DESIGN OF RCC T - GIRDER DECK USING MORICE & LITTLE METHOD

DESIGN OF RCC T - GIRDER DECK USING MORICE & LITTLE METHOD :(All blue coloured fonts depict inputs)

BASIC DESIGN DATA

1 Effective span Leff 19.500 m

2 Clear carriage way Bcw 11.000 m

3 Spacing of main girder c/c Spmg 2.650 m

4 Spacing of cross girder c/c Spcg 9.750 m

5 Width of crash barier Wkerb 0.550 m

6 Thk of deck slab Df 0.250 m

7 Thk of wearing coat Wc 0.065 m

8 Length of cantilever Lcan 2.075 m

9 Cantilever slab thk at fixed end Dcan1 0.300 m

10 Cantilever slab thk at free end Dcan2 0.200 m

11 No of main girder Nomg 4 m

12 Depth of main girder Dmg 2.000 m

13 Web thk of main girder ( at center ) bwmc 0.325 m

14 Web thk of main girder ( at support ) bwms 0.625 m

15 Length of extra widening ( varrying ) Lwv 0.900 m

16 Length of extra widening ( uniform ) Lwu 0.600 m

17 Top haunch Thw x Thh 0.300 x 0.150 m

18 Bottom haunch Bhw x Bhh 0.150 x 0.150 m

19 Bottom bulb Bbw x Bbh 0.625 x 0.250 m

20 No of cross girder Nocg 3 m

21 Depth of cross girder Dcg 1.750 m

22 Web thk of cross girder bwcg 0.325 m

23 Grade of concrete Cgrade 30

24 Grade of reinforcement Sgrade 415

25 Clear cover cov 0.04 m

26 Unit weight of concrete wcon 2.400

27 Weight of wearing course wwc 0.200

28 Weight of crash barrier wrail 1.000 t/m

29 Stress in concrete (compression) fc 1000

30 Stress in steel (tension) ft 2000031 Modular ratio m 10

N/mm2

N/mm2

t/m3

t/m2

t/m2

t/m2

Calculation of distribution coefficients by Morrice - Little method :

Effective span (2a) = 19.500 mTotal width (2b) = 12.100 m

pComputation of longitudinal rigidity

beffbeff = [ Cl. 305.15.2 IRC 21 ]

y = 4.225 m lo = 19.5 m> 2.650 m [ c/c distance of

beff = 2.650 m longitudinal girder]

Distance of cg from top fibre (y) = 0.666 m

= 0.602

= 0.227EComputation of transverse rigidity

19.50 m

For end cross girderIts behave like L - beam

beff

0.25 beff = [ Cl. 305.15.2 IRC 21 ]lo = 0.7*2.65 1.855 m

beff = 0.511 m1.5

0.325Distance of cg from top fibre (y) = 0.818 m

= 0.170

lo/5 + bw

Moment of inertia of longitudinal girder (IL) m4

Flextural rigidity per unit width ( Dx ) = (IL x E) /p

lo/10 + bw

Moment of inertia of end cross girder (IT1) m4

N A

N A

For intermediate cross girderIts behave like T - beam

beff

0.25 beff = [ Cl. 305.15.2 IRC 21 ]lo = 3*2.65 ###

beff = 1.915 m1.5

0.325Distance of cg from top fibre (y) = 0.566 m

= 0.279For deck slab

16.8890.25

= 0.0220

= 0.033E

d/b K1.00 0.141

b = Shorter side 1.20 0.166d = longer side 1.50 0.196K corresponds to d/b from table. 2.00 0.229For longitudinal girder 2.25 0.240(Consider shaded portion only) 2.50 0.249

3.00 0.2634.00 0.2815.00 0.291

10.00 0.312> 10 0.333

d/b for segment 1 = 4.615 K = 0.287d/b for segment 2 = 2.500 K = 0.249

= 0.003E

lo/5 + bw

Moment of inertia of intermediate cross girder (IT2) m4

Moment of inertia of deck slab (IT3) m4

Flextural rigidity per unit length ( Dy ) = (SIT x E )/leff

Torsional rigidity of rectangle (Ri) = G x K x b3 x dModulus of rigidity (G) = E/2x(1+m)

Torsional rigidity of long girder per unit width (Rxy) = (G x K x b3 x d)/p

AN

AN

2

1

For cross girder(Consider shaded portion only)

d/b for cross girder = 5.385K = 0.293

= 0.001E

For deck slab

= 0.003E

= 0.503

= 0.038

Where 2H = Rxy + Ryx + Rdeck

Torsional rigidity of cross girder per unit length (Ryx) = (G x K x b3x d)/leff

Torsional rigidity of deck slab per unit length (Rdeck) = E x t3/6

Fletural parameter (q ) = (b/leff) x (Dx/Dy)0.25

Torsional parameter ( a ) = H/(Dx*Dy)0.5

q 0.250

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.900 0.970 0.985 1.040 1.080 1.040 0.985 0.970 0.900b/4 0.220 0.410 0.630 0.850 1.040 1.200 1.350 1.540 1.700b/2 -0.530 -0.150 0.240 0.630 0.985 1.350 1.720 2.100 2.470

3b/4 -0.170 -0.640 -0.150 -0.410 -0.970 1.540 2.100 2.710 3.280b -1.850 -1.170 -0.530 -0.220 0.900 1.700 2.470 3.280 4.000

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.960 0.980 1.000 1.020 1.040 1.020 1.000 0.980 0.960b/4 0.880 0.910 0.960 0.970 1.020 1.050 1.050 1.050 1.040b/2 0.810 0.860 0.910 0.960 1.000 1.050 1.100 1.130 1.160

3b/4 0.750 0.800 0.860 0.910 0.980 1.050 1.130 1.220 1.300b 0.690 0.750 0.810 0.880 0.960 1.040 1.160 1.300 1.460

q 0.275

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.880 0.960 0.980 1.045 1.090 1.045 0.980 0.960 0.880b/4 0.210 0.405 0.630 0.860 1.045 1.210 1.355 1.535 1.690b/2 -0.535 -0.155 0.240 0.630 0.980 1.355 1.725 2.100 2.465

3b/4 -1.160 -0.635 -0.155 0.405 0.960 1.535 2.100 2.720 3.295b -1.820 -1.160 -0.535 0.210 0.880 1.690 2.465 3.295 4.050

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.950 0.975 1.000 1.020 1.045 1.020 1.000 0.975 0.950b/4 0.865 0.900 0.950 0.970 1.020 1.055 1.055 1.050 1.050b/2 0.790 0.840 0.900 0.950 1.000 1.055 1.115 1.150 1.185

3b/4 0.725 0.775 0.840 0.900 0.975 1.050 1.150 1.255 1.340b 0.660 0.725 0.790 0.865 0.950 1.050 1.185 1.340 1.525

q 0.300

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.860 0.950 0.970 1.050 1.100 1.050 0.970 0.950 0.860b/4 0.200 0.400 0.630 0.870 1.050 1.220 1.360 1.530 1.680b/2 -0.540 -0.160 0.240 0.630 0.970 1.360 1.730 2.100 2.460

3b/4 -1.150 -0.630 -0.160 0.400 0.950 1.530 2.100 2.730 3.310b -1.790 -1.150 -0.540 0.200 0.860 1.680 2.460 3.310 4.100

K0

Ref. Pt Load at

K1

Ref. Pt Load at

K0

Ref. Pt Load at

K1

Ref. Pt Load at

K0

Ref. Pt Load at

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.940 0.970 1.000 1.020 1.050 1.020 1.000 0.970 0.940b/4 0.850 0.890 0.940 0.970 1.020 1.060 1.060 1.050 1.060b/2 0.770 0.820 0.890 0.940 1.000 1.060 1.130 1.170 1.210

3b/4 0.700 0.750 0.820 0.890 0.970 1.050 1.170 1.290 1.380b 0.630 0.700 0.770 0.850 0.940 1.060 1.210 1.380 1.590

q 0.325

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.830 0.940 0.975 1.065 1.125 1.065 0.975 0.940 0.830b/4 0.185 0.395 0.630 0.880 1.065 1.235 1.370 1.515 1.650b/2 -0.540 -0.165 0.240 0.630 0.975 1.370 1.740 2.100 2.445

3b/4 -1.130 -0.615 -0.165 0.395 0.940 1.515 2.100 2.740 3.325b -1.745 -1.130 -0.540 0.185 0.830 1.650 2.445 3.325 4.150

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.940 0.965 1.000 1.030 1.055 1.030 1.000 0.965 0.940b/4 0.830 0.870 0.930 0.970 1.030 1.070 1.070 1.060 1.060b/2 0.740 0.795 0.870 0.930 1.000 1.070 1.150 1.190 1.230

3b/4 0.675 0.725 0.795 0.870 0.965 1.060 1.190 1.320 1.420b 0.595 0.675 0.740 0.830 0.940 1.060 1.230 1.420 1.655

q 0.350

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.800 0.930 0.980 1.080 1.150 1.080 0.980 0.930 0.800b/4 0.170 0.390 0.630 0.890 1.080 1.250 1.380 1.500 1.620b/2 -0.545 -0.170 0.240 0.630 0.980 1.380 1.750 2.100 2.430

3b/4 -1.110 -0.600 -0.170 0.390 0.930 1.500 2.100 2.750 3.340b -1.700 -1.110 -0.545 0.170 0.800 1.620 2.430 3.340 4.200

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.940 0.960 1.000 1.040 1.060 1.040 1.000 0.960 0.940b/4 0.810 0.850 0.900 0.970 1.040 1.080 1.080 1.070 1.060b/2 0.710 0.770 0.850 0.920 1.000 1.080 1.170 1.210 1.250

3b/4 0.650 0.700 0.770 0.850 0.960 1.070 1.210 1.350 1.460b 0.560 0.650 0.710 0.810 0.940 1.060 1.250 1.460 1.720

K1

Ref. Pt Load at

K0

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K1

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K0

Ref. Pt Load at

K1

Ref. Pt Load at

q 0.375

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.760 0.900 0.990 1.100 1.180 1.100 0.990 0.900 0.760b/4 0.150 0.390 0.640 0.860 1.100 1.270 1.380 1.480 1.600b/2 -0.540 -0.160 0.230 0.640 0.990 1.380 1.750 2.090 2.400

3b/4 -1.090 -0.600 0.160 0.390 0.900 1.480 2.090 2.770 3.360b -1.670 -1.090 -0.540 0.150 0.760 1.600 2.400 3.360 4.300

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.910 0.960 1.000 1.040 1.070 1.040 1.000 0.960 0.910b/4 0.790 0.840 0.910 0.960 1.040 1.100 1.090 1.090 1.070b/2 0.680 0.750 0.830 0.910 1.000 1.100 1.190 1.240 1.290

3b/4 0.600 0.670 0.750 0.850 0.960 1.090 1.240 1.400 1.520b 0.520 0.600 0.680 0.790 0.910 1.070 1.290 1.530 1.810

q 0.400

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.710 0.900 0.990 1.110 1.200 1.110 0.990 0.900 0.710b/4 0.120 0.360 0.640 0.910 1.110 1.290 1.400 1.470 1.560b/2 -0.550 -0.170 0.230 0.630 0.990 1.370 1.760 2.100 2.400

3b/4 -1.070 -0.580 -0.170 0.360 0.900 1.470 2.100 2.770 3.380b -1.650 -1.070 -0.550 0.120 0.710 1.560 2.400 3.380 4.300

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.900 0.950 1.000 1.050 1.080 1.050 1.000 0.950 0.900b/4 0.770 0.830 0.900 0.960 1.050 1.100 1.100 1.090 1.070b/2 0.660 0.730 0.810 0.900 1.000 1.100 1.200 1.260 1.300

3b/4 0.580 0.650 0.730 0.830 0.950 1.090 1.260 1.410 1.550b 0.500 0.580 0.660 0.770 0.900 1.070 1.300 1.550 1.880

q 0.425

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.670 0.875 0.995 1.130 1.220 1.130 0.995 0.875 0.670b/4 0.100 0.350 0.640 0.925 1.130 1.310 1.410 1.455 1.500b/2 -0.545 -0.170 0.230 0.635 0.995 1.375 1.770 2.095 2.375

3b/4 -1.045 -0.570 -0.170 0.350 0.875 1.455 2.095 2.785 3.405b -1.600 -1.045 -0.545 0.100 0.670 1.530 2.370 3.405 4.400

K0

Ref. Pt Load at

K1

Ref. Pt Load at

K0

Ref. Pt Load at

K1

Ref. Pt Load at

K0

Ref. Pt Load at

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.890 0.950 1.000 1.055 1.090 1.055 1.000 0.950 0.890b/4 0.750 0.810 0.885 0.960 1.055 1.120 1.120 1.095 1.080b/2 0.630 0.700 0.785 0.885 1.000 1.120 1.225 1.280 1.325

3b/4 0.540 0.615 0.700 0.810 0.950 1.095 1.280 1.455 1.610b 0.470 0.540 0.630 0.750 0.390 1.080 1.325 1.610 1.940

q 0.450

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.630 0.850 1.000 1.150 1.250 1.150 1.000 0.850 0.630b/4 0.080 0.340 0.640 0.940 1.150 1.340 1.420 1.440 1.500b/2 -0.540 -0.170 0.230 0.640 1.000 1.380 1.780 2.090 2.350

3b/4 -1.020 -0.560 -0.170 0.340 0.850 1.440 2.090 2.800 3.430b -1.550 -1.020 -0.540 0.080 0.630 1.500 2.350 3.430 4.500

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.880 0.950 1.000 1.060 1.100 1.060 1.000 0.950 0.880b/4 0.730 0.790 0.870 0.960 1.060 1.140 1.140 1.100 1.090b/2 0.600 0.670 0.760 0.870 1.000 1.140 1.250 1.300 1.350

3b/4 0.500 0.580 0.670 0.790 0.950 1.100 1.300 1.500 1.670b 0.440 0.500 0.600 0.730 0.880 1.090 1.350 1.670 2.000

q 0.475

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.590 0.820 1.000 1.180 1.285 1.180 1.000 0.820 0.590b/4 0.040 0.320 0.635 0.950 1.180 1.370 1.430 1.420 1.450b/2 -0.540 -0.170 0.225 0.635 1.000 1.390 1.790 2.085 2.325

3b/4 -0.990 -0.550 -0.170 0.320 0.820 1.420 2.085 2.820 3.465b -1.490 -0.990 -0.540 0.040 0.590 1.450 2.325 3.465 4.650

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.865 0.935 1.000 1.065 1.115 1.065 1.000 0.935 0.865b/4 0.705 0.775 0.865 0.960 1.065 1.150 1.145 1.110 1.090b/2 0.575 0.650 0.745 0.865 1.000 1.145 1.275 1.325 1.370

3b/4 0.475 0.555 0.650 0.775 0.935 1.110 1.325 1.540 1.715b 0.410 0.475 0.575 0.705 0.865 1.090 1.370 1.715 1.075

K1

Ref. Pt Load at

K0

Ref. Pt Load at

K1

Ref. Pt Load at

K0

Ref. Pt Load at

K1

Ref. Pt Load at

q 0.500

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.550 0.790 1.000 1.210 1.320 1.210 1.000 0.790 0.550b/4 0.000 0.300 0.630 0.960 1.210 1.400 1.440 1.400 1.400b/2 -0.540 -0.170 0.220 0.630 1.000 1.400 1.800 2.080 2.300

3b/4 -0.960 -0.540 -0.170 0.300 0.790 1.400 2.080 2.840 3.500b -1.430 -0.960 -0.540 0.000 0.550 1.400 2.300 3.500 4.800

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.850 0.920 1.000 1.070 1.130 1.070 1.000 0.920 0.850b/4 0.680 0.760 0.860 0.960 1.070 1.160 1.150 1.120 1.090b/2 0.550 0.630 0.730 0.860 1.000 1.150 1.300 1.350 1.390

3b/4 0.450 0.530 0.630 0.760 0.920 1.120 1.350 1.580 1.760b 0.380 0.450 0.550 0.680 0.850 1.090 1.390 1.760 2.150

q 0.525

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.485 0.765 1.010 1.240 1.360 1.240 1.010 0.765 0.485b/4 -0.050 0.275 0.630 0.970 1.240 1.425 1.450 1.375 1.330b/2 -0.535 -0.175 0.215 0.630 1.010 1.415 1.820 2.075 2.275

3b/4 -0.925 -0.520 -0.175 0.275 0.765 1.375 2.075 2.855 3.600b -1.365 -0.925 -0.535 -0.050 0.485 1.330 2.275 3.600 4.950

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.830 0.910 1.000 1.080 1.140 1.080 1.000 0.910 0.830b/4 0.665 0.735 0.850 0.960 1.080 1.170 1.160 1.130 1.090b/2 0.525 0.605 0.710 0.850 1.000 1.160 1.325 1.375 1.415

3b/4 0.425 0.505 0.605 0.735 0.910 1.130 1.375 1.615 1.815b 0.355 0.425 0.525 0.665 0.830 1.090 1.415 1.815 2.240

q 0.550

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.420 0.740 1.020 1.270 1.400 1.270 1.020 0.740 0.420b/4 -0.100 0.250 0.630 0.980 1.270 1.450 1.460 1.350 1.260b/2 -0.530 -0.180 0.210 0.630 1.020 1.430 1.840 2.070 2.250

3b/4 -0.890 -0.500 -0.180 0.250 0.740 1.350 2.070 2.870 3.700b -1.300 -0.890 -0.530 -0.100 0.420 1.260 2.250 3.700 5.100

K0

Ref. Pt Load at

K1

Ref. Pt Load at

K0

Ref. Pt Load at

K1

Ref. Pt Load at

K0

Ref. Pt Load at

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.810 0.900 1.000 1.090 1.150 1.090 1.000 0.900 0.810b/4 0.650 0.710 0.840 0.960 1.090 1.180 1.170 1.140 1.090b/2 0.500 0.580 0.690 0.840 1.000 1.170 1.350 1.400 1.440

3b/4 0.400 0.480 0.580 0.710 0.900 1.140 1.400 1.650 1.870b 0.330 0.400 0.500 0.650 0.810 1.090 1.440 1.870 2.330

q 0.575

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.350 0.700 1.020 1.330 1.460 1.330 1.020 0.700 0.350b/4 -0.130 0.220 0.620 1.000 1.330 1.500 1.480 1.340 1.100b/2 -0.530 -0.180 0.210 0.620 1.020 1.480 1.860 2.080 2.260

3b/4 -0.840 -0.490 -0.180 0.220 0.700 1.340 2.080 2.900 3.800b -1.160 -0.840 0.530 0.130 0.350 1.100 2.220 3.800 5.300

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.800 0.890 1.000 1.110 1.170 1.110 1.000 0.890 0.800b/4 0.600 0.700 0.810 0.950 1.110 1.210 1.200 1.140 1.080b/2 0.470 0.550 0.660 0.810 1.000 1.200 1.380 1.440 1.450

3b/4 0.370 0.450 0.550 0.700 0.890 1.140 1.440 1.720 1.920b 0.300 0.370 0.470 0.600 0.800 1.080 1.450 1.920 2.420

q 0.600

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.310 0.660 1.020 1.350 1.500 1.350 1.020 0.660 0.310b/4 -0.170 0.210 0.620 1.020 1.350 1.530 1.470 1.310 1.030b/2 -0.520 -0.180 0.200 0.620 1.020 1.470 1.870 2.060 2.190

3b/4 -0.800 -0.470 -0.180 0.210 0.660 1.310 2.060 2.920 3.080b -1.050 -0.800 -0.520 -0.200 0.310 1.100 2.190 3.080 5.450

.

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.800 0.890 1.000 1.120 1.190 1.120 1.000 0.890 0.800b/4 0.580 0.670 0.800 0.950 1.120 1.230 1.200 1.150 1.080b/2 0.440 0.520 0.660 0.800 1.000 1.200 1.400 1.450 1.460

3b/4 0.340 0.410 0.520 0.670 0.890 1.150 1.450 1.750 1.960b 0.280 0.340 0.440 0.580 0.800 1.080 1.460 1.960 2.500

K1

Ref. Pt Load at

K0

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K1

Ref. Pt Load at

K0

Ref. Pt Load at

K1

Ref. Pt Load at

q 0.625

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.230 0.635 1.023 1.390 1.540 1.390 1.023 0.630 0.230b/4 -0.220 0.180 0.615 1.030 1.390 1.570 1.490 1.290 0.965b/2 -0.520 -0.180 0.200 0.615 1.023 1.490 1.890 2.060 2.160

3b/4 -0.755 -0.455 -0.180 0.180 0.635 1.290 2.060 2.935 3.045b -0.920 -0.755 -0.520 -0.235 0.230 1.010 2.160 3.045 5.250

.

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.775 0.870 0.990 1.013 1.210 1.130 0.990 0.870 0.775b/4 0.515 0.655 0.785 0.950 1.130 1.250 1.220 1.150 1.070b/2 0.420 0.495 0.615 0.785 0.990 1.220 1.425 1.480 1.480

3b/4 0.320 0.385 0.495 0.655 0.870 1.150 1.480 1.845 2.010b 0.260 0.320 0.420 0.555 0.775 1.070 1.480 2.010 2.775

q 0.650

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.150 0.610 1.025 1.420 1.580 1.420 1.025 0.610 0.150b/4 -0.260 0.150 0.610 1.040 1.420 1.600 1.510 1.260 0.900b/2 -0.520 -0.180 0.200 0.610 1.025 1.510 1.910 2.060 2.130

3b/4 -0.710 -0.440 -0.180 -0.150 0.610 1.260 2.060 2.950 3.010b -0.800 -0.710 -0.520 -0.270 0.150 0.920 2.130 3.010 5.070

.

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.750 0.850 0.980 1.140 0.980 0.850 0.750 0.870 0.775b/4 0.550 0.640 0.770 0.950 1.140 1.270 1.240 1.150 1.060b/2 0.400 0.470 0.600 0.770 0.980 1.240 1.450 1.500 1.500

3b/4 0.300 0.360 0.470 0.640 0.850 1.150 1.500 1.840 2.060b 0.240 0.300 0.400 0.530 0.750 1.060 1.500 2.060 2.650

q 0.675

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.055 0.570 1.027 1.470 1.630 1.465 1.027 0.570 0.055b/4 -0.315 0.130 0.605 1.050 1.470 1.650 1.530 1.235 0.785b/2 -0.510 -0.185 0.190 0.605 1.027 1.530 1.935 2.055 2.080

3b/4 -0.640 -0.420 -0.185 0.130 0.570 1.235 2.055 2.975 3.150b -0.640 -0.640 -0.510 -0.320 0.055 0.825 2.080 3.510 5.500

.

K0

Ref. Pt Load at

K1

Ref. Pt Load at

K0

Ref. Pt Load at

K1

Ref. Pt Load at

K0

Ref. Pt Load at

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.730 0.842 0.980 1.155 1.255 1.155 0.980 0.842 0.730b/4 0.525 0.615 0.755 0.945 1.155 1.300 1.250 1.150 1.050b/2 0.365 0.450 0.575 0.755 0.980 1.250 1.480 1.525 1.510

3b/4 0.270 0.370 0.450 0.615 0.842 1.150 1.525 1.385 2.110b 0.200 0.270 0.365 0.510 0.730 1.050 1.510 2.110 2.750

q 0.700

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 -0.040 0.530 1.030 1.520 1.680 1.510 1.030 0.530 -0.040b/4 -0.370 0.110 0.000 1.060 1.510 1.700 1.550 1.210 0.670b/2 -0.500 -0.190 0.180 0.600 1.030 1.550 1.960 2.050 2.030

3b/4 -0.570 -0.400 -0.190 0.110 0.530 1.210 2.050 3.000 4.010b -0.480 -0.570 -0.500 -0.370 -0.040 0.730 2.030 4.010 6.030

.

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.710 0.835 0.980 1.170 1.280 1.170 0.980 0.835 0.710b/4 0.500 0.590 0.740 0.940 1.170 1.330 1.270 1.150 1.040b/2 0.330 0.430 0.550 0.740 0.980 1.270 1.510 1.550 1.520

3b/4 0.240 0.320 0.430 0.590 0.835 1.150 1.550 1.930 2.160b 0.180 0.240 0.330 0.490 0.710 1.040 1.520 2.160 2.850

q 0.725

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 -0.125 0.495 1.025 1.550 1.725 1.550 1.025 0.495 -0.125b/4 -0.400 0.080 0.585 1.070 1.550 1.735 1.570 1.180 0.585b/2 -0.495 -0.185 0.175 0.585 1.025 1.570 1.980 2.040 1.990

3b/4 -0.505 -0.375 -0.185 0.080 0.495 1.180 2.040 3.025 3.600b -0.390 -0.505 -0.495 -0.400 0.125 0.645 1.990 3.600 6.365

.

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.685 0.817 0.980 1.185 1.305 1.185 0.980 0.817 0.685b/4 0.475 0.570 0.730 0.940 1.185 1.350 1.285 1.150 1.030b/2 0.315 0.410 0.530 0.730 0.980 1.285 1.540 1.575 1.535

3b/4 0.225 0.300 0.410 0.570 0.817 1.150 1.575 1.920 2.205b 0.165 0.225 0.315 0.470 0.685 1.030 1.535 2.205 2.925

K1

Ref. Pt Load at

K0

Ref. Pt Load at

K1

Ref. Pt Load at

K0

Ref. Pt Load at

K1

Ref. Pt Load at

q 0.750

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 -0.210 0.460 1.020 1.580 1.770 1.580 1.020 0.460 -0.210b/4 -0.430 0.050 0.570 1.080 1.580 1.770 1.590 1.150 0.500b/2 -0.490 -0.180 0.170 0.570 1.020 1.590 2.000 2.040 1.950

3b/4 -0.440 -0.350 -0.180 0.050 0.460 1.150 2.040 3.050 3.200b -0.300 -0.440 -0.490 -0.430 -0.210 0.560 1.950 3.200 6.700

.

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.660 0.800 0.980 1.200 1.330 1.200 0.980 0.800 0.660b/4 0.450 0.550 0.720 0.940 1.200 1.370 1.300 1.150 1.020b/2 0.300 0.390 0.510 0.720 0.980 1.300 1.570 1.600 1.550

3b/4 0.210 0.280 0.390 0.550 0.500 1.150 1.600 2.010 2.250b 0.150 0.210 0.300 0.450 0.660 1.020 1.550 2.250 3.000

q 0.775

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 -0.280 0.425 1.020 1.620 1.825 1.620 1.020 0.425 -0.280b/4 -0.460 0.035 0.560 1.090 1.620 1.825 1.607 1.125 0.415b/2 -0.485 -0.180 0.160 0.560 1.020 1.607 2.030 2.030 1.885

3b/4 -0.390 -0.325 -0.180 0.350 0.425 1.125 2.030 3.075 3.610b -0.230 -0.390 -0.485 -0.455 -0.280 0.475 1.885 3.610 6.860

.

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.645 0.790 0.980 1.210 1.355 1.210 0.980 0.790 0.645b/4 0.425 0.530 0.700 0.935 1.210 1.400 1.320 1.145 1.010b/2 0.275 0.365 0.490 0.700 0.980 1.320 1.600 1.620 1.550

3b/4 0.185 0.255 0.365 0.530 0.790 1.145 1.620 2.055 2.290b 0.135 0.185 0.275 0.425 0.645 1.000 0.155 2.290 3.100

K0

Ref. Pt Load at

K1

Ref. Pt Load at

K0

Ref. Pt Load at

K1

Ref. Pt Load at

q 0.800

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 -0.350 0.390 1.025 1.660 1.880 1.660 1.025 0.390 -0.350b/4 -0.490 0.020 0.550 1.100 1.660 1.880 1.640 1.100 0.330b/2 -0.480 -0.180 0.150 0.550 1.025 1.640 2.060 2.030 1.820

3b/4 -0.340 -0.300 -0.180 0.020 0.390 1.100 2.030 3.100 4.020b -0.160 -0.340 -0.480 -0.480 -0.350 0.390 1.820 4.020 7.020

.

-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b

0.000 0.630 0.780 0.980 1.220 1.380 1.220 0.980 0.780 0.630b/4 0.400 0.510 0.680 0.930 1.220 1.430 1.340 1.140 1.000b/2 0.250 0.340 0.470 0.680 0.980 1.340 1.630 1.640 1.550

3b/4 0.160 0.230 0.340 0.510 0.780 1.140 1.640 2.100 2.330b 0.120 0.160 0.250 0.400 0.630 0.980 1.550 2.330 3.200

K0

Ref. Pt Load at

K1

Ref. Pt Load at

Unit load distribution coefficient.q 0.503

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b

0 0.541 0.787 1.001 1.214 1.325 1.214 1.001 0.787 0.541 7.87b/4 -0.007 0.297 0.630 0.961 1.214 1.403 1.441 1.397 1.391 8.04b/2 -0.539 -0.171 0.219 0.630 1.001 1.402 1.803 2.079 2.297 7.84

3b/4 -0.955 -0.537 -0.171 0.297 0.787 1.397 2.079 2.842 3.513 7.97b -1.421 -0.955 -0.539 -0.007 0.541 1.391 2.297 3.513 4.820 7.94

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b

0 0.847 0.919 1.000 1.071 1.131 1.071 1.000 0.919 0.847 7.96b/4 0.678 0.757 0.859 0.960 1.071 1.161 1.151 1.121 1.090 7.96b/2 0.547 0.627 0.727 0.859 1.000 1.151 1.303 1.353 1.393 7.99

3b/4 0.447 0.527 0.627 0.757 0.919 1.121 1.353 1.585 1.767 8.00b 0.377 0.447 0.547 0.678 0.847 1.090 1.393 1.767 2.162 8.04

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b

-b 4.300 3.172 2.120 1.332 0.601 0.127 -0.327 -0.681 -1.070 7.96

-3b/4 3.172 2.596 1.937 1.343 0.812 0.387 -0.015 -0.329 -0.681 7.98

-b/2 2.120 1.937 1.705 1.353 1.001 0.675 0.319 -0.015 -0.327 7.87

-b/4 1.332 1.343 1.385 1.356 1.186 0.961 0.675 0.387 0.127 8.020 0.601 0.812 1.001 1.186 1.287 1.186 1.001 0.812 0.601 7.89

b/4 0.127 0.387 0.675 0.961 1.186 1.356 1.385 1.343 1.332 8.02b/2 -0.327 -0.015 0.319 0.675 1.001 1.353 1.705 1.937 2.120 7.87

3b/4 -0.681 -0.329 -0.015 0.387 0.812 1.343 1.937 2.596 3.172 7.98b -1.070 -0.681 -0.327 0.127 0.601 1.332 2.120 3.172 4.300 7.96

For no torsion grillage a = 0 K0

Row integral

Ref. Pt Load at

For full torsion grillage a = 1 K1

Row integral

Ref. Pt Load at

Ka= K0+(K1-K0)x(a)0.5

Row integral

Ref. Pt Load at

RUN

Distribution coefficient K' for SIDL

0.5 t/m 0.5 t/m

2.075 2.650 2.65 2.65 2.075

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b

-b 0.43 1.87 1.38 0.92 0.58 0.26 0.06 -0.14 -0.30 -0.46-3b/4 0.07 0.21 0.17 0.13 0.09 0.05 0.03 0.00 -0.02 -0.05-b/2 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00-b/4 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00b/4 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00b/2 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

3b/4 0.07 -0.05 -0.02 0.00 0.03 0.05 0.09 0.13 0.17 0.21b 0.43 -0.46 -0.30 -0.14 0.06 0.26 0.58 0.92 1.38 1.87

1.00

1.57 1.23 0.91 0.75 0.63 0.75 0.91 1.23 1.57

1.566 1.231 0.905 0.747 0.629 0.747 0.905 1.231 1.566

Distribution coefficient K' at girder location

Girder Nr. G1 G2 G3 G4K' 1.221 0.806 0.774 1.221

Note : Coefficients have been increased by 10% to take into account the effect of higher harmonics.

lwKa

Ref. Pt Load at

Load factor (lw )

Slw

SlwKa

K' = SlwKa/Slw

G1

G2

G3

G4

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b

Distribution coefficient K' for live load (3 lane class A)

2.075 2.65 2.65 2.65 2.075

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b

-b 2.12 9.11 6.72 4.49 2.82 1.27 0.27 -0.69 -1.44 -2.27-3b/4 4.62 14.65 11.99 8.95 6.20 3.75 1.79 -0.07 -1.52 -3.15-b/2 4.99 10.58 9.67 8.51 6.75 5.00 3.37 1.59 -0.07 -1.63-b/4 5.37 7.15 7.21 7.44 7.28 6.37 5.16 3.62 2.08 0.68

0 4.95 2.97 4.02 4.95 5.87 6.37 5.87 4.95 4.02 2.97b/4 4.99 0.63 1.93 3.37 4.80 5.92 6.77 6.91 6.70 6.65b/2 4.62 -1.51 -0.07 1.47 3.12 4.62 6.25 7.87 8.95 9.79

3b/4 2.54 -1.73 -0.84 -0.04 0.98 2.07 3.42 4.93 6.60 8.07b 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

34.20

41.86 40.64 39.14 37.82 35.37 32.88 29.12 25.31 21.12

1.224 1.188 1.145 1.106 1.034 0.962 0.851 0.740 0.617


Girder Nr. G1 G2 G3 G4K' 1.289 1.207 1.087 0.860


lwKa

Ref. Pt Load at

Load factor (lw )

Slw

SlwKa

K' = SlwKa/Slw

G1

G2

G3

G4

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b

Class A 1.8m

0.95m

Class A 1.8m

1.7m

Class A 1.8m

1.7m

Distribution coefficient K' for live load (70 - R)

2.075 2.65 2.65 2.65 2.075

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b

-b 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00-3b/4 4.75 15.06 12.33 9.20 6.38 3.86 1.84 -0.07 -1.56 -3.23-b/2 6.15 13.05 11.92 10.49 8.33 6.16 4.15 1.96 -0.09 -2.01-b/4 6.10 8.12 8.19 8.44 8.27 7.23 5.86 4.11 2.36 0.78

0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00b/4 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00b/2 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

3b/4 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00b 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

17.00

36.23 32.44 28.14 22.97 17.25 11.85 6.01 0.70 -4.47

2.131 1.908 1.655 1.351 1.015 0.697 0.353 0.041 -0.263


Girder Nr. G1 G2 G3 G4K' 1.995 1.440 0.897 0.173


lwKa

Ref. Pt Load at

Load factor (lw )

Slw

SlwKa

K' = SlwKa/Slw

70 - R 1.93m

2.18m

G1

G2

G3

G4

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b

Distribution coefficient K' for live load (1lane class A + 70 - R)

2.075 2.65 2.65 2.65 2.075

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b

-b 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00-3b/4 4.75 15.07 12.33 9.20 6.38 3.86 1.84 -0.07 -1.56 -3.24-b/2 6.15 13.04 11.91 10.49 8.32 6.16 4.15 1.96 -0.09 -2.01-b/4 6.33 8.43 8.50 8.76 8.58 7.51 6.08 4.27 2.45 0.80

0 5.47 3.29 4.44 5.48 6.49 7.04 6.49 5.48 4.44 3.29b/4 4.84 0.62 1.87 3.27 4.65 5.74 6.56 6.70 6.50 6.45b/2 0.86 -0.28 -0.01 0.27 0.58 0.86 1.16 1.47 1.67 1.82

3b/4 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00b 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

28.40

40.16 39.05 37.47 35.00 31.17 26.28 19.80 13.40 7.12

1.414 1.375 1.319 1.233 1.097 0.926 0.697 0.472 0.251


Girder Nr. G1 G2 G3 G4K' 1.490 1.337 1.088 0.611


lwKa

Ref. Pt Load at

Load factor (lw )

Slw

SlwKa

K' = SlwKa/Slw

70 - R 1.93m

2.18m

Class A 1.8m

G1

G2

G3

G4

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b

DESIGN OF MAIN GIRDER

Calculation of dead load

Inner girder

1 Weight of web =(2-0.25-0.25)*0.325*2.4 = 1.17 t/m2 Weight of top haunch =2*0.5*0.3*0.15*2.4 = 0.11 t/m3 Weight of bottom haunch =2*0.5*0.15*0.15*2.4 = 0.05 t/m4 Weight of bulb =0.625*0.25*2.4 = 0.38 t/m5 Weight of deck slab =2.65*0.25*2.4 = 1.59 t/m

Running weight = 3.30 t/m

1 Weight of cross girder = 2.67 t

Web thickening at near ends

1 Wt due to extra widening (uni) = 0.97 t/m

2 Wt due to extra widening (vary) = 0.97 to 0 t/m

Main girder

0.6 0.9

Extra widening at support

Outer girder

1 Weight of web =(2-0.25-0.25)*0.325*2.4 = 1.17 t/m2 Weight of top haunch =2*0.5*0.3*0.15*2.4 = 0.11 t/m3 Weight of bottom haunch =2*0.5*0.15*0.15*2.4 = 0.05 t/m4 Weight of bulb =0.625*0.25*2.4 = 0.38 t/m5 Weight of deck slab = 1.94 t/m

Running weight = 3.65 t/m

1 Weight of cross girder = 1.33 t

Web thickening at near ends

1 Wt due to extra widening (uni) = 0.98 t/m

2 Wt due to extra widening (vary)= 0.98 to 0 t/m

=((2.65-0.325)*1.5*2.4-0.108-0.054)*0.325)

=2*0.5*(2*2-2*0.25-2*0.25-0.15-0.15)*(0.625-0.325)*2.4

=((0.5*2.65*0.25)+0.5*(0.3+ 0.2)*(2.075-0.325*0.5))*2.4

=((2.65-0.325)*1.5*2.4-0.108-0.054)*0.325)*0.5

=(0.5*(2*2-2*0.25 -2*0.25-0.15-0.15)*(0.625-0.325) + (0.5*(2*2-2*0.3-2*0.25-0.15)*(0.625-0.325))*0.5*2.4

Calculation of SIDL (uniform)

Inner girder1 Weight of wearing coat = 0.53 t/m

Outer girder1 Weight of wearing coat = 0.57 t/m

Calculation of SIDL (concentrated)2 Weight of crash barrier = 2.00 t/m

Total concentrated SIDL = 2.00 t/m

Calculation of bending moment and shear force (DL+SIDL)(Uniform SIDL like wearing coat)Inner girder

2.67 t 2.67 t 2.67 t9.75 9.75

3.83t/m 0.97t/m

0.9 0.619.5 m

A B

Support reaction at A = 42.34 t

Sl. Nr. Item

Location

1 BM (t-m) 70.2 83.4 143.5 195.5

2 SF (t) 31.0 29.3 20.0 0.0

Outer girder

1.33 t 1.33 t 1.33 t9.75 9.75

4.22t/m 0.98t/m

0.9 0.619.5 m

A B

Deff from sup

Span (L/8)

Span (L/4)

Span (L/2)


Sl. Nr. Item

Location

1 BM (t-m) 75.7 89.9 154.2 207.6

2 SF (t) 33.4 31.5 21.2 0.0

Calculation of total BM and SF due to concentrated SIDL(Concentrated SIDL like kerb,crash barrier)

2.00t/m

19.5 mA B


Sl. Nr. Item

Location

1 BM (t-m) 35.0 41.6 71.3 95.1

2 SF (t) 15.5 14.6 9.8 0.0

Calculation of short term deflection due to dead load & sidl

D2 D1 D2

L/4 L/4 L/4 L/4

D1 = = 9 mm

D2 = (considering parabolic profile) = 6 mmCalculation of bending moment and shear force (Live load)

Deff from sup

Span (L/8)

Span (L/4)

Span (L/2)

Deff from sup

Span (L/8)

Span (L/4)

Span (L/2)

=(5*19.5/16)*(2*(2*(195.5+207.6)+95.1)*0.5*19.5/3)/ (31220.186*100*2*(0.296+0.338))*1000

=D1/(2)0.5

The live load bending moment and shear force at various sections has been worked out using an inhouse fortran programme, which runs the train of wheels both in forward and reverse directions and gives the max moment with corresponding shear and max shear with corresponding moment. The results are presented in the following sheets.

Summary of bending moment

Design live load B M ( t-m)

1Inner 70.2 7.1 56.6 44.7 110.1 118.8 54.4 50.5 59.2 59.2 136.5

Outer 75.7 10.7 56.6 44.7 110.1 118.8 58.1 70.0 65.9 70.0 156.4

2Inner 83.4 8.4 70.9 55.8 138.3 149.2 68.2 63.4 74.3 74.3 166.1

Outer 89.9 12.7 70.9 55.8 138.3 149.2 72.8 87.8 82.8 87.8 190.5

3Inner 143.5 14.4 116.0 97.1 237.3 248.5 111.5 105.6 125.4 125.4 283.3

Outer 154.2 21.8 116.0 97.1 237.3 248.5 119.1 146.3 139.7 146.3 322.3

4Inner 195.5 19.2 144.1 144.1 325.3 325.3 138.5 138.2 166.7 166.7 381.3

Outer 207.6 29.0 144.1 144.1 325.3 325.3 148.0 191.5 185.7 191.5 428.1

Average BM = Total BM/no of main girdersDesign concentrated SIDL BM = Average BM x DF(K')Design live load BM = Average BM x IF x DF(K')Reduced the BM by 10% for each additional loaded traffic lane in excess of 2 lanes. [ Cl.208.2 IRC 6, 1966]

Calculation of impact factor for live load.

1 For class A = 1+ 4.5/(6+L) 1.182 For 70 R (Wheeled) 1.18 From curve IRC 6 1966 Cl. 211.3

SL. Nr.

Section considered

Girder location

BM (t-m) (dl+uni

sidl)

BM (t-m) (con sidl)

Total BM for 1L Cl A (Reverse)

Total BM for 1L Cl A (Forward)

Total BM for 70 - R (Reverse)

Total BM for 70 - R (Forward)

Max design LL BM

Design BM (t-m)3 Lane

Class A 70 - R (wheel)

1L Cl A + 70 - R

At Deff from

support

At 1/8th span (L/8)

At quarter span (L/4)

At middle span (L/2)

Design of section for flexure

Inner girder Outer girder

SECTION

DATA M (t.m) 136.5 166.1 283.3 381.3 156.4 190.5 322.3 428.1 h (m) 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 bf (m) 2.650 2.650 2.650 2.650 3.400 3.400 3.400 3.400 df (m) 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 bw (m) 0.325 0.325 0.325 0.325 0.325 0.325 0.325 0.325 Ast (m^2) 0.00482 0.00482 0.00804 0.01126 0.00563 0.00563 0.00965 0.01286 c (m) 0.115 0.115 0.124 0.132 0.109 0.109 0.120 0.148 Asc (m^2) 0.00080 0.00040 0.00040 0.00040 0.00080 0.00040 0.00040 0.00040 dc (m) 0.064 0.064 0.064 0.064 0.064 0.064 0.064 0.064 m 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 RESULTS

d (m) 1.885 1.885 1.876 1.868 1.891 1.891 1.880 1.852 Asf (m^2) 0.00515 0.00511 0.00513 0.00516 0.00656 0.00652 0.00656 0.00667 AA (m^2) 0.0000 0.0000 0.5812 0.5812 0.0000 0.0000 0.7688 0.7688 A (m) 2.6500 2.6500 0.3250 0.3250 3.4000 3.4000 0.3250 0.3250

B (m^2) 0.1110 0.1037 1.3305 1.3949 0.1270 0.1198 1.7377 1.8020 C (m^3) -0.1828 -0.1823 -0.4474 -0.5663 -0.2138 -0.2133 -0.5554 -0.6691 n (m) 0.243 0.243 0.312 0.373 0.233 0.233 0.303 0.349

CC (m^2) 0.0332 0.0336 0.0635 0.0902 0.0388 0.0391 0.0783 0.1053 jd (m) 1.804 1.804 1.778 1.761 1.814 1.813 1.784 1.749

fc (t/m^2) 231 283 396 481 215 263 359 442 fs (t/m^2) -15677 -19083 -19815 -19232 -15321 -18665 -18723 -19030

0.224 0.296 0.272 0.338 d=h-c Asf=(bf*df^2+2*(m-1)*Asc*(df-dc))/(2*m*(d-df)) AA=(bf-bw)*df for As<Asf , else 0 A=bw for As<Asf , else bf B=2*(AA+(m-1)*Asc+m*As) C=-(AA*df+2*(m-1)*Asc*dc+2*m*As*d) n=(-B-sqrt(B^2-4*A*C))/(2*A) CC=(bf-bw)*(min(df,n))^2*(3*n-2*min(df,n)) jd=d-(CC+bw*n^3+6*(m-1)*Asc*(n-dc)*dc)/(6*m*As*(d-n)) fs=-M/(As*jd) fc=-(fs/m)*n/(d-n)

Deff from support

L/8 of span

L/4 of span

L/2 of span

Deff from support

L/8 of span

L/4 of span

L/2 of span

Cracked moment of inertia Ir (m4)

Calculation of shear force (Live load)

a) For loads at within 5.5m : Greater of the followings.i) Assuming the deck slab continuous with supports being assumed as unyielding.

ii) By distribution coefficient ie. Morice-Little as used for calculation of bending moments.

b) For loads beyond 5.5m from either supports : By distribution coefficient ie. Morice-Little as used for calculation of bending moments.

At Deff from support

For class A (Forward train)

Total shear force (from computer print out on previous sheets) = 24.2 tComponent of shear force due to loads within 5.5 m from support. = 11.9 tComponent of shear force due to loads beyond 5.5 m from support. = 12.2 t

For 70 - R (wheel) (Forward train)


Distribution of shear force for 70 - R (wheel)

A. By Morrice - Little's method1 For inner girder =1.440*64.24*1.18/4 = 27.3 t2 For outer girder =1.995*64.24*1.18/4 = 37.8 t

B. By continuous beam method [ For loads with in 5.5 m from support ]

15.66 t 15.66 t

1.525 2.65 2.65 2.65

FEM -3.233 5.742 Balance 3.233 -2.871 -2.871Carryover -1.435 1.616 0.000 -1.435Balance 1.435 -0.808 -0.808 0.718 0.718Total M 0.000 3.679 -3.679 -0.718 0.718

Simple SF 18.674 12.646 Elastic SF -1.388 1.388 1.659 -1.659 -0.271 0.271Reaction 17.29 15.69 -1.93 0.27

The shear forces in beams has been calculated as per the provisions of Cl 305.12.2 of IRC: 21 ie,

1.63m

1.93m

1 For inner girder = (32.92*1.440/4+15.69)*1.18 = 32.5 t2 For outer girder = (32.92*1.995/4+17.29)*1.18 = 39.8 t

Design Shear force =Average SF x IF x DF

1 For inner girder = 32.5 t2 For outer girder = 39.8 t

Distribution of shear force for 1 L Class A + 70 - R (wheel)

A. By Morrice - Little's method1 For inner girder = =1.34*(24.16*1.18+64.24*1.18)*0.9/4 = 31.4 t2 For outer girder = =1.49*(24.16*1.18+64.24*1.18)*0.9/4 = 35 t


15.66 t 15.66 t 5.97 t 5.97 t

1.525 2.65 2.65 2.65

FEM -3.233 5.742 -2.063 1.884 -1.762 0.327Balance 3.233 -1.840 -1.840 -0.061 -0.061 -0.327Carryover -0.920 1.616 -0.030 -0.920 -0.164 -0.030Balance 0.920 -0.793 -0.793 0.542 0.542 0.030Total M 0.000 4.726 -4.726 1.445 -1.445 0.000

Simple SF 18.674 12.646 3.120 2.850 5.035 0.935Elastic SF -1.783 1.783 1.238 -1.238 0.545 -0.545Reaction 16.89 18.79 7.19 0.39

1 For inner girder = ((12.22+32.92)*1.34/4+18.79)*1.18*0.9 = 36.0 t2 For outer girder = ((12.22+32.92)*1.49/4+16.89)*1.18*0.9 = 35.8 t


Reduced the SF by 10% for each additional loaded traffic lane in excess of 2 lanes.[As per clause 208.2 IRC 6, 1966]

1 For inner girder = 36 t2 For outer girder = 35.8 t

1.63m

1.93m

1.8m

1.88m

At 1/8th span (L/8)








15.05 t 15.05 t

1.525 2.65 2.65 2.65






1.63m

1.93m


A. By Morrice - Little's method1 For inner girder =1.34*(22.9*1.18+61.2*1.18)*0.9/4 = 29.9 t2 For outer girder =1.49*(22.9*1.18+61.2*1.18)*0.9/4 = 33.3 t


15.05 t 15.05 t 6.1 t 6.1 t

1.525 2.65 2.65 2.65







1.63m

1.93m

1.8m

1.88m

At quarter span (L/4)








8.20 t 8.20 t

1.525 2.65 2.65 2.65






1.63m

1.93m


A. By Morrice - Little's method1 For inner girder =1.34*(18.8*1.18+48.7*1.18)*0.9/4 = 24.0 t2 For outer girder =1.49*(18.8*1.18+48.7*1.18)*0.9/4 = 26.7 t


8.20 t 8.20 t 1.55 t 1.55 t

1.525 2.65 2.65 2.65







1.63m

1.93m

1.8m

1.88m

Summary of shear force

SL. Nr.

1Inner 31.0 3.1 32.5 36.0 36.0 70.1

Outer 33.4 4.7 39.8 35.8 39.8 77.9

2Inner 29.3 2.9 31.0 34.2 34.2 66.5

Outer 31.5 4.5 37.9 33.7 37.9 73.9

3Inner 20.0 2.0 23.4 26.6 26.6 48.6

Outer 21.2 3.0 29.7 28.5 29.7 53.9

2.1

[ Cl. 304.7.3 IRC - 21 1987 ]Where

1.14 - 0.7 d >= 0.5

>= 1.0

0.45

SL. Nr.

1Inner 70.1 1.14 0.787 0.5 1.00 0.23

Outer 77.9 1.27 0.916 0.5 1.00 0.23

2Inner 66.5 1.09 0.787 0.5 1.00 0.23

Outer 73.9 1.20 0.916 0.5 1.00 0.23

3Inner 48.6 0.80 1.319 0.5 1.00 0.23

Outer 53.9 0.88 1.579 0.5 1.00 0.23

4Inner 0.0 0.00 1.854 0.5 1.00 0.23

Outer 0.0 0.00 2.137 0.5 1.03 0.23

SL. Nr.

1Inner 18.6 2 16 216 210

Outer 20.6 2 16 195 190

2Inner 17.6 2 16 228 220

Outer 19.5 2 16 206 200

3Inner 12.9 2 12 175 170

Outer 14.3 2 12 158 150

4Inner 9.1 2 12 248 170

Outer 9.0 2 12 251 150

Section considere

dGirder

location

SF (t) (dl+uni

sidl)SF (t)

(con sidl)

70 - R (wheel)

1Lane class A +

70 - R

Design LL SF

Design SF (t-m)

Deff from sup

Span (L/8)

Span (L/4)

Shear stress tv (N/mm2) < tmax = N/mm2

tc = K1 x K2 x tco

K1 =

K2 = 0.5 + 0.25 r tco =

Section considere

dGirder

locationDesign SF (t)

tv (N/mm2)

r % K1 K2 tc (N/mm2)

Deff from sup

Span (L/8)

Span (L/4)

Span (L/2)

Section considere

dGirder

location

Reinf required (Asv / Sv) (cm2/m)

Reinf provided (Asv) (cm2/m)

Spacing required

(mm)

Spacing Provided

(mm)No of legs

Bar dia (mm)

Deff from sup

Span (L/8)

Span (L/4)

Span (L/2)

DESIGN OF CROSS GIRDER

End cross girder

50.12 t ### ### ###

2.650 2.650 2.650

0.65 1.35 0.65 0.65 1.35 0.65 0.65 1.350 0.65

A B C D E FDF 1.00 0.49 0.51 0.51 0.49 0.49 0.51 0.51 0.49 1.00FEM 32.58 0.00 0.00 -7.52 7.52 0.00 0.00 -7.49 7.49 0.00 0.00 -32.58Balance -32.58 3.68 3.83 -3.83 -3.68 3.67 3.82 -3.82 -3.67 32.58C O -16.29 -1.92 1.92 1.84 -1.84 -1.91 1.91 16.29Balance 8.92 9.29 -1.91 -1.84 1.84 1.91 -9.28 -8.92C O 0.00 -0.96 4.64 0.92 -0.92 -4.64 0.96 0.00Balance 0.47 0.49 -2.84 -2.73 2.72 2.84 -0.49 -0.47Total M 32.58 -32.58 -3.22 3.22 5.49 -5.49 5.47 -5.47 -3.23 3.23 32.58 -32.58

Max support moment (DL+SIDL) = 32.58 t-mMax span moment (DL+SIDL) = 10.68 t-m

Designed of deep beam [ As per clause 28.2, IS 456-1978 ]

For span AB L = 2.65 D = 1.75L/D = 1.514 >= 1 for contineous beam

Lever arm Z = 0.2*(2.65+1.5*1.75) = 1.055 m

For span CD L = 2.65 D = 1.75L/D = 1.514 >= 1 for contineous beam

Lever arm Z = 0.2*(2.65+1.5*1.75) = 1.055 m

The end cross girder is designed as a contineous deep beam for bearing replacement condition, contineous over knife supports at the jack locations. The CL of jacks are taken to be 650 mm from the CL of main girder. The reaction of main girder due to (DL+SIDL) are applied as load at the girder location as shown below.

Required Ast for max span M =10.682/1.055*20000 = 5.06

Minimum Ast at bottom =0.2%bd =0.002*32.5*175 = 11Provide 3 nos 16 f + 2 nos 16 f + 2 nos 12 fat bottom within a depth of (0.25D - 0.05L) = 0.305 mfrom bottom face with a development length of (0.8*35*dia of bar) = 448 mm

Provided Ast = 12.3

Required Ast for max support M =32.579/1.055*20000 = 15.44Provide 3 nos 20 f + 2 nos 16 f + 2 nos 12 fDistributed as per clause 28.3.2 (b) IS 456-1978

Provided Ast = 15.7

Hanging reinforcement [ As per clause 28.3.3, IS 456-1978 ]

Total shear =50.121+46.107+46.264+50.121 = 192.6 t

Required Ast as hanging R/F =192.6*10000/20000 = 96.3

Required Ast per m length =96.3/7.95 = 12.1 Provide 2 L 12 f @ 180 c/c as vertical reinforcement

Provided Ast = 12.6

Side face reinforcement [As per clause 31.4 IS-456, 1978]

0.1 % of web area on either face with spacing not more then 450 mm.

Required Ast =0.001 *175*32.5 = 5.69

=M/sst*Z cm2

cm2

cm2

=M/sst*Z cm2

cm2

cm2

cm2/m

cm2/m

cm2

DESIGN OF RCC T - GIRDER DECK USING MORICE & LITTLE METHOD

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