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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 N/mm2
24 Grade of reinforcement Sgrade 415 N/mm2
25 Clear cover cov 0.04 m
26 Unit weight of concrete wcon 2.400 t/m3
27 Weight of wearing course wwc 0.200 t/m2
28 Weight of crash barrier wrail 1.000 t/m
29 Stress in concrete (compression) fc 1000 t/m2
30 Stress in steel (tension) ft 20000 t/m2
31 Modular ratio m 10
Calculation of distribution coefficients by Morrice - Little method :
Effective span (2a) = 19.500 m
Total width (2b) = 12.100 m
p
Computation of longitudinal rigidity
beff
beff = lo/5 + bw [ Cl. 305.15.2 IRC 21 ]
y = 4.225 m lo = 19.5 m
> 2.650 m [ c/c distance of
N A
beff = 2.650 m longitudinal girder]
Distance of cg from top fibre (y) = 0.666 m
Moment of inertia of longitudinal girder (IL) = 0.602 m4
Flextural rigidity per unit width ( Dx ) = (IL x E) /p = 0.227E
Computation of transverse rigidity
19.50 m
For end cross girder
Its behave like L - beam
beff
0.25 beff = lo/10 + bw [ Cl. 305.15.2 IRC 21 ]
lo = 0.7*2.65 1.855 m
N A beff = 0.511 m
1.5
0.325
Distance of cg from top fibre (y) = 0.818 m
Moment of inertia of end cross girder (IT1) = 0.170 m4
For intermediate cross girder
Its behave like T - beam
beff
0.25 beff = lo/5 + bw [ Cl. 305.15.2 IRC 21 ]
lo = 3*2.65 ######
N A
beff = 1.915 m
1.5
0.325
Distance of cg from top fibre (y) = 0.566 m
Moment of inertia of intermediate cross girder (IT2) = 0.279 m4
For deck slab
16.889
0.25
N A
4
Moment of inertia of deck slab (IT3) = 0.0220 m
Flextural rigidity per unit length ( Dy ) = (SIT x E )/leff = 0.033E
Torsional rigidity of rectangle (Ri) = G x K x b3 x d d/b K
Modulus of rigidity (G) = E/2x(1+m) 1.00 0.141
b = Shorter side 1.20 0.166
d = longer side 1.50 0.196
K corresponds to d/b from table. 2.00 0.229
For longitudinal girder 2.25 0.240
(Consider shaded portion only) 2.50 0.249
3.00 0.263
4.00 0.281
5.00 0.291
1
10.00 0.312
> 10 0.333
2
d/b for segment 1 = 4.615
K = 0.287
d/b for segment 2 = 2.500
K = 0.249
Torsional rigidity of long girder per unit width (Rxy) = 0.003E
= (G x K x b3 x d)/p
For cross girder
(Consider shaded portion only)
d/b for cross girder = 5.385
K = 0.293
Torsional rigidity of cross girder per unit length (Ryx) = 0.001E
= (G x K x b3x d)/leff
For deck slab
Torsional rigidity of deck slab per unit length (Rdeck) = E x t 3/6 = 0.003E
Fletural parameter (q ) = (b/leff) x (Dx/Dy)0.25 = 0.503
Torsional parameter ( a ) = H/(Dx*Dy)0.5 = 0.038
Where 2H = Rxy + Ryx + Rdeck
q 0.250
K0
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.900 0.970 0.985 1.040 1.080 1.040 0.985 0.970 0.900
b/4 0.220 0.410 0.630 0.850 1.040 1.200 1.350 1.540 1.700
b/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 3.280
b -1.850 -1.170 -0.530 -0.220 0.900 1.700 2.470 3.280 4.000
K1
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.960 0.980 1.000 1.020 1.040 1.020 1.000 0.980 0.960
b/4 0.880 0.910 0.960 0.970 1.020 1.050 1.050 1.050 1.040
b/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 1.300
b 0.690 0.750 0.810 0.880 0.960 1.040 1.160 1.300 1.460
q 0.275
K0
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.880 0.960 0.980 1.045 1.090 1.045 0.980 0.960 0.880
b/4 0.210 0.405 0.630 0.860 1.045 1.210 1.355 1.535 1.690
b/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 3.295
b -1.820 -1.160 -0.535 0.210 0.880 1.690 2.465 3.295 4.050
K1
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.950 0.975 1.000 1.020 1.045 1.020 1.000 0.975 0.950
b/4 0.865 0.900 0.950 0.970 1.020 1.055 1.055 1.050 1.050
b/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 1.340
b 0.660 0.725 0.790 0.865 0.950 1.050 1.185 1.340 1.525
q 0.300
K0
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.860 0.950 0.970 1.050 1.100 1.050 0.970 0.950 0.860
b/4 0.200 0.400 0.630 0.870 1.050 1.220 1.360 1.530 1.680
b/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 3.310
b -1.790 -1.150 -0.540 0.200 0.860 1.680 2.460 3.310 4.100
K1
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.940 0.970 1.000 1.020 1.050 1.020 1.000 0.970 0.940
b/4 0.850 0.890 0.940 0.970 1.020 1.060 1.060 1.050 1.060
b/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 1.380
b 0.630 0.700 0.770 0.850 0.940 1.060 1.210 1.380 1.590
q 0.325
K0
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.830 0.940 0.975 1.065 1.125 1.065 0.975 0.940 0.830
b/4 0.185 0.395 0.630 0.880 1.065 1.235 1.370 1.515 1.650
b/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 3.325
b -1.745 -1.130 -0.540 0.185 0.830 1.650 2.445 3.325 4.150
K1
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.940 0.965 1.000 1.030 1.055 1.030 1.000 0.965 0.940
b/4 0.830 0.870 0.930 0.970 1.030 1.070 1.070 1.060 1.060
b/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 1.420
b 0.595 0.675 0.740 0.830 0.940 1.060 1.230 1.420 1.655
q 0.350
K0
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.800 0.930 0.980 1.080 1.150 1.080 0.980 0.930 0.800
b/4 0.170 0.390 0.630 0.890 1.080 1.250 1.380 1.500 1.620
b/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 3.340
b -1.700 -1.110 -0.545 0.170 0.800 1.620 2.430 3.340 4.200
K1
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.940 0.960 1.000 1.040 1.060 1.040 1.000 0.960 0.940
b/4 0.810 0.850 0.900 0.970 1.040 1.080 1.080 1.070 1.060
b/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 1.460
b 0.560 0.650 0.710 0.810 0.940 1.060 1.250 1.460 1.720
q 0.375
K0
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.760 0.900 0.990 1.100 1.180 1.100 0.990 0.900 0.760
b/4 0.150 0.390 0.640 0.860 1.100 1.270 1.380 1.480 1.600
b/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 3.360
b -1.670 -1.090 -0.540 0.150 0.760 1.600 2.400 3.360 4.300
K1
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.910 0.960 1.000 1.040 1.070 1.040 1.000 0.960 0.910
b/4 0.790 0.840 0.910 0.960 1.040 1.100 1.090 1.090 1.070
b/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 1.520
b 0.520 0.600 0.680 0.790 0.910 1.070 1.290 1.530 1.810
q 0.400
K0
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.710 0.900 0.990 1.110 1.200 1.110 0.990 0.900 0.710
b/4 0.120 0.360 0.640 0.910 1.110 1.290 1.400 1.470 1.560
b/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 3.380
b -1.650 -1.070 -0.550 0.120 0.710 1.560 2.400 3.380 4.300
K1
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.900 0.950 1.000 1.050 1.080 1.050 1.000 0.950 0.900
b/4 0.770 0.830 0.900 0.960 1.050 1.100 1.100 1.090 1.070
b/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 1.550
b 0.500 0.580 0.660 0.770 0.900 1.070 1.300 1.550 1.880
q 0.425
K0
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.670 0.875 0.995 1.130 1.220 1.130 0.995 0.875 0.670
b/4 0.100 0.350 0.640 0.925 1.130 1.310 1.410 1.455 1.500
b/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 3.405
b -1.600 -1.045 -0.545 0.100 0.670 1.530 2.370 3.405 4.400
K1
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.890 0.950 1.000 1.055 1.090 1.055 1.000 0.950 0.890
b/4 0.750 0.810 0.885 0.960 1.055 1.120 1.120 1.095 1.080
b/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 1.610
b 0.470 0.540 0.630 0.750 0.390 1.080 1.325 1.610 1.940
q 0.450
K0
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.630 0.850 1.000 1.150 1.250 1.150 1.000 0.850 0.630
b/4 0.080 0.340 0.640 0.940 1.150 1.340 1.420 1.440 1.500
b/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 3.430
b -1.550 -1.020 -0.540 0.080 0.630 1.500 2.350 3.430 4.500
K1
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.880 0.950 1.000 1.060 1.100 1.060 1.000 0.950 0.880
b/4 0.730 0.790 0.870 0.960 1.060 1.140 1.140 1.100 1.090
b/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 1.670
b 0.440 0.500 0.600 0.730 0.880 1.090 1.350 1.670 2.000
q 0.475
K0
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.590 0.820 1.000 1.180 1.285 1.180 1.000 0.820 0.590
b/4 0.040 0.320 0.635 0.950 1.180 1.370 1.430 1.420 1.450
b/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 3.465
b -1.490 -0.990 -0.540 0.040 0.590 1.450 2.325 3.465 4.650
K1
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.865 0.935 1.000 1.065 1.115 1.065 1.000 0.935 0.865
b/4 0.705 0.775 0.865 0.960 1.065 1.150 1.145 1.110 1.090
b/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 1.715
b 0.410 0.475 0.575 0.705 0.865 1.090 1.370 1.715 1.075
q 0.500
K0
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.550 0.790 1.000 1.210 1.320 1.210 1.000 0.790 0.550
b/4 0.000 0.300 0.630 0.960 1.210 1.400 1.440 1.400 1.400
b/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 3.500
b -1.430 -0.960 -0.540 0.000 0.550 1.400 2.300 3.500 4.800
K1
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.850 0.920 1.000 1.070 1.130 1.070 1.000 0.920 0.850
b/4 0.680 0.760 0.860 0.960 1.070 1.160 1.150 1.120 1.090
b/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 1.760
b 0.380 0.450 0.550 0.680 0.850 1.090 1.390 1.760 2.150
q 0.525
K0
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.485 0.765 1.010 1.240 1.360 1.240 1.010 0.765 0.485
b/4 -0.050 0.275 0.630 0.970 1.240 1.425 1.450 1.375 1.330
b/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 3.600
b -1.365 -0.925 -0.535 -0.050 0.485 1.330 2.275 3.600 4.950
K1
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.830 0.910 1.000 1.080 1.140 1.080 1.000 0.910 0.830
b/4 0.665 0.735 0.850 0.960 1.080 1.170 1.160 1.130 1.090
b/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 1.815
b 0.355 0.425 0.525 0.665 0.830 1.090 1.415 1.815 2.240
q 0.550
K0
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.420 0.740 1.020 1.270 1.400 1.270 1.020 0.740 0.420
b/4 -0.100 0.250 0.630 0.980 1.270 1.450 1.460 1.350 1.260
b/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 3.700
b -1.300 -0.890 -0.530 -0.100 0.420 1.260 2.250 3.700 5.100
K1
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.810 0.900 1.000 1.090 1.150 1.090 1.000 0.900 0.810
b/4 0.650 0.710 0.840 0.960 1.090 1.180 1.170 1.140 1.090
b/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 1.870
b 0.330 0.400 0.500 0.650 0.810 1.090 1.440 1.870 2.330
q 0.575
K0
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.350 0.700 1.020 1.330 1.460 1.330 1.020 0.700 0.350
b/4 -0.130 0.220 0.620 1.000 1.330 1.500 1.480 1.340 1.100
b/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 3.800
b -1.160 -0.840 0.530 0.130 0.350 1.100 2.220 3.800 5.300
K1
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.800 0.890 1.000 1.110 1.170 1.110 1.000 0.890 0.800
b/4 0.600 0.700 0.810 0.950 1.110 1.210 1.200 1.140 1.080
b/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 1.920
b 0.300 0.370 0.470 0.600 0.800 1.080 1.450 1.920 2.420
q 0.600
K0
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.310 0.660 1.020 1.350 1.500 1.350 1.020 0.660 0.310
b/4 -0.170 0.210 0.620 1.020 1.350 1.530 1.470 1.310 1.030
b/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 3.080
b -1.050 -0.800 -0.520 -0.200 0.310 1.100 2.190 3.080 5.450
.
K1
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.800 0.890 1.000 1.120 1.190 1.120 1.000 0.890 0.800
b/4 0.580 0.670 0.800 0.950 1.120 1.230 1.200 1.150 1.080
b/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 1.960
b 0.280 0.340 0.440 0.580 0.800 1.080 1.460 1.960 2.500
q 0.625
K0
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.230 0.635 1.023 1.390 1.540 1.390 1.023 0.630 0.230
b/4 -0.220 0.180 0.615 1.030 1.390 1.570 1.490 1.290 0.965
b/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 3.045
b -0.920 -0.755 -0.520 -0.235 0.230 1.010 2.160 3.045 5.250
.
K1
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.775 0.870 0.990 1.013 1.210 1.130 0.990 0.870 0.775
b/4 0.515 0.655 0.785 0.950 1.130 1.250 1.220 1.150 1.070
b/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 2.010
b 0.260 0.320 0.420 0.555 0.775 1.070 1.480 2.010 2.775
q 0.650
K0
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.150 0.610 1.025 1.420 1.580 1.420 1.025 0.610 0.150
b/4 -0.260 0.150 0.610 1.040 1.420 1.600 1.510 1.260 0.900
b/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 3.010
b -0.800 -0.710 -0.520 -0.270 0.150 0.920 2.130 3.010 5.070
.
K1
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.750 0.850 0.980 1.140 0.980 0.850 0.750 0.870 0.775
b/4 0.550 0.640 0.770 0.950 1.140 1.270 1.240 1.150 1.060
b/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 2.060
b 0.240 0.300 0.400 0.530 0.750 1.060 1.500 2.060 2.650
q 0.675
K0
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.055 0.570 1.027 1.470 1.630 1.465 1.027 0.570 0.055
b/4 -0.315 0.130 0.605 1.050 1.470 1.650 1.530 1.235 0.785
b/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 3.150
b -0.640 -0.640 -0.510 -0.320 0.055 0.825 2.080 3.510 5.500
.
K1
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.730 0.842 0.980 1.155 1.255 1.155 0.980 0.842 0.730
b/4 0.525 0.615 0.755 0.945 1.155 1.300 1.250 1.150 1.050
b/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 2.110
b 0.200 0.270 0.365 0.510 0.730 1.050 1.510 2.110 2.750
q 0.700
K0
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 -0.040 0.530 1.030 1.520 1.680 1.510 1.030 0.530 -0.040
b/4 -0.370 0.110 0.000 1.060 1.510 1.700 1.550 1.210 0.670
b/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 4.010
b -0.480 -0.570 -0.500 -0.370 -0.040 0.730 2.030 4.010 6.030
.
K1
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.710 0.835 0.980 1.170 1.280 1.170 0.980 0.835 0.710
b/4 0.500 0.590 0.740 0.940 1.170 1.330 1.270 1.150 1.040
b/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 2.160
b 0.180 0.240 0.330 0.490 0.710 1.040 1.520 2.160 2.850
q 0.725
K0
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 -0.125 0.495 1.025 1.550 1.725 1.550 1.025 0.495 -0.125
b/4 -0.400 0.080 0.585 1.070 1.550 1.735 1.570 1.180 0.585
b/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 3.600
b -0.390 -0.505 -0.495 -0.400 0.125 0.645 1.990 3.600 6.365
.
K1
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.685 0.817 0.980 1.185 1.305 1.185 0.980 0.817 0.685
b/4 0.475 0.570 0.730 0.940 1.185 1.350 1.285 1.150 1.030
b/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 2.205
b 0.165 0.225 0.315 0.470 0.685 1.030 1.535 2.205 2.925
q 0.750
K0
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 -0.210 0.460 1.020 1.580 1.770 1.580 1.020 0.460 -0.210
b/4 -0.430 0.050 0.570 1.080 1.580 1.770 1.590 1.150 0.500
b/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 3.200
b -0.300 -0.440 -0.490 -0.430 -0.210 0.560 1.950 3.200 6.700
.
K1
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.660 0.800 0.980 1.200 1.330 1.200 0.980 0.800 0.660
b/4 0.450 0.550 0.720 0.940 1.200 1.370 1.300 1.150 1.020
b/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 2.250
b 0.150 0.210 0.300 0.450 0.660 1.020 1.550 2.250 3.000
q 0.775
K0
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 -0.280 0.425 1.020 1.620 1.825 1.620 1.020 0.425 -0.280
b/4 -0.460 0.035 0.560 1.090 1.620 1.825 1.607 1.125 0.415
b/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 3.610
b -0.230 -0.390 -0.485 -0.455 -0.280 0.475 1.885 3.610 6.860
.
K1
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.645 0.790 0.980 1.210 1.355 1.210 0.980 0.790 0.645
b/4 0.425 0.530 0.700 0.935 1.210 1.400 1.320 1.145 1.010
b/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 2.290
b 0.135 0.185 0.275 0.425 0.645 1.000 0.155 2.290 3.100
q 0.800
K0
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 -0.350 0.390 1.025 1.660 1.880 1.660 1.025 0.390 -0.350
b/4 -0.490 0.020 0.550 1.100 1.660 1.880 1.640 1.100 0.330
b/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 4.020
b -0.160 -0.340 -0.480 -0.480 -0.350 0.390 1.820 4.020 7.020
.
K1
Ref. Pt
-b -3b/4 -b/2 -b/4 0.000 b/4 b/2 3b/4 b
Load at
0.000 0.630 0.780 0.980 1.220 1.380 1.220 0.980 0.780 0.630
b/4 0.400 0.510 0.680 0.930 1.220 1.430 1.340 1.140 1.000
b/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 2.330
b 0.120 0.160 0.250 0.400 0.630 0.980 1.550 2.330 3.200
Unit load distribution coefficient.
RUN
q 0.503
For no torsion grillage a = 0 K0
Ref. Pt Row
-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b
Load at integral
0 0.541 0.787 1.001 1.214 1.325 1.214 1.001 0.787 0.541 7.87
b/4 -0.007 0.297 0.630 0.961 1.214 1.403 1.441 1.397 1.391 8.04
b/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 7.97
b -1.421 -0.955 -0.539 -0.007 0.541 1.391 2.297 3.513 4.820 7.94
For full torsion grillage a = 1 K1
Ref. Pt Row
-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b
Load at integral
0 0.847 0.919 1.000 1.071 1.131 1.071 1.000 0.919 0.847 7.96
b/4 0.678 0.757 0.859 0.960 1.071 1.161 1.151 1.121 1.090 7.96
b/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 8.00
b 0.377 0.447 0.547 0.678 0.847 1.090 1.393 1.767 2.162 8.04
Ka= K0+(K1-K0)x(a)
0.5
Ref. Pt Row
-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b
Load at integral
-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 8.02
0 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 8.02
b/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 7.98
b -1.070 -0.681 -0.327 0.127 0.601 1.332 2.120 3.172 4.300 7.96
Distribution coefficient K' for SIDL
-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b
0.5 t/m 0.5 t/m
2.075 2.650 2.65 2.65 2.075
G1 G2 G3 G4
lwKa
Load
Ref. Pt factor -b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b
Load at
(lw )
-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 0.00
b/4 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
b/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 0.21
b 0.43 -0.46 -0.30 -0.14 0.06 0.26 0.58 0.92 1.38 1.87
Slw 1.00
SlwKa 1.57 1.23 0.91 0.75 0.63 0.75 0.91 1.23 1.57
K' = SlwKa/Slw 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 G4
K' 1.221 0.806 0.774 1.221
Note : Coefficients have been increased by 10% to take into account the effect of higher harmonics.
Distribution coefficient K' for live load (3 lane class A)
-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b
Class A Class A Class A
0.95m 1.8m 1.7m 1.8m 1.7m 1.8m
2.075 2.65 2.65 2.65 2.075
G1 G2 G3 G4
lwKa
Load
Ref. Pt
factor -b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b
Load at
(lw )
-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 2.97
b/4 4.99 0.63 1.93 3.37 4.80 5.92 6.77 6.91 6.70 6.65
b/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 8.07
b 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Slw 34.20
SlwKa 41.86 40.64 39.14 37.82 35.37 32.88 29.12 25.31 21.12
K' = SlwKa/Slw 1.224 1.188 1.145 1.106 1.034 0.962 0.851 0.740 0.617
Distribution coefficient K' at girder location
Girder Nr. G1 G2 G3 G4
K' 1.289 1.207 1.087 0.860
Note : Coefficients have been increased by 10% to take into account the effect of higher harmonics.
Distribution coefficient K' for live load (70 - R)
-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b
70 - R
2.18m 1.93m
2.075 2.65 2.65 2.65 2.075
G1 G2 G3 G4
lwKa
Load
Ref. Pt factor -b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b
Load at
(lw )
-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 0.00
b/4 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
b/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 0.00
b 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Slw 17.00
SlwKa 36.23 32.44 28.14 22.97 17.25 11.85 6.01 0.70 -4.47
K' = SlwKa/Slw 2.131 1.908 1.655 1.351 1.015 0.697 0.353 0.041 -0.263
Distribution coefficient K' at girder location
Girder Nr. G1 G2 G3 G4
K' 1.995 1.440 0.897 0.173
Note : Coefficients have been increased by 10% to take into account the effect of higher harmonics.
Distribution coefficient K' for live load (1lane class A + 70 - R)
-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b
70 - R Class A
2.18m 1.93m 1.8m
2.075 2.65 2.65 2.65 2.075
G1 G2 G3 G4
lwKa
Load
Ref. Pt
factor -b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b
Load at
(lw )
-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 3.29
b/4 4.84 0.62 1.87 3.27 4.65 5.74 6.56 6.70 6.50 6.45
b/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 0.00
b 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Slw 28.40
SlwKa 40.16 39.05 37.47 35.00 31.17 26.28 19.80 13.40 7.12
K' = SlwKa/Slw 1.414 1.375 1.319 1.233 1.097 0.926 0.697 0.472 0.251
Distribution coefficient K' at girder location
Girder Nr. G1 G2 G3 G4
K' 1.490 1.337 1.088 0.611
Note : Coefficients have been increased by 10% to take into account the effect of higher harmonics.
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/m
2 Weight of top haunch =2*0.5*0.3*0.15*2.4 = 0.11 t/m
3 Weight of bottom haunch =2*0.5*0.15*0.15*2.4 = 0.05 t/m
4 Weight of bulb =0.625*0.25*2.4 = 0.38 t/m
5 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 =((2.65-0.325)*1.5*2.4-0.108- = 2.67 t
0.054)*0.325)
Web thickening at near ends
1 Wt due to extra widening (uni) =2*0.5*(2*2-2*0.25-2*0.25- = 0.97 t/m
2 Wt due to extra widening (vary) 0.15-0.15)*(0.625-0.325)*2.4 = 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/m
2 Weight of top haunch =2*0.5*0.3*0.15*2.4 = 0.11 t/m
3 Weight of bottom haunch =2*0.5*0.15*0.15*2.4 = 0.05 t/m
4 Weight of bulb =0.625*0.25*2.4 = 0.38 t/m
5 Weight of deck slab =((0.5*2.65*0.25)+0.5*(0.3+ = 1.94 t/m
0.2)*(2.075-0.325*0.5))*2.4
Running weight = 3.65 t/m
1 Weight of cross girder =((2.65-0.325)*1.5*2.4-0.108- = 1.33 t
0.054)*0.325)*0.5
Web thickening at near ends
=(0.5*(2*2-2*0.25 -2*0.25-0.15-
1 Wt due to extra widening (uni)
0.15)*(0.625-0.325) + = 0.98 t/m
2 Wt due to extra widening (vary) (0.5*(2*2-2*0.3-2*0.25-
0.15)*(0.625-0.325))*0.5*2.4 = 0.98 to 0 t/m
Calculation of SIDL (uniform)
Inner girder
1 Weight of wearing coat = 0.53 t/m
Outer girder
1 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 t
9.75 9.75
3.83t/m 0.97t/m
0.9 0.6
19.5 m
A B
Support reaction at A = 42.34 t
Location
Sl. Nr. Item Deff Span Span Span
from sup (L/8) (L/4) (L/2)
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 t
9.75 9.75
4.22t/m 0.98t/m
0.9 0.6
19.5 m
A B
Support reaction at A = 44.17 t
Location
Sl. Nr. Item Deff Span Span Span
from sup (L/8) (L/4) (L/2)
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 m
A B
Support reaction at A = 19.50 t
Location
Sl. Nr. Item Deff Span Span Span
from sup (L/8) (L/4) (L/2)
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 = =(5*19.5/16)*(2*(2*(195.5+207.6)+95.1)*0.5*19.5/3 = 9 mm
)/ (31220.186*100*2*(0.296+0.338))*1000
D2 = =D1/(2)0.5 (considering parabolic profile) = 6 mm
Calculation of bending moment and shear force (Live load)
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)
BM (t-m) Total BM Total BM Total BM Total BM Max
SL. Section Girder BM (t-m) Design
(dl+uni for 1L Cl A for 1L Cl A for 70 - R for 70 - R 3 Lane 70 - R 1L Cl A design
Nr. considered location (con sidl) BM (t-m)
sidl) (Reverse) (Forward) (Reverse) (Forward) Class A (wheel) + 70 - R LL BM
At Deff Inner 70.2 7.1 56.6 44.7 110.1 118.8 54.4 50.5 59.2 59.2 136.5
1 from
support Outer 75.7 10.7 56.6 44.7 110.1 118.8 58.1 70.0 65.9 70.0 156.4
At 1/8th Inner 83.4 8.4 70.9 55.8 138.3 149.2 68.2 63.4 74.3 74.3 166.1
2
span (L/8) Outer 89.9 12.7 70.9 55.8 138.3 149.2 72.8 87.8 82.8 87.8 190.5
At quarter Inner 143.5 14.4 116.0 97.1 237.3 248.5 111.5 105.6 125.4 125.4 283.3
3
span (L/4) Outer 154.2 21.8 116.0 97.1 237.3 248.5 119.1 146.3 139.7 146.3 322.3
At middle Inner 195.5 19.2 144.1 144.1 325.3 325.3 138.5 138.2 166.7 166.7 381.3
4
span (L/2) 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 girders
Design 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) 1.18
2 For 70 R (Wheeled) 1.18 From curve IRC 6 1966 Cl. 211.3
Design of section for flexure
Inner girder Outer girder
Deff from L/8 of L/4 of L/2 of Deff from L/8 of L/4 of L/2 of
SECTION
support span span span support span span span
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 0.5813 0.5813 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
Cracked moment of inertia Ir (m4) 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)
Calculation of shear force (Live load)
The shear forces in beams has been calculated as per the provisions of Cl 305.12.2 of IRC: 21 ie,
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 t
Component of shear force due to loads within 5.5 m from support. = 11.9 t
Component of shear force due to loads beyond 5.5 m from support. = 12.2 t
For 70 - R (wheel) (Forward train)
Total shear force (from computer print out on previous sheets) = 64.2 t
Component of shear force due to loads within 5.5 m from support. = 31.3 t
Component of shear force due to loads beyond 5.5 m from support. = 32.9 t
Distribution of shear force for 70 - R (wheel)
A. By Morrice - Little's method
1 For inner girder =1.440*64.24*1.18/4 = 27.3 t
2 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
1.63m 1.93m
1.525 2.65 2.65 2.65
FEM -3.233 5.742
Balance 3.233 -2.871 -2.871
Carryover -1.435 1.616 0.000 -1.435
Balance 1.435 -0.808 -0.808 0.718 0.718
Total 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 0.271
Reaction 17.29 15.69 -1.93 0.27
1 For inner girder = (32.92*1.440/4+15.69)*1.18 = 32.5 t
2 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 t
2 For outer girder = 39.8 t
Distribution of shear force for 1 L Class A + 70 - R (wheel)
A. By Morrice - Little's method
1 For inner girder = =1.34*(24.16*1.18+64.24*1.18)*0.9/4 = 31.4 t
2 For outer girder = =1.49*(24.16*1.18+64.24*1.18)*0.9/4 = 35. t
B. By continuous beam method [ For loads with in 5.5 m from support ]
15.66 t 15.66 t 5.97 t 5.97 t
1.63m 1.93m 1.88m 1.8m
1.525 2.65 2.65 2.65
FEM -3.233 5.742 -2.063 1.884 -1.762 0.327
Balance 3.233 -1.840 -1.840 -0.061 -0.061 -0.327
Carryover -0.920 1.616 -0.030 -0.920 -0.164 -0.030
Balance 0.920 -0.793 -0.793 0.542 0.542 0.030
Total 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 0.935
Elastic SF -1.783 1.783 1.238 -1.238 0.545 -0.545
Reaction 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 t
2 For outer girder = ((12.22+32.92)*1.49/4+16.89)*1.18*0.9 = 35.8 t
Design Shear force =Average SF x IF x DF
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. t
2 For outer girder = 35.8 t
At 1/8th span (L/8)
For class A (Forward train)
Total shear force (from computer print out on previous sheets) = 22.9 t
Component of shear force due to loads within 5.5 m from support. = 12.2 t
Component of shear force due to loads beyond 5.5 m from support. = 10.7 t
For 70 - R (wheel) (Forward train)
Total shear force (from computer print out on previous sheets) = 61.2 t
Component of shear force due to loads within 5.5 m from support. = 30.1 t
Component of shear force due to loads beyond 5.5 m from support. = 31.1 t
Distribution of shear force for 70 - R (wheel)
A. By Morrice - Little's method
1 For inner girder =1.440*61.2*1.18/4 = 26.0 t
2 For outer girder =1.995*61.2*1.18/4 = 36.0 t
B. By continuous beam method [ For loads with in 5.5 m from support ]
15.05 t 15.05 t
1.63m 1.93m
1.525 2.65 2.65 2.65
FEM -3.107 5.518
Balance 3.107 -2.759 -2.759
Carryover -1.380 1.554 0.000 -1.380
Balance 1.380 -0.777 -0.777 0.690 0.690
Total M 0.000 3.536 -3.536 -0.690 0.690
Simple SF 17.946 12.154
Elastic SF -1.334 1.334 1.595 -1.595 -0.260 0.260
Reaction 16.61 15.08 -1.85 0.26
1 For inner girder = (31.1*1.440/4+15.08)*1.18 = 31.0 t
2 For outer girder = (31.1*1.995/4+16.61)*1.18 = 37.9 t
Design Shear force =Average SF x IF x DF
1 For inner girder = 31.0 t
2 For outer girder = 37.9 t
Distribution of shear force for 1 L Class A + 70 - R (wheel)
A. By Morrice - Little's method
1 For inner girder =1.34*(22.9*1.18+61.2*1.18)*0.9/4 = 29.9 t
2 For outer girder =1.49*(22.9*1.18+61.2*1.18)*0.9/4 = 33.3 t
B. By continuous beam method [ For loads with in 5.5 m from support ]
15.05 t 15.05 t 6.1 t 6.1 t
1.63m 1.93m 1.88m 1.8m
1.525 2.65 2.65 2.65
FEM -3.107 5.518 -2.108 1.925 -1.801 0.334
Balance 3.107 -1.705 -1.705 -0.062 -0.062 -0.334
Carryover -0.853 1.554 -0.031 -0.853 -0.167 -0.031
Balance 0.853 -0.761 -0.761 0.510 0.510 0.031
Total M 0.000 4.605 -4.605 1.520 -1.520 0.000
Simple SF 17.946 12.154 3.188 2.912 5.145 0.955
Elastic SF -1.738 1.738 1.164 -1.164 0.574 -0.574
Reaction 16.21 18.24 7.47 0.38
1 For inner girder = ((10.7+31.1)*1.34/4+18.24)*1.18*0.9 = 34.2 t
2 For outer girder = ((10.7+31.1)*1.49/4+16.21)*1.18*0.9 = 33.7 t
Design Shear force =Average SF x IF x DF
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 = 34.2 t
2 For outer girder = 33.7 t
At quarter span (L/4)
For class A (Forward train)
Total shear force (from computer print out on previous sheets) = 18.8 t
Component of shear force due to loads within 5.5 m from support. = 3.1 t
Component of shear force due to loads beyond 5.5 m from support. = 15.7 t
For 70 - R (wheel) (Forward train)
Total shear force (from computer print out on previous sheets) = 48.7 t
Component of shear force due to loads within 5.5 m from support. = 16.4 t
Component of shear force due to loads beyond 5.5 m from support. = 32.3 t
Distribution of shear force for 70 - R (wheel)
A. By Morrice - Little's method
1 For inner girder =1.440*48.7*1.18/4 = 20.7 t
2 For outer girder =1.995*48.7*1.18/4 = 28.7 t
B. By continuous beam method [ For loads with in 5.5 m from support ]
8.20 t 8.20 t
1.63m 1.93m
1.525 2.65 2.65 2.65
FEM -1.693 3.007
Balance 1.693 -1.503 -1.503
Carryover -0.752 0.846 0.000 -0.752
Balance 0.752 -0.423 -0.423 0.376 0.376
Total M 0.000 1.927 -1.927 -0.376 0.376
Simple SF 9.778 6.622
Elastic SF -0.727 0.727 0.869 -0.869 -0.142 0.142
Reaction 9.05 8.22 -1.01 0.14
1 For inner girder = (32.3*1.440/4+8.22)*1.18 = 23.4 t
2 For outer girder = (32.3*1.995/4+9.05)*1.18 = 29.7 t
Design Shear force =Average SF x IF x DF
1 For inner girder = 23.4 t
2 For outer girder = 29.7 t
Distribution of shear force for 1 L Class A + 70 - R (wheel)
A. By Morrice - Little's method
1 For inner girder =1.34*(18.8*1.18+48.7*1.18)*0.9/4 = 24.0 t
2 For outer girder =1.49*(18.8*1.18+48.7*1.18)*0.9/4 = 26.7 t
B. By continuous beam method [ For loads with in 5.5 m from support ]
8.20 t 8.20 t 1.55 t 1.55 t
1.63m 1.93m 1.88m 1.8m
1.525 2.65 2.65 2.65
FEM -1.693 3.007 -0.536 0.489 -0.458 0.085
Balance 1.693 -1.236 -1.236 -0.016 -0.016 -0.085
Carryover -0.618 0.846 -0.008 -0.618 -0.042 -0.008
Balance 0.618 -0.419 -0.419 0.330 0.330 0.008
Total M 0.000 2.198 -2.198 0.186 -0.186 0.000
Simple SF 9.778 6.622 0.810 0.740 1.307 0.243
Elastic SF -0.830 0.830 0.759 -0.759 0.070 -0.070
Reaction 8.95 9.02 1.36 0.17
1 For inner girder = ((15.7+32.3)*1.34/4+9.02)*1.18*0.9 = 26.6 t
2 For outer girder = ((15.7+32.3)*1.49/4+8.95)*1.18*0.9 = 28.5 t
Design Shear force =Average SF x IF x DF
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 = 26.6 t
2 For outer girder = 28.5 t
Summary of shear force
Section SF (t) 1Lane
70 - R Design Design
SL. Nr. considere Girder (dl+uni SF (t) class A +
(wheel) LL SF SF (t-m)
d location sidl) (con sidl) 70 - R
Deff Inner 31.0 3.1 32.5 36.0 36.0 70.1
1
from sup Outer 33.4 4.7 39.8 35.8 39.8 77.9
Span Inner 29.3 2.9 31.0 34.2 34.2 66.5
2
(L/8) Outer 31.5 4.5 37.9 33.7 37.9 73.9
Span Inner 20.0 2.0 23.4 26.6 26.6 48.6
3
(L/4) Outer 21.2 3.0 29.7 28.5 29.7 53.9
Shear stress tv (N/mm )
2
< tmax = 2.1 N/mm
2
tc = K1 x K2 x tco [ Cl. 304.7.3 IRC - 21 1987 ]
Where
K1 = 1.14 - 0.7 d >= 0.5
K2 = 0.5 + 0.25 r >= 1.0
tco = 0.45
Section
considere Girder Design tv r% K1 K2 tc
2 2
SL. Nr. d location SF (t) (N/mm ) (N/mm )
Deff Inner 70.1 1.14 0.787 0.5 1.00 0.23
1
from sup Outer 77.9 1.27 0.916 0.5 1.00 0.23
Span Inner 66.5 1.09 0.787 0.5 1.00 0.23
2
(L/8) Outer 73.9 1.20 0.916 0.5 1.00 0.23
Span Inner 48.6 0.80 1.319 0.5 1.00 0.23
3
(L/4) Outer 53.9 0.88 1.579 0.5 1.00 0.23
Span Inner 0.0 0.00 1.854 0.5 1.00 0.23
4
(L/2) Outer 0.0 0.00 2.137 0.5 1.03 0.23
Reinf provided
Reinf required 2
Section (Asv) (cm /m) Spacing Spacing
2
considere Girder (Asv / Sv) (cm /m) No of Bar dia required Provided
SL. Nr. d location legs (mm) (mm) (mm)
Deff Inner 18.6 2 16 216 210
1
from sup Outer 20.6 2 16 195 190
Span Inner 17.6 2 16 228 220
2
(L/8) Outer 19.5 2 16 206 200
Span Inner 12.9 2 12 175 170
3
(L/4) Outer 14.3 2 12 158 150
Span Inner 9.1 2 12 248 170
4
(L/2) Outer 9.0 2 12 251 150
DESIGN OF CROSS GIRDER
End cross girder
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.
50.12 t 46.26 t 46.11 t 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 F
DF 1.00 0.49 0.51 0.51 0.49 0.49 0.51 0.51 0.49 1.00
FEM 32.58 0.00 0.00 -7.52 7.52 0.00 0.00 -7.49 7.49 0.00 0.00 -32.58
Balance -32.58 3.68 3.83 -3.83 -3.68 3.67 3.82 -3.82 -3.67 32.58
CO -16.29 -1.92 1.92 1.84 -1.84 -1.91 1.91 16.29
Balance 8.92 9.29 -1.91 -1.84 1.84 1.91 -9.28 -8.92
CO 0.00 -0.96 4.64 0.92 -0.92 -4.64 0.96 0.00
Balance 0.47 0.49 -2.84 -2.73 2.72 2.84 -0.49 -0.47
Total 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-m
Max 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 = 1.75
L/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 = 1.75
L/D = 1.514 >= 1 for contineous beam
Lever arm Z = 0.2*(2.65+1.5*1.75) = 1.055 m
=M/sst*Z
2
Required Ast for max span M =10.682/1.055*20000 = 5.06 cm
2
Minimum Ast at bottom =0.2%bd =0.002*32.5*175 = 11 cm
Provide 3 nos 16 f + 2 nos 16 f + 2 nos 12 f
at bottom within a depth of (0.25D - 0.05L) = 0.305 m
from bottom face with a development length of (0.8*35*dia of bar) = 448 mm
Provided Ast = 12.3 cm2
Required Ast for max support M =M/sst*Z
2
=32.579/1.055*20000 = 15.44 cm
Provide 3 nos 20 f + 2 nos 16 f + 2 nos 12 f
Distributed as per clause 28.3.2 (b) IS 456-1978
2
Provided Ast = 15.7 cm
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 cm2
Required Ast per m length =96.3/7.95 = 12.1 cm2/m
Provide 2L 12 f @ 180 c/c as vertical reinforcement
Provided Ast = 12.6 cm2/m
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.
2
Required Ast =0.001 *175*32.5 = 5.69 cm
