T Beam Design

DESIGN OF T-BEAB 10.7 1.600

7.500

1.600

0.250

1.500

A

B

0.50 1.125

C

0.50

0.50 2.500

2.500

D

0.50 2.500

1.125

9.75 CROSS SECTION OF DECK Required data Effective Span Total length of Deck Carriage way width Width of Parapet including Kerb Width of Footpath Thickness of Slab No of Longitudinal Girder Hight of Longitudinal Girder Spacing of Longitudinal Girder Cantiliver Length Thickness of Web Thickness of Footpath Thickness of Kerb Thickness of Parapet Hight of Parapet above Kerb No of Cross Girder Spacing of Cross Girder Spacing Thickness of Cross Girder Hight of Cross Girder Density of RCC Wearing Coat Thickness Density of Wearing Coat

= = = = = = = = = = = = = = = = = = = = =

16.000 8.700 7.500 0.600 1.000 0.250 4.000 1.500 2.500 1.125 0.250 0.350 0.450 0.200 0.900 5.000 4.000 0.300 1.500 25.000 0.080 22.000

m m m m m m m m m m m m m m m m m m m kN/m3 m kN/m3

Haunches and Bulbs of Longitudinal Girder Girder 'A' and 'D' Bottom Bulb Width = Bottom Bulb Thickness = Bottom Haunch 0.125 x Top Haunch 0.500 x Girder 'B' and 'C' Bottom Bulb Width = Bottom Bulb Thickness = Bottom Haunch 0.125 x Top Haunch 0.150 x

0.500 0.250 0.125 0.100

m m m m

0.500 0.250 0.125 0.050

m m m m

DESIGN OF DECK INTERIOR SLAB PANNEL x x

Conatact ares of vehicle is, 0.84 m in transevers direction 4.57 m in longitudinal direction

6.25 1.76 8.01

B=

2.500 m

u=

1.00

L=

u = 0.84+2x0.08 1.00 m

= = =

4.000

Considering 70R Tracked vehicle, which is placed at the centre of pannel as shown in fig

25.000 22.000

v = 4.57+2x0.08 4.73 m > 4.000 m hence v= 4.000 m

u/B = 1/2.5 v/L = 4/4 K = B/L =

2.5/4

= = =

0.4 1.00 0.625

Refering to Pigeaud's curves corresponding to 'K'=7' values, the values of moment Co-efficients are, m1 = 0.085 m2 = 0.034 Impact factor for 70R tracked vehicle = as per IRC-6:2000,Cl:208.3, page No 21, 70R Tracked load for two track 70R Tracked load for one track Total load per track including impact Effective load on span (W)

10%

= = = = =

kN/m2 kN/m2 kN/m2

4.730

0.250 0.080

v=

Dead weight of slab Dead weight of wearing coat Total weight

700.00 kN 350.00 kN 385.00 kN 385x(4/4.73) 325.58 kN

m

Moment along shorter span ( MB) MB = W*(m1+1.5*m2) = 325.581395348837x(0.085+1.5x0.034) = 44.28 Kn-m Moment along longer span ( ML) ML = W*(m2+1.5*m1) = 325.581395348837x(0.034+1.5x0.085) = 52.58 Kn-m As the slab is continuous, the design bending moments are obtained by applying the continuity factor as, MB = 0.8x44.2790697674419 = 35.42 Kn-m ML = 0.8x52.5813953488372 = 42.07 Kn-m Dead load bending moments are computed using Pigeaud's Curves Dead Load = 8.01 kN/m2 Ttal DL on pannel = 8.01x4x2.5 = 80.10 kN (u/B) = (v/L) K = B/L

= 1 as pannel is loaded with UDL = 2.500 / 4.000 = 0.625 1/K = 1.6 from Pigeaud's Curves read out the Co-efficients are m1 = 0.047 m2 = 0.025 Taking the continuity effect, the design moments are, MB = (0.8*W)*(m1+1.5*m2) = 0.8x80.1(0.047+1.5x0.025) = 5.415 kN-m ML = (0.8*W)*(m2+1.5*m1) = 0.8x80.1(0.025+1.5x0.047) = 6.12 kN-m Hence final design moments in the slabs are obtained as, MB = 35.42 + 5.4148 = 40.838 kN-m ML = 42.07

+

Design parameters Grade of concrete Grade of Steel Fe According to IRC-21:2000

6.1196

= =

=

48.185 kN-m

M- 35 Fe- 415

= =

35 415

N/mm2 N/mm2

Design Constants: σcbc = 11.67 N/mm2 σst = 200 N/mm2 m = 10 k = m σcbc/( mσcbc + σst) = 10 x 11.667 10 x 11.667 + 200 = 0.37 j = 1-(k/3) =

1 -

0.37 3

= 0.88 Q = 0.5 x σcbc x j x k =

0.5 x 11.667 x 0.88 x 0.37

= 1.89 dreq =

48.18 x 1.89 x = 159.9 mm

Overall Depth Provided = Clear Cover = Center of reinforcement = Effective depth Provided = Are of Steel Required =

1E+06 1000

250 40 8 202

dia of rod =16 mm mm mm mm mm < dreq Hence O.K.

M x 106 j x σst x d

For Shorter span Are of Steel Required = x40.84 xx 1000000 x x x0.877 xx 200 x x 202 x x x = 1152.4 mm2/m Minimum reinforcement required = 0.12 % of cross sectional area = 0.12% x 1000 x 250 Astreq Hence required Ast = Steel Provided = Provide

16 mm dia

300 mm2/m > Astmin 1152.4 mm2/m

150

mm c/c

Total Steel Provided on Embankment Face = 1340.41 mm2/m OK and SAFE

Pro steel/m = 1340.41

For Longer span Are of Steel Required = x48.18 xx 1000000 x x x0.877 xx 200 x x 202 x x x = 1359.7 mm2/m Minimum reinforcement required = 0.12 % of cross sectional area = 0.12% x 1000 x 250 300 mm2/m > Astmin

Astreq Hence required Ast = Steel Provided = Provide

16 mm dia

1359.7 mm2/m

150

Pro steel/m = 1340.41

mm c/c

Total Steel Provided on Embankment Face = 1340.41 mm2/m NOT OK DESIGN OF CANTILIVER SLAB Bellow figure shows the cantiliver portion of the Tee beam and slab bridge deck with dimensional details of cantiliver projection, kerb, hanrails and footpath. 0.20

1.00

0.60 0.90

0.35

0.45 0.25 0.50 0.50 x 0.10 1.00

CROSS SECTIONAL DETAILS OF CANTILIVER SLAB a). Dead Load Calculation i) Dech slab ii) Haunch at sopprt iii) Foot path iv) Kerb above Footpath v) Parapet

= = = = =

0.25 0.10 0.35 0.10 0.90

x 1.00 x x x 1.00 x x 0.60 x x 0.20 x

25 25 25 25 25

= = = = =

6.25 2.5 8.75 1.5 4.5

kN/m kN/m kN/m kN/m kN/m

2.5 kN/m 4.5 kN/m 1.5 kN/m 6.25 kN/m 8.75 kN/m

0.20 m

0.50 m 0.60 m 1.00 m LOADING DETAILS OF CANTILIVER SLAB

Taking Moments at the support i) Dech slab ii) Haunch at sopprt iii) Foot path iv) Kerb above Footpath v) Parapet Total Moment at support

= = = = =

6.25 0.5 8.75 1.5 4.5

x 1.00 x 0.50 x 1.25 x 0.17

x 1.00 x 0.50 x 0.60 x 0.70 x 0.20 x 0.90

3.13 0.10 4.38 0.63 0.81 9.04

= = = = =

kN-m kN-m kN-m kN-m kN-m kN-m

b). Live Load Calculation Here only footpath live load is considered, becouse footpath is covering the whole cantiliver portion. According to IRC-6:2010, Cl:209.4(b) Footpath load is taken 5.00 kN/m2 5.00 x 0.40 =

2

kN/m

0.40 m Taking Moments at the support

=

2

c). Maximum Bending Moment at Support i) Dead Load Moment = ii) Live Load Moment = Toatl Moment = Design parameters Grade of concrete = Grade of Steel Fe = According to IRC-21:2000 Design Constants: σcbc = 11.67 N/mm2 σst = 200 N/mm2 m = 10 k = 0.37 j = 0.88 Q = 1.89 dreq = =

9.20 x 1.89 x 69.9 mm

x

0.40 x 0.2

0.16 kN-m

=

9.04 kN-m 0.16 kN-m 9.20 kN-m

M- 35 Fe- 415

= =

35 415

N/mm2 N/mm2

1E+06 1000

dia of rod =10 mm Overall Depth Provided = 350.00 mm Clear Cover = 40 mm Center of reinforcement = 5 mm Effective depth Provided = 305 mm < dreq Hence O.K. Are of Steel Required =

M x 106 j x σst x d

For Shorter span Are of Steel Required = x 9.20 xx 1000000 x x x0.877 xx 200 x x 305 x x x = 172.0 mm2/m

Minimum reinforcement required = 0.12 % of cross sectional area = 0.12% x 1000 x 350 420 mm2/m < Astmin

Astreq Hence required Ast = Steel Provided = Provide

10 mm dia

420.0 mm2/m

150

Pro steel/m = 523.60

mm c/c

Total Steel Provided on Embankment Face = 523.60 mm2/m OK and SAFE DESIGN OF LONGITUDINAL GIRDER Using Courbon's theory, IRC Class 70R Tracked vehicle loads are arranged for maximum eccentricity as shown in bellow figer. Wheel position of vehicle is taken as per IRC-6:2000. e = 1.10 1.62

2.06

C/L of Bridge deck W1

W1

W

3.750

3.750

1.25 1.25 TRANSVERSE POSITION OF IRC CLASS 70R TRACKED VEHICLE W= W1 =

700 kN 350 kN

a). Reaction Factors The reaction factor for outer girder 'A' and 'D' is given by 2W1 neX1 RA = 1 + n SX2 Wheare, W= n= e= X1 =

the eccentric concentrated load The number of longitudinal girder the eccentricity of the wheel load from the centre line of the deck the distance of the girder under consideration from the central axis of the deck. SX2 = the sum of the distances of longitudinal girders from the centre line of the deck.

RA = =

2 x 350 4 267.4 kN

1 +

2 x

4 x 1.10 x 3.750 3.750 x 3.750 + 1.25 x 1.25

The reaction factor for inner girder 'B' and 'C' is given by 2W1 neX1 RA = 1 + here X1 is 0 n SX2

= =

2 x 350 4 175

1 +

2 x

4 x 1.10 x 0.0 3.750 x 3.750 + 1.25 x 1.25

kN

b). Dead load from slab per girder Dead load of slab is calculated as bellow, 1) Parapet railing 0.20 x 0.90 x 2) Kerb and deck slab 0.70 x 0.60 x 3) Foot path 0.35 x 1.00 x Total Total Dead load of Deck = 2 x 23.8 =

+

25 25 25

= = = =

4.5 10.5 8.75 23.75

kN/m kN/m kN/m kN/m

7.500 x 8.01

107.6 kN/m

It is assumed that the dead load of deck is shared equally by all the four girders. There fore Dead load per girder = 107.58 / 4 = 26.894 kN/m c). Live Load Bending Moment in Girder-'A' Effective span of girder = Impact factor for 70R tracked vehicle =

16.00 m 0.10

The live load is placed centrally as shown in figer, 4.57 m

a=

8 m

####

####

####

700.00 kN

b=

8 m

d). Dead load Bending Moment in girder 'A' and 'D' 0.25 0.15 1.50

0.25 0.05

0.25 0.125

0.250 0.50 Girder 'B' and 'C' C/S

0.50 x 0.10 1.50

0.125

0.25 0.125 x 0.125 0.250 0.50 Girder 'A' and 'D' C/S

Self weight of girder 'A' and 'D' Top haunch 2 x 0.5 x 0.50 x Bottom haunch 2 x 0.5 x 0.125 x Web 1 x 0.25 x Bottom bulb 1 x 0.50 x Total

0.10 x 0.125 x 1.00 x 0.25 x

16.00 16.00 16.00 16.00

x x x x

25 25 25 25

= = = =

20 6.25 100 50 176.25 11.016

kN kN kN kN kN kN/m

Self weight of girder 'B' and 'C' Top haunch 2 x 0.5 x 0.15 x Bottom haunch 2 x 0.5 x 0.125 x Web 1 x 0.25 x Bottom bulb 1 x 0.50 x Total

0.05 x 0.125 x 1.00 x 0.25 x

16.00 16.00 16.00 16.00

x x x x

25 25 25 25

= = = =

3 6.25 100 50 159.25 9.9531

kN kN kN kN kN kN/m

Weight of each Cross Girder = 0.30 x 1.250 x 25 = 9.375 kN/m Reaction on Main Girder = 9.375 x 2.50 = 23.438 kN Reaction from Dead load on each girder = 26.894 kN/m There fore total Dead load on girder 'A' & 'D' = 26.894+ 11.016= 37.91 kN/m There fore total Dead load on girder 'B' & 'C' = 26.894+ 9.9531= 36.85 kN/m

Maximum Bending Moment for Girder 'A' and 'D' 23.44 kN

23.44 kN

23.44 kN 37.91 kN/m

4 m

4 m

4 m

4 m

16.00 m Mmax =

37.91x16.00x16.00/8+ 23.44x16.00/4.00+ 23.44x16.00/4.00

=

1213.1 93.75 93.75

=

1400.6 kN-m

Maximum Bending Moment for Girder 'B' and 'C' 23.44 kN

23.44 kN

23.44 kN 36.85 kN/m

4 m

4 m

4 m

4 m

16.00 m Mmax =

36.85x16.00x16.00/8+ 23.44x16.00/4.00+ 23.44x16.00/4.00

=

1179.1 93.75 93.75

=

1366.6 kN-m

e). Design Moment Design Moments in Girder 'A' and 'D' Dead Load Moment Live Load Moment Total design Moment

= = =

1400.6 kN-m kN-m 1400.6 kN-m

Design Moments in Girder 'A' and 'D' Dead Load Moment Live Load Moment Total design Moment

= = =

1366.6 kN-m kN-m 1366.6 kN-m

f). Design of Reinforcement in Girder