I-Beam Girder Computions.xls

Prestressed Precast I-Girder Design for Intermediate Beams - CE767 Geometrical Properties Girder Span Length Girder Depth Spacing of Girders

L h S

24 182.88 0.85

m cm m

Deck Thickness

tdeck

20

cm

0 0

cm cm

Haunch Thickness Haunch Width

Please choose the type of the beam cross section (1/2) Please enter the dimensions of the section in "SectionComposer"

Material Properties of Concrete Elastic Modulus - AASHTO LRFD 5.4.2.4-1 Descrip. fc` Unit W (MPA) (kg/m3) CIP Deck 30 2500 Beam@transfer 40 2500 Beam@service 50 2500

Loads DW, Dead Load Placed on Structural Components Thickness of wearing surface 6 cm Unit weight of wearing surface 2200 kg/m3

1

Cross sectional Properties for a Single Beam Girder from LARSA Section Composer Area Istrong Iweak bw yb (cm2) (cm4) (cm4) (cm) (cm) 6070.9556 2.79E+07 2095094 15.24 92.55 Cross Diaphragms width height Quantity

25 94 3

Cross sectional Properties for the Composite Beam Descript. Area yb A.yb A(ycb-yb)2 (cm2) (cm) (cm3) (cm4) Beam 6070.96 92.6 561896 1941330.8 Haunch 0.00 0 0 0 Deck 1316.81 192.88 253987 8950186.1 Sum 7387.77 8.16E+05 Section, ycb =

110.4

Ec (MPA) 29440 33994 38007

DC, Dead Load of Structural Components and non-structural elements Self Weight 1.518 t/m Deck Weight 0.425 t/m Haunch 0.000 t/m Sum 1.943 t/m

cm cm two at ends and one at mid-span

Istrong (cm4) 2.79E+07 0 43894

Istr+Ay2 (cm4) 2.99E+07 0.00E+00 8.99E+06 3.89E+07

Cross Diaphragms

0.499375 0.499375

tons per girder at mid-span tons per girder at each end

Barrier Wearing Surface Sum

0.100 0.112 0.212

t/m per beam t/m per beam t/m per beam

LL, Distrubution Factors for LiveLoad H30 truck Distribution Factor for Bending Moment - lane/beam

S= ts = L= Nb = Kg

cm

Effective Flange Width (AASHTO LRFD 4.6.2.6.1) 1/4 Span = 6 m 12ts + web 2.908 m Spacing = 0.85 m Use 0.85 m

Kg = DFM =

Prestressing steel # of strands Area of 1 strand

Spacing for prestressing strands

5

DFS =

Layer 1 - # of strands Layer 2 - # of strands Layer 3 - # of strands Layer 4 - # of strands Layer 5 - # of strands Layer 6 - # of strands Layer 7 - # of strands Layer 8 - # of strands Layer 9 - # of strands

11 11 0 0 0 0 0 0 0

c.g of prestressing tendons from bottom

cm

Check for fitting x y,from bottom (cm) (cm) 60 5 60 10 5 15 5 20 5 25 5 30 5 35 5 40 5 45

7.50

cm

mm mm mm mm4

NOT OK OK OK OK OK

Table 4.6.2.2.3a-1

0.77 13

(1/2 in. Dia. Seven wire, low relaxation) 22 Ab 98.71 mm2

850 200 24000 >=4 1.15E+12

1.15E+12 mm4 0.369 lanes/beam

Distribution Factor for Shear - lane/beam Modular Ratio of Deck to Beam = Span to Depth Ratio

Table 4.6.2.2.2b-1

Prestressing force Ultimate strength Yield strength Initially (=0.75 fpu) Initial loss Initial loss At Transfer after initial losses Total Prestressing Force

Reinforcing Bars Yield strength

fpy

fpu fpy fpi

1861.65 1675.485 1396.2 4.3 60.0 1336.2 2901.7

420

MPa

MPa MPa MPa % MPa MPa kN

0.430

lanes/beam

(LRFD Table 5.4.4.1-1) (LRFD Table 5.9.3-1)

STRESSES AT TRANSFER

Moment due to prestressing Moment due to SW of the beam

Mp at c/g of beam Mbeam at c.g of beam

2468.0 1072.0

kN-m kN-m

Stress check at transfer - midspan Bottom Fiber - Compression

`=-P/A-Mp/Sb+Mb/Sb

-9.405

MPa

<

-24

MPa

OK

Top Fiber - Tension Check

`=-P/A+Mp/St-Mb/St

-0.265

MPa

<

1.581

MPa

OK

without bonded reinf. Check Total Loss due to Initial Prestressing Loss = n * elastic shortening stress n = Es/Ec 5.78 Elastic Shortening Stress

`=(-P/A)-(Mp*e)/I+(Mb*e)/I

Loss

iterate for loss

-52.20

-9.031 60.0 (estimated)

MPa

MPa

Check Stresses at Transfer Length Section Transfer Length =

60 dia =

mm

LRFD Art. 5.8.2.3

Mbeam @ end of Transfer Length =

131.82

kN-m

P= Mp at c.g of beam =

0.00 0.00

kN kN-m

Debonded strands =

762 22

Bottom Fiber Stresses =

`=-P/A-Mp/Sb+Mb/Sb

0.437

MPa

<

-24

MPa

OK

Top fiber Stresses =

`=-P/A+Mp/St-Mb/St

-0.426

MPa

<

1.581

MPa

OK

Not checked but say at every meter activate 8 strands from the end zone.

STRESSES AT SERVICE LOADS

Prestress Losses at Service Level Elastic Shortening

-52.20

MPa

fpi Aps Ag gamma-k gamma-st delta fpr

(see above comp.)

delta fpl

1396.24 MPa 2171.61 mm2 607095.56 mm2 0.8 0.74 17 MPa (AASHTO LRFD Section 5.9.5.3) 96.20 MPa

Total Prestress Loss at Service Total Prestress loss (%) Total Prestress Stress after losses

-148.40 10.6 1247.84

Total Prestress Force Mp Mdc Mdw Mll Mll+im Stresses at Mid-Span

Beam Top Fiber Stresses =

2709.8 2304.8 1372.2 149.9 3464.6 1698.5

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

Live Load Table H30-S24

MPa

Span m

MPa

(iterative) Finding the number of strands

Compute stresses using non-composite non-composite non-composite composite from the table in "live loads" sheet composite

Service I = P/A (MPa) -4.46

Mp term (MPa) 7.45

-4.46

7.45

Service III = -4.46

-7.64

-4.46

-7.64

fbc fpb ybs ec Ppe Final loss #

1.00(DC+DW) + 1.00 (LL+IM) Check compressive Stresses in prestressed comp. Mdc term Mdw term Mll+im term Total (MPa) (MPa) (MPa) (MPa) -4.44 -0.28 -1.73

8.83 5.30 9.144 83.41 1.20E+03 10.6 10

<

-22.50

OK

-0.28

-3.17

-4.89

<

-22.50

OK

-0.28

-3.13

-3.41

<

-13.5

OK

1.00(DC+DW) + 0.80 (LL+IM) Check tensile stresses in prestressed concrete comp. 4.55 0.43 -7.13

<

3.54

OK

<

3.54

OK

-4.44

Top of Deck Fiber Stresses

Beam Bottom Fiber Stresses =

from AASHTO Table

4.55

0.43

3.86

-3.27

Mpa MPa cm cm Kn %

0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3 3.4 3.7 4 4.3 4.6 4.9 5.2 5.5 5.8 6.1 6.4 6.7 7 7.3 7.6 7.9 8.2 8.5 8.8

Moment kN-m 16.2 32.55 48.75 65.1 81.3 97.65 113.85 130.2 146.4 162.75 178.95 195.3 211.5 227.7 244.05 260.25 276.6 292.8 309.15 325.35 341.7 357.9 374.25 391.95 421.8 451.8 481.95 512.4 543

FATIGUE CHECK Fatigue is typically checked for one lane load instead of multiple lanes however for simplicity use above Mll+IM Distribution Factor for 1 lane loading Bottom Compressive Stress due to permanent loads and prestress = Bottom Tensile Stress due to( 0.75 Mll+IM) = Ratio comp/tension =

2.51

>

2

-7.13 2.84 don't check fatigue

MPa MPa LRFD 5.5.3.1

check of fatigue is not provided in this spreadsheet STRENGTH LIMIT STATE Mu1 = 1.25(DC)+1.5(DW)+1.75(LL+IM) Mu2 =0.9(DC)+0.65(DW)+1.75(LL+IM) Mu = 4912.5 kN-m Mu = 4304.8 kN-m dp

195.38

β 0.75

k 0.38

c=

23.72

cm

cm

>

20

Top flange thickness of the PC beam = c=

33.38

>

cm T-section behaviour

12.7

cm

32.7

cm

Average stress in prestressing tendons fps = 1775.7592 MPa Mn = 7145.5724 kN-m for rectangular Mn= 71078.885 kN-m for T-section Mr =Ø n Ø= 1 Mr =

LRFD 5.5.4.2.1

71078.89

>

4912.5

kN-m

OK

SHEAR DESIGN Vp =

0

kN

no draped tendons exist

Critical shear section approax. = de = h-ybs = Vdc = Vdw = Vll= Vll+im =

193.9 20.9 424.35 242.6

kN kN kN kN

Vu = Vc = Vu =

698.3 349.5 698.3

kN kN >

157.3

Vn >

Vu/phi =

775.8

kN

426.3

kN

Req'd Vs =

195.38

cm

from the live loads table

kN

provide stirrups

θ = 45 deg Av/s =

0.520

mm2/mm

Say S =

15

mm

Required Av =

7.8

mm2

Bar Dia =

8

mm

2 Bars, Av =

100.48

mm2

OK

Use

dia

@

15

8

mm

stirrups

Check minumum required reinforcement and maximum nominal capacity that can be provided by shear reinforcement Not done in this spreadsheet

DFS

0.290

lanes/beam

9.1 9.4 9.8 10.1 10.4 10.7 11 11.3 11.6 11.9 12.2 12.8 13.4 14

573.75 604.65 635.55 666.6 698.55 734.55 770.55 806.55 842.55 878.7 914.7 986.85 1059.3 1131.75

14.6 14.6 15.2 15.8 16.5 17.1 17.7 18.3 18.9 19.5 20.1 20.7 21.3 22.9 24.4 25.9 27.4 29 30.5 33.5 36.6 39.6 42.7 45.7 48.8 51.8 54.9 57.9 61 67.1 73.2 79.2 85.3 91.4

1204.05 1204.05 1276.05 1349.55 1422.15 1494.9 1567.5 1640.1 1713.15 1785.75 1858.8 1931.4 2004.3 2186.4 2368.95 2551.65 2734.05 2916.45 3099.3 3464.55 3829.95 4195.35 4561.05 5033.4 5629.05 6257.7 6918.6 7612.05 8337.9 9887.55 11567.25 13377.15 15317.25 17387.55

H30-S24 End shear and end reaction kN 213.45 213.45 213.45 213.45 213.45 213.45 213.45 213.45 213.45 213.45 213.45 213.45 213.45 213.45 227.55 240.15 251.55 260.85 269.55 277.5 284.85 290.85 296.85 302.25 307.65 312.3 316.2 320.25 325.65

330.9 335.55 340.2 344.25 348.3 352.35 355.65 358.95 362.25 365.7 368.25 373.65 378.3 382.35 387 387 390.3 394.35 397.65 400.35 403.05 405.6 408.3 410.4 412.95 414.3 416.4 421.05 424.35 427.65 430.35 433.05 435.75 439.65 442.95 451.05 472.35 493.8 515.1 536.4 557.85 579.15 600.45 643.2 685.95 728.55 771.3 814.05

GIRDER TYPE

1 Input lenghts (cm) X1 66.04 X2 101.6 X3 15.24 X4 10.16 Y1 20.32 Y2 25.4 Y3 106.68 Y4 10.16 Y5 7.62 Y6 12.7

Calculation of IXX A(cm2) 1341.9328 645.16 387.096 1625.8032 103.2256 154.8384 251.6124 270.9672 1290.32

A1 A2 A3 A4 A5 A6 A7 A8 A9

XX --> Strong axis

yb (cm) 10.16 28.79 33.02 99.06 159.17 157.48 167.64 166.37 176.53

A yb'

6070.9556 cm2 92.55 cm

IXX

27,932,801.336 cm4

A*yb 13634.03725 18572.00587 12781.90992 161052.065 16430.76284 24383.95123 42180.30274 45080.81306 227780.1896 Σ 561896.0375

Ix 46173.94 23123.97 20811.57 1541887.69 591.97 1331.94 811.65 1311.13 17342.98 1653386.842

A*yb 8437.5 5041.666667 4000 26812.5 12890.625 9187.5 52500 Σ 118869.7917

Ix 21093.75 1527.78 1666.67 57213.54 644.53 703.13 6250.00 89099.39

6.711E+05 YY --> Weak Axis

GIRDER TYPE

A yl' IYY

6070.9556 cm2 50.80 cm 2.095E+06 cm4

2 Required lenghts (cm)

Calculation of IXX

X1 X2 X3 Y1 Y2 Y3 Y4 Y5

A1 A2 A3 A4 A5 A6 A7

75 75 20 15 10 32.5 7.5 10

A(cm2) 1125 275 200 650 206.25 150 750

yb (cm) 7.5 18.33 20 41.25 62.5 61.25 70

XX --> Strong axis

A yb' IXX

3356.25 cm2 35.42 cm 2.264E+06 cm4

YY --> Weak Axis

A yl' IYY

3356.25 cm2 37.50 cm 1.109E+06 cm4

Calculation of IYY A*(yb-yb')^2 9110250.10 2623461.79 1372019.79 68800.29 458118.30 652687.60 1418537.46 1476414.87 9099124.29 26279414.4938

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12

A 1341.9328 322.58 322.58 387.096 1625.8032 51.6128 51.6128 154.8384 125.8062 125.8062 270.9672 1290.32

yl 50.80 34.71 66.89 50.80 50.80 39.79 61.81 50.80 22.01 79.59 50.80 50.80

A*yl 68170.19 11197.83 21576.30 19664.48 82590.80 2053.85 3190.02 7865.79 2769.41 10012.50 13765.13 65548.26 Σ 308404.54

Iy 487712.24 11561.98 11561.98 7492.17 31467.10 295.99 295.99 2996.87 7620.50 7620.50 28553.48 1109950.47 1707129.26

A*(yl-yl')^2 0.00 83477.52 83477.52 0.00 0.00 6252.72 6252.72 0.00 104252.10 104252.10 0.00 0.00 387964.69

yl 37.50 18.33 56.67 37.5 37.50 18.33 56.67 37.5 37.50

A*yl 42187.50 2520.83 7791.67 7500.00 24375.00 1890.63 5843.75 5625.00 28125.00 Σ 125859.38

Iy 527343.75 5776.91 5776.91 6666.666667 21666.67 4332.68 4332.68 5000 351562.50 932458.77

A*(yl-yl')^2 0.00 50512.15 50512.15 0.00 0.00 37884.11 37884.11 0.00 0.00 176792.53

Calculation of IYY A*(yb-yb')^2 876806.55 80263.37 47539.51 22112.17 151277.14 100098.15 896964.96 2175061.85

A1 A2 A3 A4 A5 A6 A7 A8 A9

A 1125 137.5 137.5 200 650 103.125 103.125 150 750