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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


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