Prestressed Precast I-Girder Design for Intermediate Beams - CE767

Geometrical Properties Material Properties of ConcreteElastic Modulus - AASHTO LRFD 5.4.2.4-1

Girder Span Length L 24 m Descrip. fc` Unit W EcGirder Depth h 182.88 cm (MPA) (kg/m3) (MPA)Spacing of Girders S 0.85 m CIP Deck 30 2500 29440

Beam@transfer 40 2500 33994Deck Thickness tdeck 20 cm Beam@service 50 2500 38007

Haunch Thickness 0 cmHaunch Width 0 cm Loads

DW, Dead Load Placed on Structural ComponentsPlease choose the type of the beam cross section (1/2) 1 Thickness of wearing surface 6 cmPlease enter the dimensions of the section in "SectionComposer" Unit weight of wearing surface 2200 kg/m3

Cross sectional Properties for a Single Beam DC, Dead Load of Structural Components and non-structural elementsGirder from LARSA Section Composer Self Weight 1.518 t/mArea Istrong Iweak bw yb Deck Weight 0.425 t/m(cm2) (cm4) (cm4) (cm) (cm) Haunch 0.000 t/m6070.9556 2.79E+07 2095094 15.24 92.55 Sum 1.943 t/m

Cross Diaphragms Cross Diaphragms 0.499375 tons per girder at mid-spanwidth 25 cm 0.499375 tons per girder at each endheight 94 cmQuantity 3 two at ends and one at mid-span Barrier 0.100 t/m per beam

Wearing Surface 0.112 t/m per beam Cross sectional Properties for the Composite Beam Sum 0.212 t/m per beam Descript. Area yb A.yb Istrong

(cm2) (cm) (cm3) (cm4) (cm4) (cm4) LL, Distrubution Factors for LiveLoad H30 truckBeam 6070.96 92.6 561896 1941330.8 2.79E+07 2.99E+07Haunch 0.00 0 0 0 0 0.00E+00 Distribution Factor for Bending Moment - lane/beam Table 4.6.2.2.2b-1Deck 1316.81 192.88 253987 8950186.1 43894 8.99E+06Sum 7387.77 8.16E+05 3.89E+07 S = 850 mm NOT OK

ts = 200 mm OKSection, ycb = 110.4 cm L = 24000 mm OK

Nb = >=4 OKEffective Flange Width (AASHTO LRFD 4.6.2.6.1) Kg 1.15E+12 mm4 OK1/4 Span = 6 m12ts + web 2.908 m Kg = 1.15E+12 mm4Spacing = 0.85 m DFM = 0.369 lanes/beamUse 0.85 m

Distribution Factor for Shear - lane/beam Table 4.6.2.2.3a-1

Modular Ratio of Deck to Beam = 0.77Span to Depth Ratio 13 DFS = 0.430 lanes/beam

Prestressing steel (1/2 in. Dia. Seven wire, low relaxation)# of strands 22 Prestressing forceArea of 1 strand Ab 98.71 mm2 Ultimate strength fpu 1861.65 MPa

Yield strength fpy 1675.485 MPa (LRFD Table 5.4.4.1-1)Spacing for prestressing strands 5 cm Check for fitting Initially (=0.75 fpu) fpi 1396.2 MPa (LRFD Table 5.9.3-1)

x y,from bottom Initial loss 4.3 %(cm) (cm) Initial loss 60.0 MPa

Layer 1 - # of strands 11 60 5 At Transfer after initial losses 1336.2 MPaLayer 2 - # of strands 11 60 10 Total Prestressing Force 2901.7 kNLayer 3 - # of strands 0 5 15Layer 4 - # of strands 0 5 20Layer 5 - # of strands 0 5 25Layer 6 - # of strands 0 5 30Layer 7 - # of strands 0 5 35Layer 8 - # of strands 0 5 40Layer 9 - # of strands 0 5 45

c.g of prestressing tendons from bottom 7.50 cm

Reinforcing BarsYield strength fpy 420 MPa

A(ycb-yb)2 Istr+Ay2

STRESSES AT TRANSFER

Moment due to prestressing Mp at c/g of beam 2468.0 kN-mMoment due to SW of the beam Mbeam at c.g of beam 1072.0 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 stressn = Es/Ec 5.78

Elastic Shortening Stress `=(-P/A)-(Mp*e)/I+(Mb*e)/I -9.031 MPa

Loss -52.20 iterate for loss 60.0 MPa(estimated)

Check Stresses at Transfer Length Section

Transfer Length = 60 dia = 762 mm LRFD Art. 5.8.2.3

Debonded strands = 22

Mbeam @ end of Transfer Length = 131.82 kN-m

P = 0.00 kNMp at c.g of beam = 0.00 kN-m

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 (see above comp.)

fpi 1396.24 MPaAps 2171.61 mm2Ag 607095.56 mm2gamma-k 0.8gamma-st 0.74delta fpr 17 MPa

(AASHTO LRFD Section 5.9.5.3) from AASHTO Tabledelta fpl 96.20 MPa Live Load Table

H30-S24

Total Prestress Loss at Service -148.40 MPa Span MomentTotal Prestress loss (%) 10.6 m kN-mTotal Prestress Stress after losses 1247.84 MPa (iterative) 0.3 16.2

Finding the number of strands 0.6 32.55Compute stresses using 0.9 48.75

Total Prestress Force 2709.8 kN non-composite fbc 8.83 Mpa 1.2 65.1Mp 2304.8 kN-m non-composite fpb 5.30 MPa 1.5 81.3Mdc 1372.2 kN-m non-composite ybs 9.144 cm 1.8 97.65Mdw 149.9 kN-m composite ec 83.41 cm 2.1 113.85Mll 3464.6 kN-m from the table in "live loads" sheet Ppe 1.20E+03 Kn 2.4 130.2Mll+im 1698.5 kN-m composite Final loss 10.6 % 2.7 146.4

# 10 3 162.75Stresses at Mid-Span Service I = 1.00(DC+DW) + 1.00 (LL+IM) 3.4 178.95

Check compressive Stresses in prestressed comp. 3.7 195.3P/A Mp term Mdc term Mdw term Mll+im term Total 4 211.5

(MPa) (MPa) (MPa) (MPa) (MPa) (MPa) 4.3 227.7Beam Top Fiber Stresses = -4.46 7.45 -4.44 -0.28 -1.73 < -22.50 OK 4.6 244.05

4.9 260.25-4.46 7.45 -4.44 -0.28 -3.17 -4.89 < -22.50 OK 5.2 276.6

5.5 292.85.8 309.15

Top of Deck Fiber Stresses -0.28 -3.13 -3.41 < -13.5 OK 6.1 325.356.4 341.76.7 357.9

Service III = 1.00(DC+DW) + 0.80 (LL+IM) 7 374.25Check tensile stresses in prestressed concrete comp. 7.3 391.95

Beam Bottom Fiber Stresses = -4.46 -7.64 4.55 0.43 -7.13 < 3.54 OK 7.6 421.87.9 451.8

-4.46 -7.64 4.55 0.43 3.86 -3.27 < 3.54 OK 8.2 481.958.5 512.48.8 543

FATIGUE CHECK 9.1 573.75Fatigue is typically checked for one lane load instead of multiple lanes however for simplicity use above Mll+IM 9.4 604.65

Distribution Factor for 1 lane loading 9.8 635.5510.1 666.6

Bottom Compressive Stress due to permanent loads and prestress = -7.13 MPa 10.4 698.55Bottom Tensile Stress due to( 0.75 Mll+IM) = 2.84 MPa 10.7 734.55

11 770.55Ratio comp/tension = 2.51 > 2 don't check fatigue LRFD 5.5.3.1 11.3 806.55

11.6 842.55check of fatigue is not provided in this spreadsheet DFS 0.290 lanes/beam 11.9 878.7

12.2 914.7STRENGTH LIMIT STATE 12.8 986.85

13.4 1059.3Mu1 = 1.25(DC)+1.5(DW)+1.75(LL+IM) 14 1131.75Mu2 =0.9(DC)+0.65(DW)+1.75(LL+IM)Mu = 4912.5 kN-m 14.6 1204.05Mu = 4304.8 kN-m 14.6 1204.05

15.2 1276.05dp 195.38 cm 15.8 1349.55

16.5 1422.15 k 17.1 1494.90.75 0.38 17.7 1567.5

18.3 1640.1c= 23.72 cm > 20 cm 18.9 1713.15

T-section behaviour 19.5 1785.7520.1 1858.8

Top flange thickness of the PC beam = 12.7 cm 20.7 1931.421.3 2004.3

c= 33.38 > 32.7 cm 22.9 2186.424.4 2368.95

Average stress in prestressing tendons 25.9 2551.65fps = 1775.7592 MPa 27.4 2734.05Mn = 7145.5724 kN-m for rectangular 29 2916.45Mn= 71078.885 kN-m for T-section 30.5 3099.3

33.5 3464.5536.6 3829.95

= 1 LRFD 5.5.4.2.1 39.6 4195.3542.7 4561.05

Mr = 71078.89 > 4912.5 kN-m OK 45.7 5033.448.8 5629.0551.8 6257.7

SHEAR DESIGN 54.9 6918.657.9 7612.05

Vp = 0 kN no draped tendons exist 61 8337.967.1 9887.55

Critical shear section approax. = de = h-ybs = 195.38 cm 73.2 11567.2579.2 13377.15

Vdc = 193.9 kN 85.3 15317.25Vdw = 20.9 kN 91.4 17387.55Vll= 424.35 kN from the live loads tableVll+im = 242.6 kN

Vu = 698.3 kNVc = 349.5 kNVu = 698.3 > 157.3 kN provide stirrups

Vn > Vu/phi = 775.8 kN

Req'd Vs = 426.3 kN

= 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 8 dia @ 15 mm stirrups

Check minumum required reinforcement and maximum nominal capacity that can be provided by shear reinforcementNot done in this spreadsheet

Mr = n

H30-S24

kN213.45213.45213.45213.45213.45213.45213.45213.45213.45213.45213.45213.45213.45213.45227.55240.15251.55260.85269.55

277.5284.85290.85296.85302.25307.65

312.3316.2

320.25325.65

End shear and end reaction

330.9335.55

340.2344.25

348.3352.35355.65358.95362.25

365.7368.25373.65

378.3382.35

387387

390.3394.35397.65400.35403.05

405.6408.3410.4

412.95414.3416.4

421.05424.35427.65430.35433.05435.75439.65442.95451.05472.35

493.8515.1536.4

557.85579.15600.45

643.2685.95728.55

771.3814.05

GIRDER TYPE 1

Input lenghts (cm)X1 66.04 A(cm2) yb (cm) A*yb IxX2 101.6 A1 1341.9328 10.16 13634.03725 46173.94X3 15.24 A2 645.16 28.79 18572.00587 23123.97X4 10.16 A3 387.096 33.02 12781.90992 20811.57Y1 20.32 A4 1625.8032 99.06 161052.065 1541887.69Y2 25.4 A5 103.2256 159.17 16430.76284 591.97Y3 106.68 A6 154.8384 157.48 24383.95123 1331.94Y4 10.16 A7 251.6124 167.64 42180.30274 811.65Y5 7.62 A8 270.9672 166.37 45080.81306 1311.13Y6 12.7 A9 1290.32 176.53 227780.1896 17342.98

561896.0375 1653386.842

XX --> A 6070.9556 cm2Strong axis yb' 92.55 cm

IXX 27,932,801.336 cm4

6.711E+05

YY --> A 6070.9556 cm2Weak Axis yl' 50.80 cm

IYY 2.095E+06 cm4

GIRDER TYPE 2

Required lenghts (cm)X1 75 A(cm2) yb (cm) A*yb IxX2 75 A1 1125 7.5 8437.5 21093.75X3 20 A2 275 18.33 5041.666667 1527.78Y1 15 A3 200 20 4000 1666.67Y2 10 A4 650 41.25 26812.5 57213.54Y3 32.5 A5 206.25 62.5 12890.625 644.53Y4 7.5 A6 150 61.25 9187.5 703.13Y5 10 A7 750 70 52500 6250.00

118869.7917 89099.39

XX --> A 3356.25 cm2Strong axis yb' 35.42 cm

IXX 2.264E+06 cm4

YY --> A 3356.25 cm2Weak Axis yl' 37.50 cm

IYY 1.109E+06 cm4

Calculation of IXX

Calculation of IXX

A*(yb-yb')^2 A yl A*yl Iy A*(yl-yl')^29110250.10 A1 1341.9328 50.80 68170.19 487712.24 0.002623461.79 A2 322.58 34.71 11197.83 11561.98 83477.521372019.79 A3 322.58 66.89 21576.30 11561.98 83477.5268800.29 A4 387.096 50.80 19664.48 7492.17 0.00458118.30 A5 1625.8032 50.80 82590.80 31467.10 0.00652687.60 A6 51.6128 39.79 2053.85 295.99 6252.721418537.46 A7 51.6128 61.81 3190.02 295.99 6252.721476414.87 A8 154.8384 50.80 7865.79 2996.87 0.009099124.29 A9 125.8062 22.01 2769.41 7620.50 104252.1026279414.4938 A10 125.8062 79.59 10012.50 7620.50 104252.10

A11 270.9672 50.80 13765.13 28553.48 0.00A12 1290.32 50.80 65548.26 1109950.47 0.00

308404.54 1707129.26 387964.69

A*(yb-yb')^2 A yl A*yl Iy A*(yl-yl')^2876806.55 A1 1125 37.50 42187.50 527343.75 0.0080263.37 A2 137.5 18.33 2520.83 5776.91 50512.1547539.51 A3 137.5 56.67 7791.67 5776.91 50512.1522112.17 A4 200 37.5 7500.00 6666.666667 0.00151277.14 A5 650 37.50 24375.00 21666.67 0.00100098.15 A6 103.125 18.33 1890.63 4332.68 37884.11896964.96 A7 103.125 56.67 5843.75 4332.68 37884.112175061.85 A8 150 37.5 5625.00 5000 0.00

A9 750 37.50 28125.00 351562.50 0.00 125859.38 932458.77 176792.53

Calculation of IYY

Calculation of IYY

AASHTOLRFDSectionComposer