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Bridge Design Manual - 2002

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Appendix GB

Girder Bridge Design

Project:

Name of River:

Span : 16.60 m c/c , T-girder bridge

Consultant: Louis Berger Group in association with SABA Engineering plcDesigned by : Henok Aberra ( Str. Engineer)

Checked by : Lennart Rahm (Bridge Engineer)

Case: Statical calculation

Given data:

No of girders = 3

c/c of support = 16. 60 m

Clear bridge wi dt h B = 7. 32 m

No of lane = 2

Face of railing/curb to end of slab = 0.40 m

Multiple presence factor = 1.00

Specification used : ERA Bridge Design Manual 2002

Rear Axle load = P = 145.00 kN

= 72.50 kN

Lane load in the transverse direction = 9.30 kN/3m

= 3.10 kN/m

Design tandem axle load = 110.00 kN

wearing surface = 1. 10 kN/m2

Highway railing design loading, PH= 44.48 kN

Material Properties

Type of concrete: C25 concrete cube or C20 cylinderfc'= 20.00 Mpa

fc=0.4fc'= 8.000 Mpa

gc = 24.000 KN/m3

Type of steel :

For bars greater than f20 For bars less than or equal to f20

fyk = 400.00 MPa fyk = 350.00 MPa

fs = 160.00 Mpa fs = 175.00 Mpa

Es = 200000 Mpa

Ec = 0.043*gc*1.5*sqrt(fc') = 22610 Mpa

Others

modular ratio n=Es/Ec= 9

fmoment = 0.9

fshear = 0.85

b = 0.85Modulus of rupture =fr =0.63sqrt(fc') = 2.82 MPa Eq. 9.5

z in Eq. 9.15 = 30000 kPa

For rebar f > 20 mm

rb = 0.85b1fc'/fy*(599.843/(599.843+fy)) = 0.0217

For rebar f


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Appendix GB


Load Factors

Dead load limit state factor = 1.25

Live load limit state factor = 1.75

Dead load service state factor = 1.00

Live load service state factor = 1.30

Fatique Live load factor = 0.75

Preliminary dimensions

girder depth =0.070*s = 1.162 m

girder depth provided = Dgirder = 1.300 m

c/c of girder spacing = 2.600 m

End of slab to center of exterior girder = 1.460 m

web width recommended = 0.376 m

web width provided = 0.380 m

clear span b/n girders = 2.220 m

Top slab thickness = Tslab = 0.220 m

overhang slab thickness provided = 0.220 m

overhang slab thickness near edge beam = 0.180 m

Edge beam depth from side = 0.400 mEdge beam depth beneath the bottom slab level = 0.205 m

Width of edge beam = 0.400 m

Total top width = 8.120 m

fillet = 0.000 m

Exterior diapragm depth = 1.000 m

Interior diapragm depth = 1.000 m

width of diphragm = 0.250 m

Total No of diaphragm = 3

c/c distance b/n diaphragm = 8.300 m

TYPICAL CROSS SECTION

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Ethiopian Roads Authority Page GB-2


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Appendix GB


GB.1 Design of overhang

GB.1.1 Dead loadtotal overhang length = 1.270 m

Item weight moment Moment depth of railing = 0.300 m

[KN/m] arm [m] [KNm/m] breadth of railing = 0.250 m

Top slab 6.096 0.635 3.871 distance b/n post and curb end = 0.050 m

Bottom Part of

Edge beam 1.972 1.070 2.110 distance b/n back of railing and end of curb = 0.15 m

railing 1.800 0.995 1.791 depth of post = 0.250 m

post 0.960 1.095 1.051 width of post = 0.300 mwearing su. 0.957 0.435 0.416 c/c of post = 1.500 m

total 11.785 9.239 height of post = 0.800 m

GB.1.2 Live load

a) Railing loadRailing loads shall be applied on an effective length of E =1140+0.833X, Eq. 7.14

E = 1140+0.833X [mm] where: X- is the distance in mm from the center of the post to

= 1.565 m the point under investigation

According to Art. 2.7 of the AASHTO 1996, the design load, P is ,

P = 44.51 kN height of top of rail from top of curb = 0.90 m

Moment arm = 1.010 m

Therefore the railing live load is as follows:

MRLL = 28.73 kNm/m

b) Truck loadAccording to Art. 7.4 Slabs/Longitudinal Edges, the wheel is put 300mm from face of rail

Eoverhang = 1140+0.833X Where : X = Distance from load to point of support [mm]

= 1614.8 mm = 570 mm

MLL = 25.59 kNm/m

MLL+I = 34.04 kNm/m

dist. from face of rail to overhanging gir. face = 0.870 m

Lane load moment = 1.173 kNm/m

MTotal = 35.21 kNm/m

OVERHANG SLAB

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Appendix GB


GB.1.3 Total moment

a) Dead load plus rail live load

MTR = 1.25MDL+1.75MRLL

= 61.82 kNm/m

b) Dead load plus truck live load

MTT = 1.25MDL+1.75MLL= 73.17 kNm/m

c) Design moment

MD = max(MTR,MTT)

= 73.17 kNm/m

GB.1.4 Design for flexure

Mu= 73.17 kNm/m fmoment = 0.9

dreqd =sqrt(Mu/(frmaxbfy(1-.6rmaxfy/fc')) = 110.76 mm fy = 350.000 MPa

Dreqd =Dreqd+f/2+cover = 168.76 mm fc' = 20.000 MPa

Dprov = 220 mm

dprov=Dprov-f/2-cover = 162.00 mm b = 1000 mm

a=Asfy/(.85fc'b) = 32.85 mm dia. of bar =f = 16 mm

As =Mu/(ffy(d-a/2)) = 1595.550 mm2/m cover = 50 mm

r max= 0.020

r prov=As/bd = 0.010 OK !

Smax = 330 mm

use f 16 c/c 120 mm

As prov. = 1675.52 mm2

ALTERNATIVE

use f 16 c/c 190 mm

and

f 12 c/c 210 mm

GB.2 Design of slab

GB.2.1 Design of Interior spans

GB.2.1.1 Dead load

a) Overhang part ( Upto middle of ext. girder)

total overhang length = 1.460 m

Item weight

moment

arm Moment depth of railing = 0.300 m

[KN/m] [m] [KNm/m] breadth of railing = 0.250 m

Top slab 7.709 0.730 5.627 distance b/n post and curb end = 0.050 m

Bottom Part of

Edge beam 1.972 1.260 2.485 distance b/n back of railing and end of curb = 0.15 m

railing 1.800 1.185 2.133 depth of post = 0.250 m

post 0.960 1.285 1.234 width of post = 0.300 m

wearing su. 1.166 0.530 0.618 c/c of post = 1.500 m

total 13.607 12.097 height of post = 0.800 m

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Appendix GB


b) Middle part

slab = 5.28 KN/m2

wearing surfac e = 1.10 "

total 6.38 KN/m2

C

GB.2.1.2 Dead load momenta) Slab with two girders A B

Dead load Moment at the midspan

Conservatively, the flooring system is assumed simply supported b/n girder centers.

M = 5.39 kNm

b) Slab with more than two girders

In slabs continuous over more than two supports the dead load moment at support and midspan can be taken

as midspan moment for simply supported beam reduced by 20%.

Md =wl2/8*.8 =wl

2/10 = 4.31 KNm/m

GB.2.2 Live load moment a b a = 0.50 mmb = 1.30 mm

a) Slab with two girders

C

Distribution Widths A B

Eoverhang = 1140+0.833X Where : X = Distance from load to point of support [mm]

= 1614.8 mm = 570 mm

Epositive = 660+0.55*S S = girder spacing [mm]

= 2090 mm

Enegitive = 1220+0.25*S

1870 mm

Moverhang = PX/E

= 25.59 kNm

Live load Moment at the interior wheel location

Reaction at Support A = 122.69 kN

Minterior wheel = 13.88 kNm

b) Slab with more than two girders

Two charts were prepared and equations are drived from the "Trend line" both forpositive and negative moments. Though the spacing is center to center of support, consideration

is taken for the reduction with monoliticity and width of the web. For the derivation of the equation

look at the "Slab design coeff." calculations. For slab supported on two girders, the overhang cantilever

moment is compared with this value and the maximum is taken.

Let x be the center to center of girder spacing.

Mneg = 0.1815x5-3.9473x

4+29.948x

3-100.41x

2+160.34x-86.671

= 18.99 kNm/m

and

Mpos = -0.8166x3+7.8442x

2-16.085x+30.271

= 27.12 kNm/m

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Appendix GB


Impact

According to subchapter 3.13, Table 3-8, the dynamic load allowance is taken to be 33% for the strength limit state

design considerations.

Therefore take I = 0.33

SummaryDead load moments

Negative moment at support = 4.31 kNm

Positive moment at midspan = 4.31 "Live load moments

Negative moment at support = 18.99 kNm

Positive moment at midspan = 27.12 "

GB.2.3 Factored design moment

Mneg =1.25MD+1.75(ML+I)= 49.59 KNm/m

Mpos =1.25MD+1.75(ML+I)= 68.52 KNm/m

GB.2.4 Design for flexure

GB.2.4.1 Slab top reinforcementMu= 49.59 KNm/m

dreqd =sqrt(Mu/(frmaxbfy(1-.6rmaxfy/fc')) = 91.18 mm fmoment = 0.9fy = 350.000 MPaDreqd =Dreqd+f/2+cover = 149.18 mm fc' = 20.000 MPa

Dprov = 220 mm


a=Asfy/(.85fc'b) = 21.42 mm a. of bar =f = 16 mm


r max= 0.020

r =As/bd = 0.006 OK !

Smax = 330 mm

use f 16 c/c 190 mm

As prov. = 1058.22 mm2

GB.2.4.2 Slab bottom reinforcementMu= 68.52 KNm/m

dreqd =sqrt(Mu/(frmaxbfy(1-.6rmaxfy/fc')) = 107.18 mm fmoment = 0.9fy = 350.0 MPa

Dreqd =Dreqd+f/2+cover = 140.18 mm fc' = 20.0 MPa

Dprov = 220 mm


a=Asfy/(.85fc'b) = 25.72 mm a. of bar =f = 16 mm


r =As/bd = 0.007 OK !

Smax = 330 mm

use f 16 c/c 160 mm

As prov. = 1256.64 mm2

GB.2.4.3 Distribution reinforcement

According to Eq. 12.12, the amount of distribution reinforcement shall be the percentage of the main

reinforcement steel required for positive moment as given by the following formula:

Percentage = 3840/sqrt(s)


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Appendix GB


GB.3. Design of Girder

GB.3.1 Exterior Girder

GB.3.1.1 Dead load

GB.3.1.1.1 Dead load of girder

Item Weight[KN/m]

overhang 11.785

Top slab 5.861

girder 11.856

fillet 0.000

wearing surface 1.639

Total 31.141

GB.3.1.1.2 Dead load of diaphragm

a) Near center of span b) Near end of span

Item Weight[KN] Item Weight[KN]

Diaphragm 5.19 Diaphragm 5.19

Fillet 0.00 Fillet 0.00

Total 5.19 Total 5.19

EXTERIOR GIRDER CROSS SECTION

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Appendix GB


GB.3.1.1.3 Dead load shear and moment

a Girder

Reaction at support =wL/2 = 258.47 KN

* Point of maximum live load moment =(L/2-.711)/L = 0.457

a x [m] VA [KN] Mo[KNm]

0.00 0.00 258.47 0.000.05 0.83 232.62 203.80

0.10 1.66 206.77 386.15

0.15 2.49 180.93 547.05

0.20 3.32 155.08 686.49

0.25 4.15 129.23 804.48

0.30 4.98 103.39 901.02

0.35 5.81 77.54 976.10

0.40 6.64 51.69 1029.73

0.45 7.47 25.85 1061.91

0.50 8.30 0.00 1072.64

b Diaphragm

Reaction at support due to the midway diaphragms = 2.60 KN


0.00 0.00 2.60 0.00

0.05 0.83 2.60 2.16

0.10 1.66 2.60 4.31

0.15 2.49 2.60 6.47

0.20 3.32 2.60 8.62

0.25 4.15 2.60 10.78

0.30 4.98 2.60 12.94

0.35 5.81 2.60 15.09

0.40 6.64 2.60 17.25

0.45 7.47 2.60 19.40

0.50 8.30 2.60 21.56

GB.3.1.2 Live load

GB.3.1.2.1 Lane load ( Uniformly distributed load)

The design lane load shall consist of a load of 9.3 N/mm, uniformly distributed in the longitudinal direction.

Transversely, the design lane load shall be assumed to be uniformly distributed over a 3000 mm width. The

force effects from the design lane load shall not be subject to a dynamic load allowance.

Line load per meter on the int. gir.for shear = 7.73 kN/m

Reaction at support =wL/2 = 64.13 kN

Line load per meter on the int. gir.for moment = 7.73 kN/m


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Appendix GB



0.00 0.00 64.13 0.00

0.05 0.83 57.71 50.56

0.10 1.66 51.30 95.81

0.15 2.49 44.89 135.72

0.20 3.32 38.48 170.32

0.25 4.15 32.06 199.60

0.30 4.98 25.65 223.550.35 5.81 19.24 242.18

0.40 6.64 12.83 255.48

0.45 7.47 6.41 263.47

0.50 8.30 0.00 266.13

GB.3.1.2.2 Standard truck load

a) Transversal distribution of wheel load

I) Distribution coefficient for moment in exterior girder

For one design lane loaded the lever rule method is applied.

Distance of first line of wheel from face of rail = 0.60 m

Distance of second line of wheel from face of rail = 2.40 mAccording to Art. 3.8 Live Load/Multiple Presence of Live Load, the multiple presence factor is applied where the lever rule is used.

Rex moment(1) = 1.662

The live load flexural moment for exterior beams with concrete decks may be determined by applying the lane load

fraction specified as follows:

For two or more design lanes are loaded: Where : de is the distance in mm from the face of

rail to exterior face of exterior girder. It is positive

de = 870 m if the exterior web is inboard and vise versa.

Rex moment(2) = (0.77+de/2800)*Rin moment -300


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Appendix GB


b) Longitudinal distribution of wheel load

Case -1 Moment and shear at rear wheel position ( truck moving to the right )

a x x1 x2 x3 VA Mo

0.00 0.00 8.000 12.300 16.600 1.861 0.000

0.05 0.83 7.170 11.470 15.770 1.749 1.452

0.10 1.66 6.340 10.640 14.940 1.636 2.717

0.15 2.49 5.510 9.810 14.110 1.524 3.795

0.20 3.32 4.680 8.980 13.280 1.411 4.686

0.25 4.15 3.850 8.150 12.450 1.299 5.391

0.30 4.98 3.020 7.320 11.620 1.186 5.909

0.35 5.81 2.190 6.490 10.790 1.074 6.240

0.40 6.64 1.360 5.660 9.960 0.961 6.384

0.45 7.47 0.530 4.830 9.130 0.849 6.342

0.50 8.30 0.000 4.000 8.300 0.741 6.150

Case -2 Moment and shear at middle wheel position ( truck moving to the left )

a x x1 x2 x3 VA Mo

0.25 4.15 8.150 12.450 0.000 1.241 5.150

0.30 4.98 7.320 11.620 15.920 1.381 5.801

0.35 5.81 6.490 10.790 15.090 1.268 6.293

0.40 6.64 5.660 9.960 14.260 1.156 6.599

0.45 7.47 4.830 9.130 13.430 1.043 6.718

0.50 8.3 4.000 8.300 12.600 0.931 6.650

CASE-2P/4 P P

PCASE-1 P P/4

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Appendix GB


Summary of maximum live load shear and moments plus impact at different points

Impact

Take I = 0.330

1+I = 1.330

a x VA Mo VA [KN/m] Mo[KNm/m]

0.00 0.00 2.476 0.000 362.36 0.000.05 0.83 2.326 1.931 337.92 283.13

0.10 1.66 2.176 3.613 313.48 531.03

0.15 2.49 2.027 5.047 289.05 743.68

0.20 3.32 1.877 6.232 264.61 921.08

0.25 4.15 1.728 7.170 240.17 1063.25

0.30 4.98 1.578 7.858 215.74 1170.17

0.35 5.81 1.428 8.370 191.30 1250.46

0.40 6.64 1.279 8.777 166.86 1312.73

0.45 7.47 1.129 8.935 142.43 1339.76

0.50 8.30 0.985 8.845 118.71 1331.55

GB.3.1.2.3 Design Tandem

P' for shear = 91.38 kN

P' for moment = 91.38 kN

Spacing b/n the axles = 1.20 m

Case -1 Moment and shear at the left wheel position

P'P'

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Appendix GB


a x [m] x1 [m] x2 [m] VA [KN] Mo[KNm]

0.00 0.00 15.40 16.60 1.928 0.00

0.05 0.83 14.57 15.77 1.828 1.52

0.10 1.66 13.74 14.94 1.728 2.87

0.15 2.49 12.91 14.11 1.628 4.05

0.20 3.32 12.08 13.28 1.528 5.07

0.25 4.15 11.25 12.45 1.428 5.930.30 4.98 10.42 11.62 1.328 6.61

0.35 5.81 9.59 10.79 1.228 7.13

0.40 6.64 8.76 9.96 1.128 7.49

0.45 7.47 7.93 9.13 1.028 7.68

0.50 8.30 7.10 8.30 0.928 7.70

Case -2 Moment and shear at the right wheel position

a x [m] x1 [m] x2 [m] VA [KN] Mo[KNm]

0.00 0.00 16.60 0.00 1.000 0.00

0.05 0.83 15.77 0.00 0.950 0.79

0.10 1.66 14.94 16.14 1.872 1.91

0.15 2.49 14.11 15.31 1.772 3.21

0.20 3.32 13.28 14.48 1.672 4.35

0.25 4.15 12.45 13.65 1.572 5.33

0.30 4.98 11.62 12.82 1.472 6.13

0.35 5.81 10.79 11.99 1.372 6.77

0.40 6.64 9.96 11.16 1.272 7.25

0.45 7.47 9.13 10.33 1.172 7.56

0.50 8.30 8.30 9.50 1.072 7.70

Summary :- The maximum live load shear and flexure with impact at different points are as follows


0.00 0.00 298.4 0.00

0.05 0.83 279.9 234.94

0.10 1.66 261.3 444.39

0.15 2.49 242.7 628.33

0.20 3.32 224.2 786.78

0.25 4.15 205.6 919.73

0.30 4.98 187.0 1027.18

0.35 5.81 168.5 1109.13

0.40 6.64 149.9 1165.59

0.45 7.47 131.3 1196.54

0.50 8.30 112.8 1202.00

P' P'

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Appendix GB


GB.3.1.2.4 Summary of total dead and live load moments

According to subchapter 3.3, the coefficients for load factor service load design are as follows:

For standard truck & lane , design tandem loading

Vu = 1.25VDL+1.75VLL+I Vs = VDL+VLL+I

Mu = 1.25MDL+1.75MLL+I Ms = MDL+MLL+I

The load summary adds up the dead loads and the maximum of the two live load cases,

(i.e standard truck & lane loading).

a x Vu[KN/m] Mu[KNm/m] Vs[KN/m] Ms[KNm/m]

0.00 0.00 960.45 0.00 732.13 0.00

0.05 0.83 885.38 752.93 674.51 574.03

0.10 1.66 810.31 1417.37 616.90 1080.80

0.15 2.49 735.24 1993.33 559.28 1520.29

0.20 3.32 660.16 2480.79 501.67 1892.52

0.25 4.15 585.09 2879.76 444.06 2197.48

0.30 4.98 510.02 3190.24 386.44 2435.17

0.35 5.81 434.95 3427.30 328.83 2616.79

0.40 6.64 359.87 3606.01 271.21 2753.53

0.45 7.47 284.80 3696.23 213.60 2823.01

0.50 8.30 210.99 3697.96 156.92 2825.21

GB.3.2 Interior Girder

GB.3.2.1 Dead load

GB.3.2.1.1 Dead load of girder

Item Weight[KN/m]

Top slab 11.722

girder 9.850

fillet 0.000

wearing surface 2.860

Total 24.431

GB.3.2.1.2 Dead load of diaphragm

a) Near center of span b) Near end of span

Item Weight[KN] Item Weight[KN]

Diaphragm 10.39 Diaphragm 10.39

Fillet 0.00 Fillet 0.00

Total 10.39 Total 10.39

INTERIOR GIRDER CROSS SECTION

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Appendix GB


GB.3.2.1.3 Dead load shear and moment

a) GirderReaction at support =wL/2 = 202.78 KN

* Point of maximum live load moment =(L/2-.711)/L = 0.457


0.00 0.00 202.78 0.00

0.05 0.83 182.50 159.890.10 1.66 162.22 302.95

0.15 2.49 141.95 429.18

0.20 3.32 121.67 538.58

0.25 4.15 101.39 631.15

0.30 4.98 81.11 706.89

0.35 5.81 60.83 765.79

0.40 6.64 40.56 807.87

0.45 7.47 20.28 833.12

0.50 8.30 0.00 841.53

b) Diaphragm

Reaction at support due to the midway diaphragms = 5.19 KN


0.00 0.00 5.19 0.00

0.05 0.83 5.19 4.31

0.10 1.66 5.19 8.62

0.15 2.49 5.19 12.94

0.20 3.32 5.19 17.25

0.25 4.15 5.19 21.56

0.30 4.98 5.19 25.87

0.35 5.81 5.19 30.18

0.40 6.64 5.19 34.49

0.45 7.47 5.19 38.81

0.50 8.30 5.19 43.12

GB.3.2.2 Live load

GB.3.2.2.1 Lane load

Remark: In the following Table impact and the transversal distribution factors are included.

Line load per meter on the int. gir.for shear = 8.03 kN/m


Line load per meter on the int. gir.for moment = 6.71 kN/m


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Appendix GB


a x VA [KN/m] Mo[KNm/m]

0.00 0.00 66.63 0.00

0.05 0.83 59.97 43.91

0.10 1.66 53.30 83.20

0.15 2.49 46.64 117.86

0.20 3.32 39.98 147.90

0.25 4.15 33.31 173.330.30 4.98 26.65 194.12

0.35 5.81 19.99 210.30

0.40 6.64 13.33 221.86

0.45 7.47 6.66 228.79

0.50 8.30 0.00 231.10

GB.3.2.2.2 Standard truck load

a) Transversal distribution of wheel load

I) Distribution coefficient for moment in interior girder

The live load flexural moment for interior beams with concrete decks may be determined by applying the lane load

fraction specified as follows:

For one design lane loaded:According to Art. 3.8 Live Load/Multiple Presence of Live Load, the distribution factor where single lane approximation distribution

is used has to be divided by 1.20.

Rin moment(1) = 0.06+(S/4300)0.4

(S/L)0.3

(Kg/Lts3)

0.1Where :

= 0.441 (Kg/Lts3) may be taken as 1.0

1100


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Appendix GB


b) Longitudinal distribution of wheel load

Summary of maximum live load shear and moments plus impact at different points

a x VA Mo VA [KN/m] Mo[KNm/m]

0.00 0.00 2.476 0.000 376.49 0.00

0.05 0.83 2.326 1.931 351.10 245.87

0.10 1.66 2.176 3.613 325.71 461.130.15 2.49 2.027 5.047 300.32 645.80

0.20 3.32 1.877 6.232 274.93 799.85

0.25 4.15 1.728 7.170 249.54 923.31

0.30 4.98 1.578 7.858 224.15 1016.16

0.35 5.81 1.428 8.370 198.76 1085.88

0.40 6.64 1.279 8.777 173.37 1139.95

0.45 7.47 1.129 8.935 147.98 1163.43

0.50 8.30 0.985 8.845 123.34 1156.29

GB.3.2.2.3 Design tandem

P' for shear = 64.36 kN

P' for moment = 48.48 kN


0.00 0.00 231.6 0.00

0.05 0.83 216.4 141.72

0.10 1.66 201.2 268.12

0.15 2.49 186.0 379.20

0.20 3.32 170.7 474.94

0.25 4.15 155.5 555.36

0.30 4.98 140.3 620.46

0.35 5.81 125.1 670.23

0.40 6.64 109.9 704.68

0.45 7.47 94.6 723.80

0.50 8.30 79.4 727.59

GB.3.2.2.4 Summary of total dead and live load moments

According to subchapter 3.3, the coef. for load factor service load design are as follows:

For standard truck & lane , and design tandem loading

Vu = 1.25VDL+1.75VLL+I Vs = VDL+VLL+I

Mu = 1.25MDL+1.75MLL+I Ms = MDL+MLL+I

The load summary adds up the dead loads and the maximum of the two live load cases,

(i.e standard truck & lane loading).

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Appendix GB



0.00 0.00 918.83 0.00 697.41 0.00

0.05 0.83 849.05 635.52 644.13 483.83

0.10 1.66 779.27 1196.45 590.84 911.05

0.15 2.49 709.49 1682.79 537.56 1281.65

0.20 3.32 639.71 2094.53 484.27 1595.64

0.25 4.15 569.93 2431.67 430.99 1853.010.30 4.98 500.15 2694.22 377.70 2053.76

0.35 5.81 430.37 2895.26 324.42 2207.62

0.40 6.64 360.59 3047.88 271.13 2324.31

0.45 7.47 290.81 3125.90 217.85 2384.38

0.50 8.30 222.34 3129.33 165.54 2387.83

GB.3.3 Summary of Girder shear and moment for design


0.00 0.00 960.45 0.00 732.13 0.00

0.05 0.83 885.38 752.93 674.51 574.03

0.10 1.66 810.31 1417.37 616.90 1080.80

0.15 2.49 735.24 1993.33 559.28 1520.29

0.20 3.32 660.16 2480.79 501.67 1892.520.25 4.15 585.09 2879.76 444.06 2197.48

0.30 4.98 510.02 3190.24 386.44 2435.17

0.35 5.81 434.95 3427.30 328.83 2616.79

0.40 6.64 360.59 3606.01 271.21 2753.53

0.45 7.47 290.81 3696.23 217.85 2823.01

0.50 8.30 222.34 3697.96 165.54 2825.21

FACTORED LOADS MOMENT DIAGRAM

y = -59.586x2

+ 937.13x + 15.07

0

500

1000

1500

2000

2500

3000

3500

4000

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00

x [m]

Mu[KNm]

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Appendix GB


GB.3.4 Design for Flexure

GB.3.4.1. Exterior girder design

The reinforcement c/c spacing limits according to subchaper 7.3 are as follows:

min. horizontal c/c spacing b/n bars in the web = 0.11 m

min. horizontal c/c spacing b/n bundle bars = 0.11 m

Prov. No of bar in the bottom flange =a= 4

min.vertical c/c spacing b/n bars =s= 0.09 mma x. No of ba r per row in the web =b= 4

center of bottom bar to bottom of girder =x= 0.07 m

center of bottom corner bar to nearest side of girder = 0.07 m

GB.3.4.1.1 Effective flange width for flexural compression

The total width of slab effective as a T-girder flange shall not exceed one fourth of

the span length of the girder, c/c spacing b/n girders( if total No of girders is greater or equal to 3), half of c/c spacing

b/n girders plus over hang length (where the effective flange width overhanging on one side of the web shall not exceed

six times the thickness of slab) plus half web width.

The effective flange width may be taken as one-half the effective width of the adjacent interior beam plus the least of:

- one-eighth of the effective span length

- 6.0 times the average thickness of the slab, plus the greater of half the web thickness or one quarter of thewidth of the top flange of the basic girder, or

- the width of the overhang

befff comp.= 2.760 m

SERVICE LOADS MOMENT DIAGRAM

y = -45.376x2

+ 714.8x + 11.195

0

400

800

1200

1600

2000

2400

2800

3200

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00x [m]

Ms[KNm]

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___________________________________________________________________________________________________

Appendix GB


GB.3.4.1.2 Web width for computation of equivalent concrete area for Serviceability requirements

befff dist.= 0.380 m

GB.3.4.1.3 Serviceability RequirementsFor flexural members designed with reference to load factor and strengths by strength design method, stresses at service

load shall be limited to satisfy the requirements for fatigue and for distribution of reinforcement.

The requirements for control of deflection shall also be checked.

GB.3.4.1.3.1 Fatigue stress limits

Spacing b/n the 35kN and 145kN axels = 4.30 m

Spacing b/n the 145kN and 145kN axels = 9.00 m

Impact

Take I = 0.150

1+I = 1.150

Design Truck moment

Case -1 Moment at rear wheel position (truck moving to the right )

a = x/L x x1 x2 x3 VA Mo

0.00 0.00 3.300 7.600 16.600 1.508 0.000

0.05 0.83 2.470 6.770 15.770 1.395 1.158

0.10 1.66 1.640 5.940 14.940 1.283 2.129

0.15 2.49 0.810 5.110 14.110 1.170 2.913

0.20 3.32 0.000 4.280 13.280 1.058 3.512

0.25 4.15 0.000 3.450 12.450 0.958 3.975

0.30 4.98 0.000 2.620 11.620 0.858 4.272

0.35 5.81 0.000 1.790 10.790 0.758 4.403

0.40 6.64 0.000 0.960 9.960 0.658 4.368

0.45 7.47 0.000 0.130 9.130 0.558 4.167

0.50 8.30 0.000 0.000 8.300 0.500 4.150

Case -2 Moment and shear at middle wheel position (truck moving to the left )

a = x/L x x1 x2 x3 VA Mo

0.25 4.15 3.450 12.450 0.000 0.958 3.975

0.30 4.98 2.620 11.620 15.920 1.098 4.399

0.35 5.81 1.790 10.790 15.090 0.985 4.657

0.40 6.64 0.960 9.960 14.260 0.873 4.727

0.45 7.47 0.130 9.130 13.430 0.760 4.611

0.50 8.3 0.000 8.300 12.600 0.690 4.658

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Appendix GB


Summary:- The maximum of the above moments is taken

Remark :- The maximum of the two live load distribution coefficient is taken.

- The multiple presence factor is not considered for fatique limit state analysis.

a = x/L

Mdead

Exterior

Mdead

Interior

M truck

Exterior

M truck

Interior

0.00 0.00 0.00 0.0 0.0

0.05 205.96 164.20 153.2 96.80.10 390.46 311.58 283.6 179.7

0.15 553.51 442.12 391.1 249.0

0.20 695.11 555.83 475.8 304.5

0.25 815.26 652.71 543.0 349.1

0.30 913.95 732.76 589.4 381.1

0.35 991.19 795.98 615.2 400.4

0.40 1046.98 842.36 620.2 407.2

0.45 1081.32 871.92 604.5 401.3

0.50 1094.20 884.65 604.5 402.1

Max 1094.20 884.65 620.22 407.15

The stress range in straight reinfororcement resulting from the fatique load combination, specified in Table 3-2, shall

not exceed :

ff= 145-0.33fmin+55(r/h) [MPa] r/h = 0.3

fLL = 50.37 MPa

fDL =fmin = 88.86 MPa

ff = 132.18 MPa OK !

GB.3.4.1.3.2 Distribution of Flexural Reinforcements

To control flexural cracking of the concrete, tension reinforcement shall be well distributed within the maximum

flexural zones. To prevent this kind of cracking, the calculated stress in the reinforcement at service load ,fs, in

ksi shall not exceed the value computed by ,

fs = z/(dcA)1/3


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Appendix GB


GB.3.4.1.4 Reinforcement proportioning

Mmax = 3698 KNm coef. of d = 1.000

The following parameters are read from trendline eq. on the moment diagram charts.

y = ax2+bx+c

Factored moment a= -59.586 b= 937.13 c= 15.07

Service load moment a= -45.38 b= 714.8 c= 11.195

No of bar(or N) 15 14 12 10 8 6 OK !

bar size [mm] 32 32 32 32 32 32 OK !!

As[mm2] 12063.7 11259.5 9651.0 8042.5 6434.0 4825.5

No of row(or k) 4 4 3 3 2 2

x bar [m] 0.196 0.186 0.160 0.142 0.115 0.100

d [m] 1.10 1.11 1.14 1.16 1.19 1.20

r 0.0040 0.0037 0.0031 0.0025 0.0020 0.0015

fy[Mpa] 400.000 400.000 400.000 400.000 400.000 400.000

a[mm] 102.845 95.989 82.276 68.563 54.851 41.138

Asf[mm2

] - - - - - -

As-Asf[mm2

] 12063.72 11259.47 9650.97 8042.48 6433.98 4825.49

a'[mm] - - - - - -

Mu[KNm] 4571.28 4322.11 3817.83 3253.49 2681.21 2048.88theo. dist. from midspan of Mu - 0.000 0.000 3.173 4.571 5.700

Remark Rect.Beam Rect.Beam Rect.Beam Rect.Beam Rect.Beam Rect.Beam

rn 0.0356 0.0329 0.0276 0.0226 0.0177 0.0131

t/d 0.199 0.197 0.193 0.190 0.186 0.183

k 0.236 0.228 0.210 0.191 0.172 0.152

kd [mm] 260.78 253.63 238.90 221.62 203.59 182.76

j 0.925 0.926 0.931 0.936 0.943 0.949

A [mm2/bar] 9930.67 10081.63 10133.33 10792.00 10925.00 12666.67

fs of eq.8-61 [MPa] 240.00 240.00 240.00 240.00 240.00 240.00

Ms [KNm] 2955.37 2789.74 2458.20 2092.59 1725.03 1319.19

theo.dist.from midspan of Ms[m] - 1.320 3.272 4.445 5.350 6.187

Where:

xbar - centroid of rein. from bottom of girderxbar = (ax+b((k-1)x+s(k-1)k/2))/N

d = D-xbar

r =As/beff*d

a =Asfy/.85fc'b

If T-Beam

Asf=0.85fc'(b-bw)h f /fy

a' =(As-Asf)fy/0.85fc'bw

Mu =Muf+Muw ,if T-Beam

Muf =fAsf fy(d-hf/2)

Muw=f(As-Asf)fy(d-a/2)

If Rect. Beam

Mu=fAsfy(d-a/2)

k =(rn+0.5(t/d)2

)/(rn+t/d)

j =(6+6t/d+2(t/d)2+(t/d)3(1/2rn))/(6-3t/d),for kd>t

j =1-k/3, for kd


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Appendix GB


Extension length required at bar cutoffExtension length reqd beyond the point at which it is no longer required is given by ;

Lext reqd = max( 15*dia of bar,d eff,1/20 of clear span length )

= 1129.1 mm

Bar cut-off locations

Length of standard hook = 0.635 m

cover to hooked bar at end = 0.05 m

Total superstructure length = 16.90 m

G6 32 1 4322.11 2.641 4.899

G5 32 2 3817.83 6.543 8.801

G4 32 2 3253.49 8.889 11.147

G3 32 2 2681.21 10.700 12.958

G2 32 2 2048.88 12.373 14.631G1 32 6 - 17.751 17.751

GB.3.4.2. Interior girder design

The reinforcement c/c spacing limits according to subchapter 7.3 are as follows:

min. horizontal c/c spacing b/n bars in the web = 0.11 m

min. horizontal c/c spacing b/n bundle bars = 0.11 m

Prov. No of bar in the bottom flange =a= 4

min.vertical c/c spacing b/n bars =s= 0.09 m

ma x. No of ba r per row in the web =b= 4

center of bottom bar to bottom of girder =x= 0.07 m

center of bottom corner bar to nearest side of girder = 0.07 m

GB.3.4.2.1 Effective flange width for flexural compression

The total width of slab effective as a T-girder flange shall not exceed one fourth of

the span length of the girder,c/c spacing b/n girders( if total No of girders is greater or equal to 3).

For interior girder, the effective flange width may be taken as the least of:

- one-quarter of the effective span length

- 12.0 times the average thickness of the slab, plus the greater of half the web thickness or one quarter of the

width of the top flange of the girder, or

- the average spacing of the adjacent beams

befff comp.= 2.600 m

GB.3.4.2.2 Web width for computation of equivalent concrete area for Serviceability requirements

befff dist.= 0.380 m

Bar type

Bar size

[mm]

No.of

bar/gir.

Moment at

theor.

Cutoff

[KNm]

Theor.

Length [m]

Length with

extension

[m]

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Appendix GB


GB.3.4.2.3 Reinforcement proportioning

Mmax = 3697.96 KNm

The following parameters are read from trendline equation in the moment diagram charts.

y = ax2+bx+c

Factored moment a= -59.586 b= 937.13 c= 15.07

Service load moment a= -45.38 b= 714.8 c= 11.195

No of bar(or N) 15 14 12 10 8 6

bar size [mm] 32 32 32 32 32 32

As[mm2] 12063.7 11259.5 9651.0 8042.5 6434.0 4825.5

No of row(or k) 4 4 3 3 2 2

x bar [m] 0.196 0.186 0.160 0.142 0.115 0.100

d [m] 1.10 1.11 1.14 1.16 1.19 1.20

r 0.0042 0.0039 0.0033 0.0027 0.0021 0.0015

fy[Mpa] 400.000 400.000 400.000 400.000 400.000 400.000

a[mm] 109.174 101.896 87.339 72.783 58.226 43.670

Asf[mm2

] - - - - - -

As-Asf[mm2

] 12063.72 11259.47 9650.97 8042.48 6433.98 4825.49

a'[mm] - - - - - -

Mu[KNm] 4557.54 4310.14 3809.04 3247.38 2677.30 2046.68

theo. dist. from midspan of Mu - 0.000 0.000 3.192 4.579 5.703Remark Rect.Beam Rect.Beam Rect.Beam Rect.Beam Rect.Beam Rect.Beam

rn 0.0378 0.0350 0.0293 0.0240 0.0188 0.0139

t/d 0.199 0.197 0.193 0.190 0.186 0.183

k 0.243 0.234 0.216 0.197 0.176 0.156

kd [mm] 268.58 261.14 245.79 227.72 208.82 186.92

j 0.923 0.925 0.930 0.935 0.941 0.948

A [mm2/bar] 9930.67 10081.63 10133.33 10792.00 10925.00 12666.67

fs of eq.8-61 [MPa] 240.00 240.00 240.00 240.00 240.00 240.00

Ms [KNm] 2951.56 2785.97 2454.52 2088.98 1722.34 1317.58

theo.dist.from midspan of Ms[m] - 1.366 3.286 4.454 5.356 6.190

Where:

xbar - centroid of rein. from bottom of girder

xbar = (ax+b((k-1)x+s(k-1)k/2))/Nd = D-xbar

r =As/beff*d

a =Asfy/.85fc'b

If T-Beam

Asf=0.85fc'(b-bw)h f /fy

a' =(As-Asf)fy/0.85fc'bw

Mu =Muf+Muw ,if T-Beam

Muf =fAsf fy(d-hf/2)

Muw=f(As-Asf)fy(d-a/2)

If Rect. Beam

Mu=fAsfy(d-a/2)

k =(rn+0.5(t/d)2

)/(rn+t/d)

j =(6+6t/d+2(t/d)2+(t/d)

3(1/2rn))/(6-3t/d),for kd>t

j =1-k/3, for kd


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Appendix GB


Bar curtailment

The following parameters are read from trendline equation in the moment diagram chart.

y = ax2+bx+c

a= -59.586 b= 937.13 c= 15.07

Length of standard hook = 0.635 m

cover to hooked bar at end = 0.05 mTotal superstructure length = 16.90 m

G5 32 1 4310.14 2.731 4.989

G4 32 2 3809.04 6.571 8.830

G3 32 2 3247.38 8.909 11.167

G2 32 2 2677.30 10.712 12.970

G1 32 2 2046.68 12.379 14.637

G 32 6 - 17.751 17.751

GB.3.5 Design for Shear for Exterior and Interior girdersAccording to Eq. 12.25 and 12.26, Design of cross sections subject to shear shall be based on:

Vu s


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Appendix GB


Therefore, the max. spacing is the smaller of the two.

smax = 300 mm

Sections located less than a distance d from support may be designed for the same shear,V,

as that computed at a distance d. But in this case the shear at support is considered.

Vd = 859.4 kNSpacing at different points

vmax=Vd/bw*d = 2.048 MPa davg = 1129.07 mm

smin=fAvfy/(v-fvc)bw = 130.0 mm bw = 380 mm

The shear eq. from the shear force trendline is as follows : V = -ax+b

a = 89.471

b = 958.16

spacing bar size No of legs fy v-fvc v V ist.from su No of sp.

[mm] [mm] [MPa] [MPa] [MPa] [KN] [m]

60 12 2 350.00 - - - - 1

130 12 2 350.00 1.442 2.110 885.39 0.813 12

150 12 2 350.00 1.250 1.918 822.98 1.511 10

200 12 2 350.00 0.938 1.606 688.90 3.009 4

250 12 2 350.00 0.750 1.418 608.45 3.909 0

250 12 2 350.00 0.750 1.418 608.45 3.909 18

Total length = 8420 mm

N.B . The first bar shall be put at a distance not farther than half the minimum spacing from c/l of support.

FACTORED LOADS SHEAR FORCE DIAGRAM

y = -89.471x + 958.16

0

100

200

300

400

500

600

700800

900

1000

1100

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00

x [m]

Vu[KNm]

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Appendix GB


GB.4 Computation of skin reinforcementThe skin reinforcement on each face is given by the following formula.

N.B. Skin reinforcement is needed for D>900mm.

Ask>=0.001(d-760) ; but the spacing of bar shall not be greater than the lesser of d/6 or 300.

Ask >= 0.001(d-30) [mm2/mm] Where: d is in inches.

>= 369.071 mm2/m f of bar for skin rein. = 16 mm

smax = 180 mm

Use 2 f 16 c/c 180.0 mm

GB.5 Computation of Deflection

GB.5.1 Calculation of moment of inertias

GB.5.1.1 Calculation of gross moment of inertia

Remark : For simplifying the calculation the slab surface is assumed level, i.e. without crossfall.

The center of gravity from bottom of girder is calculated as follows:

Part

Area

[m2]

ycg

[m] Area*ycg

Slab 2.12 1.19 2.52 Ycg = S[Area*ycg]/S[Area]

Girder 1.2312 0.54 0.66 = 0.95 m

Sum 3.35 3.18

y* = ABS(ycg-Ycg)

Part

Area

[m2]

y*

[m] Icg A*(y*)2

Icg+A*(y*)2

Slab 2.12 0.24 0.01198 0.12096 0.1329

Girder 1.2312 0.41 0.11967 0.20789 0.3276

Sum, Ig = 0 .4 60 5 m

GB.5.1.2 Calculation of effective moment of inertia

Ie = [Mcr/Ma]3Ig+[1-(Mcr/Ma)

3]Icr


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Appendix GB


Part

Area

[m2]

ycg

[m] Area*ycg

Slab 2.116 1.17 2.48 Ycg = S[Area*ycg]/S[Area]

Girder 0.046 1.06 0.05 = 1.17 m

Transformed reinf. 0.109 0.20 0.02

Sum 2.16 2.52 y* = ABS(ycg-Ycg)

Part

Area

[m2]

y*

[m] Icg A*(y*)2

Icg+A*(y*)2

Slab 2.116 0.0024 0.01198 0.00001 0.0120

Girder 0.046 0.1077 0.00001 0.00054 0.0005

Transformed reinf. 0.109 0.9713 0.00000 0.10244 0.1024

Sum, Icr = 0.1150 m4

Therefore, the effective moment of inertia is,

Ie = [Mcr/Ma]3Ig+[1-(Mcr/Ma)

3]Icr


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Appendix GB


GB.5.1.4 Calculation of live load deflection using the effective moment of inertia

The live load deflection at middspan for different loading conditions that is analogous to the moving

load pattern is given as follows:

- When investigating the maximum absolute deflection, all design lanes should be loaded; and all

supporting components should be assumed to deflect equally.

- The live load portion of load combination Service I of Table 3-3( i.e, load factors for both live

and dead load equal to 1.0) with dynamic load allowance factor should be applied.

P with IM = 385.7 kN w lane load = 18.6 N/mm

x =l/2 = 8.3 def. Lane =5wl4/(384EI) = 5.50 mm

Px/(6eIl) = 9.61E-12 mm-2

According to Chapter 3,- The live load deflection should be taken as the larger of :

* That resulting from the design truck alone, or

* That resulting from 25 percent of the design truck together with the design lane load.

a x x1 x2 x3

Def at

midspan

(axle)

[mm]

Def at

midspan

(0.25*Axle

+

Lane)

[mm]

0.00 0.00 8.000 12.300 16.600 10.52 8.13

0.05 0.83 7.170 11.470 15.770 13.21 8.80

0.10 1.66 6.340 10.640 14.940 15.59 9.40

0.15 2.49 5.510 9.810 14.110 17.61 9.900.20 3.32 4.680 8.980 13.280 19.20 10.30

0.25 4.15 3.850 8.150 12.450 20.32 10.58

0.30 4.98 3.020 7.320 11.620 20.91 10.73

0.35 5.81 2.190 6.490 10.790 20.98 10.74

0.40 6.64 1.360 5.660 9.960 20.54 10.64

0.45 7.47 0.530 4.830 9.130 19.61 10.40

0.50 8.30 0.000 4.000 8.300 18.32 10.08

Therefore, the maximum live load deflection is the maximum of the tabulated values above.

Def. Live load Max = 20.98 mm

For Vehicular load, the deflection limit is equal to Span/800.

Span/def. Live load Max = 791 ~ 800, OK !

P

P P P/4

appendix gb

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