from Sopport of Girder

Mu-0.150m.

119.500 kN-m

d) Moment at a Distance L/8 from Sopport of Girder

Mu-L/8.

1,810.421 kN-m

e) Moment at a Distance L/4 from Sopport of Girder

Mu-L/4.

3,110.232 kN-m

f) Moment at a Distance 3L/8 from Sopport of Girder

Mu-3L/4.

3,847.423 kN-m

g) Moment at Absolute Max. Moment Loaction (c.g. Position) of Girder

Mu-c.g.

4,127.905 kN-m

h) Moment at a Distance L/2 (Middle of Span) from Sopport of Girder

Mu-L/2.

4,074.004 kN-m

i) Sketch Diagram of T-Beam/Girder : bFln. 2.000 hFln. = 0.200 d=

1.826

hGir. =

2.000

bWeb = 0.350 iv) Factored Flexural Resistance for Prestressed or RCC Structural Components (AASHTO-LRFD-5.7.3.2.1): a) Factored Flexural Resistance for any Section of Component, Mr = fMn, where;

Mr

N-mm

i) Mn is Nominal Resistance Moment for the Section in N-mm ii) f is Resistance Factor for Flexural in Tension of Reinforcement/Prestressing.

Mn

N-mm

f

b) For a Nonprestressing Structural Component either of I or T Section having Flenge & Web Elements, at any Section the Nominal Resistance, Mn = Asfy(ds-a/2) + 0.85f/c(b-bw)b1hf(a/2-hf/2) c) For a Nonprestressing Structural Component of Rectangular Elements having Singly Reinforced, , at any Section the Nominal Resistance, Mn = Asfy(de-a/2) v) Related Features for Working Stressed Design of Main Girder with Max, Moment value (At c.g. Position) : a) The Absolute Max. Moments on Interior Girder is at c.g. Point. Since it is very close to Middle Position of Span having value MMex. = 4,127.905 kN-m, thus this value is Considerd as the Moment at Middle Position of Span. b) Let the Clear Cover at Bottom Surface of Girder, C-Cov.Bot. = 50mm, Let the Clear Cover at Top of Girder, C-Cov.Top = 50mm, Let the Clear Cover at Vertical Faces of Girder, C-Cov.Vert.. =38mm,

MMax.

4,127.905 kN-M 4127.905*10^6 N-mm

C-Cov-Bot. C-Cov-Top. C-Cov-Side.

50 mm 50 mm 38 mm

c) Let the Main Reinforcements are 32f Bars in 4 Layers,

DBar

32 mm

2 2 d) X-Sectional Area of Main Reinforcements Af = p*DBar /4mm

Af-32

e) The Vertical Spacing between Reinforcement Bars, SVer. = 32 mm

SVer.

32 mm

f) Let the Transverse/Shear Reinforcements (Stirrups) are of 12f Bars,

DStir.

12 mm

g) Thus Effective Depth of Reinforcements from Top of Girder up to Center of the Provided Reinforcements d = (hGir - C-Cov-Bot - DStri -2*DBar- 1.50*SVer.)

dL/2

1,826.00 mm

h) Flange Width of T-Girder, b = 2.000 m

2 804.25 mm

b

2000 mm

i) Thickness of T-Girder Flange, hf = 200mm

hf

200 mm

j) According to WSD Method the Balanced-Stress Steel Ratio for Girder Section pe = n/2r(n + r)

pe.

0.008

vi) Checking's Whether the Bridge Girder would Designed as T-Beam or Rectangular Beam Provisions : a) According to Working Stressed Design Provisions a Rectangular having Flange with Reasonable Thickness on its Top should be Designed as T-Beam if Depth of Netural Axis 'kd' is Less than the Flange Thickness. b) Let Consider the T-Girder will behave as Rectangular Beam for which the Total Flange Width-'b' will be the Width of Rectangular Beam. c) According to WSD Provisions the depth of Neutral Axis from Compressiof Face

kd

548.552 mm

is Expressed by kd.

hf Mr, the Allowable Minimum Moment for the Section, thus (-) MF-Extr-Out-USD is the Design Moment MU.

Mr

MU

261.967 261.967*10^6 207.866 207.866*10^6

kN-m/m N-mm/m kN-m/m N-mm/m

261.967 kN-m/m 261.967*10^6 N-mm/m

ii) Provision of Reinforcement on Top Surface of Abutment Cap : a) Let provide 25f Bars as Main Reinforcement on Top Surface of Abutment Cap.

DAb-Cap-Top

25 mm

Af-25.

2 490.874 mm

c) The provided Effective Depth for the Section with Reinforcement on Top Surface, dpro = (h -CCov-Top -DAb-Cap-Top/2)

de-pro-Top.

537.500 mm

d) With Design Moment MU , Design Width of Cap b & Effective Depth dpro; the required value of a = dpro*(1 - (1 - (2MU)/(b1f/cbdpro2))(1/2))

areq.

28.035 mm

b) X-Sectional of 25f Bars = p*DAb-Cap-Top2/4

e) Steel Area required for the Section, As-req. = MU/(ffy(dpro - a/2))

As-req-Ab-Cap-Top

1,356.181

mm2/m

f) Number of 25f bars Requred for the Section= As-req-Ab-Earth-V./Af-20

NBer-req.

2.763 nos.

g) Let the Provided 8 nos. 25f bars as Main Reinforcement on Top Surface of Abutment Cap.

NBer-pro.

8 nos.

h) The provided Steel Area with 8 nos. 25f bars as Main Reinforcement on Top Surface of = Af-25.*NBer-pro.

As-pro-Ab-Cap-Top

3,926.991

mm2/m

iii) Chacking in respect of Design Moment & Max. Steel Ratio : a) Steel Ratio for the Section, ppro = As-pro/bdpro

ppro

/ b) With provided Steel Area the value of 'a' = As-pro*fy/(b1*f c*b)

apro

c) Resisting Moment for the Section with provided Steel Area, = As-pro*fy(d - apro/2)/10^6

Mpro

d) Relation between Provided Resisting Moment Mpro and Calculated Design Moment MU. e) Relation between Provided Steel Ration rpro and Allowable Max. Steel Ratio rMax.

0.007 90.200 mm 792.797 kN-m/m

Mpro>Mu

OK

ppro Mr, the Allowable Minimum Moment for the Section, thus (+) MInt-Mid-USD is the Design Moment MU.

MU

kN-m/m N-mm/m kN-m/m N-mm/m

207.866 kN-m/m 206.986*10^6 N-mm/m

ii) Provision of Reinforcement on Bottom Surface of Abutment Cap : a) Let provide 25f Bars as Main Reinforcement on Bottom Surface of Abutment Cap.

DAb-Cap-Bot.

25 mm

b) X-Sectional of 25f Bars = p*DAb-Cap-Bot2/4 c) The provided Effective Depth for the Section with Reinforcement on Bottom Surface, dpro = (h -CCov-Bot -DAb-Cap-Bot/2) d) With Design Moment MU , Design Width of Cap b & Effective Depth dpro; the required value of a = dpro*(1 - (1 - (2MU)/(b1f/cbdpro2))(1/2)) e) Steel Area required for the Section, As-req. = MU/(ffy(dpro - a/2))

Af-25.

2 490.874 mm

de-pro-Bot.

537.500 mm

areq.

22.121 mm

As-req-Ab-Cap-Bot

1,065.531

mm2/m

f) Number of 25f bars Requred for the Section= As-req-Ab-Earth-V./Af-20

NBer-req.

2.171 nos.

g) Let the Provided 6 nos. 25f bars as Main Reinforcement on Top Surface of Abutment Cap.

NBer-pro.

8 nos.

h) The provided Steel Area with 6 nos. 25f bars as Main Reinforcement on Top Surface of = Af-25.*NBer-pro.

As-pro-Ab-Cap-Bot

3,926.991

mm2/m

iii) Chacking in respect of Design Moment & Max. Steel Ratio : a) Steel Ratio for the Section, ppro = As-pro/bdpro

ppro

/ b) With provided Steel Area the value of 'a' = As-pro*fy/(b1*f c*b)

apro

c) Resisting Moment for the Section with provided Steel Area, = As-pro*fy(d - apro/2)/10^6

Mpro

d) Relation between Provided Resisting Moment Mpro amd Calculated Design Moment MU. e) Relation between Provided Steel Ration rpro and Allowable Max. Steel Ratio rMax.

0.007 90.200 mm 792.797 kN-m/m

Mpro>Mu

OK

ppro 0.50 ≤ 1.00 , thus values of q & b of these Sections can obtain from Table -5.8.3.4.2-1 in respect of values of vc/f/c. viii) Computation of Values of q & b from AASHTO-LRFD'sTable -5.8.3.4.2-1. against the Respective Calculated values of esx1000, Ratio vc/f/c : a)

Table for Values of q & b at Different Location of Girder. Location of Abutment Cap Section a) On Exterior Girder Outer Face b) On Exterior Girder Outer Face c) On Interior Girder Inner Face b) On Middle of Interior Girders

Referece of Table 5.8.3.4.2.-1 5.8.3.4.2.-2 5.8.3.4.2.-2 5.8.3.4.2.-2

vc/f/c 0.051 0.045 0.045 0.000

exx1000 1.000 0.800 0.825 0.362

Value of q b 36.40 2.23 36.40 2.23 36.40 2.23 30.50 2.59

b) Value of Cotq at different Locaion of Girder : i) On Outer Face of Exterior Girder value of Cotq

Cotq

1.356

ii) On Inner Face of Exterior Girder value of Cotq

Cotq

1.356

iii) On Interior Girder Position value of Cotq

Cotq

1.356

iv) On Mid of Interior Girders value of Cotq

Cotq

1.698

ix) Computation of Value for Nominal Shearing Strength of Concrete (Vc) using the Values of q & b : a) Since Critical Section is at the Outer Face of Exterior Girder, thus Values of q & b of that Section are Governing for Computation of Nominal Shearing Strength of Concrete (Vc) for the Abutment Cap. b) Nominal Shear Resistance of Conrete of Girder Vc = 0.083bf/cbvdv, AASHTO-LRFD-5.8.3.3-(Equ. 5.8.3.3-1);

Vc

39,485.944 kN 39485.944*10^3 N

x) Regions Requiring Transverse or Shear/Web Reinforcements under AASHTO-LRFD-5.8.2.4 :

a) The Transverse or Shear Reinforcements are required for those Sections where the Factored Shearing Force due to the Applied Loads (DL & LL), Vu > 0.5f (Vc + Vp); AASHTO-LRFD-5.8.2.4; Equ-5.8.2.4-1; Here, b) Vu is Factored Shearing Force due to the Applied Loads for the Selected Section in N, c) Vc is Nominal Shear Resistance for the Section having value = 0.083bf/cbvdv according to AASHTO-LRFD-5.8.3.3. Equation-5.8.3.3-4. d) Vp is component of Prestressing Force in direction of Shear Force in N; For Nonprestressing RCC Structural Component, the value of Vp = 0.

Vp.

-

N

e) b a is Factor for the Diagonally Cracked Concrete to transmit Tension according to AASHTO-LRFD-5.8.3.4; f) f is Resistance Factor as per to AASHTO-LRFD-5.5.4.2. having value 0.90

f

0.90

g) Thus for Nonprestressing Structure the Eqution-5.8.2.4-1 Stands to Vu > 0.5Vc h) Table showing the values of b, Vu, Vc, 0.5Vc & Relation between Vu & 0.5Vc at Different Location of Girder. Location of Abutment Cap Section a) On Exterior Girder Outer Face b) On Exterior Girder Outer Face c) On Interior Girder Inner Face b) On Middle of Interior Girders

Relation Equation Between Satisfied/ Vu & Vc Not Satisfied

Values of

b

Vu N

2.230

465718.685

39,485.944

17768.675

Vu>0.5Vc

Satisfied

2.230

413972.164

39,485.944

17768.675

Vu>0.5Vc

Satisfied

2.230

413972.164

39,485.944

17768.675

Vu>0.5Vc

Satisfied

2.590

0.000

45,860.356

20637.160

Vu 0.5f (Vc + Vp). AASHTO-LRFD-Equation-5.8.2.4-1. Other than that on Middle in-between Girders. Thus the Abutment Cap requires Transverse or Shear/Web Reinforcements. xi) Computation of Values of Vs,the Shear Resistance against Provided Shear Reinforcement & Spacings at Different Sections according to Vs = Avfydv(cotq + cota)sina /s (AASHTO-LRFD-Equ. 5.8.3.3-3) : a) With Vertical Shear Reinforcement the value of a = 900 & the Equation Vs = Avfydv(cotq + cota)sina /s stands to Vs = Avfydvcotq /s, b) On Outer Faces of Exterior Girder, Vs= Avfydv-Ext-Gir-OuterCotq/spro.

VS-Ext-Gir-Outer

405.670 kN 405.670*10^3 N

c) On Inner Face of Exterior Girder, Vs=Avfydv-Ext-Gir-InnerCotq/spro.

VS-Ext-Gir-Inner

405.670 kN 405.670*10^3 N

d) On Position of Interior Girders, Vs=Avfydv-On-Inner-GirCotq/spro.

VS-On-Inner-Gir

405.670 kN 405.670*10^3 N

xii) Computation of values for Nominal Shear Resistance (Vn) at Different Section of Abutment Cap under the

Provisions of AASHTO-LRFD-5.8.3.3 against Equation Vn = Vc + Vs + Vp (Equ. 5.8.3.3-2) : a) The Nominal Shear Resistanceat any Section of Girder is Vn = Vc + Vs + Vp (Equ. 5.8.3.3-1) b) For RCC Girder the value of Vp = 0, thus Equation stands to Vn-1 = Vc + Vs c) On Outer Faces of Exterior Girder Vn= Vc-Ext-Outer. + Vs-Ext-Outer.

Vn-Ext-Outer

445.156 kN 445.156*10^3 N

d) On Inner Face of Exterior Girder, Vn = Vc-Ext-Gir-Inner + Vs-Ext-Gir-Inner

Vn-Ext-Gir-Inner

445.156 kN 445.156*10^3 N

e) On Position of Interior Girders, Vn = Vc-On-Inner+ Vs-On-Inner-Gir

Vn-On-Inner-Gir

405.670 kN 405.670*10^3 N

xiii) Computation of values for Nominal Shear Resistance (Vn) at Different Section of Abutment Cap under the Provisions of AASHTO-LRFD-5.8.3.3 against Equation Vn = 0.25f/cbvdv + Vp (Equ. 5.8.3.3-2) : a) According to Equ. 5.8.3.3-1 the Nominal Shear Resistanceat any Section of Girder is Vn = 0.25f/cbvdv + Vp b) For RCC Girder the value of Vp = 0, thus Equation stands to Vn = 0.25f/cbvdv c) On Outer Faces of Exterior Girder Vn= 0.25f/c-bv-Ext-Gir-Outer.dv-Ext-Gir-Outer.

Vn-Ext-Gir-Outer. 2,539.688 kN 2539.688*10^3 N

d) On Inner Face of Exterior Girder, Vn= 0.25f/c-bv-Ext-Gir-Innerdv-Ext-Gir-Inner

Vn-Ext-Gir-Inner 2,539.688 kN 2539.688*10^3 N

e) On Position of Interior Girders, Vn= 0.25f/c-bv-On-Inner-Girdv-On-Inner-Gir

Vn-On-Inner-Gir 2,539.688 kN 2539.688*10^3 N

xiv) Chacking for requirment of Shear Reinforcement based on Computed Nominal Shear Resistance-V n & the Factored Shearing Resistance-Vr of Abutment Cap Accordting to the Provisions of AASHTO-LRFD-5.8.3.3 & AASHTO-LRFD-5.8.2.1: a) Nominal Shear Resistance, Vn at any Section of Component is the Lesser value of of the Equqtions as mentioned below ; b) Vn = Vc + Vs + Vp (Equ. 5.8.3.3-1; AASHTO-LRFD-5.8.3.3) c) Vn = 0.25f/cbvdv + Vp (Equ. 5.8.3.3-2; AASHTO-LRFD-5.8.3.3) : d) For RCC Component, Vp = 0. e) The Factored Shear Resitance at any Section of Component is Expressed by the Equation-5.8.2.1-2. Having the value, Vr = fVn in which; f) Vr is the Factored Shear Resitance at a Section in N

Vr.

N

f

g) f is Resistance Factor according to AASHTO-LRFD-5.5.4.2.

0.90

h) Checking for requirment of Shear Reinforcement in respect of Acceptable Nominal Shear Resistance, Vn, Respective Factored Shear Resitance-Vr on Different Section of the Abutment Cap Computed under provision of Equ. 5.8.3.3-1 & Equ. 5.8.3.3-2 are shown in the Table below :. i) Table :- Checking for Requirement of Shear Reinforcement in respect of Computed values of Vn & Vr : Location

Calculated

Vn-1

Vn-2

Relation

Accepted

Factored

Relation

If VU > Vr

of

Factored

As per

As per

between

Value of

Shear

between

Shear Rein (SR)

Abutment

Shear

Equation.

Equation

Values of

Vn

Resitance

Values of

Requires

Cap

Force-Vu

5.8.3.3-1

5.8.3.3-2

Vn-1 & Vn-2

Vr

Vu& Vr

otherwise SR

Vn-1 > Vn-2

Section

kN

kN

kN

kN

Vu> Vr

Not Require.

On Outer

465.719

445.156

2539.688

Vn-1< Vn-2

445.156

kN

400.64

Vu> Vr

Require SR

413.972

445.156

2539.688

Vn-1< Vn-2

445.156

400.64

Vu> Vr

Require SR

413.972

405.670

Vn-1< Vn-2

405.670

365.10

Vu> Vr

Require SR

Face of Ext.-Girder On Inner Face of Ext.-Girder On

2,539.69

Int.-Girder Position

xv) Checking of Required Max. Spacing for Transvers/Shear Reinforcement due to Applied Shearing Stress on Abutment Cap under provision of AASHTO-LRFD-5.8.2.7 : a) Due to applied Shearing Stress, vu < 0.125f/c, the Max. Spacing of Transverse/Shear Reinforcement at a Section is smax.-1 = 0.8dv ≤ 600mm, (AASHTO-LRFD-Equ. 5.8.2.7-1). b) Due to applied Shearing Stress, vu > 0.125f/c, the Max. Spacing of Transverse/Shear Reinforcement at a Section is smax.-2 = 0.4dv ≤ 300mm (AASHTO-LRFD-Equ. 5.8.2.7-2) c) Value of 0.125f/c in respect of Max. Spacing of Transvers/Shear Reinforcement due to Applied Shearing Stress at Defferent Section of Girder.

0.125f/c

2 2.63 N/mm

d) Table Showing values of vu, 0.8dv, 0.4dv againest the respective values of 0.125f/c : Table- ; Showing Spacing of Transverse/Shear Reinforcements in respect of Max. Spacing & Status :

Sections

Value of dv for the Section mm

End Edge

483.750

Segment. Between Abutment Cap

Ext.-Girder Face

N/mm2

N/mm2

vu0.12f/c

Value of 0.8dv for the Section mm

1.070

2.625

vuppro

OK

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

a) Accodring to AASHTO-LRFD-.7.3.3.1; In Flexural Design c/de  0.42; where,

c/de-Max.

0.450

b) c is the Distance between Neutral Axis& the Extrime Compressive Face, having c = b1apro, in mm.

c

c) b1 is Factor for Rectangular Stress Block for Flexural Design

b1

0.85

c/de-pro

0.143

d) Thus for the Section the Ratio c/de = 0.143 n) Relation between c/de-Max. & c/de-pro (Whether c/de-pro< c/de-Max. or Not)

52.340 mm

c/de-proVu Satisfied VU for the Section (Whether Vn > VU or Vn < VU & Provisions of AASHTO-LRFD-5.8.3 have Satisfied or Not). e) Since Nominal Shear Resitance for the Section Vn > VU the Calculated Ultimate Shearing Force for the Section, thus the Cantilever Wing Wall on Strip-2 does not require any Shear Reinforcement. f) Since Resisting Moment > Designed Moment, Provided Steel Ratio < Max. Steel Ratio, the Cantilever Wing Wall on Strip-2 Section does not Require any Shear Reinforcement, thus Flexural Design for Provisio of Horizontal Reinforcement on Earth Face of Cantilever Wing Wall on Strip-2 is OK. vi) Checking for Factored Flexural Resistance under Provision of AASHTO-LRFD-5.7.3.2: a) Factored Flexural Resistance for any Section of Component, Mr = fMn, where; i) Mn is Nominal Resistance Moment for the Section in N-mm ii) f is Resistance Factor of Flexural in Tension of Reinforcement/Prestressing.

Mr

332.589 N-mm 255.152*10^6 kN-m

Mn

369.543 N-mm 283.503*10^6 kN-m

f

0.90

b) The Nominal Resistance of Rectangular Section with One Axis Stress having both Prestressing & Nonprestessing AASHTO-LRFD-5.7.3.2.3 is Mn = Apsfps(dp-a/2) + Asfy(ds-a/2) - A/sf/y(d/s-a/2) c) In a Nonprestressing Structural Component having Rectangular Elements, at any Section the Nominal Resistance, Mn = Asfy(ds-a/2) d) Since Cantilever Wing Wall on Strip-2 is being considered as a Cantilever Mn-Strip-2 369.543 kN-m Beam having 1.000 m Wide Strips. The Steel Area against Factored Max. Moments 283.503*10^6 N-mm at its Support Face will have value of Nominal Resistance, Mn = Asfy(ds-a/2) e) Calculated Factored Moment MU at Support Face of Cantilever Beam is on its Earth Face = MStrip-2-USD

MStrip-2-USD

f) Relation between the Computed Factored Flexural Resistance Mr & the Actual Factored Moment M at Support Face ( Which one is Greater, if Mr  M the Flexural Design for the Section has Satisfied otherwise Not Satisfied)

226.280 kN-m 226.280*10^6 N-mm

Mr>MStrip-2-USD Satisfied

vii) Checking in respect of Control of Cracking By Distribution of Reinforcement, (AASHTO-LRFD-5.7.3.4) :

Page 521

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

a) Under Service Limit State Load Condition, Developed Tensile Stress of Reinforcement fs-Dev. of Concrete Elements, should not exceed fs the Computed Tensile Stress of Reinforcement under provision of AASHTO-LRFD-5.7.3.4. Where; b) fs-Dev. is Developed Tensile Stress in Provided Reinforcements of Section under the Service Limit State of Loads = M/As-prode in which, i) M is Calculated Moment for the Section under Service Limit State

ii) As-pro is the Steel Area for the Section under USD Design Calculation. iii) de is Effective Depth between Extreme Compression Fiber to Centroid of the Tensile Reinforcement for the Section. c) fsa is Computed Tensile Stress of Reinforcement having its value = Z/(dcA)1/3  0.6fy, in Which;

fs-Dev.

MStrip-2-WSD

As-pro

2 146.98 N/mm

144.605 kN-m 144.605*10^6 N-mm 2 2,680.826 mm

de

367.000 mm

fsa

2 288.899 N/mm

i) dc= Depth of Concrete Extreme Tension Face from the Center of the Closest dc Tension Bar. The Depth is Summation Earth/Water Clear Cover & Radius of the Closest Bar to Tension Face. The Max. Clear Cover = 50mm. In a Component of Rectangular Section, dc = DBar/2 + CCov-Earth. Since Clear Cover on Earth Face of Back Wall, CCov-Earth = 75mm & Bar Dia, DBar = 16f ; thus dc = (16/2 + 50)mm ii) A = Area of Concrete Surrounding a Single Tension Bar, which is Calculated A by Dividing the Total Concrete Area bounded in between Extreme Tension Face & a Straight Line parallel to Neutral Axis of Component having equal distance from the Centrioed of Main Tension Reinforcement Bars on both side & Diving the Area by the total Number of Main Bars as Tensile Reinforcement having Max. Clear Cover = 50mm.In Abutment Wall the Tension Bars in One Layer & as per Condition Distance of Neutral Axis from Tension Face = dc, thus Area of Concrete that Surrounding a Single Tension Bar can Compute by A = 2dc*spro. Here spro is Spacing between Provided Tension Bars. iii) Z = Crack Width Parameter for Cast In Place Components in N/mm. For a) Structure with Moderate Exposure Components the Max. value of Z = 30000 b) Structure with Severe Exposure Components the Max. value of Z = 23000 c) Structure with Buried Components the Max. value of Z = 17000 Since the Structure is very close to Sea, thus it’s Components are of Severe Exposure Category having Allowable Max. value of ZMax. = 23000N/mm

ZMax.

iv) The Computed value of 0.6*fy for the Concrete Element.

0.6*fy

58.000 mm

2 8,700.000 mm

23,000.000 N/mm

2 246.000 N/mm

d) Since the Calculated value of fs-Dev. is responsible for Controlling the formation of Cracks under Applied Loads to the Cant. Wing Wall Structure, thus value of Crack Width Parameter Z should calculate based the value of fs-Dve. e) Based on fs-Dve. the value of Crack Width Parameter ZDev. = fs-Dev.*(dcA)1/3

Page 522

ZDev.

11,701.238 N/mm

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

f) Relation between of Developed Tensile Stress fs-Dev. & Allowable Tensile Stress fs

fs-Dev.< fs

g) Relation between Computed Tensile Stress fsa & Calculated value of 0.6fy

fsa > 0.6fy Not Satisfy

h) Relation between Allowable Max. value of ZMax. & Developed value ZDev.

Zdev.< Zmax.

Satisfy

Satisfy

i) Since Developed Tensile Stress of Tension Reinforcement of Cant. Wing Wall fs-Dev.< fsa Computed Tensile Stress; though Computed Tensile Stress fsa>0.6fy;but Developed Crack Width Parameter ZDev. Mr, the Allowable Minimum Moment for the Section, thus MStrip-3 is the Design Moment MU.

MU

Mr

124.373 124.373*10^6 116.924 116.924*10^6

kN-m/m N-mm/m kN-m/m N-mm/m

124.373 kN-m/m 124.373*10^6 N-mm/m

ii) Provision of Reinforcement for the Section : a) Let provide 16f Bars as Horizontal Reinforcement on Earth Face of Strip-3.

DStrip-3

16.000 mm

b) X-Sectional of 16f Bars = p*DStrip-32/4

Af-16.

2 201.062 mm

c) The provided Effective Depth for the Section with Reinforcement on Earth Face, dpro = (tCant.-WW -CCov-Earth. -DStrip-3/2)

de-pro.

367.000 mm

areq.

19.504 mm

d) With Design Moment MU , Design Strip Width b & Effective Depth dpro; the required value of a = dpro*(1 - (1 - (2MU)/(b1f/cbdpro2))(1/2)) e) Steel Area required for the Section, As-req. = MU/(ffy(dpro - a/2))

As-req-Strip-3-Earth

f) Spacing of Reinforcement with 16f bars = Af-16b/As-req-Strip-3

sreq

g) Let the provided Spacing of Reinforcement with 16f bars for the Section spro = 175mm,C/C

spro.

Page 523

943.470

mm2/m

213.109

mm,C/C

175 mm,C/C

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

h) The provided Steel Area with 16f bars having Spacing 175mm,C/C = Af-16.b/spro

As-pro-Strip-3-Earth

1,148.925

mm2/m

iii) Chacking in respect of Design Moment & Max. Steel Ratio : a) Steel Ratio for the Section, ppro = As-pro/bdpro

ppro

/ b) With provided Steel Area the value of 'a' = As-pro*fy/(b1*f c*b)

apro

c) Resisting Moment for the Section with provided Steel Area, = As-pro*fy(d - apro/2)/10^6

Mpro

d) Relation between Provided Resisting Moment Mpro amd Calculated Design Moment MU. e) Relation between Provided Steel Ration rpro and Allowable Max. Steel Ratio rMax.

0.003 26.390 mm 166.663 kN-m/m

Mpro>Mu

OK

pmax>ppro

OK

iv) Checking according to Provisions of AASHTO-LRFD-5.7.3.3.1 : a) Accodring to AASHTO-LRFD-.7.3.3.1; In Flexural Design c/de  0.42; where,

c/de-Max.

0.450

b) c is the Distance between Neutral Axis& the Extrime Compressive Face, having c = b1apro, in mm.

c

c) b1 is Factor for Rectangular Stress Block for Flexural Design

b1

0.85

c/de-pro

0.061

d) Thus for the Section the Ratio c/de = 0.061 n) Relation between c/de-Max. & c/de-pro (Whether c/de-pro< c/de-Max. or Not)

22.431 mm

c/de-proVu Satisfied VU for the Section (Whether Vn > VU or Vn < VU & Provisions of AASHTO-LRFD-5.8.3 have Satisfied or Not). e) Since Nominal Shear Resitance for the Section Vn > VU the Calculated Ultimate Shearing Force for the Section, thus the Cantilever Wing Wall on Strip-3 does not require any Shear Reinforcement. f) Since Resisting Moment > Designed Moment, Provided Steel Ratio < Max. Steel Ratio, the Cantilever Wing Wall on Strip-3 Section does not Require any Shear Reinforcement, thus Flexural Design for Provisio of Horizontal Reinforcement on Earth Face of Cantilever Wing Wall on Strip-3 is OK. vi) Checking for Factored Flexural Resistance under Provision of AASHTO-LRFD-5.7.3.2: a) Factored Flexural Resistance for any Section of Component, Mr = fMn, where; i) Mn is Nominal Resistance Moment for the Section in N-mm ii) f is Resistance Factor of Flexural in Tension of Reinforcement/Prestressing.

Page 525

Mr

149.997 N-mm 173.909*10^6 kN-m

Mn

166.663 N-mm 193.232*10^6 kN-m

f

0.90

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

b) The Nominal Resistance of Rectangular Section with One Axis Stress having both Prestressing & Nonprestessing AASHTO-LRFD-5.7.3.2.3 is Mn = Apsfps(dp-a/2) + Asfy(ds-a/2) - A/sf/y(d/s-a/2) c) In a Nonprestressing Structural Component having Rectangular Elements, at any Section the Nominal Resistance, Mn = Asfy(ds-a/2) d) Since Cantilever Wing Wall on Strip-2 is being considered as a Cantilever Mn-Strip-3 Beam having 1.000 m Wide Strips. The Steel Area against Factored Max. Moments at its Support Face will have value of Nominal Resistance, Mn = Asfy(ds-a/2) e) Calculated Factored Moment MU at Support Face of Cantilever Beam is on its Earth Face = MStrip-3-USD

MStrip-3-USD

166.663 kN-m 193.232*10^6 N-mm

124.373 kN-m 124.373*10^6 N-mm

f) Relation between the Computed Factored Flexural Resistance Mr & the Actual Mr>MStrip-3-USD Factored Moment MStrip-2-USD at Support Face ( Which one is Greater, if Mr  MStrip-2-USD the Flexural Design for the Section has Satisfied otherwise Not Satisfied)

Satisfied

vii) Checking in respect of Control of Cracking By Distribution of Reinforcement, (AASHTO-LRFD-5.7.3.4) : a) Under Service Limit State Load Condition, Developed Tensile Stress of Reinforcement fs-Dev. of Concrete Elements, should not exceed fs the Computed Tensile Stress of Reinforcement under provision of AASHTO-LRFD-5.7.3.4. Where; b) fs-Dev. is Developed Tensile Stress in Provided Reinforcements of Section under the Service Limit State of Loads = M/As-prode in which, i) M is Calculated Moment for the Section under Service Limit State of Loads

fs-Dev.

MStrip-3-WSD

ii) As-pro is the Steel Area for the Section under USD Design Calculation. iii) de is Effective Depth between Extreme Compression Fiber to Centroid of the Tensile Reinforcement for the Section. c) fsa is Computed Tensile Stress of Reinforcement having its value = Z/(dcA)1/3  0.6fy, in Which;

As-pro

Page 526

80.138 kN-m 80.138*10^6 N-mm 2 1,148.925 mm

de

367.000 mm

fsa

2 217.814 N/mm

i) dc= Depth of Concrete Extreme Tension Face from the Center of the Closest dc Tension Bar. The Depth is Summation Earth/Water Clear Cover & Radius of the Closest Bar to Tension Face. The Max. Clear Cover = 50mm. In a Component of Rectangular Section, dc = DBar/2 + CCov-Earth. Since Clear Cover on Earth Face of Back Wall, CCov-Earth = 75mm & Bar Dia, DBar = 16f ; thus dc = (16/2 + 50)mm ii) A = Area of Concrete Surrounding a Single Tension Bar, which is Calculated by Dividing the Total Concrete Area bounded in between Extreme Tension Face & a Straight Line parallel to Neutral Axis of Component having equal distance from the Centrioed of Main Tension Reinforcement Bars on both side & Diving the Area by the total Number of Main Bars as Tensile Reinforcement having Max. Clear

2 190.056 N/mm

A

58.00 mm

2 20,300.000 mm

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

Cover = 50mm.In Abutment Wall the Tension Bars in One Layer & as per Condition Distance of Neutral Axis from Tension Face = dc, thus Area of Concrete that Surrounding a Single Tension Bar can Compute by A = 2dc*spro. Here spro is Spacing between Provided Tension Bars. iii) Z = Crack Width Parameter for Cast In Place Components in N/mm. For a) Structure with Moderate Exposure Components the Max. value of Z = 30000 b) Structure with Severe Exposure Components the Max. value of Z = 23000 c) Structure with Buried Components the Max. value of Z = 17000 Since the Structure is very close to Sea, thus it’s Components are of Severe Exposure Category having Allowable Max. value of ZMax. = 23000N/mm

ZMax.

iv) The Computed value of 0.6*fy for the Concrete Element.

0.6*fy

23,000.000 N/mm

2 246 N/mm

d) Since the Calculated value of fs-Dev. is responsible for Controlling the formation of Cracks under Applied Loads to the Cant. Wing Wall Structure, thus value of Crack Width Parameter Z should calculate based the value of fs-Dve. e) Based on fs-Dve. the value of Crack Width Parameter ZDev. = fs-Dev.*(dcA)1/3

ZDev.

20,068.839 N/mm

f) Relation between of Developed Tensile Stress fs-Dev. & Allowable Tensile Stress fs

fs-Dev.< fs

Satisfy

g) Relation between Computed Tensile Stress fsa & Calculated value of 0.6fy

fsa< 0.6fy

Satisfy

Zdev.< Zmax.

Satisfy

h) Relation between Allowable Max. value of ZMax. & Developed value ZDev.

i) Since Developed Tensile Stress of Tension Reinforcement of Cant. Wing Wall fs-Dev.< fsa Computed Tensile Stress; the Computed Tensile Stress fsa < 0.6fy ;the Developed Crack Width Parameter ZDev. < ZMax. Allowable Max.Crack Width Parameter, thus Provisions of Tensile Reinforcement in Cant. Wing Wall Strip-3 Earth Surface in respect of Control of Cracking & Distribution of Reinforcement are OK. j) More over though the Structure is a Nonprestressed one & value of dc have not Exceeds 900 mm, thus Component does require any Longitudinal Skein Reinforcement. 16 Flexural Design of Horizontal Reinforcements on Earth Face of Cantilever Wing Wall against Calculated the Moments on Strips-4 : i) Design Moment for the Section : a) Calculated Flexural Moment in Horizontal Span Strip-4 of Cantilever Wing Wall is Less than the Allowable Minimum Moment Mr. Thus Mr is the Governing Moment for Provision of Reinforcement against Moment value. Since the Strip is facing Earth Loads, thus requird Reinforcements will be on Earth Side.

MStrip-4-USD

b) Since MStrip-4 -USD < Mr, the Allowable Minimum Moment for the Section,thus Mr is the Design Moment MU.

MU

ii) Provision of Reinforcement for the Section :

Page 527

Mr

4.259 4.259*10^6 58.462 58.462*10^6

kN-m/m N-mm/m kN-m/m N-mm/m

58.462 kN-m/m 58.462*10^6 N-mm/m

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

a) Let provide 16f Bars as Horizontal Reinforcement on Earth Face of Strip-4.

DStrip-4

b) X-Sectional of 16f Bars = p*DStrip-42/4

Af-16.

2 201.062 mm

c) The provided Effective Depth for the Section with Reinforcement on Earth Face, dpro = (tCant.-WW -CCov-Earth. -DStrip-4/2)

de-pro.

367.000 mm

areq.

18.305 mm

d) With Design Moment MU , Design Strip Width b & Effective Depth dpro; the required value of a = dpro*(1 - (1 - (2MU)/(b1f/cbdpro2))(1/2)) e) Steel Area required for the Section, As-req. = MU/(ffy(dpro - a/2))

As-req-Strip-4-Earth

f) Spacing of Reinforcement with 16f bars = Af-16b/As-req-Strip-4

sreq

g) Let the provided Spacing of Reinforcement with 16f bars for the Section spro = 175mm,C/C

spro.

h) The provided Steel Area with 16f bars having Spacing 175mm,C/C = Af-16.b/spro

As-pro-Strip-4-Earth

16 mm

442.742

mm2/m

227.064

mm,C/C

175 mm,C/C

574.463

mm2/m

iii) Chacking in respect of Design Moment & Max. Steel Ratio : a) Steel Ratio for the Section, ppro = As-pro/bdpro

ppro

/ b) With provided Steel Area the value of 'a' = As-pro*fy/(b1*f c*b)

apro

26.390 mm

c) Resisting Moment for the Section with provided Steel Area, = As-pro*fy(d - apro/2)/10^6

Mpro

83.332 kN-m/m

d) Relation between Provided Resisting Moment Mpro amd Calculated Design Moment MU. e) Relation between Provided Steel Ration rpro and Allowable Max. Steel Ratio rMax.

0.003

Mpro>Mu

OK

pmax>ppro

OK

iv) Checking according to Provisions of AASHTO-LRFD-5.7.3.3.1 : a) Accodring to AASHTO-LRFD-.7.3.3.1; In Flexural Design c/de  0.42; where,

c/de-Max.

0.450

b) c is the Distance between Neutral Axis& the Extrime Compressive Face, having c = b1apro, in mm.

c

c) b1 is Factor for Rectangular Stress Block for Flexural Design

b1

0.85

c/de-pro

0.061

d) Thus for the Section the Ratio c/de = 0.061 n) Relation between c/de-Max. & c/de-pro (Whether c/de-pro< c/de-Max. or Not)

Page 528

22.431 mm

c/de-proVu Satisfied VU for the Section (Whether Vn > VU or Vn < VU & Provisions of AASHTO-LRFD-5.8.3 have Satisfied or Not).

Page 529

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

e) Since Nominal Shear Resitance for the Section Vn > VU the Calculated Ultimate Shearing Force for the Section, thus the Cantilever Wing Wall on Strip-4 does not require any Shear Reinforcement. f) Since Resisting Moment > Designed Moment, Provided Steel Ratio < Max. Steel Ratio, the Cantilever Wing Wall on Strip-4 Section does not Require any Shear Reinforcement, thus Flexural Design for Provisio of Horizontal Reinforcement on Earth Face of Cantilever Wing Wall on Strip-4 is OK. vi) Checking for Factored Flexural Resistance under Provision of AASHTO-LRFD-5.7.3.2: a) Factored Flexural Resistance for any Section of Component, Mr = fMn, where; i) Mn is Nominal Resistance Moment for the Section in N-mm ii) f is Resistance Factor of Flexural in Tension of Reinforcement/Prestressing.

Mr

74.998 N-mm 74.998*10^6 kN-m

Mn

83.332 N-mm 83.332*10^6 kN-m

f

0.90

b) The Nominal Resistance of Rectangular Section with One Axis Stress having both Prestressing & Nonprestessing AASHTO-LRFD-5.7.3.2.3 is Mn = Apsfps(dp-a/2) + Asfy(ds-a/2) - A/sf/y(d/s-a/2) c) In a Nonprestressing Structural Component having Rectangular Elements, at any Section the Nominal Resistance, Mn = Asfy(ds-a/2) d) Since Cantilever Wing Wall on Strip-4 is being considered as a Cantilever Mn-Strip-4 Beam having 0.500 m Wide Strips. The Steel Area against Factored Max. Moments at its Support Face will have value of Nominal Resistance, Mn = Asfy(ds-a/2)

83.332 kN-m 83.332*10^6 N-mm

e) Calculated Factored Moment MU at Support Face of Cantilever Beam is on its Earth Face = MStrip-4-USD

4.259 kN-m 4.259*10^6 N-mm

MStrip-4-USD

f) Relation between the Computed Factored Flexural Resistance Mr & the Actual Mr>MStrip-4-USD Factored Moment MStrip-4-USD at Support Face ( Which one is Greater, if Mr  MStrip-4-USD the Flexural Design for the Section has Satisfied otherwise Not Satisfied)

Satisfied

vii) Checking in respect of Control of Cracking By Distribution of Reinforcement, (AASHTO-LRFD-5.7.3.4) : a) Under Service Limit State Load Condition, Developed Tensile Stress of Reinforcement fs-Dev. of Concrete Elements, should not exceed fs the Computed Tensile Stress of Reinforcement under provision of AASHTO-LRFD-5.7.3.4. Where; b) fs-Dev. is Developed Tensile Stress in Provided Reinforcements of Section under the Service Limit State of Loads = M/As-prode in which, i) M is Calculated Moment for the Section under Service Limit State of Loads

ii) As-pro is the Steel Area for the Section under USD Design Calculation.

Page 530

fs-Dev.

MStrip-4-WSD

As-pro

2 13.055 N/mm

2.752 kN-m 2.752*10^6 N-mm 2 574.463 mm

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

iii) de is Effective Depth between Extreme Compression Fiber to Centroid of the Tensile Reinforcement for the Section. c) fsa is Computed Tensile Stress of Reinforcement having its value = Z/(dcA)1/3  0.6fy, in Which;

de

367.000 mm

fsa

2 217.814 N/mm

i) dc= Depth of Concrete Extreme Tension Face from the Center of the Closest dc Tension Bar. The Depth is Summation Earth/Water Clear Cover & Radius of the Closest Bar to Tension Face. The Max. Clear Cover = 50mm. In a Component of Rectangular Section, dc = DBar/2 + CCov-Earth. Since Clear Cover on Earth Face of Back Wall, CCov-Earth = 75mm & Bar Dia, DBar = 16f ; thus dc = (16/2 + 50)mm

58.00 mm

ii) A = Area of Concrete Surrounding a Single Tension Bar, which is Calculated A by Dividing the Total Concrete Area bounded in between Extreme Tension Face & a Straight Line parallel to Neutral Axis of Component having equal distance from the Centrioed of Main Tension Reinforcement Bars on both side & Diving the Area by the total Number of Main Bars as Tensile Reinforcement having Max. Clear Cover = 50mm.In Abutment Wall the Tension Bars in One Layer & as per Condition Distance of Neutral Axis from Tension Face = dc, thus Area of Concrete that Surrounding a Single Tension Bar can Compute by A = 2dc*spro. Here spro is Spacing between Provided Tension Bars.

2 20,300.000 mm

iii) Z = Crack Width Parameter for Cast In Place Components in N/mm. For a) Structure with Moderate Exposure Components the Max. value of Z = 30000 b) Structure with Severe Exposure Components the Max. value of Z = 23000 c) Structure with Buried Components the Max. value of Z = 17000 Since the Structure is very close to Sea, thus it’s Components are of Severe Exposure Category having Allowable Max. value of ZMax. = 23000N/mm

ZMax.

23,000.000 N/mm

iv) The Computed value of 0.6*fy for the Concrete Element.

0.6*fy

2 246 N/mm

d) Since the Calculated value of fs-Dev. is responsible for Controlling the formation of Cracks under Applied Loads to the Cant. Wing Wall Structure, thus value of Crack Width Parameter Z should calculate based the value of fs-Dve. e) Based on fs-Dve. the value of Crack Width Parameter ZDev. = fs-Dev.*(dcA)1/3

ZDev.

1,378.492 N/mm

f) Relation between of Developed Tensile Stress fs-Dev. & Allowable Tensile Stress fs

fs-Dev.< fs

Satisfy

g) Relation between Computed Tensile Stress fsa & Calculated value of 0.6fy

fsa< 0.6fy

Satisfy

Zdev.< Zmax.

Satisfy

h) Relation between Allowable Max. value of ZMax. & Developed value ZDev.

i) Since Developed Tensile Stress of Tension Reinforcement of Cant. Wing Wall fs-Dev.< fsa Computed Tensile Stress; the Computed Tensile Stress fsa < 0.6fy ;the Developed Crack Width Parameter ZDev. < ZMax. Allowable Max.Crack Width Parameter, thus Provisions of Tensile Reinforcement in Cant. Wing Wall Strip-4 Earth Surface in respect of Control of Cracking & Distribution of Reinforcement are OK. 17 Provision of Shrinkage & Temperature Reinforcements both on Earth & Water Faces of Cantilever Wing

Page 531

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

Walls in Vertical & Horizontal Directions : i) Requiment of Shrinkage & Temperature Reinforcements for Cantilever Wing Walls : a) The Flexural Design of Cantilever Wing Walls are being done Considering the Structure as Constituents of Multiple Cantilever Beam Strips having Span Length in Longitudinal, Width in Vertical & Depth in Transverse Direction. Since the Cantilever Wing Walls are Subject to Horizontal Earth & Surcharge Pressures, thus under Concept of Flexural Design the Longitudinal Reinforcements are on Earth Face in Vertical Plane. According to Principle of RCC Design all Concrete Surfaces should have Reinforcements in both Directions either under Flexural Tension/Compression or under Flexural Shear/Web/Torsion. The Surfaces where there is no such type of Reinforcements on that surface Shrinkage & Temperature Reinforcements should arrange according to AASHTO-LRFD-5.10.8.1. Provisions. b) On Earth Surface Cantilever Wing Walls the Main Reinforcements are in Horizontal Direction, thus on Earth Face Shrinkage & Temperature Reinforcements are required in Vertical Direction. Whereas on Water Face Provision of Shrinkage & Temperature Reinforcements are required both in Vertical & Horizontal Directions. ii) Provision of Shrinkage & Temperature Reinforcements on Earth Face in Vertical and for Wate Face both in Vertical & Horizontal Direction : a) Since the Thickness/Depth of Cantilever Wing Walls is less than1200mm, thus to Calculate the Shrinkage & Temperature Reinforcements on both Faces in Vertical & Horizontal Directions a Strip is being Considered having Length of each Arm b = 1000mm.

LHor. hVer. b

c) According to AASHTO-LRFD-5.10.8.1. Steel Area required as Shrinkage Temperature Reinforcement for Structural Components having its Thickness 1200mm or Less; As  0.11Ag/fy in both way.(Here Thickness = 450mm).

As-req-S&T

d) Here Ag is Gross Area of Strip on Vertical Surface = LHor.*hVer.

Ag-Strip

e) Let provide 16f bars as Shrinkage & Temperature in Vertical Direction on Earth Face Both in Vertical & Horizontal Direction on Water Face. f) X-Sectional Area of 16f bar = pDBar-S&T-V&H2/4 g) Spacings required for 16f Bars as Shrinkage & Temperature in Vertical Direction on Earth Face Both Vertical & Horizontal Direction on Water Face. = Af-16*b/As-req-S&T-V&H

DBar-S&T-V&H

1.000 m 1.000 m 1.000 m

2 268.293 mm

2 1000000.000 mm

16 mm

Af-16

2 201.062 mm

sreq-S&T-V&H

749.413 nos.

h) According to AASHTO-LRFD-5.10.8.1. In a Component having Less 1200mm Thickness, Shrinkage & Temperature Reinforcements should not Spaced further Apart than 3.00 Times the Component's Thickness or 450mm. i) 3.00 Times of Cantilever Wing Wall Thickness = 3.00*tCont.-WW ii) Allowable Max. Spacing for Shrinkage & Temperature Reinforcements i) Let provide 300 mm Spacing for Shrinkage & Temperature Reinforcements with 16f Bars in Vertical Direction on Earth Face, Both in Vertical & Horizontal Direction on Water Face.

Page 532

3.00*tCont.-WW sAllow-S&T-V&H-1

1,350.000 mm 450.000 mm

spro-S&T-V&H

300 mm

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

j) The provided Steel Area with 16f Bars as Shrinkage & Temperature Reinforcements having Spacing 300mm,C/C = Af-16.b/spro-S&T-V&H

As-pro-S&T-V&H

670.206

mm2/m

k) According to AASHTO-LRFD-5.10.8.1. For Components of Solid Structural Concrete Wall & Footing having Less 1200mm Thickness, the Spacing of Shrinkage & Temperature Reinforcements Bars should not Exceed 300mm in Each Direction on all Faces and Steel Area of Shrinkage & Temperature Reinforcements need not Exceed value of Ab = 0.0015Ag. Since the Cantilever Wing Walls are Concrete Wall Structure, thus i) Allowable Max. Spacing for Shrinkage & Temperature Reinforcements sAllow-S&T-V&H-2 300.000 mm 2 Ab = ii) Calculated value of Ab = 0.0015Ag. åAb = 1,500.000 mm /m i) Status between Provided Steel Area of Shrinkage & Temperature Reinforcement & Allowable Max, Steel Area for Shrinkage & Temperature Reinforcement (Whether Ab > As-pro-S&T-V&H or not. If Ab < As-pro-S&T-V&H ; then Provisions of Shrinkage & Temperature Reinforcement have Satisfied, otherwise Not Satisfied) åAb > As-pro-S&T Satisfied l) Since Calculated Ab > As-pro-S&T-V&H. > As-req-S&T-V&H. & spro-S&T-V&H. = sAllow-S&T-V&H-2, thus Provisions for the Shrinkage & Temperature on Surfaces of Cantilever Wing Wall is OK.

Page 533

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

Page 534

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

Page 535

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

Page 536

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

Page 537

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

Page 538

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

Page 539

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

Page 540

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

Page 541

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

Page 542

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

Page 543

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

Page 544

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

Page 545

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

Page 546

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

Page 547

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

Page 548

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

Page 549

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

Page 550

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

Page 551

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

Page 552

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

Satisfy

Page 553

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

Page 554

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

Page 555

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

Page 556

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

Page 557

DESIGN OF SUB-STRUCTURE FOR CHAMPATOLI BRIDGE AT 11.90km ON BAGHAIHUT-MACHALONGSEZEK ROAD

Satisfy

Page 558

O. Structural Design of Abutment Well Cap :

5225

12750 3000 3450

600 C 2000

RL-5.00m

A

2750

2150

2525

600 450

300

RL-2.20m 750

2525 1200

1775

1200

3000

450

1900

1500 1447

2750

600 2150

1775 450

3000

3450

9350

6350

2450

450

3450 450

5500

450 300

B

10250

C

600

4300

600

5500

2 Dimension of Different Sub-Structural Components & RCC Well for Foundation: Description

Notation Dimensions

Unit.

i) Dimensions of Sub-Structure. a) Height of Abutment Wall from Bottom of Well Cap up to Top of Back Wall,

H

6.147 m

b) Height of Abutment Wall from Top of Well Cap up to Top of Back Wall,

H1

4.947 m

hWell-Cap.

1.200 m

d) Height of Abutment Steam

hSteam.

1.900 m

e) Height of Back Wall

hb-wall

2.147 m

f) Height of Wing Wall

H-W-Wall

4.947 m

c) Height of Abutment Well Cap,

H = 6147

600

2147

3450

700

2100

H1 = 4947

600

3450

600

600

300

1 Sketch Diagram of Abutment & Wing wall:

g) Width of Wall Cap on Heel Side (From Abutment Wall Face).

WWell-Cap-Hell

2.975 m

h) Width (Longitudinal Length) of Abutment Well Cap,

LAb-Cap-Long.

i) Length (Transverse Length) of Abutment Well Cap,

LW-Cap-Trans

12.750 m

LAB-Wall-Trans.

10.250 m

LAb-T-Inner

9.350 m

j) Transverse Length of Abutment Wall (Outer Face to Outer Face) in X-X Direction. k) Inner Length of Abutment Wall in between Wing Walls (Transverse), l) Thickness of Abutment Wall (Stem) at Bottom

5.500

m

t.-Ab-wal-Bot.

0.750

t.-Ab-wal-Top.

0.450 m

n) Thickness of Counterfort Wall (For Wing Wall)

tWW-Countf.

0.450 m

o) Number of Wing-Wall Counterforts (on each side)

NW-W-count

1.000 No's

m) Thickness of Abutment Wall (Stem) at Top

p) Clear Spacing between Counerfort & Abutment Wall at Bottom q) Average Spacing between Counerfort & Abutment Wall = (tAB-Wall-Bot + tAb-Wall-Top)/2+SClear-Count& Ab-Bot. r) Effective Span of Wing Wall Counterfort = SAver-Count + tWW-Countf s) Thickness of Wing Walls within Well Cap, t) Thickness of Cantilever Wing Walls u) Length of Cantilever Wing Walls v) Height of Rectangular Portion of Cantilever Wing Walls w) Height of Triangular Portion of Cantilever Wing Walls x) Longitudinal Length of Well Cap on Toe Side from Abutment Wall Outer Face. y) Average Length (Longitudinal) of Well Cap on Heel Side from Abutment Wall Face.= SAver.-Count.& Ab. + tWW-Count. z) Surface Area of Well Cap

m

SClear-Count& Ab-Bot.

1.775 m

SAver-Count&Ab.

2.375 m

SEfft-Count.

2.825 m

t-Wing-wall

0.450 m

tw-wall-Cant.

0.450 m

Lw-wall-Cant.

3.000 m

hw-wall-Cant.-Rec.

2.000 m

hw-wall-Cant.-Tri.

1.500 m

L-W-Cap-Toe.

2.525 m

L-W-Cap-Heel-Aver.

2.825 m

AWell-Cap.

2 66.879 m

ii) Dimensions of RCC Well for Foundation. a) Width of Well in Y-Y Direction (In Longitudinal Direction)

WWell-Y-Y

5.500 m

b) Length of Well in X-X Direction (In Transverse Direction)

LWell-X-X

12.750 m

c) Depth of Well from Bottom of Well Cap up to Bottom of Well Curb

HWell-pro.

6.325 m

tWell.

0.600 m

tWall-Perti

0.600 m

g) Diameter of Outer Circle,

DOuter.

5.500 m

h) Diameter of Inner Circle = DOuter - 2* tWall

DInner.

4.300 m

i) Transverse Length of Rectangular Portion of Well Cap =LWell-X-X - DOuter

LRect.

7.250 m

j) Length of Partition Walls = DOuter - 2*tWall

LParti.

4.300 m

k) Number of Pockets within Well

NPock.

3.000 Nos

SPock-Y-Y.

4.300 m

m) Distance between Inner Faces of Outer Pockets in X-X Direction (Transverse Span Length).

SPock-X-X-Outer.

3.450 m

n) Distance between Inner Faces of Central Pocket in X-X Direction (Transverse Span Length).

SPocket-X-X-Central.

3.450 m

d) Wall thickness of Well, f) Thickness of Partition Walls of Well,

l) Distance between Inner Faces of Pockets in Y-Y Direction (Longitudinal Span Length).

o) Effective Span Length in Y-Y Direction (C/C Distance between Well Walls.) = SPock-Y-Y. + tWall

SEff-Y-Y.

4.900 m

p) Effective Span Length in X-X Direction (C/C Distance between Well Walls.) = SPock-X-X-Central/Outer + tWall(tWall-Perti)

SEff-X-X

4.050 m

3 Information about Soil, Foundation, Abutment & Wing-walls: a) Type of Sub-soil

:

a) At Borehole No-BH07 (Cox's Bazar End), from GL (GL is - 2.25m from Road Top Level) up to 2.50m depth Sub-soil posses Loss gray fine Silty sand having SPT Value ranging 7 to 12. Whereas in next 0.75m from depth 2.50m to 3.75m there exists Medium dense gray fine sand with SPT value ranging from 12 to 40. From depth about 3.75m there exists Bed-rock (Gray Shale) having 50 and over SPT values . b) At Borehole No-BH08 (Teknuf End), from GL (GL is - 2.25m from Road Top Level) upto 2.75m depth Sub-soil posses Medium dency gray sandy silt having SPT Value renging 12 to 37. In next 2.15m (About depth 2.75m to 4.80m) there exists Medum densey gray fine sand with SPT value renging from 37 to 50. From depth about 4.80m there exists Bed rock (Gray Shale) having SPT value 50 over.

b) Type of Foundation

:

Due to its Geographical position, Marin Drive Road have every risk to effected by Wave action & Cyclonic Strom from Sea. More over the Slain Water is also an important factor for RCC Construction Works in these area. In Designing of any Permanent Bridge/Structure on this Road, specially in Foundation Design all the prevalling adverse situations should be considered for their Survival and Durability. Though as per Soil Investigation Report there exist Loss to Medium dency gray sandy silt on Seashore Sub-soil, but due to ground their formation those posses a very poor Mechanical bonding among it contitutent.But there exites Bed-rock at a considerably short depth (About 3.75m to 4.80m) from the Ground Level.Presence of Bed-rock is an important for the Foundation of any Structue on this Road. To encounter all mentioned adverse situations Provision of RCC Caissons embedded into the Bed-rock will be best one as Foundation of Bridges on this Road. RCC Caissons embedded into the Bed-rock will be a Solid mass to save guard the Structure against Errosion, Sliding, Overturning etc. which caused by the Wave action & Cyclonic Strom. More over against Salinity effect necessary meassary can provide for RCC Caissions. Thus it is recommended to Provide RCC Caissions embedded into the Bed-rock at least 1.50m into Bed-rock as Foundation of Delpara Bridge.

c) Type of Abutment

:

Wall Type Abutment.

d) Type of Wing-walls

:

Wall Type Wing Walls Integrated with Abutment Wall having Counterforts over Well & Cantilever Wings beyond Well.

e) Design Criteria

:

Strength Limit State of Design (USD) According to AASHTO-LRFD-2004.

4 Design Data in Respect of Unit Weight, Flexural Multiplier Factors, Material Strength & Soil Pressure: 3 i) Unit Weight of Different Materials in kg/m : (Having value of Gravitional Acceleration, g =

a) b) c) d) e)

2 9.807 m/sec )

Unit weight of Normal Concrete Unit weight of Wearing Course Unit weight of Normal Water Unit weight of Saline Water Unit weight of Earth (Compected Clay/Sand/Silt)

gc gWC gW-Nor. gW-Sali. gs

2,447.232 2,345.264 1,019.680 1,045.172 1,835.424

wc wWC wW-Nor. wW-Sali. wE

24.000 23.000 10.000 10.250 18.000

kg/m3 kg/m3 kg/m3 kg/m3 kg/m3

3 ii) Unit Weight of Materials in kN/m Related to Design Forces :

a) b) c) d) e)

Unit weight of Normal Concrete Unit weight of Wearing Course Unit weight of Normal Water Unit weight of Saline Water Unit weight of Earth (Compected Clay/Sand/Silt)

iii) Design Data for Resistance Factors for Conventional Construction (AASHTO LRFD-5.5.4.2.1). : (Respective Resistance Factors are mentioned as f or b value)

kN/m^3 kN/m^3 kN/m^3 kN/m^3 kN/m^3

a) b) c) d) e) f) g) h) i) j) k)

For Flexural & Tension in Reinforced Concrete For Flexural & Tension in Prestressed Concrete For Shear & Torsion of Normal Concrete For Axil Comression with Spirals or Ties & Seismic Zones at Extreme Limit State (Zone 3 & 4). For Bearing on Concrete For Compression in Strut-and-Tie Modeis For Compression in Anchorage Zones with Normal Concrete For Tension in Steel in Anchorage Zones For resistance during Pile Driving Value of b 1 for Flexural Compression in Reinforced Concrete (AASHTO LRFD-5.7.2..2.) Value of b for Flexural Tension of Reinforcement in Concrete

fFlx-Rin. fFlx-Pres. fShear. fSpir/Tie/Seim. fBearig. fStrut&Tie. fAnc-Copm-Conc. fAnc-Ten-Steel. fPile-Resistanc. b1 b

0.90 1.00 0.90 0.75 0.70 0.70 0.80 1.00 1.00 0.85 0.85

vi) Strength Data related to Ultimate Strength Design( USD & AASHTO-LRFD-2004) : a) Concrete Ultimate Compressive Strength, f/c (Normal Concrete) b) Concrete Allowable Strength under Service Limit State (WSD) = 0.40f/c c) Modulus of Elasticity of Concrete, Ec = 0.043gc1.50f/c (AASHTO LRFD-5.4.2.4). d) Poisson's Ration = 0.63f/c = 0.63*21^(1/2), subject to cracking and considered to be neglected (AASHTO LRFD-5.4.2.5). e) Modulus of Rupture of Concrete, fr = 0.63f/c Mpa (AASHTO LRFD-5.4.2.6). f) Steel Ultimate strength, fy (60 Grade Steel) g) Steel Allowable Strength under Service Limit State (WSD) = 0.40fy h) Modulus of Elasticity of Reinforcement, Es for fy = 410 MPa

f/c fc Ec

21.000 8.400 23,855.620

MPa MPa MPa

2.887 fr fy fs ES

2.887

MPa

410.000 MPa 164.000 MPa 200000.000 MPa

v) Strength Data related to Working Stress Design & Service Load Condition ( WSD & AASHTO-SLS ) : a) b) c) d) e)

Modular Ratio, n = Es/Ec  6 8.384 Value of Ratio of Steel & Concrete Flexural Strength, r = fs/fc Value of k = n/(n + r) = 9.000/(9.000 + 20) Value of j = 1 - k/3 = 1 - 0.307/3 Value of R = 0.5*(fckj)

n r k j R

kN/m3

vi) Sub-soil Investigation Report & Side Codition Data: a) SPT Value as per Soil Boring Test Report, / b) Corrected SPT Value for N>15, N = 15 + 1/2(N - 15) = 15 + 1/2(50 - 15) = 15 + 1/2(50 - 15) = 32.5 . Say N/ = 33 c) Recommended Allowable Bearing Capacity of Soil as per Soil Investigation Report witht SPT Value 50 over, p = 7.2 Ton/ft2. = 770kN/m2 5 Intensity of Different Imposed Loads, Load Coefficients & Multiplier Factors : i) Coefficient for Lateral Earth Pressure (EH) :

8 19.524 0.291 0.903 1.102

N N/

50 Over 33

p

2 770 kN/m

a) Coefficient of Active Horizontal Earth Pressure, ko = (1-sinff ) ,Where; f is Effective Friction Angle of Soil

ko

b) For Back Filling with Clean fine sand, Silty or clayey fine to medium sand

f

0.441

34

O

Effective Friction Angle of Soil, f = 340 .(Table 12.9, Page-138, RAINA,s Book) c) Angle of Friction with Concrete surface & Soli AASHTO-LRFD-3.11.5.3 ;Table 3.11.5.3-1. d) Value of Tan d (dim) for Coefficient of Friction. = 0.34 to 0.45 (AASHTO-LRFD-3.11.5.3 ;Table 3.11.5.3-1.)

d

Tan d

19 to 24

O

0.34 to 0.45 dim

ii) Dead Load Surcharge Lateral/Horizontal Pressure Intensity (ES); AASHTO-LRFD-3.11.6.1. : a) Constant Horizontal Earth Pressur due to Uniform Surcharge, Dp-ES = ksqs in Mpa. Where; b) ks is Coefficien of Earth Pressure due to Surcharge = ko for Active Earth Pressure, c) qs is Uniform Surcharge applied to upper surface of Active Earth Wedge(Mpa)

Dp-ES

2 7.935 kN/m 2 0.007935 N/mm

ks

0.441 2 0.018 N/mm

wE*10-3

= wE*10-3N/mm2 iii) Live Load Surcharge Vertical & Horizontal Pressure Intensity (LS); AASHTO-LRFD-3.11.6.4. : a) Constant Earth Pressur both Vertical & Horizontal for Live Load Surcharge on Abutment Wall (Perpendicular to Traffic), Where; Dp-LS = kgsgheq*10-9

b) Constant Horizontal Earth Pressur due to Live Load Surcharge for Wing Walls (Parallel to Traffic), Where; Dp-LS = kgsgheq*10-9 ,

Dp-LL-Ab Designed Moment, Provided Steel Ratio < Max. Steel Ratio, the Shear Forces for the Section in X-X Direction > the Critical Shear Forces in Y-Y Direction, thus the Flexural Design of Bottom Surface Reinforcement of Well Cap in X-X Direction (Perpendicular to Traffic) is OK.

iv) Checking for Factored Flexural Resistance under Provision of AASHTO-LRFD-5.7.3.2: a) Factored Flexural Resistance for any Section of Component, Mr = fMn, where;

i) Mn is Nominal Resistance Moment for the Section in N-mm ii) f is Resistance Factor of Flexural in Tension of Reinforcement/Prestressing.

Mr

959.379 N-mm 959.379*10^6 kN-m

Mn

1,065.977 N-mm 1065.977*10^6 kN-m

f

0.90

b) The Nominal Resistance of Rectangular Section with One Axis Stress having both Prestressing & Nonprestessing AASHTO-LRFD-5.7.3.2.3 is Mn = Apsfps(dp-a/2) + Asfy(ds-a/2) - A/sf/y(d/s-a/2) c) In a Nonprestressing Structural Component having Rectangular Elements, at any Section the Nominal Resistance, Mn = Asfy(ds-a/2) d) Since Well Cap is being considered as s Simple Supported Rectangular Beam having 1.000 m Wide Strips. The Steel Area against Factored (+) Moments in X-X at its Mid Span will have value of Nominal Resistance, Mn = Asfy(ds-a/2) e) Calculated Factored Moment (+) M at Mid Span of assumed Rectangular Beam in X-X Direction = (+) MMidd-X-X-USD

(+)Mn-X-X 1,065.977 kN-m 1065.977*10^6 N-mm

(+)MMidd-X-X-USD

110.519 kN-m 110.519*10^6 N-mm

f) Relation between the Computed Factored Flexural Resistance Mr & the Actual Factored Moment M for the Section ( Which one is Greater, if Mr  M the Flexural Design for the Section has Satisfied otherwise Not Satisfied)

Mr>MMidd-X-X-USD Satisfied

v) Checking in respect of Control of Cracking By Distribution of Reinforcement, (AASHTO-LRFD-5.7.3.4) : a) Under Service Limit State Load Condition, Developed Tensile Stress of Reinforcement fs-Dev. of Concrete Elements, should not exceed fs the Computed Tensile Stress of Reinforcement under provision of AASHTO-LRFD-5.7.3.4. Where; b) fs-Dev. is Developed Tensile Stress in Provided Reinforcements of Section under the Service Limit State of Loads = M/As-prode in which, i) M is Calculated Moment for the Section under Service Limit State

(+)MMidd-X-X-USD

ii) As-pro is the Steel Area for the Section under USD Design Calculation. iii) de is Effective Depth between Extreme Compression Fiber to Centroid of the Tensile Reinforcement for the Section. c) fsa is Computed Tensile Stress of Reinforcement having its value = Z/(dcA)1/3  0.6fy, in Which;

fs-Dev.

2 37.052 N/mm

98.895 kN-m 98.895*10^6 N-mm

As-pro

2 2,454.369 mm

de

1,087.500 mm

fsa

2 170.000 N/mm

i) dc=Depth of Concrete Extreme Tension Face from the Center of the Closest Tension Bar. The Depth is Summation Bottom/Top Clear Cover & Radius of the Closest Bar to Tension Face. The Max. Clear Cover = 50mm. In a Component of Rectangular Section, dc = DBar/2 + CCov-Bot. Since Clear Cover at Bottom of Well Cap, CCover-Bot = 75mm & Bar Dia, DBar = 25f ; thus dc = (25/2 + 50)mm

dc

ii) A = Area of Concrete Surrounding a Single Tension Bar, which is Calculated by Dividing the Total Concrete Area bounded in between Extreme Tension Face & a Straight Line parallel to Neutral Axis of Component having equal distance from the Centrioed of Main Tension Reinforcement Bars on both side & Diving the Area by the total Number of Main Bars as Tensile Reinforcement having Max. Clear Cover = 50mm.In Well Cap the Tension Bars in One Layer & as per Condition Distance of Neutral Axis from Tension Face = dc, thus Area of Concrete that Surrounding a Single Tension Bar can Compute by A = 2dc*spro. Here spro is Spacing between Provided Tension Bars.

A

iii) Z = Crack Width Parameter for Cast In Place Components in N/mm. For a) Structure with Moderate Exposure Components the Max. value of Z = 30000 b) Structure with Severe Exposure Components the Max. value of Z = 23000 c) Structure with Buried Components the Max. value of Z = 17000 Since the Structure will be a Buried Components thus the Allowable Max. value is ZMax. = 17000N/mm

ZMax.

iv) The Computed value of 0.6*fy for the Concrete Element.

0.6*fy

50.000 mm

2 20,000.000 mm

17,000.000 N/mm

2 246.000 N/mm

d) Since the Calculated value of fs-Dev. is responsible for Controlling the formation of Cracks under Applied Loads to the T-Girder Structure, thus value of the Crack Width Parameter Z should calculate based the value of fs-Dve. e) Based on fs-Dve. the value of Crack Width Parameter ZDev. = fs-Dev.*(dcA)1/3

ZDev.

3,705.150 N/mm

f) Relation between of Developed Tensile Stress fs-Dev. & Allowable Tensile Stress fs

fs-Dev.< fs

Satisfy

g) Relation between Computed Tensile Stress fsa & Calculated value of 0.6fy

fsa< 0.6fy

Satisfy

h) Relation between Allowable Max. value of ZMax. & Developed value ZDev.

Zdev.< Zmax. Satisfy

i) Since Developed Tensile Stress of Tension Reinforcement of Well Cap fs-Dev.< fsa the Computed Tensile Stress; the Computed Tensile Stress fsa < 0.6fy ;the Developed Crack Width Parameter ZDev. < ZMax. Allocable Max. Crack Width Parameter, thus Provisions of Tensile Reinforcement in Y-Y Direction at Well Cap Bottom Surface in respect of Control of Cracking & Distribution of Reinforcement are OK. j) More over though the Structure is a Nonprestressed one & value of dc have not Exceeds 900 mm, thus Component does require any additional Longitudinal Skein Reinforcement. 14 Flexural Design of Reinforcements for Well Cap in X-X Directions for (-) Moment on Top Surface : i) Design of Reinforcements in X-X Direction (Perpendicular to Traffic) against (-) ve Moment:

a) The Calculated (-)ve Moments occur at Support Positions of Well (-)MWall-R1&R2-X-X-USD 154.726 Cap in X-X Direction having equal value. (-) MWall-R1&R2-X-X-USD < Mr, the 154.726*10^6 Required Minimum Flexural Strength Moment which Governs the Design. For Mr 831.463 (-) ve Moment value the Reinforcement will be on Top Surface of Well Cap in 831.463*10^6 X-X Direction. b) Since (-) MWall-R1&R2-X-X-USD > Mr, the Allowable Minimum Moment for the Section, thus (-) MWall-R1&R2-X-X-USD is the Design Moment MU.

b) Let provide 25f bars as Reinforcement on Top Surface in X-X Direction of Well Cap.

MU

kN-m/m N-mm/m kN-m/m N-mm/m

831.463 kN-m/m 831.463*10^6 N-mm/m

DBar-X-X.-Top

25.000 mm

c) X-Sectional of 25f Bars = p*DBar-X-X-Bot.2/4

Af-25.

2 490.874 mm

e) The provided Effective Depth for the Section with Main Reinforcement on Top Surface, dpro = (hWell-Cap. - CCov-Top - DBarX-X.-Top/2)

dpro.

1,112.500 mm

f) With Design Moment MU , Design Strip Width b & Effective Depth dpro; the required value of a = dpro*(1 - (1 - (2MU)/(b1f/cbdpro2))(1/2))

areq.

42.689 mm

g) Steel Area required for the Section, As-req. = MU/(ffy(dpro - a/2))

As-req-Top.-X-X

h) Spacing of Reinforcement with 25f bars = Af-25.b/As-req-Bot.-Y-Y i) Let the provided Spacing of Reinforcement with 25f bars for the Section spro = 200mm,C/C j) The provided Steel Area with 25f bars having Spacing 200mm,C/C = Af-25b/spro

/ l) With provided Steel Area the value of 'a' = As-pro*fy/(b1*f c*b)

m) Resisting Moment for the Section with provided Steel Area, = As-pro*fy(d - apro/2)/10^6

mm2/m

sreq

237.706

mm,C/C

spro.

200.000

mm,C/C

As-pro-Top-X-X.

k) Steel Ratio for the Section, ppro = As-pro/bdpro

2,065.046

ppro

2,454.369

mm2/m

0.002

apro

56.375 mm

Mpro

1,091.134 kN-m/m

n) Relation between Provided Resisting Moment Mpro amd Calculated Design Moment MU. o) Relation between Provided Steel Ration rpro and Allowable Max. Steel Ratio rMax.

Mpro>Mu

OK

ppro VU or Vn < VU & Provisions of AASHTO-LRFD-5.8.3 have Satisfied or Not). e) Since Nominal Shear Resitance for the Section Vn > VU the Calculated Ultimate Shearing Force for the Section, thus the Well does not require any Shear Reinforcement. f) Since Resisting Moment > Designed Moment, Provided Steel Ratio < Max. Steel Ratio, the Shear Forces for the Section in X-X Direction > the Critical Shear Forces in Y-Y Direction, thus the Flexural Design of Bottom Surface Reinforcement of Well Cap in X-X Direction (Perpendicular to Traffic) is OK. iv) Checking for Factored Flexural Resistance under Provision of AASHTO-LRFD-5.7.3.2: a) Factored Flexural Resistance for any Section of Component, Mr = fMn, where;

i) Mn is Nominal Resistance Moment for the Section in N-mm ii) f is Resistance Factor of Flexural in Tension of Reinforcement/Prestressing.

Mr

956.493 N-mm 956.493*10^6 kN-m

Mn

1,062.770 N-mm 1062.770*10^6 kN-m

f

0.90

b) The Nominal Resistance of Rectangular Section with One Axis Stress having both Prestressing & Nonprestessing AASHTO-LRFD-5.7.3.2.3 is Mn = Apsfps(dp-a/2) + Asfy(ds-a/2) - A/sf/y(d/s-a/2) c) In a Nonprestressing Structural Component having Rectangular Elements, at any Section the Nominal Resistance, Mn = Asfy(ds-a/2) d) Since Well Cap is being considered as s Simple Supported Rectangular Beam having 1.000 m Wide Strips. The Steel Area against Factored (-) Moments in X-X Well Wall Face will have value of Nominal Resistance, Mn = Asfy(ds-a/2) e) Calculated Factored Moment (-) M at Well Wall Face of assumed Rectangular Beam in X-X Direction = (-) MWall-R1&R2-X-X-USD

(-)Mn-X-X 1,062.770 kN-m 1062.770*10^6 N-mm

(-)MWall-R1&R2-X-X-USD

154.726 kN-m 154.726*10^6 N-mm

f) Relation between the Computed Factored Flexural Resistance Mr & the Mr>MWall-R1&R2-X-X-USD Satisfied Actual Factored Moment M for the Section ( Which one is Greater, if Mr  M the Flexural Design for the Section has Satisfied otherwise Not Satisfied) v) Checking in respect of Control of Cracking By Distribution of Reinforcement, (AASHTO-LRFD-5.7.3.4) : a) Under Service Limit State Load Condition, Developed Tensile Stress of Reinforcement fs-Dev. of Concrete Elements, should not exceed fs the Computed Tensile Stress of Reinforcement under provision of AASHTO-LRFD-5.7.3.4. Where; b) fs-Dev. is Developed Tensile Stress in Provided Reinforcements of Section under the Service Limit State of Loads = M/As-prode in which, i) M is Calculated Moment for the Section under Service Limit State

fs-Dev.

2 50.706 N/mm

(-)MWall-R1&R2-X-X-USD 138.453 kN-m 138.453*10^6 N-mm

ii) As-pro is the Steel Area for the Section under USD Design Calculation. iii) de is Effective Depth between Extreme Compression Fiber to Centroid of the Tensile Reinforcement for the Section. c) fsa is Computed Tensile Stress of Reinforcement having its value = Z/(dcA)1/3  0.6fy, in Which;

As-pro

2 2,454.369 mm

de

1,112.500 mm

fsa

i) dc=Depth of Concrete Extreme Tension Face from the Center of the Closest Tension Bar. The Depth is Summation Bottom/Top Clear Cover & Radius of the Closest Bar to Tension Face. The Max. Clear Cover = 50mm. In a Component of Rectangular Section, dc = DBar/2 + CCov-Bot. Since Clear Cover at Bottom of Well Cap, CCover-Bot = 75mm & Bar Dia, DBar = 25f ; thus dc = (25/2 + 50)mm

dc

ii) A = Area of Concrete Surrounding a Single Tension Bar, which is Calculated by Dividing the Total Concrete Area bounded in between Extreme Tension Face & a Straight Line parallel to Neutral Axis of Component having equal distance from the Centrioed of Main Tension Reinforcement Bars on both side & Diving the Area by the total Number of Main Bars as Tensile Reinforcement having Max. Clear Cover = 50mm.In Well Cap the Tension Bars in One Layer & as per Condition Distance of Neutral Axis from Tension Face = dc, thus Area of Concrete that Surrounding a Single Tension Bar can Compute by A = 2dc*spro. Here spro is Spacing between Provided Tension Bars.

A

iii) Z = Crack Width Parameter for Cast In Place Components in N/mm. For a) Structure with Moderate Exposure Components the Max. value of Z = 30000 b) Structure with Severe Exposure Components the Max. value of Z = 23000 c) Structure with Buried Components the Max. value of Z = 17000 Since the Structure will be a Buried Components thus the Allowable Max. value is ZMax. = 17000N/mm

ZMax.

iv) The Computed value of 0.6*fy for the Concrete Element.

0.6*fy

2 170.000 N/mm

50.000 mm

2 20,000.000 mm

17,000.000 N/mm

2 246.000 N/mm

d) Since the Calculated value of fs-Dev. is responsible for Controlling the formation of Cracks under Applied Loads to the T-Girder Structure, thus value of the Crack Width Parameter Z should calculate based the value of fs-Dve. e) Based on fs-Dve. the value of Crack Width Parameter ZDev. = fs-Dev.*(dcA)1/3

ZDev.

5,070.644 N/mm

f) Relation between of Developed Tensile Stress fs-Dev. & Allowable Tensile Stress fs

fs-Dev.< fs

Satisfy

g) Relation between Computed Tensile Stress fsa & Calculated value of 0.6fy

fsa< 0.6fy

Satisfy

h) Relation between Allowable Max. value of ZMax. & Developed value ZDev.

Zdev.< Zmax. Satisfy

i) Since Developed Tensile Stress of Tension Reinforcement of Well Cap fs-Dev.< fsa the Computed Tensile Stress; the Computed Tensile Stress fsa < 0.6fy ;the Developed Crack Width Parameter ZDev. < ZMax. Allocable Max. Crack

Width Parameter, thus Provisions of Tensile Reinforcement in Y-Y Direction at Well Cap Bottom Surface in respect of Control of Cracking & Distribution of Reinforcement are OK. j) More over though the Structure is a Nonprestressed one & value of dc have not Exceeds 900 mm, thus Component does require any additional Longitudinal Skein Reinforcement. 15 Arrangement of Reinforcement on Top & Bottom Surface of Well Cap under Provision of Distribution Reinforcement or as Temperature & Shrinkage Reinforcement in Y-Y (Parallel to Traffic) & also X-X (Perpendicular to Traffic) Directions Including the Vertical Faces. i) Arrangement of Reinforcement on Horizontal Surfaces : a) Since on Bottom Surface of Well Cap, Reinforcements are being Provided both in Y-Y & X-X Directions, but on Top Surface the Provided Reinforcements are in X-X Direction only. Thus it requires provision of Reinforcements in Y-Y Direction. On Top Surface in Y-Y Direction (Parallel to Traffic) Reinforcements can Provide as Shrinkage & Temperature Reinforcement on same Surface according to provisions of AASHTO-LRFD.- 5.10.8. b) Let consider a 1.000m X 1.000m Strip of Surface of Well Cap for Calculation of Shrinkage & Temperature Reinforcement on Top Surface in Y-Y Direction. c) Under Provision of AASHTO1996-8.20.1&.2. the Required Steel Area against Temperature & Shrinkage Reinforcement on any Cocrete Exposed Surface in both Directions = (1/8)*25^2*3.28mm 2/m

bY-Y. bX-X

1.000 m 1.000 m 2 256.250 mm /m

AS-S&T

2 268.293 mm

d) According to AASHTO-LRFD-5.10.8.1. Steel Area required as Shrinkage As-req-S&T-Top.Y-Y Temperature Reinforcement for Structural Components having its Thickness 1200mm or Less; As  0.11Ag/fy in both way.(Here Well Cap Thickness = 1200mm). e) Here Ag is Gross Area of Strip on Top Surface = bY-Y*bX-X f) Let provide 16f bars as Shrinkage & Temperature on Top of Well Cap in Y-Y Direction. g) X-Sectional Area of 16f bar = pDBar2/4 h) Spacing of 16f bars as Shrinkage & Temperature on Top of Well Cap in Y-Y Direction = Af-16.bX-X/As-req-S&T-Top.Y-Y

Ag-Strip

2 1000000.000 mm

DBar.S&T-Y-Y

16.000 mm

Af-16

2 201.062 mm

sreq-S&T-Top-Y-Y.

i) Spacing of Shrinkage & Temperature Reinforcements will less of 3-times spro-S&T-Top-Y-Y. the Component thickness or 450mm. Since the Thickness of Component is 1200mm; thus let provide Specing of Shrinkage & Temperature Reinforcements for Top Surface in Y-Y Direction = 300m C/C.

2 749.413 mm

300.000 mm

j) Since As-pro-Top. > As-req-Top & spro-Top> s-req-Top, thus the provision of Shrinkage & Temperature on Top Surface of Wel Cap in Y-Y Direction is OK. ii) Arrangement of Reinforcements on Vertical Faces both in Vertical & Horizontal Direction :

a) The Vertical Faces of Well Cap Require Reinforcements in both Vertical & Horizontal Directions, those can also provide as Shrinkage & Temperature Reinforcement under Provisions of AASHTO-LRFD.- 5.10.8. b) Since the Well Cap has a Thickness/Depth of 1200mm, thus let consider a Strip of Well Cap Vertical Surface having Horizontal Length LHor. = 1000mm & Vertical Height hVer. = 1200mm (Depth of Well Cap) for Calculations of its Shrinkage & Temperature Reinforcements on both Directions.

LHor. hVer.

c) According to AASHTO-LRFD-5.10.8.1. Steel Area required as Shrinkage As-req-S&T-V-Face Temperature Reinforcement for Structural Componentshaving its Thickness 1200mm or Less; As  0.11Ag/fy in both way.(Here Well Cap Thickness = 1200mm).

1.000 m 1.200 m

2 321.951 mm

2 1200000.000 mm

d) Here Ag is Gross Area of Strip on Vertical Surface = LHor.*hVer.

Ag-Strip

e) Let provide 16f bars as Shrinkage & Temperature on Well Cap Vertical Faces in Horihontal Direction.

DBar-Hor

16.000 mm

Af-16

2 201.062 mm

f) X-Sectional Area of 16f bar = pDBar-Hor2/4 g) Number of 16f Bars required as Shrinkage & Temperature on Vertical Faces in Horihontal Direction = As-req-S&T-V-Face/Af-16.

NBar-Hor-req.

1.601 nos.

h) Let provide 4 nos 16f Bars as Shrinkage & Temperature on Vertical Faces in Horihontal Direction.

NBar-Hor-pro.

4.000 nos.

i) Spacing of 4nos. 16f bars as Shrinkage & Temperature on Well Cap Vertical Faces in Horizopntal Direction = hVer./(NBar-Hor-pro.- 1)

spro-S&T-Hor.

400.000 mm

h) Spacing of Shrinkage & Temperature Reinforcements will less of 3-times spro-S&T-Top-Y-Y. the Component thickness or 450mm. Since the Thickness of Component is 1200mm; thus let provide Specing of Shrinkage & Temperature Reinforcements for Top Surface in Y-Y Direction = 300m C/C.

300.000 mm

j) Since As-pro-Top. > As-req-Top & spro-Top> s-req-Top, thus the provision of Shrinkage & Temperature on Top Surface of Wel Cap in Y-Y Direction is OK. k) Since the Well Cap Bottom & Top Surfaces are being Provided with Flexural as well Shrinkage & Temperature Reinforcement Bars having Spacing ranging 150mm to 300mm C/C, thus it is Recommended to bent up & down those Bars alternately from Bottom & Top. These arrangement will fulfill the requirements of Vertical Shrinkage & Temperature Reinforcements for Vertical Faces of Well Cap. 16 Checking against Shearing Forces at Critical Sections of Well Cap. i) Checking of Shearing Forces at Critical Sections of Well Cap along X-X Direction due to Vertical Loads from Superstructure (DL + LL), Loads of Abutment Wall (DL), Soil & Surcharge Loads (DL + LL). a) According to AASHTO-LRFD-5.8.3.2; 5.13.3.6.1 & C 5.13.3.6.1 the Critical Sections of Footings (Here Well Cap) prevaile on 2 (Two) Loactions; i) At a Distance dv from Face of Abutment Wall Toe Side (River Face), ii) Just on the

Back Face of Abutment Well on Heel Side (Earth Face). b) Since the Well Cap is being Designed Considering it has One Way Action; thus the Shear Resistances for both the Locations should Satisfy the Provisions of AASHTO-LRFD-5.8.3. c) The Calculated Factored Shearing Forces on Toe Side of Well Cap at Critical Section at a Distance dv from the = RB-USD - (LY-Y/2 - tAb-Wal-Bot/2 - dv)*pSelf-Wt.-USD d) The Nominal Shear Resitance Vn for the Section is the Lesser value of any of Equations as mentioned in Aritical 5.8.3.3 : i) Vn-1 = Vc + Vs + Vp

Equ.- 5.8.3.3-1, or

VU-dv-Toe

348.492 kN/m

Vn-Heel 5,256.563 kN/m 52563.563*10^3 N/m Vn-1

7,616.584 kN/m 7616.584*10^3 N/m

Vn-2

5,256.563 kN/m 52563.563*10^3 N/m

d-i) Vc is Nominal Shear Resistance of Conrete in N & value = 0.083bf/cbvdv, (AASHTO-LRFD- Equ. 5.8.3.3-1);

Vc

7,616.584 kN/m 7616.584*10^3 N/m

d-ii) Vs is Shear Resistance Provided by Shear Reinforcement in N having value = Avfydv(cotq + cota)sina /s. (AASHTO-LRFD-Equ. 5.8.3.3-3) in which, For Footing/Foundation Slab Vs = 0.

Vs

-

d-iii) b is Factor for the Diagonally Cracked Concrete to transmit Tension as per AASHTO-LRFD-5.8.3.4. For Footing/Foundation Slab b = 2.00.

b

2.000

Vp.

-

ii) Vn-2 = 0.25f/cbvdv + Vp Equ.- 5.8.3.3-2. In which,

d-iv) Vp is component of Prestressing Force in direction of Shear Force in N; (For RCC Structure Elements, Vp = 0. AASHTO-8.16.6.3.1.)

N/m

N

e) Statue between Computed Nominal Shear Resitance Vn & Factored Shearing Forces VU Vn>Vu Satisfied For the Section (Whether Vn > VU or Vn < VU & Provisions of AASHTO-LRFD-5.8.3 have Satisfied or Not). f) Since Nominal Shear Resitance for the Section Vn > VU the Calculated Ultimate Shearing Force for the Section, thus the Well does not require any Shear Reinforcement. g) Checking of Shearing Forces at Critical Section on Abutment Wall Heel Face of Well Cap along X-X Direction due to Vertical Loads from Superstructure (DL + LL), Loads of Abutment Wall (DL), Soil & Surcharge Loads (DL + LL) have already been done in Serial No-12-ii & found Satisfactory, thus no further Checking ie Required. ii) Checking of Punching Shear Forces at Critical Sections of Well Cap along X-X Direction due to Vertical Loads from Superstructure (DL + LL), Loads of Abutment Wall (DL), Soil & Surcharge Loads (DL + LL) as Two-Way Action According to Provision of AASHTO-LRFD-5.13.3.6 : a) According to AASHTO-LRFD-5.13.3.6.1 the Critical is Located at a Distance not Less than 0.5dv to Calcutate the Parimeter bo of the Concetrated Loads. b) According to AASHTO-LRFD-5.13.3.6.3 for Two-Way Action without Transverse/Shear Reinforcement the Nominal

Shear Resitance of Concrete for the Section, Vn = (0.17+0.33/bc)f/cbodv  0.33 f/cbodv ; where, c) bc is Ratio of Long Side to Short Side of Rectangule through which the Horces bc Concentrated Load or Reaction Transmitted having value = LAb-Wall-Trans./LAb-Cap-Long.

1.864

d) bo is Perimeter of the Critial Section at a distance 0.5*dv from Face of Load bo 3 Action Face having value, bo = 2*{(2*0.5dv +LAB-Wall-Trans) + (tAb-Wall-Bot+2*0.5dv)} /10 m

26.005 m 26.005*10^3 mm

e) dv is Effective Shear Depth in mm.

dv

1,001.250 mm

f) The Calculated Factored Total Shearing Forces at Critical on Toe Side at a Distance 0.5*dv from the Abutment Wall Face = ((RB-USD - (LY-Y/2 - tAb-Wal-Bot/2 - 0.5*dv)*pSelf-Wt.-USD)*LW-Cap-Trans.

VU-Total-Crit-Toe-1

4,075.105 kN

g) The Calculated Factored Total Shearing Forces at Critical on Heel Side at a Distance 0.5*dv from the Abutment Wall Face = ((RA-USD - (LY-Y/2 - tAb-Wal-Bot/2 - 0.5*dv)*pSelf-Wt.-USD+ pHeel)*LW-Cap-Trans.

VU-Total-Crit-Toe-2

7,130.067 kN

h) Computed value on Toe Side for Vn-1 = (0.17+0.33/bc)f/cbodv i) Computed value on Toe Side for Vn-2 = 0.33 f/cbodv

j) Relation betweenComputed values of Vn-1 & Vn-2 for Tor Side

Vn-1

41,412.369 kN

Vn-2

180439.918 kN 180439.918*10^3 N

Vn1 VC-d1 > VU, Thus the Well Cap does not Require any Punching Shear Reinforcement. m) Since the Resisting Moment > Designed Moment, the Provided Steel Ratio < Max. Steel Ratio, the Calculated Imposed Max. Shear Forces (Nominal & Punching) < the Computed Shear Forces (Nominal & Punching) and the Well Cap does not require any Shear Reinforcement, thus the Flexural Design of the Well Cap for Reinforcement on Top & Bottom Surface in all respect (both in X-X & Y-Y Direction) is OK.

ximum

the

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

P. Structural Design of RCC Wells for Bridge foundation:

5225

12750 3000 600

3450

600 C 2000

RL-5.00m

A

2750

2150

2525

600

1775

750

2525 1200

450

1447

3000

RL-2.20m

1200

3000

1900 H1 = 4947

450

300

1500

2150 600

1775 450

2750

5500

450 300

B

3450

9350

6150

2450

450

450

3450

10250

C

600

4300

600

5500

2 Dimensions of Bridge Superstructur, Substructure & RCC Well for Foundation : Description

Notation Dimensions

Unit.

SL SAddl. LGir. WCarr-Way. WS-Walk. WCurb. WR-Post. WB-Deck. RW&D. PW&B.

m m m m m m m m m m

i) Dimentions of Superstructure : a) b) c) d) e) f) g) h) i) j)

Span Length (Clear C/C distance between Bearings) Addl.Length of Girder beyond Bearing Center Line. Total Girder Length (a+2b) Carriageway Width Width of Side Walk on Each Side Width of Curb/Wheel Guard Width of Railing Curb/Post Guard Total Width of Bridge Deck Width & Depth of Railings Width & Breath of Railing Post

Page 637

24.400 0.300 25.000 7.300 1.250 0.350 0.225 10.250 0.175 0.225

H = 6147

3450

700

2100

2147

600

3450

600

600

300

1 Sketch Diagram of Abutment & Wing wall:

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

k) l) m) n) o) p) q) r) s) t) u) v) w) w-i) x) y)

Height of Railing Post Height of Wheel Guard/Curb Number of Railings on each Side C/C distance between Railing Posts Thickness of Deck Slab Thickness of Wearing Course Number of Main Girders Number of Cross Girders Depth of Main Girders (Including Slab as T-Girder) Depth of Cross Girders (Including Slab as T-Girder) Width of Main Girders Width of Cross Girders C/C Distance Between Main Girders Distance of Slab Outer Edge to Exterior Girder Center Clear Distance Between Main Interior Girders Filets : i) Main Girder in Vertical Direction ii) Main Girder in Horizontal Direction iii) X-Girder in Vertical Direction vi) X-Girder in Horizontal Direction z) Vertical Surface Area of Superstructure's Exposed Elements

hR-Post. hCurb. Rnos. C/CD-R-Post. tSlab. tWC NGirder. NX-Girder. hGirder. hX-Girder. bGirder. bX-Girder. C/CD-Girder. CD-Ext.-Girder-Edg. ClD-Int.-Girder. FM-Girder-V. FM-Girder-H. FX-Girder-V. FX-Girder-H. ASup-Vert.

1.070 m 0.300 m 3.000 nos 2.000 m 0.200 m 0.075 m 5.000 nos 5.000 nos 2.000 m 1.900 m 0.350 m 0.250 m 2.000 m 1.125 m 1.650 m 0.150 m 0.150 m 0.075 m 0.075 m 2 87.108 m

ii) Dimensions of Sub-Structure. a) Height of Abutment Wall from Bottom of Well Cap up to Top of Back Wall,

H

6.147 m

b) Height of Abutment Wall from Top of Well Cap up to Top of Back Wall,

H1

4.947 m

hWell-Cap.

1.200 m

d) Height of Abutment Steam

hSteam.

1.900 m

e) Height of Back Wall

hb-wall

2.147 m

f) Height of Wing Wall

H-W-Wall

4.947 m

c) Height of Abutment Well Cap,

g) Width of Wall Cap on Heel Side (From Abutment Wall Face).

WWell-Cap-Hell

2.525 m

h) Width (Longitudinal Length) of Abutment Well Cap,

WAb-Cap

i) Length (Transverse Length) of Abutment Well Cap,

LAb-T-W-Cap

12.750 m

j) Transverse Length of Abutment Wall (Outer Face to Outer Face) in X-X Direction.

LAB-Trans.

10.250 m

k) Inner Length of Abutment Wall in between Wing Walls (Transverse),

LAb-T-Inner

9.350 m

l) Thickness of Abutment Wall (Stem) at Bottom

t.-Ab-wal-Bot.

Page 638

5.500

0.750

m

m

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

m) Thickness of Abutment Wall (Stem) at Top

t.-Ab-wal-Top.

0.450 m

n) Thickness of Counterfort Wall (For Wing Wall)

tWW-Countf.

0.450 m

o) Number of Wing-Wall Counterforts (on each side)

NW-W-count

1.000 No's

p) Clear Spacing between Counerfort & Abutment Wall at Bottom

SClear-Count& Ab-Bot.

1.775 m

SAver-Count&Ab.

2.375 m

SEfft-Count.

2.825 m

t-Wing-wall

0.450 m

t) Thickness of Cantilever Wing Walls

tw-wall-Cant.

0.450 m

u) Length of Cantilever Wing Walls

Lw-wall-Cant.

3.000 m

hw-wall-Cant.-Rec.

2.000 m

hw-wall-Cant.-Tri.

1.500 m

L-W-Cap-Toe.

2.525 m

L-W-Cap-Heel-Aver.

2.825 m

a) Width of Well in Y-Y Direction (In Longitudinal Direction)

WWell-Y-Y

5.500 m

b) Length of Well in X-X Direction (In Transverse Direction)

LWell-X-X

12.750 m

c) Depth of Well from Bottom of Well Cap up to Bottom of Well Curb

HWell-pro.

6.325 m

d) Wall thickness of Well,

tWell-Wall.

0.600 m

f) Thickness of Partition Walls of Well,

tWall-Perti

0.600 m

g) Diameter of Outer Circle,

DOuter.

5.500 m

h) Diameter of Inner Circle = DOuter - 2* tWall

DInner.

4.300 m

LRect.

7.250 m

q) Average Spacing between Counerfort & Abutment Wall = (tAB-Wall-Bot + tAb-Wall-Top)/2+SClear-Count& Ab-Bot. r) Effective Span of Wing Wall Counterfort = SAver-Count + tWW-Countf s) Thickness of Wing Walls within Well Cap,

v) Height of Rectangular Portion of Cantilever Wing Walls w) Height of Triangular Portion of Cantilever Wing Walls x) Longitudinal Length of Well Cap on Toe Side from Abutment Wall Outer Face. y) Average Length (Longitudinal) of Well Cap on Heel Side from Abutment Wall Face.= SAver.-Count.& Ab. + tWW-Count. iii) Dimensions of RCC Well for Foundation.

i) Transverse Length of Rectangular Portion of Well Cap =LWell-X-X - DOuter

Page 639

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

j) Length of Partition Walls = DOuter - 2*tWall

LParti.

4.300 m

k) Number of Pockets within Well

NPock.

3.000 Nos

l) Distance between Inner Faces of Pockets in Y-Y Direction (Longitudinal Span Length).

SPock-Y-Y.

4.300 m

m) Distance between Inner Faces of Outer Pockets in X-X Direction (Transverse Span Length).

SPock-X-X-Outer.

3.450 m

n) Distance between Inner Faces of Central Pocket in X-X Direction (Transverse Span Length).

SPocket-X-X-Central.

3.450 m

W1/2-Well-Y-Y

2.750 m

o) Width of Well from its c.g. Line in X-X. = WWell-Y-Y/2

2 63.633 m

p) Surface Area of Well at Top & Bottom Level = pDOuter2/4 + LRect*DOuter

AWell.

q) Total Length of Staining of Well (Main & Partitions) through Center line = p*(DOuter+ DInner)/2 + 2*LRect. + 2*LParti

LStaining.

38.494 m

r) Surface Area of Well Cap = LAb-T-W-Cap*W1/2-Well-Y-Y + 0.5*pDOuter2/4 + LRect*W1/2-Well-Y-Y

AWell-Cap.

2 66.879 m

s) Distance of c.g. (X-X) Line from Well Cap Toe Face = (LAb-T-W-Cap*(W1/2-Well-Y-Y)2*1.50+ (0.5*pDOuter2/4)*0.50*DOuter*3/4 + LRect*W1/2-Well-Y-Y2/2)/AWell-Cap.

bc.g.-Y-Y.

2.939 m

t) RL of Height Flood Level (HFL)

HFLRL

2.100 m

u) RL of Maximum Scoring Level (MSL)

MSLRL

(4.750) m

v) Depth of Well Portion within Bed-rock,

HB-Rock

1.500 m

3 Design Data in Respect of Unit Weight & Strength of Materials : i) Unit Weight of Different Materials : 3 i) Unit Weight of Different Materials in kg/m : (Having value of Gravitional Acceleration, g =

a) b) c) d) e)

2 9.807 m/sec )

gc gWC

Unit weight of Normal Concrete Unit weight of Wearing Course Unit weight of Normal Water Unit weight of Saline Water Unit weight of Earth (Compected Clay/Sand/Silt)

gW-Nor. gW-Sali. gs

3 ii) Unit Weight of Materials in kN/m Related to Design Forces :

Page 640

2,447.23 2,345.26 1,019.68 1,045.17 1,835.42

kg/m3 kg/m3 kg/m3 kg/m3 kg/m3

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

a) b) c) d) e)

Unit weight of Normal Concrete Unit weight of Wearing Course Unit weight of Normal Water Unit weight of Saline Water Unit weight of Earth (Compected Clay/Sand/Silt)

wc wWC wW-Nor. wW-Sali. wE

24.00 23.00 10.00 10.25 18.00

kN/m3 kN/m3 kN/m3 kN/m3 kN/m3

ii) Design Data for Resistance Factors for Conventional Construction (AASHTO LRFD-5.5.4.2.1). : (Respective Resistance Factors are mentioned as f or b value) a) b) c) d) e) f) g) h) i) j) k)

For Flexural & Tension in Reinforced Concrete For Flexural & Tension in Prestressed Concrete For Shear & Torsion of Normal Concrete For Axil Comression with Spirals or Ties & Seismic Zones at Extreme Limit State (Zone 3 & 4). For Bearing on Concrete For Compression in Strut-and-Tie Modeis For Compression in Anchorage Zones with Normal Concrete For Tension in Steel in Anchorage Zones For resistance during Pile Driving Value of b1 for Flexural Compression in Reinforced Concrete (AASHTO LRFD-5.7.2..2.) Value of b for Flexural Tension of Reinforcement in Concrete

fFlx-Rin. fFlx-Pres. fShear. fSpir/Tie/Seim. fBearig. fStrut&Tie. fAnc-Copm-Conc. fAnc-Ten-Steel. fPile-Resistanc. b1 b

0.90 1.00 0.90 0.75 0.70 0.70 0.80 1.00 1.00 0.85 0.85

iii) Strength Data related to Ultimate Strength Design( USD & AASHTO-LRFD-2004) : a) Concrete Ultimate Compressive Strength, f/c (Normal Concrete) b) Concrete Allowable Strength under Service Limit State (WSD) = 0.40f/c c) Modulus of Elasticity of Concrete, Ec = 0.043gc1.50f/c (AASHTO LRFD-5.4.2.4). d) Poisson's Ration = 0.63f/c = 0.63*21^(1/2), subject to cracking and considered to be neglected (AASHTO LRFD-5.4.2.5). e) Modulus of Rupture of Concrete, fr = 0.63f/c Mpa (AASHTO LRFD-5.4.2.6). f) Steel Ultimate strength, fy (60 Grade Steel) g) Steel Allowable Strength under Service Limit State (WSD) = 0.40fy h) Modulus of Elasticity of Reinforcement, Es for fy = 410 MPa

f/c fc Ec

21.000 8.400 23,855.620 2.887

fr fy fs ES

2.887

Modular Ratio, n = Es/Ec>6 8.384 Value of Ratio of Steel & Concrete Flexural Strength, r = fs/fc = 164/8.400 Value of k = n/(n + r) = 9.000/(9.000 + 20) Value of j = 1 - k/3 = 1 - 0.307/3 Value of R = 0.5*(fckj) = 0.5*(8.400*0.307*0.898) = 1.156

v) Sub-soil Investigation Report & Bearing Capacity of Bed-rock :

Page 641

n r k j R

MPa

410.000 MPa 164.000 MPa 200000.000 MPa

iv) Strength Data related to Working Stress Design & Service Load Condition ( WSD & AASHTO-SLS ) : a) b) c) d) e)

MPa MPa MPa

8 19.524 0.291 0.903 1.102

STRUCTURAL DESIGN OF DELPARA BRIDGE AT 18.25km ON COX'S BAZAR-TEKNUF MARIN DRIVE ROAD UNDER COX'S BAZAR ROAD DIVISION (IMPLEMENTION AUTHORITY ;- 16 ECB BANGLADESH ARMY).

a) SPT Value as per Soil Boring Test Report, / b) Corrected SPT Value for N>15, N = 15 + 1/2(N - 15) = 15 + 1/2(50 - 15) = 15 + 1/2(50 - 15) = 32.5 . Say N/ = 33 c) Recommended Allowable Bearing Capacity of Bed-rock (Soil Investigation Report witht SPT Value 50 over, p = 7.2 Ton/ft2. = 770kN/m2)

N N/

50 Over 33

p

2 770 kN/m

4 Intensity of Different Imposed Loads, Load Coefficients & Multiplier Factors : i) Coefficient for Lateral Earth Pressure (EH) : a) Coefficient of Active Horizontal Earth Pressure, ko = (1-sinff ) ,Where; f is Effective Friction Angle of Soil

ko

b) For Back Filling with Clean fine sand, Silty or clayey fine to medium sand Effective Friction Angle of Soil, f = 340 .(Table 12.9, Page-138, RAINA,s Book)

f

c) Angle of Friction with Concrete surface & Soli AASHTO-LRFD-3.11.5.3 ;Table 3.11.5.3-1.

d

19 to 24

Tan d

0.34 to 0.45

d) Value of Tan d (dim) for Coefficient of Friction. = 0.34 to 0.45 (AASHTO-LRFD-3.11.5.3 ;Table 3.11.5.3-1.)

0.441

34

O

O

dim

ii) Dead Load Surcharge Lateral/Horizontal Pressure Intensity (ES); AASHTO-LRFD-3.11.6.1. : Dp-ES

a) Constant Horizontal Earth Pressur due to Uniform Surcharge, Dp-ES = ksqs in Mpa. Where; b) ks is Coefficien of Earth Pressure due to Surcharge = ko for Active Earth Pressure, c) qs is Uniform Surcharge applied to upper surface of Active Earth Wedge(Mpa) = wE*10-3N/mm2

2 0.007935 N/mm 2 7.935 kN/m

ks

0.441 2 0.018 N/mm

wE*10-3

iii) Live Load Surcharge Vertical & Horizontal Pressure Intensity (LS); AASHTO-LRFD-3.11.6.4. : a) Constant Earth Pressur both Vertical & Horizontal for Live Load Surcharge on Abutment Wall (Perpendicular to Traffic), Where; Dp-LS = kgsgheq*10-9

b) Constant Horizontal Earth Pressur due to Live Load Surcharge for Wing Walls (Parallel to Traffic), Where; Dp-LS = kgsgheq*10-9 ,

c) ks is Coefficien of Latreal Earth Pressure = ko for Active Earth Pressure. d) gs is Unit Weight of Soil (kg/m3)

Page 642

Dp-LL-AbAsS-req.

c) Relation between Provided Area & Required Area of Elastomeric Bearing for Compressive Shear Stress under Shear Deformation for Live Load only:

Apro-Plan.>AsL-req.

c) Relation between Provided Area & Required Area of Elastomeric Bearing for Compressive Shear Stress under Shear Deformation for Total Load:

Apro-Plan.>AsS-Fix-req.

d) Relation between Provided Area & Required Area of Elastomeric Bearing for Compressive Shear Stress under Shear Deformation for Live Load only:

Apro-Plan.>AsL-Fix-req.

iv) Developed Compressive Shear Stress for Elastomeric Bearing under Service Limit State (WSD) : a) Developed Compressive Shear Stress on Elastomeric Bearing due to Applied Total Loads (DL + LL) = PMax.-WSD/(L*W)

sS-Dev.

5.786

b) Developed Compressive Shear Stress on Elastomeric Bearing due to Applied Live Load (LL) only = PMin.-WSD-LL/(L*W)

sL-Dev.

2.150

c) Relation between Developed Compressive Stress on Elastomeric Bearing and Allowable Compressive Stress for Bearing Subject to Shear Deformation due to Applied Total Loads (DL + LL) under Service Limit State (WSD).

sS-Dev.6 8.384 Value of Ratio of Steel & Concrete Flexural Strength, r = fs/fc = 164/8.400 Value of k = n/(n + r) = 9.000/(9.000 + 20) Value of j = 1 - k/3 = 1 - 0.307/3 Value of R = 0.5*(fckj) = 0.5*(8.400*0.307*0.898) = 1.156

n r k j R

8 19.524 0.291 0.903 1.102

2 Dimentional Data of RCC Bearing Pads for Abutment : i) Provided Dimensions of RCC Bearing Pad for Central Girder : a) Length of Bearing Pad (Parallel to Traffic)

LPad

500 mm

b) Width of Bearing Pad (Transverse to Traffic)

WPad

930 mm

c) Depth of Bearing Pad (Under Central Girder)

hPad

115 mm

a) Length of Bearing Plate (Parallel to Traffic)

LB-Plate

400 mm

b) Width of Bearing Plate (Transverse to Traffic)

WB-Plate

300 mm

c) Depth of Bearing Plate

hB-Plate

72 mm

d) Clear Cover on Vertical Faces

CCov.-V

25 mm

e) Clear Cover on Horizontal Face on Top

CCov.-H

25 mm

f) Width of Abutment Cap

bAb-Cap

1000 mm

g) Depth of Abutment Cap

hAb-Cap

600 mm

ii) Provided Dimensions of Elastomeric Bearing Pad for Central Girder :

3 Philosophy in Structural Design of RCC Bearing Pad : a) The RCC Bearing Pads for Girders are absolutely Compressive Components & their Structural shall be accordingly. b) Since the Pads are of very short Depth, thus the Structural Design will based on Short Column Phenomenon.

c) Design shall be according to Provisions of AASHTO-LRFD-5.7.5 & the Design Phenomenon for RCC Structure. d) Since Total Vertical Loads from Girder would be Placed Directly upon the Elastomeric Bearing Pad, afterward upon the RCC Pad & Finally to the Abutment Cap. Thus it is require to Design Flexural Design as Compression Member for Reinforcement & Subsequent Checking for Shear. e) Initial Structural Design will be done under Strength Limit State (USD) & Subsequent Checking will done based on Service Limit State (WSD). 4 Applied Factored Loads upon Bearing Pad for Central Girder : a) Applied Factored Loads (DL + LL) under Strength Limit State (USD)

PUSD

1,149.477 kN

b) Applied Factored Loads (DL + LL) under Service Limit State (WSD)

PWSD

694.340 kN

5 Structural Design of RCC Bearing Pad for Central Girder under Strength Limit State (USD) : i) Structural Design of Compression Reinforcement as Short Column : a) Surface Area of RCC Pad under Elastomeric Bearing Pad = LB-Plate *WB-Plate

AC

b) Vertical Concentrated Load upon the Elastomeric Bearing Pad PUSD is the Ultimate Load for Design. Thus PUSD = PU

PU

c) Steel Area Required for Compressive Member = (PU - 0.85f/cAC)/fy

2 120000.000 mm

1,149.477 kN 1149.477*10^3 N

AS-req

2 (2,420.787) mm

d) The (-) ve value of As-req indicates that No Compression Reinforcement is require for RCC Pad. But for Safe Guard of RCC Pads the under Mentioned Reinforcements are being Proposed to Provide. e) Let Provide 12f Bars as Reinforcement for RCC Pad on all Faces

DBar

f) Cross-sional Ares of 12f Bar = pDBar-Comp2/4

Af-12

g) Let Provide the Vertical Bars on Width Faces (Transverse to Traffic) of RCC Pad having Spacing 100 mm C/C. h) Number of Vertical Bars reqired on Width Face of RCC Pad = (WPad -2*CCov-V)/sW-Pad-pro-V + 1

sW-Pad-pro-V

12 mm 2 113.097 mm

100 mm C/C

NBar-W-req

9.800 nos

i) Let Provide 8 nos. Vertical Bars on Each Width Face of RCC Pad

NBar-W-V-pro

10 nos.

j) Let Provide 2 (Two) Rows of Vertical Bars on Length Faces (Parallel to Traffic) of RCC Pad having Spacing 100 mm C/C.

sL-Pad-pro-V

100 mm C/C

k) Number of Compression Bars reqired on Length Face of RCC Pad on Eacg Row = (LPad -2*CCov-V)/sL-Pad-pro-V+ 1

NBar-L-req

4.500 nos

l) Let Provide 5 nos. Bars on Length Face of RCC Pad for Each Row

NBar-L-Face-1Set-pro

5 nos.

ii) Arrangement of Tie Reinforcement : a) According to ACI Code against 12f Compression Bars the Tie Reinforcement will of 10f Bars.

DBar-Tie

10 mm

b) Under same Code. Spacing of Tie Reinforcement with of 10f Bars will be the Lesser value of 16 times of Main Bar Diameter or 48 times of Tie Bar Diameter or the Least Dimension of Compressive Member. c) 16 times of Main Bar Diameter = 16*DBar-Comp

sMain

192 mm

d) 48 times of Tie Bar Diameter = 48*DBar-Tie

sTie

480 mm

sDimn

500 mm

e) Least Dimension of RCC Pad = LPad f) Let Provide 100 mm C/C Spacing for 10f Tie Bars .

sTie-pro

100 mm C/C

iii) Arrangement of Reinforcement on Top Surface of of RCC Bearing Pad : a) Alternate Compression Bars from Inner Row of Length Faces would be bend Horizontally and will Continue up to the Outer Row on Opposite Face. b) Each Compression Bar of Outer Row on Length Faces would Continue up to Guide Wall Top & then after those will Turned Downward to Continue through Inner Row Position to Enter inside of the Horizontal Face of RCC Pad. c) Each Compression Bar on Width Face will Bend Horizontally to Continue up to opposite Face and again those will Bend Downward to become the Compression Bar for that Face. 6 Structural Design of RCC Bearing Pad for Central Girder under Service Limit State (WSD) : a) Under Service Limit State or WSD the Applied Load upon Bearing Pad is Expressed by P = fc Ac + fsAs; where, b) P is th Applied Concentrated load upon Bearing Pad = PWSD

P

694.340 kN

/ c) fc is Concrete Allowable Strength under Service Limit State (WSD) = 0.40f c

fc

8.400

MPa

d) fs is Steel Allowable Strength under Service Limit State (WSD) = 0.40fy

fs

164.000

MPa

e) Ac is Area of RCC Pad under Elastomeric Bearing Pad = LB-Plate *WB-Plate

AC

2 120000.000 mm

f) As is Total Cpompresive Steel Area Required for RCC Pad against Applied Load = (P - Acfc)/fs

AS

2 (1,912.56) mm

g) The (-) ve value of As-req indicates that No Compression Reinforcement is require for RCC Pad. But for Safety of Pads Reinforcements are being Proposed under to Provide as mentioned on Strength Limit State (USD) Section. 5 Checking for Shear of RCC Bearing Pad according to Article AASHTO-LRFD-5.7.5 : i) Provisions of Article AASHTO-LRFD-5.7.5 :

a) Sketch Diagram of RCC Bearing Pad:Elastomeric Bearing Pad 150 mm

150 mm Girder

115mm 530 mm 930 mm W=

930 mm

b) The Factored Bearing Resistance of Bearing Device Pr = fPn; in which, (Equ.-5.7.5-1).

Pr

3,855.600 kN 3855.600*10^3 N

c) Pn = 0.85f/cA1m is Nominal Bearing Resistance in N, (Equ.-5.7.5-2).

Pn

4,284.000 kN 4284.000*10^3 N

d) f is Multipluing Factor for Shear

f

0.900

e) A1 is Area under Bearing Device in mm2 = AC

A1

2 120000.000 mm

f) m is a Modification Factor related to Area A2 i) If the Supporting Surface is Wider than the Loaded or Bearing Device Area m = (A2/A1)  2.00 (The Present Case Wider Loaded Area with Uniformly Distributed Load).(Equ.-5.7.5-3). ii) If the loaded Area is subject to Non-uniformly Distributed Load in that Case m = 0.75 (A2/A1)  1.50 (Equ.-5.7.5-4).

m

2.000

m-1

2.784

m-2

2 g) A2 is Notational Area in mm within RCC Pad & Abutment = W*bAb-Cap

h) Relation between Applied Factored (USD) Load upon Bearing Pad PU & Computed Factored Bearing Resistance Pr.& whether the Provisions of Equation.-5.7.5-3 have Satisfied or Not. i) Since all required Provisions are being Satisfied, thus the Design of RCC Pad is OK.

A2

>2.00

NA

2 930000.000 mm

Pu L/2. d) L is the Span Length (C/C Distance between Bearings/Supports) = SL

L

e) Ma is Moment for the respective Load under Service Limit Staete of Design (WSD)

Ma

f) Modulus of Elasticity of Concrete,

Ec

24.400 m N-mm 23,855.620

MPa

g) Ie is the Effective Moment of Inertia of Girder Crack Section under Service Limit State of Design (WSD).

4 0.269 mm

Ie

7 Calculation of Factored Dead Loads (DL) & Live Loads (LL) on Intermediate Girder under Service Limit State : i) Sketch Diagram Showing Different Loads (DL & LL) on Intermediate Girder Under Service Limit State: X-Girder-1 17.053 kN 6.100

X-Girder-2 17.053 kN m 6.100 X-Gir-3 =

0.300 m

X-Gir-2 =

6.100

CL of Bearing

L /2 = X-Rear = X-Mid. = X-Front =

12.200

X-Girder-3 17.053 kN m 6.100

X-Girder-4 17.053 kN m 6.100

X-Girder-5 17.053 kN m

m

m 108.750 kN 0.728 108.750 kN 12.200 m 8.628 m 12.928 m 17.228 m

0.300 m

c.g. of Wheels. CL of Bearing Rear Wheel under c.g Provisions. Midd. Wheel under c.g Provisions. Front Wheel under c.g Provisions. 26.250 kN

m

A

 FDLInt = 28.7100kN/m  FLLInt. = 6.200kN/m

CL of Girder

B  FDLint-All =  FLLint-Lane-Ped =

LSpan =

24.400 m

LTotal =

25.000 m

28.710 kN/m

6.200 kN/m

ii) Dead Loads on 1 no. Interior Girder from Different Components & Attachments : a) Uniformly Distributed Dead Load (DL) on.Interior Girder due to Self Wt. & Attachments (Without WC & Utilies) for per meter Length of Girder.

DLIntt-Gir-Self

25.260

kN/m

b) Uniformly Distributed Dead Load (DL)on Interior Girder from WC. for per meter Length of Girder

DLInt-Gir-WC.

3.450

kN/m

c) Concentrated Dead Load on Interior Girder from to 1 no. Cross Girder

DLInt-X-Gir.

17.053

kN

d) Sumation of Uniformly Distributed Dead Loads on Interior Girder (a + b) for

DL-Int.UD

28.710

kN/m

iii) Live Loads (LL) on 1 no. Interior Girder due to Wheel Load & Lane Load according to Provisions of AASHTO-LRFD-3.6.1.2.2, 3.6.1.2.4 & 3.6.1.6 : a) Concentrated Live Load (LL) on 1 no.Interior Girder from Front Wheel

LLInt-Wheel-Front.

26.250

kN

b) Concentrated Live Load (LL) on 1 no.Interior Girder from Mid. Wheel

LLInt-Wheel-Mid.

108.750

kN

c) Concentrated Live Load (LL) on 1 no.Interior Girder from Rear Wheel d) Uniformly Distributed Live Lane Load (LL) on 1 no. Interior Girder

LLInt-Wheel-Rear.

108.750

kN

LLInt-Lane.

6.200

kN/m

iv) Factored Dead Loads on 1 no. Interior Girder from Different Components & Attachments : a) Factored Dead Load (DL)on Interior Girder due to Self Wt.& Attachments (Without WC) for per Meter Length = gDC*DLInt-Gir-Self

FDLIntt-Gir-Self

25.260

kN/m

b) Factored Dead Load (DL) on Interior Girder due to WC. & Utilities for per Merter Length = gDW*DLInt.-Gir-WC

FDLInt-Gir-WC+ Utility.

3.450

kN/m

FDLInt-X-Gir.

17.053

kN

FDL-Int.UD-DL

28.710

kN/m

a) Factored Concentrated Live Load (LL) on 1 no.Interior Girder from Front Wheel = mgLL-Truck*LLInt-Wheel-Front

FLLInt-Wheel-Front.

26.250

kN

b) Factored Concentrated Live Load (LL) on 1 no.Interior Girder from Middle Wheel = mgLL-Truck*IM*LLInt-Wheel-Mid

FLLInt-Wheel-Mid.

108.750

kN

c) Factored Concentrated Live Load (LL) on 1 no.Interior Girder from Rear Wheel = mgLL-Truck*IM*LLInt-Wheel-Rear

FLLInt-Wheel-Rear

108.750

kN

FLLInt-Lane.

6.200

kN/m

c) Factored Concentrated Dead Load (DL) on Interior Girder from to 1 no. Cross Girder = gDC*DLInt-X-Gir. d) Sumation of Factored Uniformly Distributed Dead Loads (DL) on Interior Girder (a + b) for per Meter Length of Girder. v) Factored Live Loads of Different Components for 1 no. Interior Girder :

d) Factored Uniformly Distributed Live Lane Load (LL) on 1 no. Interior Girder = mgLL-Lane*LLInt-Lane

8 Calculation of Moments due to Factored Loads (DL & LL) at Mid Span of Intermediate Girder : i) Moment due to Uniformly Distributed Loads (DL & LL) on Interior Girder : a) Moments due to Uniformely Distributed Factored Dead Loads (DL) = FDL-Int.UD-DL*L2/8

MUD-DL.

2,136.598

kN-m

b) Moments due to Uniformely Distributed Factored Live Lane Loads (LL) = FLLInt.Lane*L2/8

MUD-LL.

461.404

kN-m

ii) Moment due to Concentrated Loads (DL & LL) on Interior Girder : a) Moments due to Factored Concentrated Dead Loads (DL) for 1st & 5th Cross Girder = FDLInt.X-Gir.*L/2 - FDLInt.X-Gir.*L/2

MCDL-X-1&5.

0.000 kN-m

b) Moments due to Factored Concentrated Dead Loads (DL) for 2nd & 4th Cross Girder (Case for X < L/2) = FDLInt.X-Gir.*X-Gir-2 /2

MCDL-X-2&4.

52.011

kN-m

c) Moments due to Factored Concentrated Dead Loads (DL) for 3rd Cross Girder (Case for X = L/2) = FDLInt.X-Gir.*X-Gir-3 /4

MCDL-X-3.

52.011

kN-m

d) Moments due to Factored Concentrated Wheel Live Load (LL) for Front Wheel (Case for X > L/2) = FLLInt-Wheel-Front.*(L - X-Front)/2

MCLL-W-Front.

94.137

kN-m

e) Moments due to Factored Concentrated Wheel Live Load (LL) for Mid Wheel (Case for X > L/2) = FLLInt-Wheel-Mid.*(X-Mid)/2

MCLL-W-Mid.

702.943

kN-m

f) Moments due to Factored Concentrated Wheel Live Load (LL) for Rear Wheel (Case for X < L/2) = FLLInt-Wheel-Rear.*(X-Rear)/2

MCLL-W-Rear.

469.131

kN-m

9 Values of Deflection Coefficient 'K' for Different Applied Loads to Compute the respective Deflections at Mid Span of Intermediate Girder : a) Deflection Coefficient for Uniformly Distributed Load (DL & LL), the value = 5/48 (Applicable for Dead Loads of Main Girder, Slab, W-Course & Lane Live Load). b) Deflection Coefficient for Concentrated Load (DL) for 1st & 5th Cross Girders having Position at Support Position the value = 0.

KUD-DL&LL

KCL-DL-1&5-X-Gir-Supp

0.104

0.000

c) Deflection Coefficient for Concentrated Dead Load (DL) for 2nd & 4th KCL-DL2&4-X-Gir(XL/2)

0.101

f) Deflection Coefficient for Concentrated Live Load (LL) for Middle KCL-LL-Wheel-Mid-(X L/2, the value of K = ((L-X)*(3L2 - 4(L - X)2) + (L - 2X)3)/(24(L-X)L2).

0.088

g) Deflection Coefficient for Concentrated Live Load (LL) for Rear KCL-LL-Wheel-Rear-(X L/2, the value of K = ((L-X)*(3L2 - 4(L - X)2) + (L - 2X)3)/(24(L-X)L2);

10 Moment of Inertia of Different Component Sections Related to Flexural Design under AASHTO-LRFD : i) Events related to Flexural Design of Interior Girder against Max. Moment under Service Limit State : a) Provided Steel Area at Mid Span against Max. (+) ve. Moment

As-pro.

2 14,476.459 mm

b) Effective Depth of Provided Tensial Reinforcement

dpro.

c) Depth of Neutral Axis from Top of Extreme Compression Face = kdpro

1,808.222 mm

dComp.

525.573 mm

d) Depth of Tensial Bar Centriod from Neutral Axis = dpro - kd

dTen

1,282.649 mm

e) Diameter of Provided Main Tensial Reinforcement Bars

DBar

32.000 mm

f) Number of Provided Main Tensial Reinforcement Bars

NBar

18.000 nos.

g) Number of Layers for Provided Main Tensial Reinforcement Bars

NLayer

5.000 nos.

h) Total Height of 5 Layers 32f Steel Bars if placed without Spacing = NLayer*DBar

hSteel

160.000 mm 0.160 m

h) Transformed Steel Area as Equivalent Concrete Area Provided for Tensile Reinforcement = nAs-pro

As-Trans.

i) Width of Transformed Steel Area as Equivalent Concrete Area = As-Trans./hSteel

2 115,811.672 mm 2 0.115811672 m

bSteel

723.823 mm 0.724 m

ii) Calculations for Moment of Inertia of Main T-Girder Section about its Natural Axis for Un-crack Section : a) Sketch Diagram of T-Girder Section : bFln = hFln =

0.200

2.000

m

m

dNeut-Axis dFln = 0.612

hWeb/2 =

0.900

0.712

m

hGir = dWeb = 0.388

bWeb =

0.350

m

m 2.000 m

m

m

b) Flange Width of T-Girder

bFln.

2.000 m

c) Flange Height of T-Girder.

hFln.

0.200 m

d) Depth of T-Girder.

hGir.

2.000 m

e) Width of T-Girder Web

bWeb.

0.350 m

f) Distance of T-Girder Neutral Axis from Flange Top, dNeut-Gir. = (bFal*hFln.*hFln./2+bWeb.*(hGir.-hFln.)*((hGir-hFln.)/2+hFln))/ (bFln.*hFln.+bWeb*(hGir-hFln.))

dNeut-Gir

0.712 m

g) Distance between Neutral Axis of T-Girder & Neutral Axis of Flange Portion = dNeut-Axis - hFln./2

dFln.

0.612 m

h) Distance between Neutral Axis of Web Portion & Neutral Axis of T-Girder = ((hGir.- hFln.)/2+ hFln.)-dNeut-Axis

dWeb.

0.388 m

i) Moment of Inertia of Flange Portion about its Neutral Axis, IFln. = bFln.*hFln.3/12

IFln.

4 0.001 m

j) Moment of Inertia of Web Portion about its Neutral Axis, IWeb. = bWeb.*(hWeb - hFln.)3/12

IWeb.

4 0.170 m

IFln.-Neut.

4 0.151 m

IWeb.-Neut.

4 0.265 m

m) Moment of Inertia of T-Girder about its Neutral Axis, = IFln.-Neut. + IWeb.-Neut.

IT-Gir.

4 0.416 m

n) Gross Moment of Inertia for (Un-cracke) under Service Limit State = IT-Gir.

Ig.

k) Moment of Inertia of Flange Portion about T-Girder Neutral Axis, IFln.-Neut = IFln. + bFln.*hFln.*dFln.2 l) Moment of Inertia of Web Portion about T-Girder Neutral Axis, IWeb.-Neut = IWeb. + bWeb.*(hWeb-hFln.)*dWeb.2

4 0.416 m 4 4.161E+11 mm

iii) Calculations for Moment of Inertia of T-Girder Crack Section about Natural Axis of Section : a) Sketch Diagram of T-Girder Crack Section : bFln = hFln =

2.000

m

0.200 m dWeb = 0.326

m

dFln. =

dpro = 1.808

m

dTen = 1.283 m hGir = 2.000

b) Flange Width of T-Girder

As-Trans. =

2 0.116 m

bWeb =

0.350 m

0.426

kd =

0.526 yt =

m 1.474 m

m

bFln.

2.000 m

c) Flange Height of T-Girder.

hFln.

0.200 m

kd

0.526 m

e) Width of T-Girder Web

bWeb.

0.350 m

f) Distance between Neutral Axis of Crack Section & Neutral Axis of Flange Portion = kd - hFln./2

dFln.

0.426 m

g) Depth of Un-crack Web Portion of T-Girder = (kd.- hFln.)

dWeb.

0.326 m

h) Distance between Neutral Axis of Crack Section & Centroid of Tensile Reinforcement = dpro - kd

dTen.

1.283 m

IFln.-Self

4 0.001 m

IWeb.

4 0.004 m

IFln.-Neut.

4 0.074 m

m) Moment of Inertia of Un-crack Portion of T-Girder about Neutral Axis of Crack Section IUn-Crack = IFln.-Neut. + IWeb.

IUn-Crack

4 0.078 m

n) Moment of Inertia of Transformed Tensial Steel Area as Equivalent Concrete Area about Neutral Axis of Crack Section, = As-Trans.*dTen2

ISteel-Trans

4 0.191 m

d) Depth of T-Girder Crack Section (Distance from Extreme Compression Fiber up to Flexural Neutral Axis of the Section).

i) Moment of Inertia of Flange Portion about its Neutral Axis, IFln.-Self = bFln.*hFln.3/12 j) Moment of Inertia of Uncrack Web Portion about Neutral Axis of Crack Section IWeb.-Self =bWeb.*(kd - hFln.)3/3 k) Moment of Inertia of Flange Portion about T-Girder Neutral Axis, IFln.-Neut = IFln.-Self+ bFln.*hFln.*dFln.2

o) Moment of Inertia for Crack Section under Service Limit State = IUn-Crack + ISteel-Trans.

Icr

4 0.268 m 4 2.683E+11 mm

iv) Instantinous Deflection at Mid Span due to Applied Uniformly Distributed Dead Loads upon Interior Girder: a) EcIe is Flexural Regidity of the Component as mentioned

EcIe

6 8.853E-08 N/mm 4 2.695E+11 mm IeL/2)MCLL-W-Mid.L2/EcIe.

DInst-CLL-W-Mid.

5.725

mm

f) Deflection due to Factored Concentrated Wheel Live Load (LL) for Rear Wheel = KCL-LL-Wheel-Rear(X5 0.33

p) Calculated value of g for Different Rectangular Sections of T-Girder in respect of y/x Ratio is Shown in Table below : Notation of Notation of g Factor Long Arm

Value of Long Arm m

Notation of Short Arm

Value of Short Arm m

Value of Ratio y/x

Value of g

g1

hGir

2.000

bWeb

0.350

5.714

0.290

g2

(bFln-bWeb)/2

0.825

hFln

0.200

4.125

0.290

g3

(bFln-bWeb)/2

0.825

hFln

0.200

4.125

0.290

iii) Calculation of Rotation at Support Position Under Strength Limit State (USD) for Main Girder : a) Roational Angle at Support, q = (40J/A4)*((MTL/2)/N); where,

q

b) J is Torsional Constant Relate to Moment of Inertia & RCC T-Girder Section.

J

c) A is Total Area of RCC T-Girder Section = bFln*hFln +(hGir - hFln)*bWeb

A

d) MT is Tortional Moment at Support Position under Strength Limit State (USD )

MT-USD

2.449E-15 radian 0.021 2 1.030 m 2 1030000.000 mm

430.383 kN-m 397.168*10^6 N-mm

e) L is Span Length of Girder ( C/C Distance between Support Points) = SL

L

24.400 24,400.000

m mmy

f) N is Modulus of Regidity or Shear Modulus of Elesticity of Support Section = Shear Stress/Shear Strain.

N

1,596.325

Mpa

g) under Strength Limit State (USD) Total Torsional Forces at Support, VT = VSupp. the Calculated Total Shearing Forces at Support. h) Based on the assumption of Torsional Forces (DL & LL) action Positions, the Eccentricity or Torsional Moment Arm, eTor. = b/4 from Center of Girder. i) Tortional Moment MT = VT*eTor

VT-USD

860.766 kN

eTor.

0.500 m 500.000 mm

MT-USD

430.383 kN-m

j) Calculated Shear Stress for Support Section = vSupp

vSupp

2 1.596 N/mm

k) Calculated Shear Strain for Support Section = eSupp.

eSupp.

0.001 mm/mm

l) N is Modulus of Regidity or Shear Modulus of Elesticity of Support Section = Shear Stress/Shear Strain = vSupp/eSupp m) For T-Girder Section the value of J is Expressed by the Equation J = g1*bWeb3*hGir + g2*hFln3(bFln - bWeb)/2 + g3*hFln3(bFln - bWeb)/2; Here,

N

2 1,596.325 N/mm

J

0.021

iv) Calculation of Rotation at Support Position Under Service Limit State (WSD) for Main Girder : a) Roational Angle at Support, q = (40J/A4)*((MTL/2)/N); where,

q

b) J is Torsional Constant Relate to Moment of Inertia & RCC T-Girder Section.

J

c) A is Total Area of RCC T-Girder Section = bFln*hFln +(hGir - hFln)*bWeb

A

d) MT is Tortional Moment at Support Position of Girder

MT

1.588E-15 radian 0.021 2 1.030 m 2 1030000.000 mm

279.032 kN-m 320.596*10^6 N-mm

e) L is Span Length of Girder ( C/C Distance between Support Points) = SL

L

24.400 24,400.000

m mmy

f) N is Modulus of Regidity or Shear Modulus of Elesticity of Support Section = Shear Stress/Shear Strain.

N

1,596.325

Mpa

g) Under Service Limit State the Total Torsional Forces at Support, VT = VSupp. the Calculated Total Shearing Forces at Support.

VT

558.064 kN

eTor.

0.500 m 500.000 mm

MT

279.032 kN-m

h) Based on the assumption of Torsional Forces (DL & LL) action Positions, the Eccentricity or Torsional Moment Arm, eTor. = b/4 from Center of Girder. i) Tortional Moment MT = VT*eTor j) Calculated Shear Stress for Support Section = vSupp

vSupp

2 1.596 N/mm

k) Calculated Shear Strain for Support Section = eSupp.

eSupp.

0.001 mm/mm

l) N is Modulus of Regidity or Shear Modulus of Elesticity of Support Section = Shear Stress/Shear Strain = vSupp/eSupp m) For T-Girder Section the value of J is Expressed by the Equation J = g1*bWeb3*hGir + g2*hFln3(bFln - bWeb)/2 + g3*hFln3(bFln - bWeb)/2; Here,

N

J

2 1,596.325 N/mm

0.021

v) Calculation of Rotation at Support Position due to Live Loads only Under Service Limit State (WSD) :

a) Roational Angle at Support, q = (40J/A4)*((MTL/2)/N); where,

q

b) J is Torsional Constant Relate to Moment of Inertia & RCC T-Girder Section.

J

c) A is Total Area of RCC T-Girder Section = bFln*hFln +(hGir - hFln)*bWeb

A

d) MT is Tortional Moment at Support Position of Girder

MT

1.588E-15 radian 0.021 2 1.030 m 2 1030000.000 mm

279.032 kN-m 397.168*10^6 N-mm

e) L is Span Length of Girder ( C/C Distance between Support Points) = SL

L

24.400 24,400.000

m mmy

f) N is Modulus of Regidity or Shear Modulus of Elesticity of Support Section = Shear Stress/Shear Strain.

N

1,596.325

Mpa

g) Under Service Limit State the Total Torsional Forces at Support, VT = VSupp. the Calculated Total Shearing Forces at Support.

VT

558.064 kN

eTor.

0.500 m 500.000 mm

MT

279.032 kN-m

h) Based on the assumption of Torsional Forces (DL & LL) action Positions, the Eccentricity or Torsional Moment Arm, eTor. = b/4 from Center of Girder. i) Tortional Moment MT = VT*eTor j) Calculated Shear Stress for Support Section = vSupp

vSupp

2 1.596 N/mm

k) Calculated Shear Strain for Support Section = eSupp.

eSupp.

0.001 mm/mm

l) N is Modulus of Regidity or Shear Modulus of Elesticity of Support Section = Shear Stress/Shear Strain = vSupp/eSupp m) For T-Girder Section the value of J is Expressed by the Equation J = g1*bWeb3*hGir + g2*hFln3(bFln - bWeb)/2 + g3*hFln3(bFln - bWeb)/2; Here,

N

2 1,596.325 N/mm

J

1,596.325

15 Calculation of Instantaneous Deflections at Mid Span of Cross Girders against Applied Forces : (In Computation of Rotations of Interior Girders the Provisions of Book " Concrete Bridge Practice, Analysis, Design And Economics; by Dr. V. K. Raina, Chapter-20, Practical Structural Analysis, Table-20.5; for Moment; Shear; Deflection; Special Cases are being Followed. Necessary Modifications are being made to introduce Moment in Place of Load for Particular Cases. AASHTO-LRFD Service Limit State of Design (WSD) are being followed in Calculation Loads both for Dead & Live Loads.) i) Dimensional Data of Cross-Girder : a) Span Length of Cross-Girder (Clear distance between Main Girder Faces) b) Thickness of Deck Slab c) Thickness of Wearing Course

SL-X-Gir. tSlab. tWC

1.650 0.200 0.075

m m m

d) e) f) g) h) i) j) k)

Number of Cross Girders Depth of Cross Girders (Including Slab as T-Girder) Width of Cross-Girder Web Width of Main-Girder Web C/C Distance Between Main Girders Flenge Width of Cross-Girder C/C Distance in between Cross-Girders in Longitudinal Direction Filets : i) X-Girder in Vertical Direction ii) X-Girder in Horizontal Direction

NX-Gir. hX-Gir. bX-Web. bMain-Web. C/CD-Gir. bFln-X-Gir. CD-X-Gir. FX-Gir-V. FX-Gir-H.

5.000 nos 1.900 m 0.250 m 0.350 m 2.000 m 0.413 m 6.250 m 0.075 m 0.075 m

a) Dead Load due Self Weight (Excluding Slab & W/C but including Fillets) in kN for per Meter Span Length = wc*((hX-Gir - tSlab)*bX-Web + 2*0.5*FX-Gir-V*FX-Gir-H)

DLX-Gir-Self

10.335 kN/m

b) Dead Load from Slab (Within Flange Width) in kN for per Meter Span Length = gc*bFln-X-Gir.*tSlab

DLX-Gir-Slab.

1.980 kN/m

c) Dead Load from Wearing Course (Within Flange Width) in kN for per Meter Span Length = gWC*bFln-X-Gir.*tWC

DLX-Gir-WC.

0.557 kN/m

ii) Computation of Daed Loads on Cross-Girders :

d) Summation of Dead Loads of Cross-Girder for per meter Length

DLX-Gir.

12.872

kN/m

iii) Computation of Live Loads on Cross-Girders : a) Concentrated Live Load Reaction due to Rear/Middle Single Wheel from Truck in kN = LLRSW-Load or LLMSW-Load b) Uniformly Distributed Live Load due to Loan Load Reaction in kN per Meter Span Length = LLLane/3*bFln-X-Gir.

LLX-Gir.-Wheel.

LLX-Gir-Lane.

72.500 kN

1.279 kN/m

iv) Factored Dead Load for per meter Length of Cross-Girder under Service Limit State (WSD): a) Factored Dead Load of Cross-Girder due to Self & Slab in kN/m = gDC*(DLX-Gir-Self + DLX-GirSlab)

FDLX-Gir+Slab.

12.315

kN/m

FDLX-Gir-WC

0.557

kN/m

FDLX-Gir.

12.872

kN/m

a) Factored LL of Cross-Girder due to Wheel Load in kN; = mgLL-Truck*IM*LLX-Gir-Wheel

FLLX-Gir.-Wheel.

72.500

kN

b) Factored LL of Cross-Girder due to Lane Load in kN/m

FLLX-Gir-Lane.

1.279

b) Factored Dead Load of Cross-Girder due to Wearing Course in kN/m = gDW*DLX-Gir-WC c) Summation of Factored DL of Cross-Girder for per meter Length vii) Factored Live Loads of Cross-Girder under Service Limit State (WSD):

kN/m

= mgLL-Lane*LLX-Gir-Lane. viii) Calculation of Factored Moments at Mid Span of Cross-Girder due to Applied Loads (DL & LL) : a) Span Length of Cross-Girder (Distance between Main Girder Faces) = SL-X-Gir. a) Moment due to Dead Loads (DL) under Service Limit State (WSD) = FDLX-Gir.*(LX-Gir.)2/16

LX-Gir.

1.650

m

MX-Gir.-DL

2.190 kM-m

MX-Lane-LL.

0.218 kM-m

c) Moment due to Factored Wheel Load (LL) at Middle of Cross-Girder in kN; under Service Limit State (WSD) = FLLX-Gir.-Wheel.*(L-X-Gir.)2/16

MX-Wheel-LL.

12.34 kM-m

d) Total Factored Moment at Middle of Cross-Girder in kN; due all Applied Loads (DL + LL )under Service Limit State (WSD) = MX-Gir.-DL+MX-Lane-LL.+ MX-Wheel-LL

MTotal-X-Mid.

14.744 kM-m

b) Moment due to Factored Live Lane Load (LL) at Middle of Cross-Girder in kN; under Service Limit State (WSD) = FLLX-Gir.-Wheel.*(LX-Gir.)2/16

viii) Events related to Flexural Design of Cross Girder against Max. Moment under Service Limit State : a) Provided Steel Area at Mid Span against Max. (+) ve. Moment b) Effective Depth of Provided Tensial Reinforcement

As-pro.

2 474,737.910 mm

dpro.

10.000 mm

dComp.

2.907 mm

d) Depth of Tensial Bar Centriod from Neutral Axis = dpro - kd

dTen

7.093 mm

e) Diameter of Provided Main Tensial Reinforcement Bars

DBar

20.000 mm

f) Number of Provided Main Tensial Reinforcement Bars

NBar

4.000 nos.

g) Number of Layers for Provided Main Tensial Reinforcement Bars

NLayer

1.000 nos.

h) Total Height of 1 Layers 20f Steel Bars if placed without Spacing = NLayer*DBar

hSteel

20.000 mm 0.020 m

c) Depth of Neutral Axis from Top of Extreme Compression Face = kdpro

h) Transformed Steel Area as Equivalent Concrete Area Provided for Tensile Reinforcement = nAs-pro

As-Trans.

2 ########## mm 2 3.798 m

ix) Deflection Coefficient 'K' for Different Applied Loads to Compute the Deflections at Mid Span of cross Girder : a) Since Cross-Girders have both Fixed Ends, thus value of Deflection Coefficient K accordingly. b) Deflection Coefficient for Uniformly Distributed Load (DL & LL), the value KUD-DL&LL = 16/384 (Applicable for Dead Loads of X-Girder, Slab, W-Course & Lane Live Load).

0.042

c) Deflection Coefficient for Concentrated Live Load (LL) at Mid Span of Cross Girder having value = 8/192

KCL-LL-Mid

0.042

x) Calculations for Moment of Inertia of Cross T-Girder Section about its Natural Axis for Un-crack Section : a) Sketch Diagram of Cross-Girder Section : bX-Fln = hFln =

0.200

m

hX-Web/2 =

0.850

m

0.413

m dNeut-Axis

dFln = 0.796

0.896

m

m hX-Gir =

1.900 m

b) Flange Width of Cross-Girder

bX-Fln.

0.413 m

c) Flange Height of Cross-Girder.

hFln.

0.200 m

d) Depth of Cross-Girder.

hX-Gir.

1.900 m

e) Width of Cross-Girder Web

bWeb.

0.250 m

dNeut-Axis

0.896 m

g) Distance between Neutral Axis of Cross-Girder & Neutral Axis of Flange Portion = dNeut-Axis - hFln./2

dFln.

0.796 m

h) Distance between Neutral Axis of Web Portion & Neutral Axis of Cross-Girder = ((hX-Gir.- hFln.)/2+ hFln.)-dNeut-Axis

dWeb.

0.154 m

i) Moment of Inertia of Flange Portion about its Neutral Axis, IFln. = bFln.*hFln.3/12

IFln.

4 0.000 m

j) Moment of Inertia of Web Portion about its Neutral Axis, IWeb. = bX-Web.*(hX-Gir - hFln.)3/12

IWeb.

4 0.102 m

IFln.-Neut.

4 0.052 m

dWeb = 0.154

bX-Web =

0.250

m

m

f) Distance of Cross-Girder Neutral Axis from Flange Top, dNeut-Gir. = (bX-Fal*hFln.*hFln./2+bX-Web.*(hX-Gir.-hFln.)*((hX-Gir-hFln.)/2+hFln))/ (bX-Fln.*hFln.+bX-Web*(hX-Gir-hFln.))

k) Moment of Inertia of Flange Portion about Cross-Girder Neutral Axis, IFln.-Neut = IFln. + bX-Fln.*hFln.*dFln.2

l) Moment of Inertia of Web Portion about Cross-Girder Neutral Axis, IWeb.-Neut = IWeb. + bX-Web.*(hWeb-hFln.)*dWeb.2

IWeb.-Neut.

4 0.112 m

IX-Gir.

4 0.165 m

m) Moment of Inertia of Cross-Girder about its Neutral Axis = IX-Fln.-Neut.+ IX-Web.-Neut. n) Gross Moment of Inertia for (Un-cracke) under Service Limit State = IX-Gir.

4 0.165 m 4 1.650E+11 mm

Ig-X.

xi) Calculations for Moment of Inertia of Cross-Girder Crack Section about Natural Axis of Section : a) Sketch Diagram of Cross-Girder Crack Section : bFln = hFln =

0.200 m dWeb = -0.197 dpro = 0.010

0.413

m

dFln. =

m

dTen = 0.001 m hGir = 1.900

As-Trans. =

2 3.798 m

bWeb =

0.250 m

(0.097)

kd =

m

0.003 yt =

m 1.897 m

m

b) Flange Width of Cross-Girder

bFln.

0.413 m

c) Flange Height of Cross-Girder.

hFln.

0.200 m

kd

0.003 m

e) Width of Cross-Girder Web

bWeb.

0.250 m

f) Distance between Neutral Axis of Crack Section & Neutral Axis of Flange Portion = kd - hFln./2

dFln.

(0.097) m

g) Depth of Un-crack Web Portion of Cross-Girder = (kd.- hFln.)

dWeb.

(0.197) m

h) Distance between Neutral Axis of Crack Section & Centroid of Tensile Reinforcement = dpro - kd

dTen.

0.007 m

IFln.-Self

4 0.000 m

d) Depth of T-Girder Crack Section (Distance from Extreme Compression Fiber up to Flexural Neutral Axis of the Section).

i) Moment of Inertia of Flange Portion about its Neutral Axis, IFln.-Self = bFln.*hFln.3/12

j) Moment of Inertia of Uncrack Web Portion about Neutral Axis of Crack Section IWeb.-Self =bWeb.*(kd - hFln.)3/3 k) Moment of Inertia of Flange Portion about T-Girder Neutral Axis, IFln.-Neut = IFln.-Self+ bFln.*hFln.*dFln.2

IWeb.

4 (0.001) m

IFln.-Neut.

4 0.001 m

m) Moment of Inertia of Un-crack Portion of Cross-Girder about Neutral Axis of Crack IUn-Crack Section IUn-Crack = IFln.-Neut. + IWeb. n) Moment of Inertia of Transformed Tensial Steel Area as Equivalent Concrete Area about Neutral Axis of Crack Section, = As-Trans.*dTen2 o) Moment of Inertia for Crack Section under Service Limit State = IUn-Crack + ISteel-Trans.

ISteel-Trans

Icr-X

4 0.000 m

4 3.798E-06 m

4 0.000 m 4 4.185E+08 mm

xii) Instantinous Deflection at Mid Span due to Applied Uniformly Distributed Dead Loads upon Cross Girder: a) EcIe is Flexural Regidity of the Component as mentioned b) The Effective Moment of Inertia, Ie = (Mcr/Ma)3Ig + (1 - (Mcr/Ma)3)Icr  Ig in which;

EcIe Ie

6 1.282E-16 N/mm 4 8.126E+14 mm Ie>Ig

c) Ig-X is the Gross Moment of Inertia for Uncracked Section under Service Limit State in mm4

Ig-X

4 1.650E+11 mm

d) Icr is the Moment of Inertia of the Crack Section in mm4

Icr-X

4 4.185E+08 mm

d) Mcr is Crack Moment for the Section having value = fr(Ig/yt)

Mcr-X

2.5107E+08 N-mm 2 2.887 N/mm

e) fr is Modulus of Rupture of Concrte as per AASHTO-LRFD-5.4.2.6 in Mpa

fr

f) yt is the distance from the Neutral Axie to the Extrim Tension Fiber in mm = hGir -kd

yt

1897.093 mm

g) Ma is the Max. Moment on Component for the Section = MTotal-X-Mid.

Ma

14.744 kN-m 1.474E+07 N-mm

h) Since the the Calculated value of Effective Moment of Inertia, Ie > Ig-X the Gross Moment of Inertia, thus value of Ig-X Prevailes for Calculation Deflections of T-Girder. xiii) Instantinous Deflections due to Uniformly Distributed Loads (DL & LL) on Cross-Girder Mid Span : a) Deflection due to Uniformely Distributed Factored Dead Loads (DL) = KUD-DL&LLMX-Gir.-DL.(LX-Gir.)2/EcIg-X.

DInst-X-UDL-DL

6.271E-06 mm

b) Deflection due to Uniformely Distributed Factored Live Lane Loads (LL)

DInst-X-UDL-LL

3.556E-04 mm

= KUD-DL&LLMX-Lane-LL.(LX-Gir.)2/EcIg-X. c) Deflection due to Concentraded Factored Live Wheel Loads (LL) = KCL-LL-MidMX-Wheel-LL.(LX-Gir.)2/EcIg-X. d) Total Deflection at Mid Span of Cross Girder Due to all Applied Forces.

DInst-X-CL-LL

3.556E-04 mm

DInst-X-Total

0.001 mm

xix) Computation of Rotations at Support Position of Girder due to Different Applied Loads : a) Since the Cross-Girders have Rigid Fixed Ends, thus Rotation on their Support Position = 0.

a-X-Gir-DL+LL

0.000 Radian.

13 Calculation of Deformation due to Creep & Shrinkage under Provisions of AASHTO-LRFD-5.4.2.3 : i) Provisions of Deflections due of Creep & & Shrinkage for RCC Bridge Structures : a) In RCC Bridge Structure Calculation of Deformation under Creep & Shrinkage is not Essential Component, rather than that are Applicable for Prestressed Concrete Bridge Structures. In Calculation of Deformation/Deflections in Prestressed Concrete Bridge Structures Articles 5.9.5.3 & 5.9.5.4 in Conjunction with Article 5.7.3.6.2 are to be Considered. ii) Calculation of Creep Coefficient under AASHTO-LRFD-5.4.2.3-2: a) The Creep Coefficient is Expressed by Y(t*ti) = 3.5kckf(1.58 - H/120)*ti-0.118*(t - ti)0.6/(10.0 +(t - ti)0.6). Equation-5.4.2.3.2-1 in which, b) kf is Effect of Concrete Strength having value = 62/(42+f/c)

kf

c) H is Relative Humidity in percentage. Since Bridge is Located on Sea Shore, Let Consider Value of H = 90%

H

d) kc is a Factor for the Effect of the Volume to Surface Area Ratio of the Component as Mentioned in Figure-5.4.2.3.2-1. For (t -ts) = 1825 days, kc = 0.65 According to C-5.4.2.3.2 the Max. value of Ratio V/S is 150 mm. i) Calculated values of VGir/SArea. ii) Allowable Max. value of Ratio VGir/SArea. According to C-5.4.2.3.2

kc

0.65

V/S

150.000 mm 155.263 mm 150.000 mm

e) VGir is Volume of an Interior T-Girder = LGir*((hGir- tSlab)*bWeb + (tSlab + tWC)*bFln)

VGir.

f) SArea is the Surface Area of an Interior T-Girder and Calculations are being done Considering only Exposed Faces in Longitudinal Direction having value = LGir*(2*(hGir- tSlab) + bGir-Web + (bFln - bGir-Web) +bFln)

SArea.

0.984 90 %

3 29.500 m 2 190.000 m

g) t is the Maturity Period of Concrete in days. Since Bridge is Located very close to Sea Shore with Higher Intensity of Humidity, thus the Concrete will gain Maturity Earlier than other Areas. Considering the situation it is considered 5 years or 1825 days as Maturity Period of Concrete.

t

1825 days

h) ti is Age of Concrete when Initial Load is allowed for the Structure in days.

tf

28 days

Conventionally it is Considered Concrete gains full Strength within 28 days, thus it may also taken as Initial Load Time. i) f/c is Ultimate Compressive Strength of Concrete j) Creep Coefficient Y(t*ti) = 3.5kckf(1.58 - H/120)*ti-0.118*(t - ti)0.6/(10.0 +(t - ti)0.6).

f/c Y(t*ti)

21.000 Mpa 1.128

iii) Calculation of Shrinkage Strain under AASHTO-LRFD-5.4.2.3-3: a) For Moist Cured Concretes devoid of Shrinkage-prone Aggregates, the Strain due Shrinkage is Express by the Equation esk = -kskh *(t/(35.00 + t)*0.51*10-3,where, b) t is Drying Time in days for Curing Concrete after Casting having value = 28days.

t

c) ks is Size Factor Specified in Figure-5.4.2.3.3-2. For Ratio V/S = 150, ks = 0.10

ks

0.10

d) kh is Humidity Factor Specified in Table 5.4.2.3.3-1. For 80% of Humidity the value kh = 0.86

kh

0.86

e) Thus Strain due to Shrinkag esk = -kskh *(t/(35.00 + t)*0.51*10-3

esk

-1.385

28 days

m-Wd.

mm-Wd.

ept for

oncrete

with the

d Load,

s (DL)

2.3.2-1

uation

T. Design of Beam Ledges for Abutment : 1 Design Data in Respect of Unit Weight & Strength of Materials : Description

Notation Dimensions

Unit.

i) Unit Weight of Different Materials : 3 i) Unit Weight of Different Materials in kg/m : (Having value of Gravitional Acceleration, g =

a) b) c) d) e)

2 9.807 m/sec )

Unit weight of Normal Concrete Unit weight of Wearing Course Unit weight of Normal Water Unit weight of Saline Water Unit weight of Earth (Compected Clay/Sand/Silt)

gW-Nor. gW-Sali. gs

2,447.23 2,345.26 1,019.68 1,045.17 1,835.42

kg/m3 kg/m3 kg/m3 kg/m3 kg/m3

wc wWC wW-Nor. wW-Sali. wE

24.00 23.00 10.00 10.25 18.00

kN/m3 kN/m3 kN/m3 kN/m3 kN/m3

gc gWC

3 ii) Unit Weight of Materials in kN/m Related to Design Forces :

a) b) c) d) e)

Unit weight of Normal Concrete Unit weight of Wearing Course Unit weight of Normal Water Unit weight of Saline Water Unit weight of Earth (Compected Clay/Sand/Silt)

ii) Design Data for Resistance Factors for Conventional Construction (AASHTO LRFD-5.5.4.2.1). : (Respective Resistance Factors are mentioned as f or b value) a) b) c) d) e) f) g) h) i) j) k)

For Flexural & Tension in Reinforced Concrete For Flexural & Tension in Prestressed Concrete For Shear & Torsion of Normal Concrete For Axil Comression with Spirals or Ties & Seismic Zones at Extreme Limit State (Zone 3 & 4). For Bearing on Concrete For Compression in Strut-and-Tie Modeis For Compression in Anchorage Zones with Normal Concrete For Tension in Steel in Anchorage Zones For resistance during Pile Driving Value of b1 for Flexural Compression in Reinforced Concrete (AASHTO LRFD-5.7.2..2.) Value of b for Flexural Tension of Reinforcement in Concrete

fFlx-Rin. fFlx-Pres. fShear. fSpir/Tie/Seim. fBearig. fStrut&Tie. fAnc-Copm-Conc. fAnc-Ten-Steel. fPile-Resistanc. b1 b

0.90 1.00 0.90 0.75 0.70 0.70 0.80 1.00 1.00 0.85 0.85

iii) Strength Data related to Ultimate Strength Design( USD & AASHTO-LRFD-2004) : a) Concrete Ultimate Compressive Strength, f/c (Normal Concrete) b) Concrete Allowable Strength under Service Limit State (WSD) = 0.40f/c

f/c fc

21.000 8.400

MPa MPa

c) Modulus of Elasticity of Concrete, Ec = 0.043gc1.50f/c (AASHTO LRFD-5.4.2.4). d) Poisson's Ration = 0.63f/c = 0.63*21^(1/2), subject to cracking and considered to be neglected (AASHTO LRFD-5.4.2.5). e) Modulus of Rupture of Concrete, fr = 0.63f/c Mpa (AASHTO LRFD-5.4.2.6). f) Steel Ultimate strength, fy (60 Grade Steel) g) Steel Allowable Strength under Service Limit State (WSD) = 0.40fy h) Modulus of Elasticity of Reinforcement, Es for fy = 410 MPa

Ec

23,855.620

MPa

2.887 fr fy fs ES

2.887

MPa

410.000 MPa 164.000 MPa 200000.000 MPa

iv) Strength Data related to Working Stress Design & Service Load Condition ( WSD & AASHTO-SLS ) : a) b) c) d) e)

Modular Ratio, n = Es/Ec>6 8.384 Value of Ratio of Steel & Concrete Flexural Strength, r = fs/fc = 164/8.400 Value of k = n/(n + r) = 9.000/(9.000 + 20) Value of j = 1 - k/3 = 1 - 0.307/3 Value of R = 0.5*(fckj) = 0.5*(8.400*0.307*0.898) = 1.156

n r k j R

8 19.524 0.291 0.903 1.102

2 Dimentional Data of Beam Ledges for Abutment : i) Dimentions of Beam Ledge, Bearing Plate & other Events : a) Length of Beam Ledge (Parallel to Traffic)

LB-Ladge

0.500 m

b) Width of Beam Ledge (Transverse to Traffic)

WB-Ladge

0.930 m

c) Depth of Beam Ledge (Under Central Girder)

hB-Ladge

0.115 mm

d) Length of Bearing Plate (Parallel to Traffic)

LB-Plate

4.000 m

e) Width of Bearing Plate (Transverse to Traffic)

WB-Plate

0.300 m

f) Depth of Bearing Plate

hB-Plate

0.072 m

g) Length of Abutment Cap (Parallel to Traffic) for Beam Ledge Placing

LAb-Cap

0.700 m

h) C/C Distance (Transverse to Traffic) between Bridge Girders

SC/C-Gir.

2.000 m

i) Distance between Center of Bearing & the Face of Back Wall

av

0.325 m

j) Distance between Center of Bearing & the Face of Vertical Reinforcement

af

0.363 m

C

0.675 m

de-Cap

0.538 m

on Open Face of Back Wall = av + CCov-Open k) Distance between End Bearing Center & the Edge of Wing Wall l) Effective Depth for Tension Reinforcement of Abutment Cap

m) Provided Spacing of 2-Ledge Shear Reinforcement of Abutment Cap

spro-Cap

0.150 m

n) Cross-sectional Area of 2-Ledge Shear Reinforcement of Abutment Cap

Av-f-Cap

2 226.195 mm

o) Steel Area of Shear Reinforcement for per Meter Length of Abutment Cap = Avf-Cap(1.00/spro-Cap)

Avf-Cap/m

p) Effective Depth for Tension Reinforcement of Back Wall (From Open Face)

de-Wall

q) Provided Total Steel Area of Vertical Reinforcements on both Faces of Back

Avf-Wall

2 1,507.96 mm /m

0.244 m 2 1,809.557 mm /m

Wall for per Meter Horizontal Length = As-Earth-V + As-Open-V r) Applied Shear Force on Exteriod Pads due to Reactions from Exterior Girder under Strength Limit State (USD) = Vu-Supp-Ext.-USD

VU-Ext.-USD

832.468 kN

s) Applied Shear Force on Interiod Pads due to Reactions from Interior Girder under Strength Limit State (USD) = Vu-Supp-int.USD

VU-Int.-USD

359.356 kN

t) Applied Shear Force on Exteriod Pads due to Reactions from Exterior Girder under Service Limit State (WSD) = Vu-Supp-Ext.-WSD

VU-Ext.-WSD

49.505 kN

u) Applied Shear Force on Interiod Pads due to Reactions from Interior Girder under Service Limit State (WSD) = Vu-Supp-int.WSD

VU-Int.-WSD

215.333 kN

v) Steel Area of One no.Vertical Reinforcement of Back Wall on Open Face which is the Steel Area of One Ledge Hanger Reinforcement = Af-12.

Ahr

w) Spacing of Vertical Reinforcement of Back Wall on Open Face which is the Spacing for Ledge Hanger Reinforcement = spro.-V-Open

sHanger

2 113.097 mm

125 mm C/C

3 Design of Beam Ledges under Provisions of Article 5.13.2.5 : i) Sketch Diagram of Abutment Cap & Beam Ledge showing Effects/Cracks Caused by Applied Loads : Ahr @s

af

de aV

Centerline of Bearing. VU

2

S VU

NUC

3

4 de

1

h

W

C

1 W + 4aV For Shear Force

2C

W + 5af de/2

For Flexural & Horizontal Force W + 3av

W

For Hanger Reinforcement de/2 L de/2 ii) Requirement for Design the Beam Ledges under Provisions of Article 5.13.2.5.1 : a) According to Article 5.13.2.5.1 the Design basie of Beam Ledge will be to Resist the under Mentioned Features; b) Flexural, Shear & Horizontal Forces at the Location of Crack-1. c) Tension Force in the Supporting Element at the Location of Crack-2. d) Punching Shear at Points of Loading at the Location of Crack-3; and e) Bearing Force at Location of Crack-4. iii) Design for Shear Force (Article-5.13.2.5.2) : a) Design of Beam Ledges for Shear Force will be in accordance with the Requirements for Shear Friction Specified in Article 5.8.4. b) According to Article 5.8.2.1; the Nominal Shear Resistance of the Interface Plane is Vn = cAcv + m(Avf-Capfy + Pc), (Equation 5.8.4.1-1), where;

Vn-Comp.

1378877.086 Mpa

c) Vn is Nominal Shear Resistance & its value will be the Lesser of Equations Vn  0.2f/cAcv (Equation 5.8.4.1.2) or Vn  5.5Acv (Equation 5.8.4.1.3). c-i) Against Equation 5.8.4.1.2 the Clculated Allowable value of Vn-1 = 0.2f/cAcv

Vn-1

3047625.000 Mpa

c-ii) Against Equation 5.8.4.1.3 the Clculated Allowable value of Vn-2 = 5.5Acv

Vn-2

3,990,937.50 Mpa

Vn-Allow.

3047625.000 Mpa

Acv

2 725,625.000 mm

c-iii) Allowable value of Vn is the Minimum of Vn-1 & Vn-2 d) Acv is Area of Concrete engaged in Shear Transfer in mm. The value of Acv should be Calculated by Multiplying the Effective Depth de-Cap, for the Tension

Reinforcement from Compression Face and the Width of the Concrete Face Considering the Leasser One of S, (W + 4av) & 2C as shown in the Sketch Diagram. = de-Cap*2*C (Minimum of S, (W + 4*av) & 2*C.) d-i) From the Sketch Diagram value of S = SC/C-Gir.

S

2,000.000 mm

(W + 4av)

2,230.000 mm

d-iii) From the Sketch Diagram value of 2*C

2*C

1,350.000 mm

d-iv) Applicable value for the purpose is Minimum of S, (W + 4av) & 2*C

2*C

1,350.000 mm

Avf-Cap

2 2035.75204 mm

d-ii) From the Sketch Diagram value of (W + 4av ) = (WB-Ladge + 4av)

e) Avf is Area of Shear Reinforcement Crossing the Shear Plan in mm2. =(Av-Cap/m*2*C)/1000 f) c is Choesion Factor according to Article 5.8.4.2. in Mpa. For Concrete placed against clean, hardened Concrete with intentionally roughened surface to an amplitude of 6.00mm. C = 0.75 Mpa

c

g) m is Friction Factor according to Article 5.8.4.2. For Concrete placed against clean, hardened Concrete with intentionally roughened surface to an amplitude of 6.00mm. m = 1.00*l .

m

1.000

l

1.000

g-i) For Normal Density Concrete l = 1.00 h) Pc is Permanent Net Compressive Force Normal to Shear Plan. If Force is Tensile Pc = 0.

Pc

0.75 Mpa

0.000 Mpa

i) Relation between Computed Shear Force Vn-Comp.& Vn-Allow. the Allowable Vn-comp.