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

DESIGN OF RCC T - GIRDER DECK USING MORICE & LITTLE METHOD : (All blue coloured fonts depict inputs) BASIC DESIGN DATA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

Effective span Clear carriage way Spacing of main girder c/c Spacing of cross girder c/c Width of crash barier Thk of deck slab Thk of wearing coat Length of cantilever Cantilever slab thk at fixed end Cantilever slab thk at free end No of main girder Depth of main girder Web thk of main girder ( at center ) Web thk of main girder ( at support ) Length of extra widening ( varrying ) Length of extra widening ( uniform ) Top haunch Bottom haunch Bottom bulb No of cross girder Depth of cross girder Web thk of cross girder Grade of concrete Grade of reinforcement Clear cover Unit weight of concrete Weight of wearing course Weight of crash barrier

Leff Bcw Spmg Spcg Wkerb Df Wc Lcan Dcan1 Dcan2 Nomg Dmg bwmc bwms Lwv Lwu Thw x Thh Bhw x Bhh Bbw x Bbh Nocg Dcg bwcg Cgrade Sgrade cov wcon wwc wrail

19.500 m 11.000 m 2.650 m 9.750 m 0.550 m 0.250 m 0.065 m 2.075 m 0.300 m 0.200 m 4 m 2.000 m 0.325 m 0.625 m 0.900 m 0.600 m 0.300 x 0.150 m 0.150 x 0.150 m 0.625 x 0.250 m 3 m 1.750 m 0.325 m 30 N/mm2 415 N/mm2 0.04 m 2.400 t/m3 0.200 t/m2 1.000 t/m

29

Stress in concrete (compression)

fc

1000

t/m2

30 31

Stress in steel (tension) Modular ratio

ft m

20000 10

t/m2

Calculation of distribution coefficients by Morrice - Little method : Effective span (2a) Total width (2b)

= =

19.500 12.100

m m

p Computation of longitudinal rigidity beff beff = = > beff =

y N

A

Distance of cg from top fibre (y)

lo/5 + bw [ Cl. 305.15.2 IRC 21 ] 4.225 m lo = 19.5 m 2.650 m [ c/c distance of 2.650 m longitudinal girder]

= = =

Moment of inertia of longitudinal girder (IL) Flextural rigidity per unit width ( Dx ) = (IL x E) /p Computation of transverse rigidity

0.666 0.602 0.227E

m m4

19.50 m For end cross girder Its behave like L - beam beff 0.25 N 1.5

A

0.325 Distance of cg from top fibre (y) Moment of inertia of end cross girder (IT1)

beff = lo/10 + bw [ Cl. 305.15.2 IRC 21 ] lo = 0.7*2.65 1.855 m beff = 0.511 m

= =

0.818 0.170

m m4

For intermediate cross girder Its behave like T - beam beff 0.25 A

N

beff = lo/5 + bw [ Cl. 305.15.2 IRC 21 ] lo = 3*2.65 ###### beff = 1.915 m

1.5 0.325 Distance of cg from top fibre (y)

= =

Moment of inertia of intermediate cross girder (IT2) For deck slab 16.889 0.25

N

Moment of inertia of deck slab (IT3) Flextural rigidity per unit length ( Dy ) = (SIT x E )/leff Torsional rigidity of rectangle (Ri) = G x K x b3 x d Modulus of rigidity (G) = E/2x(1+m) b = Shorter side d = longer side K corresponds to d/b from table. For longitudinal girder (Consider shaded portion only)

1

0.566 0.279

A

= = d/b 1.00 1.20 1.50 2.00 2.25 2.50 3.00 4.00 5.00 10.00 > 10

4 0.0220 m 0.033E

K 0.141 0.166 0.196 0.229 0.240 0.249 0.263 0.281 0.291 0.312 0.333

2

d/b for segment 1 K d/b for segment 2 K Torsional rigidity of long girder per unit width (Rxy) = (G x K x b3 x d)/p

m m4

= = = = =

4.615 0.287 2.500 0.249 0.003E

For cross girder (Consider shaded portion only)

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

= = =

5.385 0.293 0.001E

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

For deck slab

Where 2H = Rxy + Ryx + Rdeck

q

0.250 K0

Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.900 0.220 -0.530 -0.170 -1.850

0.970 0.410 -0.150 -0.640 -1.170

0.985 0.630 0.240 -0.150 -0.530

1.040 0.850 0.630 -0.410 -0.220

1.080 1.040 0.985 -0.970 0.900

1.040 1.200 1.350 1.540 1.700

0.985 1.350 1.720 2.100 2.470

0.970 1.540 2.100 2.710 3.280

0.900 1.700 2.470 3.280 4.000

K1 Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.960 0.880 0.810 0.750 0.690

0.980 0.910 0.860 0.800 0.750

1.000 0.960 0.910 0.860 0.810

1.020 0.970 0.960 0.910 0.880

1.040 1.020 1.000 0.980 0.960

1.020 1.050 1.050 1.050 1.040

1.000 1.050 1.100 1.130 1.160

0.980 1.050 1.130 1.220 1.300

0.960 1.040 1.160 1.300 1.460

q

0.275 K0

Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.880 0.210 -0.535 -1.160 -1.820

0.960 0.405 -0.155 -0.635 -1.160

0.980 0.630 0.240 -0.155 -0.535

1.045 0.860 0.630 0.405 0.210

1.090 1.045 0.980 0.960 0.880

1.045 1.210 1.355 1.535 1.690

0.980 1.355 1.725 2.100 2.465

0.960 1.535 2.100 2.720 3.295

0.880 1.690 2.465 3.295 4.050

K1 Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.950 0.865 0.790 0.725 0.660

0.975 0.900 0.840 0.775 0.725

1.000 0.950 0.900 0.840 0.790

1.020 0.970 0.950 0.900 0.865

1.045 1.020 1.000 0.975 0.950

1.020 1.055 1.055 1.050 1.050

1.000 1.055 1.115 1.150 1.185

0.975 1.050 1.150 1.255 1.340

0.950 1.050 1.185 1.340 1.525

q

0.300 K0

Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.860 0.200 -0.540 -1.150 -1.790

0.950 0.400 -0.160 -0.630 -1.150

0.970 0.630 0.240 -0.160 -0.540

1.050 0.870 0.630 0.400 0.200

1.100 1.050 0.970 0.950 0.860

1.050 1.220 1.360 1.530 1.680

0.970 1.360 1.730 2.100 2.460

0.950 1.530 2.100 2.730 3.310

0.860 1.680 2.460 3.310 4.100

K1 Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.940 0.850 0.770 0.700 0.630

0.970 0.890 0.820 0.750 0.700

1.000 0.940 0.890 0.820 0.770

1.020 0.970 0.940 0.890 0.850

1.050 1.020 1.000 0.970 0.940

1.020 1.060 1.060 1.050 1.060

1.000 1.060 1.130 1.170 1.210

0.970 1.050 1.170 1.290 1.380

0.940 1.060 1.210 1.380 1.590

q

0.325 K0

Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.830 0.185 -0.540 -1.130 -1.745

0.940 0.395 -0.165 -0.615 -1.130

0.975 0.630 0.240 -0.165 -0.540

1.065 0.880 0.630 0.395 0.185

1.125 1.065 0.975 0.940 0.830

1.065 1.235 1.370 1.515 1.650

0.975 1.370 1.740 2.100 2.445

0.940 1.515 2.100 2.740 3.325

0.830 1.650 2.445 3.325 4.150

K1 Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.940 0.830 0.740 0.675 0.595

0.965 0.870 0.795 0.725 0.675

1.000 0.930 0.870 0.795 0.740

1.030 0.970 0.930 0.870 0.830

1.055 1.030 1.000 0.965 0.940

1.030 1.070 1.070 1.060 1.060

1.000 1.070 1.150 1.190 1.230

0.965 1.060 1.190 1.320 1.420

0.940 1.060 1.230 1.420 1.655

q

0.350 K0

Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.800 0.170 -0.545 -1.110 -1.700

0.930 0.390 -0.170 -0.600 -1.110

0.980 0.630 0.240 -0.170 -0.545

1.080 0.890 0.630 0.390 0.170

1.150 1.080 0.980 0.930 0.800

1.080 1.250 1.380 1.500 1.620

0.980 1.380 1.750 2.100 2.430

0.930 1.500 2.100 2.750 3.340

0.800 1.620 2.430 3.340 4.200

K1 Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.940 0.810 0.710 0.650 0.560

0.960 0.850 0.770 0.700 0.650

1.000 0.900 0.850 0.770 0.710

1.040 0.970 0.920 0.850 0.810

1.060 1.040 1.000 0.960 0.940

1.040 1.080 1.080 1.070 1.060

1.000 1.080 1.170 1.210 1.250

0.960 1.070 1.210 1.350 1.460

0.940 1.060 1.250 1.460 1.720

q

0.375 K0

Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.760 0.150 -0.540 -1.090 -1.670

0.900 0.390 -0.160 -0.600 -1.090

0.990 0.640 0.230 0.160 -0.540

1.100 0.860 0.640 0.390 0.150

1.180 1.100 0.990 0.900 0.760

1.100 1.270 1.380 1.480 1.600

0.990 1.380 1.750 2.090 2.400

0.900 1.480 2.090 2.770 3.360

0.760 1.600 2.400 3.360 4.300

K1 Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.910 0.790 0.680 0.600 0.520

0.960 0.840 0.750 0.670 0.600

1.000 0.910 0.830 0.750 0.680

1.040 0.960 0.910 0.850 0.790

1.070 1.040 1.000 0.960 0.910

1.040 1.100 1.100 1.090 1.070

1.000 1.090 1.190 1.240 1.290

0.960 1.090 1.240 1.400 1.530

0.910 1.070 1.290 1.520 1.810

q

0.400 K0

Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.710 0.120 -0.550 -1.070 -1.650

0.900 0.360 -0.170 -0.580 -1.070

0.990 0.640 0.230 -0.170 -0.550

1.110 0.910 0.630 0.360 0.120

1.200 1.110 0.990 0.900 0.710

1.110 1.290 1.370 1.470 1.560

0.990 1.400 1.760 2.100 2.400

0.900 1.470 2.100 2.770 3.380

0.710 1.560 2.400 3.380 4.300

K1 Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.900 0.770 0.660 0.580 0.500

0.950 0.830 0.730 0.650 0.580

1.000 0.900 0.810 0.730 0.660

1.050 0.960 0.900 0.830 0.770

1.080 1.050 1.000 0.950 0.900

1.050 1.100 1.100 1.090 1.070

1.000 1.100 1.200 1.260 1.300

0.950 1.090 1.260 1.410 1.550

0.900 1.070 1.300 1.550 1.880

q

0.425 K0

Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.670 0.100 -0.545 -1.045 -1.600

0.875 0.350 -0.170 -0.570 -1.045

0.995 0.640 0.230 -0.170 -0.545

1.130 0.925 0.635 0.350 0.100

1.220 1.130 0.995 0.875 0.670

1.130 1.310 1.375 1.455 1.530

0.995 1.410 1.770 2.095 2.370

0.875 1.455 2.095 2.785 3.405

0.670 1.500 2.375 3.405 4.400

K1 Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.890 0.750 0.630 0.540 0.470

0.950 0.810 0.700 0.615 0.540

1.000 0.885 0.785 0.700 0.630

1.055 0.960 0.885 0.810 0.750

1.090 1.055 1.000 0.950 0.390

1.055 1.120 1.120 1.095 1.080

1.000 1.120 1.225 1.280 1.325

0.950 1.095 1.280 1.455 1.610

0.890 1.080 1.325 1.610 1.940

q

0.450 K0

Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.630 0.080 -0.540 -1.020 -1.550

0.850 0.340 -0.170 -0.560 -1.020

1.000 0.640 0.230 -0.170 -0.540

1.150 0.940 0.640 0.340 0.080

1.250 1.150 1.000 0.850 0.630

1.150 1.340 1.380 1.440 1.500

1.000 1.420 1.780 2.090 2.350

0.850 1.440 2.090 2.800 3.430

0.630 1.500 2.350 3.430 4.500

K1 Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.880 0.730 0.600 0.500 0.440

0.950 0.790 0.670 0.580 0.500

1.000 0.870 0.760 0.670 0.600

1.060 0.960 0.870 0.790 0.730

1.100 1.060 1.000 0.950 0.880

1.060 1.140 1.140 1.100 1.090

1.000 1.140 1.250 1.300 1.350

0.950 1.100 1.300 1.500 1.670

0.880 1.090 1.350 1.670 2.000

q

0.475 K0

Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.590 0.040 -0.540 -0.990 -1.490

0.820 0.320 -0.170 -0.550 -0.990

1.000 0.635 0.225 -0.170 -0.540

1.180 0.950 0.635 0.320 0.040

1.285 1.180 1.000 0.820 0.590

1.180 1.370 1.390 1.420 1.450

1.000 1.430 1.790 2.085 2.325

0.820 1.420 2.085 2.820 3.465

0.590 1.450 2.325 3.465 4.650

K1 Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.865 0.705 0.575 0.475 0.410

0.935 0.775 0.650 0.555 0.475

1.000 0.865 0.745 0.650 0.575

1.065 0.960 0.865 0.775 0.705

1.115 1.065 1.000 0.935 0.865

1.065 1.150 1.145 1.110 1.090

1.000 1.145 1.275 1.325 1.370

0.935 1.110 1.325 1.540 1.715

0.865 1.090 1.370 1.715 1.075

q

0.500 K0

Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.550 0.000 -0.540 -0.960 -1.430

0.790 0.300 -0.170 -0.540 -0.960

1.000 0.630 0.220 -0.170 -0.540

1.210 0.960 0.630 0.300 0.000

1.320 1.210 1.000 0.790 0.550

1.210 1.400 1.400 1.400 1.400

1.000 1.440 1.800 2.080 2.300

0.790 1.400 2.080 2.840 3.500

0.550 1.400 2.300 3.500 4.800

K1 Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.850 0.680 0.550 0.450 0.380

0.920 0.760 0.630 0.530 0.450

1.000 0.860 0.730 0.630 0.550

1.070 0.960 0.860 0.760 0.680

1.130 1.070 1.000 0.920 0.850

1.070 1.160 1.150 1.120 1.090

1.000 1.150 1.300 1.350 1.390

0.920 1.120 1.350 1.580 1.760

0.850 1.090 1.390 1.760 2.150

q

0.525 K0

Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.485 -0.050 -0.535 -0.925 -1.365

0.765 0.275 -0.175 -0.520 -0.925

1.010 0.630 0.215 -0.175 -0.535

1.240 0.970 0.630 0.275 -0.050

1.360 1.240 1.010 0.765 0.485

1.240 1.425 1.415 1.375 1.330

1.010 1.450 1.820 2.075 2.275

0.765 1.375 2.075 2.855 3.600

0.485 1.330 2.275 3.600 4.950

K1 Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.830 0.665 0.525 0.425 0.355

0.910 0.735 0.605 0.505 0.425

1.000 0.850 0.710 0.605 0.525

1.080 0.960 0.850 0.735 0.665

1.140 1.080 1.000 0.910 0.830

1.080 1.170 1.160 1.130 1.090

1.000 1.160 1.325 1.375 1.415

0.910 1.130 1.375 1.615 1.815

0.830 1.090 1.415 1.815 2.240

q

0.550 K0

Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.420 -0.100 -0.530 -0.890 -1.300

0.740 0.250 -0.180 -0.500 -0.890

1.020 0.630 0.210 -0.180 -0.530

1.270 0.980 0.630 0.250 -0.100

1.400 1.270 1.020 0.740 0.420

1.270 1.450 1.430 1.350 1.260

1.020 1.460 1.840 2.070 2.250

0.740 1.350 2.070 2.870 3.700

0.420 1.260 2.250 3.700 5.100

K1 Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.810 0.650 0.500 0.400 0.330

0.900 0.710 0.580 0.480 0.400

1.000 0.840 0.690 0.580 0.500

1.090 0.960 0.840 0.710 0.650

1.150 1.090 1.000 0.900 0.810

1.090 1.180 1.170 1.140 1.090

1.000 1.170 1.350 1.400 1.440

0.900 1.140 1.400 1.650 1.870

0.810 1.090 1.440 1.870 2.330

q

0.575 K0

Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.350 -0.130 -0.530 -0.840 -1.160

0.700 0.220 -0.180 -0.490 -0.840

1.020 0.620 0.210 -0.180 0.530

1.330 1.000 0.620 0.220 0.130

1.460 1.330 1.020 0.700 0.350

1.330 1.500 1.480 1.340 1.100

1.020 1.480 1.860 2.080 2.220

0.700 1.340 2.080 2.900 3.800

0.350 1.100 2.260 3.800 5.300

K1 Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.800 0.600 0.470 0.370 0.300

0.890 0.700 0.550 0.450 0.370

1.000 0.810 0.660 0.550 0.470

1.110 0.950 0.810 0.700 0.600

1.170 1.110 1.000 0.890 0.800

1.110 1.210 1.200 1.140 1.080

1.000 1.200 1.380 1.440 1.450

0.890 1.140 1.440 1.720 1.920

0.800 1.080 1.450 1.920 2.420

q

0.600 K0

Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.310 -0.170 -0.520 -0.800 -1.050

0.660 0.210 -0.180 -0.470 -0.800

1.020 0.620 0.200 -0.180 -0.520

1.350 1.020 0.620 0.210 -0.200

1.500 1.350 1.020 0.660 0.310

1.350 1.530 1.470 1.310 1.100

1.020 1.470 1.870 2.060 2.190

0.660 1.310 2.060 2.920 3.080

0.310 1.030 2.190 3.080 5.450

. K1 Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.800 0.580 0.440 0.340 0.280

0.890 0.670 0.520 0.410 0.340

1.000 0.800 0.660 0.520 0.440

1.120 0.950 0.800 0.670 0.580

1.190 1.120 1.000 0.890 0.800

1.120 1.230 1.200 1.150 1.080

1.000 1.200 1.400 1.450 1.460

0.890 1.150 1.450 1.750 1.960

0.800 1.080 1.460 1.960 2.500

q

0.625 K0

Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.230 -0.220 -0.520 -0.755 -0.920

0.635 0.180 -0.180 -0.455 -0.755

1.023 0.615 0.200 -0.180 -0.520

1.390 1.030 0.615 0.180 -0.235

1.540 1.390 1.023 0.635 0.230

1.390 1.570 1.490 1.290 1.010

1.023 1.490 1.890 2.060 2.160

0.630 1.290 2.060 2.935 3.045

0.230 0.965 2.160 3.045 5.250

. K1 Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.775 0.515 0.420 0.320 0.260

0.870 0.655 0.495 0.385 0.320

0.990 0.785 0.615 0.495 0.420

1.013 0.950 0.785 0.655 0.555

1.210 1.130 0.990 0.870 0.775

1.130 1.250 1.220 1.150 1.070

0.990 1.220 1.425 1.480 1.480

0.870 1.150 1.480 1.845 2.010

0.775 1.070 1.480 2.010 2.775

q

0.650 K0

Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.150 -0.260 -0.520 -0.710 -0.800

0.610 0.150 -0.180 -0.440 -0.710

1.025 0.610 0.200 -0.180 -0.520

1.420 1.040 0.610 -0.150 -0.270

1.580 1.420 1.025 0.610 0.150

1.420 1.600 1.510 1.260 0.920

1.025 1.510 1.910 2.060 2.130

0.610 1.260 2.060 2.950 3.010

0.150 0.900 2.130 3.010 5.070

. K1 Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.750 0.550 0.400 0.300 0.240

0.850 0.640 0.470 0.360 0.300

0.980 0.770 0.600 0.470 0.400

1.140 0.950 0.770 0.640 0.530

0.980 1.140 0.980 0.850 0.750

0.850 1.270 1.240 1.150 1.060

0.750 1.240 1.450 1.500 1.500

0.870 1.150 1.500 1.840 2.060

0.775 1.060 1.500 2.060 2.650

q

0.675 K0

Ref. Pt Load at 0.000 b/4 b/2 3b/4 b .

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.055 -0.315 -0.510 -0.640 -0.640

0.570 0.130 -0.185 -0.420 -0.640

1.027 0.605 0.190 -0.185 -0.510

1.470 1.050 0.605 0.130 -0.320

1.630 1.470 1.027 0.570 0.055

1.465 1.650 1.530 1.235 0.825

1.027 1.530 1.935 2.055 2.080

0.570 1.235 2.055 2.975 3.510

0.055 0.785 2.080 3.150 5.500

K1 Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.730 0.525 0.365 0.270 0.200

0.842 0.615 0.450 0.370 0.270

0.980 0.755 0.575 0.450 0.365

1.155 0.945 0.755 0.615 0.510

1.255 1.155 0.980 0.842 0.730

1.155 1.300 1.250 1.150 1.050

0.980 1.250 1.480 1.525 1.510

0.842 1.150 1.525 1.385 2.110

0.730 1.050 1.510 2.110 2.750

q

0.700 K0

Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

-0.040 -0.370 -0.500 -0.570 -0.480

0.530 0.110 -0.190 -0.400 -0.570

1.030 0.000 0.180 -0.190 -0.500

1.520 1.060 0.600 0.110 -0.370

1.680 1.510 1.030 0.530 -0.040

1.510 1.700 1.550 1.210 0.730

1.030 1.550 1.960 2.050 2.030

0.530 1.210 2.050 3.000 4.010

-0.040 0.670 2.030 4.010 6.030

. K1 Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.710 0.500 0.330 0.240 0.180

0.835 0.590 0.430 0.320 0.240

0.980 0.740 0.550 0.430 0.330

1.170 0.940 0.740 0.590 0.490

1.280 1.170 0.980 0.835 0.710

1.170 1.330 1.270 1.150 1.040

0.980 1.270 1.510 1.550 1.520

0.835 1.150 1.550 1.930 2.160

0.710 1.040 1.520 2.160 2.850

q

0.725 K0

Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

-0.125 -0.400 -0.495 -0.505 -0.390

0.495 0.080 -0.185 -0.375 -0.505

1.025 0.585 0.175 -0.185 -0.495

1.550 1.070 0.585 0.080 -0.400

1.725 1.550 1.025 0.495 0.125

1.550 1.735 1.570 1.180 0.645

1.025 1.570 1.980 2.040 1.990

0.495 1.180 2.040 3.025 3.600

-0.125 0.585 1.990 3.600 6.365

. K1 Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.685 0.475 0.315 0.225 0.165

0.817 0.570 0.410 0.300 0.225

0.980 0.730 0.530 0.410 0.315

1.185 0.940 0.730 0.570 0.470

1.305 1.185 0.980 0.817 0.685

1.185 1.350 1.285 1.150 1.030

0.980 1.285 1.540 1.575 1.535

0.817 1.150 1.575 1.920 2.205

0.685 1.030 1.535 2.205 2.925

q

0.750 K0

Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

-0.210 -0.430 -0.490 -0.440 -0.300

0.460 0.050 -0.180 -0.350 -0.440

1.020 0.570 0.170 -0.180 -0.490

1.580 1.080 0.570 0.050 -0.430

1.770 1.580 1.020 0.460 -0.210

1.580 1.770 1.590 1.150 0.560

1.020 1.590 2.000 2.040 1.950

0.460 1.150 2.040 3.050 3.200

-0.210 0.500 1.950 3.200 6.700

. K1 Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.660 0.450 0.300 0.210 0.150

0.800 0.550 0.390 0.280 0.210

0.980 0.720 0.510 0.390 0.300

1.200 0.940 0.720 0.550 0.450

1.330 1.200 0.980 0.500 0.660

1.200 1.370 1.300 1.150 1.020

0.980 1.300 1.570 1.600 1.550

0.800 1.150 1.600 2.010 2.250

0.660 1.020 1.550 2.250 3.000

q

0.775 K0

Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

-0.280 -0.460 -0.485 -0.390 -0.230

0.425 0.035 -0.180 -0.325 -0.390

1.020 0.560 0.160 -0.180 -0.485

1.620 1.090 0.560 0.350 -0.455

1.825 1.620 1.020 0.425 -0.280

1.620 1.825 1.607 1.125 0.475

1.020 1.607 2.030 2.030 1.885

0.425 1.125 2.030 3.075 3.610

-0.280 0.415 1.885 3.610 6.860

. K1 Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.645 0.425 0.275 0.185 0.135

0.790 0.530 0.365 0.255 0.185

0.980 0.700 0.490 0.365 0.275

1.210 0.935 0.700 0.530 0.425

1.355 1.210 0.980 0.790 0.645

1.210 1.400 1.320 1.145 1.000

0.980 1.320 1.600 1.620 0.155

0.790 1.145 1.620 2.055 2.290

0.645 1.010 1.550 2.290 3.100

q

0.800 K0

Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

-0.350 -0.490 -0.480 -0.340 -0.160

0.390 0.020 -0.180 -0.300 -0.340

1.025 0.550 0.150 -0.180 -0.480

1.660 1.100 0.550 0.020 -0.480

1.880 1.660 1.025 0.390 -0.350

1.660 1.880 1.640 1.100 0.390

1.025 1.640 2.060 2.030 1.820

0.390 1.100 2.030 3.100 4.020

-0.350 0.330 1.820 4.020 7.020

. K1 Ref. Pt Load at 0.000 b/4 b/2 3b/4 b

-b

-3b/4

-b/2

-b/4

0.000

b/4

b/2

3b/4

b

0.630 0.400 0.250 0.160 0.120

0.780 0.510 0.340 0.230 0.160

0.980 0.680 0.470 0.340 0.250

1.220 0.930 0.680 0.510 0.400

1.380 1.220 0.980 0.780 0.630

1.220 1.430 1.340 1.140 0.980

0.980 1.340 1.630 1.640 1.550

0.780 1.140 1.640 2.100 2.330

0.630 1.000 1.550 2.330 3.200

Unit load distribution coefficient. q 0.503 For no torsion grillage a = 0 Ref. Pt -b -3b/4 Load at 0 0.541 0.787 b/4 -0.007 0.297 b/2 -0.539 -0.171 3b/4 -0.955 -0.537 b -1.421 -0.955 For full torsion grillage a = 1 Ref. Pt -b -3b/4 Load at 0 0.847 0.919 b/4 0.678 0.757 b/2 0.547 0.627 3b/4 0.447 0.527 b 0.377 0.447

RUN K0

-b/2

-b/4

0

b/4

b/2

3b/4

b

1.001 0.630 0.219 -0.171 -0.539

1.214 0.961 0.630 0.297 -0.007

1.325 1.214 1.001 0.787 0.541

1.214 1.403 1.402 1.397 1.391

1.001 1.441 1.803 2.079 2.297

0.787 1.397 2.079 2.842 3.513

0.541 1.391 2.297 3.513 4.820

K1 -b/2

-b/4

0

b/4

b/2

3b/4

b

1.000 0.859 0.727 0.627 0.547

1.071 0.960 0.859 0.757 0.678

1.131 1.071 1.000 0.919 0.847

1.071 1.161 1.151 1.121 1.090

1.000 1.151 1.303 1.353 1.393

0.919 1.121 1.353 1.585 1.767

0.847 1.090 1.393 1.767 2.162

Ka= K0+(K1-K0)x(a) Ref. Pt Load at -b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b

Row integral 7.87 8.04 7.84 7.97 7.94

Row integral 7.96 7.96 7.99 8.00 8.04

0.5

-b

-3b/4

-b/2

-b/4

0

b/4

b/2

3b/4

b

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

3.172 2.596 1.937 1.343 0.812 0.387 -0.015 -0.329 -0.681

2.120 1.937 1.705 1.385 1.001 0.675 0.319 -0.015 -0.327

1.332 1.343 1.353 1.356 1.186 0.961 0.675 0.387 0.127

0.601 0.812 1.001 1.186 1.287 1.186 1.001 0.812 0.601

0.127 0.387 0.675 0.961 1.186 1.356 1.353 1.343 1.332

-0.327 -0.015 0.319 0.675 1.001 1.385 1.705 1.937 2.120

-0.681 -0.329 -0.015 0.387 0.812 1.343 1.937 2.596 3.172

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

Row integral 7.96 7.98 7.87 8.02 7.89 8.02 7.87 7.98 7.96

Distribution coefficient K' for SIDL -b

-3b/4

-b/2

-b/4

0

b/4

b/2

0.5 t/m

0.5 t/m

2.075

2.650 G1

Ref. Pt Load at

b

3b/4

Load factor (lw ) 0.43 0.07 0.00 0.00 0.00 0.00 0.00 0.07 0.43 1.00

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b Slw SlwKa K' = SlwKa/Slw

2.65 G2

2.65

2.075 G4

G3

lwKa -b

-3b/4

-b/2

-b/4

0

b/4

b/2

3b/4

b

1.87 0.21 0.00 0.00 0.00 0.00 0.00 -0.05 -0.46

1.38 0.17 0.00 0.00 0.00 0.00 0.00 -0.02 -0.30

0.92 0.13 0.00 0.00 0.00 0.00 0.00 0.00 -0.14

0.58 0.09 0.00 0.00 0.00 0.00 0.00 0.03 0.06

0.26 0.05 0.00 0.00 0.00 0.00 0.00 0.05 0.26

0.06 0.03 0.00 0.00 0.00 0.00 0.00 0.09 0.58

-0.14 0.00 0.00 0.00 0.00 0.00 0.00 0.13 0.92

-0.30 -0.02 0.00 0.00 0.00 0.00 0.00 0.17 1.38

-0.46 -0.05 0.00 0.00 0.00 0.00 0.00 0.21 1.87

1.57 1.566

1.23 1.231

0.91 0.905

0.75 0.747

0.63 0.629

0.75 0.747

0.91 0.905

1.23 1.231

1.57 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

Class A

b/4

Class A

1.8m

0.95m

0

1.7m

2.075 G1

b

3b/4

Class A

1.8m

2.65

b/2

1.7m

2.65 G2

1.8m

2.65

2.075 G4

G3

lwKa Ref. Pt Load at -b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b Slw

Load factor (lw ) 2.12 4.62 4.99 5.37 4.95 4.99 4.62 2.54 0.00 34.20

SlwKa K' = SlwKa/Slw

-b

-3b/4

-b/2

-b/4

0

b/4

b/2

3b/4

b

9.11 14.65 10.58 7.15 2.97 0.63 -1.51 -1.73 0.00

6.72 11.99 9.67 7.21 4.02 1.93 -0.07 -0.84 0.00

4.49 8.95 8.51 7.44 4.95 3.37 1.47 -0.04 0.00

2.82 6.20 6.75 7.28 5.87 4.80 3.12 0.98 0.00

1.27 3.75 5.00 6.37 6.37 5.92 4.62 2.07 0.00

0.27 1.79 3.37 5.16 5.87 6.77 6.25 3.42 0.00

-0.69 -0.07 1.59 3.62 4.95 6.91 7.87 4.93 0.00

-1.44 -1.52 -0.07 2.08 4.02 6.70 8.95 6.60 0.00

-2.27 -3.15 -1.63 0.68 2.97 6.65 9.79 8.07 0.00

41.86 1.224

40.64 1.188

39.14 1.145

37.82 1.106

35.37 1.034

32.88 0.962

29.12 0.851

25.31 0.740

21.12 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

b

3b/4

70 - R 1.93m

2.18m

2.075

2.65 G1

2.65 G2

2.65

2.075 G4

G3

lwKa Ref. Pt Load at

Load factor (lw ) 0.00 4.75 6.15 6.10 0.00 0.00 0.00 0.00 0.00 17.00

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b Slw SlwKa K' = SlwKa/Slw

-b

-3b/4

-b/2

-b/4

0

b/4

b/2

3b/4

b

0.00 15.06 13.05 8.12 0.00 0.00 0.00 0.00 0.00

0.00 12.33 11.92 8.19 0.00 0.00 0.00 0.00 0.00

0.00 9.20 10.49 8.44 0.00 0.00 0.00 0.00 0.00

0.00 6.38 8.33 8.27 0.00 0.00 0.00 0.00 0.00

0.00 3.86 6.16 7.23 0.00 0.00 0.00 0.00 0.00

0.00 1.84 4.15 5.86 0.00 0.00 0.00 0.00 0.00

0.00 -0.07 1.96 4.11 0.00 0.00 0.00 0.00 0.00

0.00 -1.56 -0.09 2.36 0.00 0.00 0.00 0.00 0.00

0.00 -3.23 -2.01 0.78 0.00 0.00 0.00 0.00 0.00

36.23 2.131

32.44 1.908

28.14 1.655

22.97 1.351

17.25 1.015

11.85 0.697

6.01 0.353

0.70 0.041

-4.47 -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

2.075

b

3b/4

1.8m

2.65 G1

b/2

Class A

70 - R 1.93m

2.18m

b/4

2.65 G2

2.65

2.075 G4

G3

lwKa Ref. Pt Load at

Load factor (lw ) 0.00 4.75 6.15 6.33 5.47 4.84 0.86 0.00 0.00 28.40

-b -3b/4 -b/2 -b/4 0 b/4 b/2 3b/4 b Slw SlwKa K' = SlwKa/Slw

-b

-3b/4

-b/2

-b/4

0

b/4

b/2

3b/4

b

0.00 15.07 13.04 8.43 3.29 0.62 -0.28 0.00 0.00

0.00 12.33 11.91 8.50 4.44 1.87 -0.01 0.00 0.00

0.00 9.20 10.49 8.76 5.48 3.27 0.27 0.00 0.00

0.00 6.38 8.32 8.58 6.49 4.65 0.58 0.00 0.00

0.00 3.86 6.16 7.51 7.04 5.74 0.86 0.00 0.00

0.00 1.84 4.15 6.08 6.49 6.56 1.16 0.00 0.00

0.00 -0.07 1.96 4.27 5.48 6.70 1.47 0.00 0.00

0.00 -1.56 -0.09 2.45 4.44 6.50 1.67 0.00 0.00

0.00 -3.24 -2.01 0.80 3.29 6.45 1.82 0.00 0.00

40.16 1.414

39.05 1.375

37.47 1.319

35.00 1.233

31.17 1.097

26.28 0.926

19.80 0.697

13.40 0.472

7.12 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 2 3 4 5

Weight of web Weight of top haunch Weight of bottom haunch Weight of bulb Weight of deck slab

=(2-0.25-0.25)*0.325*2.4 =2*0.5*0.3*0.15*2.4 =2*0.5*0.15*0.15*2.4 =0.625*0.25*2.4 =2.65*0.25*2.4

Running weight 1

Weight of cross girder

1 2

Web thickening at near ends Wt due to extra widening (uni) =2*0.5*(2*2-2*0.25-2*0.25Wt due to extra widening (vary) 0.15-0.15)*(0.625-0.325)*2.4

=((2.65-0.325)*1.5*2.4-0.1080.054)*0.325)

= = = = =

1.17 0.11 0.05 0.38 1.59

t/m t/m t/m t/m t/m

=

3.30

t/m

=

2.67

t

= 0.97 t/m = 0.97 to 0 t/m

Main girder

0.6

0.9

Extra widening at support

Outer girder 1 2 3 4 5

Weight of web Weight of top haunch Weight of bottom haunch Weight of bulb Weight of deck slab

=(2-0.25-0.25)*0.325*2.4 =2*0.5*0.3*0.15*2.4 =2*0.5*0.15*0.15*2.4 =0.625*0.25*2.4 =((0.5*2.65*0.25)+0.5*(0.3+ 0.2)*(2.075-0.325*0.5))*2.4

Running weight 1

Weight of cross girder

=((2.65-0.325)*1.5*2.4-0.1080.054)*0.325)*0.5

= = = = =

1.17 0.11 0.05 0.38 1.94

t/m t/m t/m t/m t/m

=

3.65

t/m

=

1.33

t

Web thickening at near ends 1 2

=(0.5*(2*2-2*0.25 -2*0.25-0.15= 0.98 t/m 0.15)*(0.625-0.325) + (0.5*(2*2-2*0.3-2*0.25Wt due to extra widening (vary) = 0.98 to 0 t/m 0.15)*(0.625-0.325))*0.5*2.4 Wt due to extra widening (uni)

Calculation of SIDL (uniform)

Inner girder 1

Weight of wearing coat

=

0.53

t/m

Weight of wearing coat

=

0.57

t/m

Calculation of SIDL (concentrated) 2 Weight of crash barrier Total concentrated SIDL

= =

2.00 2.00

t/m t/m

Outer girder 1

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

Sl. Nr.

Item

=

Deff from sup

Location Span Span (L/8) (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

42.34

t

Outer girder 1.33 t

1.33 t 9.75

1.33 t 9.75

4.22t/m

0.98t/m 0.9

0.6

19.5 m A

B

Support reaction at A

Sl. Nr.

Item

=

Deff from sup

Location Span Span (L/8) (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

44.17

t

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

Sl. Nr.

Item

Deff from sup

Location Span Span (L/8) (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

=

19.50

t

=

9

mm

=

6

mm

Calculation of short term deflection due to dead load & sidl D2 L/4 D1 =

D1 L/4

D2 L/4

L/4

=(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 (considering parabolic profile) D2 = 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 SL. Section Girder Nr. considered location

1

2

3

4

At Deff from support At 1/8th span (L/8) At quarter span (L/4) At middle span (L/2)

Design live load B M ( t-m) BM (t-m) Total BM Total BM Total BM Total BM BM (t-m) (dl+uni for 1L Cl A for 1L Cl A for 70 - R for 70 - R 3 Lane 70 - R 1L Cl A (con sidl) sidl) (Reverse) (Forward) (Reverse) (Forward) Class A (wheel) + 70 - R

Inner

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

Inner

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

Inner

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

Inner

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 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 2

Max Design design BM (t-m) LL BM

For class A = 1+ 4.5/(6+L) For 70 R (Wheeled)

1.18 1.18

From curve IRC 6 1966 Cl. 211.3

Design of section for flexure Inner girder SECTION

Outer girder Deff from support

DATA M (t.m) 136.5 h (m) 2.000 bf (m) 2.650 df (m) 0.250 bw (m) 0.325 Ast (m^2) 0.00482 c (m) 0.115 Asc (m^2) 0.00080 dc (m) 0.064 m 10.0 RESULTS d (m) 1.885 Asf (m^2) 0.00515 AA (m^2) 0.0000 A (m) 2.6500 B (m^2) 0.1110 C (m^3) -0.1828 n (m) 0.243 CC (m^2) 0.0332 jd (m) 1.804 fc (t/m^2) 231 fs (t/m^2) -15677

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

166.1 2.000 2.650 0.250 0.325 0.00482 0.115 0.00040 0.064 10.0

283.3 2.000 2.650 0.250 0.325 0.00804 0.124 0.00040 0.064 10.0

381.3 2.000 2.650 0.250 0.325 0.01126 0.132 0.00040 0.064 10.0

156.4 2.000 3.400 0.250 0.325 0.00563 0.109 0.00080 0.064 10.0

190.5 2.000 3.400 0.250 0.325 0.00563 0.109 0.00040 0.064 10.0

322.3 2.000 3.400 0.250 0.325 0.00965 0.120 0.00040 0.064 10.0

428.1 2.000 3.400 0.250 0.325 0.01286 0.148 0.00040 0.064 10.0

1.885 0.00511 0.0000 2.6500 0.1037 -0.1823 0.243 0.0336 1.804 283 -19083

1.876 0.00513 0.5813 0.3250 1.3305 -0.4474 0.312 0.0635 1.778 396 -19815

1.868 0.00516 0.5813 0.3250 1.3949 -0.5663 0.373 0.0902 1.761 481 -19232

1.891 0.00656 0.0000 3.4000 0.1270 -0.2138 0.233 0.0388 1.814 215 -15321

1.891 0.00652 0.0000 3.4000 0.1198 -0.2133 0.233 0.0391 1.813 263 -18665

1.880 0.00656 0.7688 0.3250 1.7377 -0.5554 0.303 0.0783 1.784 359 -18723

1.852 0.00667 0.7688 0.3250 1.8020 -0.6691 0.349 0.1053 1.749 442 -19030

0.272

0.338

Cracked moment of inertia Ir (m4) 0.224 0.296 d=h-c Asf=(bf*df^2+2*(m-1)*Asc*(df-dc))/(2*m*(d-df)) AA=(bf-bw)*df for As= 1.0

Design SF (t) 70.1 77.9 66.5 73.9 48.6 53.9 0.0 0.0

tv 2

(N/mm ) 1.14 1.27 1.09 1.20 0.80 0.88 0.00 0.00

Reinf required 2 (Asv / Sv) (cm /m) 18.6 20.6 17.6 19.5 12.9 14.3 9.1 9.0

r% 0.787 0.916 0.787 0.916 1.319 1.579 1.854 2.137

K1 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

Reinf provided (Asv) (cm2/m) No of Bar dia legs (mm) 2 2 2 2 2 2 2 2

16 16 16 16 12 12 12 12

K2

tc

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.03

(N/mm ) 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23

2

Spacing Spacing required Provided (mm) (mm) 216 210 195 190 228 220 206 200 175 170 158 150 248 170 251 150

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

2.650

0.65

1.35

A DF FEM Balance CO Balance CO Balance Total M

1.00 32.58 0.00 -32.58

32.58 -32.58

B 0.49 0.00 3.68 -16.29 8.92 0.00 0.47 -3.22

2.650

0.65

0.51 -7.52 3.83 -1.92 9.29 -0.96 0.49 3.22

0.65 C 0.51 7.52 -3.83 1.92 -1.91 4.64 -2.84 5.49

1.35

0.49 0.00 -3.68 1.84 -1.84 0.92 -2.73 -5.49

D 0.49 0.00 3.67 -1.84 1.84 -0.92 2.72 5.47

2.650

0.65

0.51 -7.49 3.82 -1.91 1.91 -4.64 2.84 -5.47

Max support moment (DL+SIDL) Max span moment (DL+SIDL) Designed of deep beam For span AB Lever arm Z = For span CD Lever arm Z =

50.12 t

0.65 E 0.51 7.49 -3.82 1.91 -9.28 0.96 -0.49 -3.23

1.350

0.49 0.00 -3.67 16.29 -8.92 0.00 -0.47 3.23

F 1.00 0.00 -32.58 32.58

32.58 -32.58

= 32.58 t-m = 10.68 t-m

[ As per clause 28.2, IS 456-1978 ]

L= 2.65 L/D = 1.514 0.2*(2.65+1.5*1.75)

D = 1.75 >= 1 for contineous beam

L= 2.65 L/D = 1.514 0.2*(2.65+1.5*1.75)

D = 1.75 >= 1 for contineous beam

0.65

= 1.055 m

= 1.055 m

Required Ast for max span M

=M/sst*Z

=10.682/1.055*20000

2 = 5.06 cm

=

Provided Ast

= 12.3 cm2

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

11

2

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

cm

= 0.305 m = 448 mm

2 = 15.44 cm

= 15.7 cm2

Provided Ast 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 Provide 2L 12 f

=96.3/7.95 @ 180 c/c as vertical reinforcement

= 12.1 cm2/m = 12.6 cm2/m

Provided Ast 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