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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
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
Ref. Pt Load at
K1
Ref. Pt Load at
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
Ref. Pt Load at
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
Distribution coefficient K' at girder location
Girder Nr. G1 G2 G3 G4K' 1.289 1.207 1.087 0.860
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
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
Distribution coefficient K' at girder location
Girder Nr. G1 G2 G3 G4K' 1.995 1.440 0.897 0.173
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
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
Distribution coefficient K' at girder location
Girder Nr. G1 G2 G3 G4K' 1.490 1.337 1.088 0.611
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
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)
Support reaction at A = 44.17 t
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
Support reaction at A = 19.50 t
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)
Total shear force (from computer print out on previous sheets) = 64.2 tComponent of shear force due to loads within 5.5 m from support. = 31.3 tComponent 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 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
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
1.525 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
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 t2 For outer girder = 35.8 t
1.63m
1.93m
1.8m
1.88m
At 1/8th span (L/8)
For class A (Forward train)
Total shear force (from computer print out on previous sheets) = 22.9 tComponent of shear force due to loads within 5.5 m from support. = 12.2 tComponent 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 tComponent of shear force due to loads within 5.5 m from support. = 30.1 tComponent 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 method1 For inner girder =1.440*61.2*1.18/4 = 26.0 t2 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
1.525 2.65 2.65 2.65
FEM -3.107 5.518 Balance 3.107 -2.759 -2.759Carryover -1.380 1.554 0.000 -1.380Balance 1.380 -0.777 -0.777 0.690 0.690Total 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 0.260Reaction 16.61 15.08 -1.85 0.26
1 For inner girder = (31.1*1.440/4+15.08)*1.18 = 31.0 t2 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 t2 For outer girder = 37.9 t
1.63m
1.93m
Distribution of shear force for 1 L Class A + 70 - R (wheel)
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
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
1.525 2.65 2.65 2.65
FEM -3.107 5.518 -2.108 1.925 -1.801 0.334Balance 3.107 -1.705 -1.705 -0.062 -0.062 -0.334Carryover -0.853 1.554 -0.031 -0.853 -0.167 -0.031Balance 0.853 -0.761 -0.761 0.510 0.510 0.031Total 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 0.955Elastic SF -1.738 1.738 1.164 -1.164 0.574 -0.574Reaction 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 t2 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 t2 For outer girder = 33.7 t
1.63m
1.93m
1.8m
1.88m
At quarter span (L/4)
For class A (Forward train)
Total shear force (from computer print out on previous sheets) = 18.8 tComponent of shear force due to loads within 5.5 m from support. = 3.1 tComponent 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 tComponent of shear force due to loads within 5.5 m from support. = 16.4 tComponent 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 method1 For inner girder =1.440*48.7*1.18/4 = 20.7 t2 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
1.525 2.65 2.65 2.65
FEM -1.693 3.007 Balance 1.693 -1.503 -1.503Carryover -0.752 0.846 0.000 -0.752Balance 0.752 -0.423 -0.423 0.376 0.376Total 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 0.142Reaction 9.05 8.22 -1.01 0.14
1 For inner girder = (32.3*1.440/4+8.22)*1.18 = 23.4 t2 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 t2 For outer girder = 29.7 t
1.63m
1.93m
Distribution of shear force for 1 L Class A + 70 - R (wheel)
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
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
1.525 2.65 2.65 2.65
FEM -1.693 3.007 -0.536 0.489 -0.458 0.085Balance 1.693 -1.236 -1.236 -0.016 -0.016 -0.085Carryover -0.618 0.846 -0.008 -0.618 -0.042 -0.008Balance 0.618 -0.419 -0.419 0.330 0.330 0.008Total 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 0.243Elastic SF -0.830 0.830 0.759 -0.759 0.070 -0.070Reaction 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 t2 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 t2 For outer girder = 28.5 t
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