RCC T BEAM.xls

7/14/2019 RCC T BEAM.xls

http://slidepdf.com/reader/full/rcc-t-beamxls 1/33

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 m13 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 = lo/5 + bw [ 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

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

beff = 0.511 m

1.5

0.325


Moment of inertia of end cross girder (IT1) = 0.170 m4

beff

N A

N A



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 ######

beff = 1.915 m

1.5

0.325


Moment of inertia of intermediate cross girder (IT2) = 0.279 m4

For deck slab

16.889

0.25

Moment of inertia of deck slab (IT3

) = 0.0220 m4

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

10.00 0.312

> 10 0.333

d/b for segment 1 = 4.615

K = 0.287

d/b for segment 2 = 2.500

K = 0.249

= 0.003ETorsional rigidity of long girder per unit width (Rxy)

= (G x K x b3

x d)/p

A N

A N

2

1



For cross girder

(Consider shaded portion only)

d/b for cross girder = 5.385

K = 0.293

= 0.001E

For deck slab

= 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

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

Torsional rigidity of cross girder per unit length (Ryx)

= (G x K x b3x d)/leff



q 0.250

K 0Ref. Pt

Load at

-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 0.900

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

K 1Ref. Pt

Load at-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 0.960

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

K 0Ref. Pt

Load at-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 0.880

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

K 1Ref. Pt

Load at-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 0.950

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

K 0Ref. Pt

Load at-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 0.860

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



K 1Ref. 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 0.940

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

K 0Ref. Pt

Load at-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 0.830

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

K 1Ref. Pt

Load at-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 0.940

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

K 0Ref. Pt

Load at -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 0.800

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

K 1Ref. Pt

Load at-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 0.940

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

K 0Ref. Pt

Load at

-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 0.760

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

K 1Ref. Pt

Load at-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 0.910

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

K 0Ref. Pt

Load at-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 0.710

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

K 1Ref. Pt

Load at-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 0.900

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

K 0Ref. Pt

Load at-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 0.670

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



K 1Ref. 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 0.890

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

K 0Ref. Pt

Load at-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 0.630

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

K 1Ref. Pt

Load at-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 0.880

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

K 0Ref. Pt

Load at-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 0.590

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

K 1Ref. Pt

Load at-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 0.865

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

K 0Ref. Pt

Load at

-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 0.550

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

K 1Ref. Pt

Load at-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 0.850

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

K 0Ref. Pt

Load at-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 0.485

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

K 1Ref. Pt

Load at-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 0.830

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

K 0Ref. Pt

Load at-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 0.420

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



K 1Ref. 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 0.810

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

K 0Ref. Pt

Load at-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 0.350

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

K 1Ref. Pt

Load at-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 0.800

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

K 0Ref. Pt

Load at-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 0.310

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

.

K 1Ref. Pt

Load at-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 0.800

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

K 0Ref. Pt

Load at

-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 0.230

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

.

K 1Ref. Pt

Load at-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 0.775

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

K 0Ref. Pt

Load at-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 0.150

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

.

K 1Ref. Pt

Load at-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 0.775

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

K 0Ref. Pt

Load at-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 0.055

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.



K 1Ref. 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 0.730

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

K 0Ref. Pt

Load at-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 -0.040

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

.

K 1Ref. Pt

Load at-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 0.710

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

K 0Ref. Pt

Load at-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 -0.125

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

.

K 1Ref. Pt

Load at-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 0.685

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

K 0Ref. Pt

Load at

-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 -0.210

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

.

K 1Ref. Pt

Load at-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 0.660

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

K 0Ref. Pt

Load at-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 -0.280

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

.

K 1Ref. Pt

Load at-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 0.645

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

K 0Ref. Pt

Load at

-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 -0.350

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

.

K 1Ref. Pt

Load at-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 0.630

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.

q 0.503

For no torsion grillage a = 0 K 0

Ref. PtLoad at

-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 7.87

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 K 1Ref. Pt

Load at-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 7.96

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

K a= K 0+(K 1-K 0)x(a)0.5

Ref. Pt

Load at-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 8.02

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

Rowintegral

Row

integral

Row

integral

RUN



Distribution coefficient K' for SIDL

0.5 t/m 0.5 t/m

2.075 2.650 2.65 2.65 2.075

lwK a

Ref. Pt

Load at

oa

factor

(lw )

-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 0.00

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

SlwK a 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 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.

K ' = SlwK a/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

lwK a

Ref. Pt

Load at

Load

factor

(lw )

-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 2.97

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

SlwK a 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


K ' = SlwK a/Slw

G1 G2 G3 G4

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

Class A

1.8m0.95m

Class A

1.8m1.7m

Class A

1.8m1.7m



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

2.075 2.65 2.65 2.65 2.075

lwK a

Ref. Pt

Load at

Load

factor

(lw )

-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 0.00

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

SlwK a 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



K' 1.995 1.440 0.897 0.173


K ' = SlwK a/Slw

70 - R

1.93m2.18m

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

lwK a

Ref. Pt

Load at

Load

factor

(lw )

-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 3.29

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

SlwK a 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



K' 1.490 1.337 1.088 0.611


K ' = SlwK a/Slw

70 - R

1.93m2.18m

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/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 = 2.67 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/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/m4 Weight of bulb =0.625*0.25*2.4 = 0.38 t/m

5 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*0.5*(2*2-2*0.25-2*0.25-

0.15-0.15)*(0.625-0.325)*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

=((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)



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

Deff

from sup

Span

(L/8)

Span

(L/4)

Span

(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

Location

Sl. Nr. Item




Deff

from sup

Span

(L/8)

Span

(L/4)

Span

(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


Deff

from sup

Span

(L/8)

Span

(L/4)

Span

(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 = = 9 mm

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

corres ondin moment. The results are resented in the followin sheets.

=(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

Sl. Nr. Item

Location

Sl. Nr. Item

Location



Summary of bending moment

3 Lane

Class A

70 - R

(wheel)

1L Cl A

+ 70 - R

Inner 70.2 7.1 56.6 44.7 110.1 118.8 54.4 50.5 59.2 59

Outer 75.7 10.7 56.6 44.7 110.1 118.8 58.1 70.0 65.9 70

Inner 83.4 8.4 70.9 55.8 138.3 149.2 68.2 63.4 74.3 74

Outer 89.9 12.7 70.9 55.8 138.3 149.2 72.8 87.8 82.8 87

Inner 143.5 14.4 116.0 97.1 237.3 248.5 111.5 105.6 125.4 12

Outer 154.2 21.8 116.0 97.1 237.3 248.5 119.1 146.3 139.7 14

Inner 195.5 19.2 144.1 144.1 325.3 325.3 138.5 138.2 166.7 16

Outer 207.6 29.0 144.1 144.1 325.3 325.3 148.0 191.5 185.7 19

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

BM (t-m)

(dl+uni

sidl)

Girder

location

BM (t-m)

(con sidl)

Total BM

for 1L Cl A

(Reverse)

Total BM

for 70 - R

(Forward)

M

des

LL

Design live load B M ( t-m)Total BM

for 1L Cl A

(Forward)

Total BM

for 70 - R

(Reverse)

At Deff from

support

At quarter

span (L/4)

At middle

span (L/2)

SL.

Nr.

4

3

1

2At 1/8th

span (L/8)

Section

considered



Design of section for flexure

Inner g r er Outer g r er

SECTIONDeff 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

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 10.0RESULTS

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)




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

1.525

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

2.65 2.65 2.65

17.29 15.69 -1.93 0.27

1.63m 1.93m



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)


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


15.66 t 15.66 t 5.97 t 5.97 t

1.525

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

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


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


16.89 7.19 0.3918.79

2.65 2.65 2.65

1.63m 1.93m1.8m

1.88m



At 1/8th span (L/8)














15.05 t 15.05 t

1.525

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






15.08 -1.85 0.26

2.65 2.65 2.65

16.61

1.63m 1.93m





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


15.05 t 15.05 t 6.1 t 6.1 t

1.525

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








18.24 7.47 0.3816.21

2.65 2.65 2.65

1.63m 1.93m 1.8m1.88m



At quarter span (L/4)














8.20 t 8.20 t

1.525

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






2.65 2.65 2.65

9.05 8.22 -1.01 0.14

1.63m 1.93m





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


8.20 t 8.20 t 1.55 t 1.55 t

1.525

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








2.65 2.65 2.65

8.95 9.02 1.36 0.17

1.63m 1.93m 1.8m1.88m



Summary of shear force

SL. Nr.

ect on

considere

d

Girder

location

t

(dl+uni

sidl)

SF (t)

(con sidl)

70 - R

(wheel)

1Lane

class A +

70 - R

Design

LL SF

Design

SF (t-m)

Inner 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

Inner 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

Inner 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

Shear stress tv (N/mm ) < tmax 2.1 N/mm

tc = K 1 x K 2 x tco [ Cl. 304.7.3 IRC - 21 1987 ]

Where

K 1 = 1.14 - 0.7 d >= 0.5

K 2 = 0.5 + 0.25 r >= 1.0

tco = 0.45

SL. Nr.

Sectionconsidere

d

Girder

location

Design

SF (t)

tv

(N/mm2)

r % K 1 K 2tc

(N/mm2)

Inner 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

Inner 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

Inner 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

Inner 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

No of

legs

Bar dia

(mm)

Inner 2 16 216 210

Outer 2 16 195 190

Inner 2 16 228 220

Outer 2 16 206 200

Inner 2 12 175 170

Outer 2 12 158 150

Inner 2 12 248 170

Outer 2 12 251 150

Spacing

Provided

(mm)

Reinf provided

(Asv) (cm2/m)

Girder

location

Reinf required(Asv / Sv) (cm

2/m)

Spacing

required

(mm)SL. Nr.

Section

considere

d

3

4Span

(L/2)

2

Deff

from sup

Span

(L/8)

Span

(L/4)

1

2Span

(L/8)

4Span

(L/2)

3Span

(L/4)

9.1

9.0

18.6

20.6

12.9

14.3

17.6

19.5

1Deff

from sup

1Deff

from sup

3Span

(L/4)

2Span

(L/8)



DESIGN OF CROSS GIRDER

End cross girder

50.12 t 46.26 t 46.11 t 50.12 t

0.65 0.65 0.65 0.65 0.65 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

C O -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

C O 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

2.650

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.

2.650 2.650

1.35 1.3501.35



Required Ast for max span M =M/sst*Z =10.682/1.055*20000 = 5.06 cm2

Minimum Ast at bottom =0.2%bd =0.002*32.5*175 = 11 cm2

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 =32.579/1.055*20000 = 15.44 cm2

Provide 3 nos 20 f + 2 nos 16 f + 2 nos 12 f

Distributed as per clause 28.3.2 (b) IS 456-1978

Provided Ast = 15.7 cm2

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 2 L 12 f 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.

Required Ast =0.001 *175*32.5 = 5.69 cm2

@ 180 c/c

RCC T BEAM.xls

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