RCC-T-19.5

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RCC-T-19.5 Powered By Docstoc
					DESIGN OF RCC T - GIRDER DECK USING MORICE & LITTLE METHOD :
(All blue coloured fonts depict inputs)
BASIC DESIGN DATA
  1   Effective span                             Leff     19.500            m
  2   Clear carriage way                         Bcw      11.000            m
  3   Spacing of main girder c/c                Spmg       2.650            m
  4   Spacing of cross girder c/c               Spcg       9.750            m
  5   Width of crash barier                     Wkerb      0.550            m
  6   Thk of deck slab                            Df       0.250            m
  7   Thk of wearing coat                        Wc        0.065            m
  8   Length of cantilever                      Lcan       2.075            m
  9   Cantilever slab thk at fixed end          Dcan1      0.300            m
 10   Cantilever slab thk at free end           Dcan2      0.200            m
 11   No of main girder                         Nomg          4             m
 12   Depth of main girder                      Dmg        2.000            m
 13   Web thk of main girder ( at center )      bwmc       0.325            m
 14   Web thk of main girder ( at support )     bwms       0.625            m
 15   Length of extra widening ( varrying )      Lwv       0.900            m
 16   Length of extra widening ( uniform )       Lwu       0.600            m
 17   Top haunch                              Thw x Thh    0.300 x 0.150    m
 18   Bottom haunch                           Bhw x Bhh    0.150 x 0.150    m
 19   Bottom bulb                             Bbw x Bbh    0.625 x 0.250    m
 20   No of cross girder                        Nocg          3             m
 21   Depth of cross girder                      Dcg       1.750            m
 22   Web thk of cross girder                   bwcg       0.325            m
 23   Grade of concrete                        Cgrade        30          N/mm2
 24   Grade of reinforcement                   Sgrade       415          N/mm2
 25   Clear cover                                cov        0.04            m
 26   Unit weight of concrete                   wcon       2.400          t/m3
 27   Weight of wearing course                   wwc       0.200          t/m2
 28   Weight of crash barrier                   wrail      1.000           t/m
 29   Stress in concrete (compression)           fc       1000           t/m2
 30   Stress in steel (tension)                  ft       20000          t/m2
 31   Modular ratio                              m          10
Calculation of distribution coefficients by Morrice - Little method :

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




                                                  p
Computation of longitudinal rigidity

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



Distance of cg from top fibre (y)                                                 =    0.666    m
Moment of inertia of longitudinal girder (IL)                                     =    0.602    m4
Flextural rigidity per unit width ( Dx ) = (IL x E) /p                            =   0.227E
Computation of transverse rigidity




                                                      19.50 m

For end cross girder
Its behave like L - beam
                      beff
       0.25                                              beff = lo/10 + bw [ Cl. 305.15.2 IRC 21 ]
                                                           lo = 0.7*2.65 1.855 m
        N                       A                        beff = 0.511 m
        1.5


                  0.325
Distance of cg from top fibre (y)                                                 =    0.818    m
Moment of inertia of end cross girder (IT1)                                       =    0.170    m4
For intermediate cross girder
Its behave like T - beam
                   beff
     0.25                                               beff = lo/5 + bw [ Cl. 305.15.2 IRC 21 ]
                                                          lo = 3*2.65 ######
             N                   A
                                                        beff = 1.915 m
    1.5

                  0.325
Distance of cg from top fibre (y)                                               =    0.566   m
Moment of inertia of intermediate cross girder (IT2)                            =    0.279   m4
For deck slab
                          16.889
                                                          0.25
     N                                                           A

                                                                                            4
Moment of inertia of deck slab (IT3)                                            =   0.0220 m
Flextural rigidity per unit length ( Dy ) = (SIT x E )/leff                     =   0.033E

Torsional rigidity of rectangle (Ri) = G x K x b3 x d                       d/b        K
Modulus of rigidity (G) = E/2x(1+m)                                         1.00     0.141
b = Shorter side                                                            1.20     0.166
d = longer side                                                             1.50     0.196
K corresponds to d/b from table.                                            2.00     0.229
For longitudinal girder                                                     2.25     0.240
(Consider shaded portion only)                                              2.50     0.249
                                                                            3.00     0.263
                                                                            4.00     0.281
                                                                            5.00     0.291
                             1
                                                                           10.00     0.312
                                                                           > 10      0.333
                             2

d/b for segment 1                                                               =   4.615
K                                                                               =    0.287
d/b for segment 2                                                               =   2.500
K                                                                               =    0.249
Torsional rigidity of long girder per unit width (Rxy)                          =   0.003E
= (G x K x b3 x d)/p
For cross girder
(Consider shaded portion only)




d/b for cross girder                                                  =    5.385
K                                                                     =    0.293
Torsional rigidity of cross girder per unit length (Ryx)              =   0.001E
= (G x K x b3x d)/leff
For deck slab
Torsional rigidity of deck slab per unit length (Rdeck) = E x t 3/6   =   0.003E

Fletural parameter (q ) = (b/leff) x (Dx/Dy)0.25                      =   0.503

Torsional parameter ( a ) = H/(Dx*Dy)0.5                              =   0.038

Where 2H = Rxy + Ryx + Rdeck
    q         0.250
                                                   K0
    Ref. Pt
                -b     -3b/4     -b/2     -b/4    0.000     b/4     b/2    3b/4     b
Load at
  0.000        0.900    0.970    0.985    1.040    1.080   1.040   0.985   0.970   0.900
    b/4        0.220    0.410    0.630    0.850    1.040   1.200   1.350   1.540   1.700
    b/2       -0.530   -0.150    0.240    0.630    0.985   1.350   1.720   2.100   2.470
   3b/4       -0.170   -0.640   -0.150   -0.410   -0.970   1.540   2.100   2.710   3.280
     b        -1.850   -1.170   -0.530   -0.220    0.900   1.700   2.470   3.280   4.000

                                                   K1
    Ref. Pt
                -b     -3b/4     -b/2     -b/4    0.000     b/4     b/2    3b/4     b
Load at
  0.000       0.960    0.980    1.000    1.020    1.040    1.020   1.000   0.980   0.960
    b/4       0.880    0.910    0.960    0.970    1.020    1.050   1.050   1.050   1.040
    b/2       0.810    0.860    0.910    0.960    1.000    1.050   1.100   1.130   1.160
   3b/4       0.750    0.800    0.860    0.910    0.980    1.050   1.130   1.220   1.300
     b        0.690    0.750    0.810    0.880    0.960    1.040   1.160   1.300   1.460

    q         0.275
                                                   K0
    Ref. Pt
                -b     -3b/4     -b/2     -b/4    0.000     b/4     b/2    3b/4     b
Load at
  0.000        0.880    0.960    0.980   1.045    1.090    1.045   0.980   0.960   0.880
    b/4        0.210    0.405    0.630   0.860    1.045    1.210   1.355   1.535   1.690
    b/2       -0.535   -0.155    0.240   0.630    0.980    1.355   1.725   2.100   2.465
   3b/4       -1.160   -0.635   -0.155   0.405    0.960    1.535   2.100   2.720   3.295
     b        -1.820   -1.160   -0.535   0.210    0.880    1.690   2.465   3.295   4.050

                                                   K1
    Ref. Pt
                -b     -3b/4     -b/2     -b/4    0.000     b/4     b/2    3b/4     b
Load at
  0.000       0.950    0.975    1.000    1.020    1.045    1.020   1.000   0.975   0.950
    b/4       0.865    0.900    0.950    0.970    1.020    1.055   1.055   1.050   1.050
    b/2       0.790    0.840    0.900    0.950    1.000    1.055   1.115   1.150   1.185
   3b/4       0.725    0.775    0.840    0.900    0.975    1.050   1.150   1.255   1.340
     b        0.660    0.725    0.790    0.865    0.950    1.050   1.185   1.340   1.525

    q         0.300
                                                   K0
    Ref. Pt
                -b     -3b/4     -b/2     -b/4    0.000     b/4     b/2    3b/4     b
Load at
  0.000        0.860    0.950    0.970   1.050    1.100    1.050   0.970   0.950   0.860
    b/4        0.200    0.400    0.630   0.870    1.050    1.220   1.360   1.530   1.680
    b/2       -0.540   -0.160    0.240   0.630    0.970    1.360   1.730   2.100   2.460
   3b/4       -1.150   -0.630   -0.160   0.400    0.950    1.530   2.100   2.730   3.310
     b        -1.790   -1.150   -0.540   0.200    0.860    1.680   2.460   3.310   4.100
                                                  K1
    Ref. Pt
                -b     -3b/4     -b/2    -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000       0.940    0.970    1.000    1.020   1.050   1.020   1.000   0.970   0.940
    b/4       0.850    0.890    0.940    0.970   1.020   1.060   1.060   1.050   1.060
    b/2       0.770    0.820    0.890    0.940   1.000   1.060   1.130   1.170   1.210
   3b/4       0.700    0.750    0.820    0.890   0.970   1.050   1.170   1.290   1.380
     b        0.630    0.700    0.770    0.850   0.940   1.060   1.210   1.380   1.590

    q         0.325
                                                  K0
    Ref. Pt
                -b     -3b/4     -b/2    -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000        0.830    0.940    0.975   1.065   1.125   1.065   0.975   0.940   0.830
    b/4        0.185    0.395    0.630   0.880   1.065   1.235   1.370   1.515   1.650
    b/2       -0.540   -0.165    0.240   0.630   0.975   1.370   1.740   2.100   2.445
   3b/4       -1.130   -0.615   -0.165   0.395   0.940   1.515   2.100   2.740   3.325
     b        -1.745   -1.130   -0.540   0.185   0.830   1.650   2.445   3.325   4.150

                                                  K1
    Ref. Pt
                -b     -3b/4     -b/2    -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000       0.940    0.965    1.000    1.030   1.055   1.030   1.000   0.965   0.940
    b/4       0.830    0.870    0.930    0.970   1.030   1.070   1.070   1.060   1.060
    b/2       0.740    0.795    0.870    0.930   1.000   1.070   1.150   1.190   1.230
   3b/4       0.675    0.725    0.795    0.870   0.965   1.060   1.190   1.320   1.420
     b        0.595    0.675    0.740    0.830   0.940   1.060   1.230   1.420   1.655

    q         0.350
                                                  K0
    Ref. Pt
                -b     -3b/4     -b/2    -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000        0.800    0.930    0.980   1.080   1.150   1.080   0.980   0.930   0.800
    b/4        0.170    0.390    0.630   0.890   1.080   1.250   1.380   1.500   1.620
    b/2       -0.545   -0.170    0.240   0.630   0.980   1.380   1.750   2.100   2.430
   3b/4       -1.110   -0.600   -0.170   0.390   0.930   1.500   2.100   2.750   3.340
     b        -1.700   -1.110   -0.545   0.170   0.800   1.620   2.430   3.340   4.200

                                                  K1
    Ref. Pt
                -b     -3b/4     -b/2    -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000       0.940    0.960    1.000    1.040   1.060   1.040   1.000   0.960   0.940
    b/4       0.810    0.850    0.900    0.970   1.040   1.080   1.080   1.070   1.060
    b/2       0.710    0.770    0.850    0.920   1.000   1.080   1.170   1.210   1.250
   3b/4       0.650    0.700    0.770    0.850   0.960   1.070   1.210   1.350   1.460
     b        0.560    0.650    0.710    0.810   0.940   1.060   1.250   1.460   1.720
    q         0.375
                                                  K0
    Ref. Pt
                -b     -3b/4     -b/2    -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000        0.760    0.900    0.990   1.100   1.180   1.100   0.990   0.900   0.760
    b/4        0.150    0.390    0.640   0.860   1.100   1.270   1.380   1.480   1.600
    b/2       -0.540   -0.160    0.230   0.640   0.990   1.380   1.750   2.090   2.400
   3b/4       -1.090   -0.600    0.160   0.390   0.900   1.480   2.090   2.770   3.360
     b        -1.670   -1.090   -0.540   0.150   0.760   1.600   2.400   3.360   4.300

                                                  K1
    Ref. Pt
                -b     -3b/4     -b/2    -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000       0.910    0.960    1.000    1.040   1.070   1.040   1.000   0.960   0.910
    b/4       0.790    0.840    0.910    0.960   1.040   1.100   1.090   1.090   1.070
    b/2       0.680    0.750    0.830    0.910   1.000   1.100   1.190   1.240   1.290
   3b/4       0.600    0.670    0.750    0.850   0.960   1.090   1.240   1.400   1.520
     b        0.520    0.600    0.680    0.790   0.910   1.070   1.290   1.530   1.810

    q         0.400
                                                  K0
    Ref. Pt
                -b     -3b/4     -b/2    -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000        0.710    0.900    0.990   1.110   1.200   1.110   0.990   0.900   0.710
    b/4        0.120    0.360    0.640   0.910   1.110   1.290   1.400   1.470   1.560
    b/2       -0.550   -0.170    0.230   0.630   0.990   1.370   1.760   2.100   2.400
   3b/4       -1.070   -0.580   -0.170   0.360   0.900   1.470   2.100   2.770   3.380
     b        -1.650   -1.070   -0.550   0.120   0.710   1.560   2.400   3.380   4.300

                                                  K1
    Ref. Pt
                -b     -3b/4     -b/2    -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000       0.900    0.950    1.000    1.050   1.080   1.050   1.000   0.950   0.900
    b/4       0.770    0.830    0.900    0.960   1.050   1.100   1.100   1.090   1.070
    b/2       0.660    0.730    0.810    0.900   1.000   1.100   1.200   1.260   1.300
   3b/4       0.580    0.650    0.730    0.830   0.950   1.090   1.260   1.410   1.550
     b        0.500    0.580    0.660    0.770   0.900   1.070   1.300   1.550   1.880

    q         0.425
                                                  K0
    Ref. Pt
                -b     -3b/4     -b/2    -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000        0.670    0.875    0.995   1.130   1.220   1.130   0.995   0.875   0.670
    b/4        0.100    0.350    0.640   0.925   1.130   1.310   1.410   1.455   1.500
    b/2       -0.545   -0.170    0.230   0.635   0.995   1.375   1.770   2.095   2.375
   3b/4       -1.045   -0.570   -0.170   0.350   0.875   1.455   2.095   2.785   3.405
     b        -1.600   -1.045   -0.545   0.100   0.670   1.530   2.370   3.405   4.400
                                                  K1
    Ref. Pt
                -b     -3b/4     -b/2    -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000       0.890    0.950    1.000    1.055   1.090   1.055   1.000   0.950   0.890
    b/4       0.750    0.810    0.885    0.960   1.055   1.120   1.120   1.095   1.080
    b/2       0.630    0.700    0.785    0.885   1.000   1.120   1.225   1.280   1.325
   3b/4       0.540    0.615    0.700    0.810   0.950   1.095   1.280   1.455   1.610
     b        0.470    0.540    0.630    0.750   0.390   1.080   1.325   1.610   1.940

    q         0.450
                                                  K0
    Ref. Pt
                -b     -3b/4     -b/2    -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000        0.630    0.850    1.000   1.150   1.250   1.150   1.000   0.850   0.630
    b/4        0.080    0.340    0.640   0.940   1.150   1.340   1.420   1.440   1.500
    b/2       -0.540   -0.170    0.230   0.640   1.000   1.380   1.780   2.090   2.350
   3b/4       -1.020   -0.560   -0.170   0.340   0.850   1.440   2.090   2.800   3.430
     b        -1.550   -1.020   -0.540   0.080   0.630   1.500   2.350   3.430   4.500

                                                  K1
    Ref. Pt
                -b     -3b/4     -b/2    -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000       0.880    0.950    1.000    1.060   1.100   1.060   1.000   0.950   0.880
    b/4       0.730    0.790    0.870    0.960   1.060   1.140   1.140   1.100   1.090
    b/2       0.600    0.670    0.760    0.870   1.000   1.140   1.250   1.300   1.350
   3b/4       0.500    0.580    0.670    0.790   0.950   1.100   1.300   1.500   1.670
     b        0.440    0.500    0.600    0.730   0.880   1.090   1.350   1.670   2.000

    q         0.475
                                                  K0
    Ref. Pt
                -b     -3b/4     -b/2    -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000        0.590    0.820    1.000   1.180   1.285   1.180   1.000   0.820   0.590
    b/4        0.040    0.320    0.635   0.950   1.180   1.370   1.430   1.420   1.450
    b/2       -0.540   -0.170    0.225   0.635   1.000   1.390   1.790   2.085   2.325
   3b/4       -0.990   -0.550   -0.170   0.320   0.820   1.420   2.085   2.820   3.465
     b        -1.490   -0.990   -0.540   0.040   0.590   1.450   2.325   3.465   4.650

                                                  K1
    Ref. Pt
                -b     -3b/4     -b/2    -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000       0.865    0.935    1.000    1.065   1.115   1.065   1.000   0.935   0.865
    b/4       0.705    0.775    0.865    0.960   1.065   1.150   1.145   1.110   1.090
    b/2       0.575    0.650    0.745    0.865   1.000   1.145   1.275   1.325   1.370
   3b/4       0.475    0.555    0.650    0.775   0.935   1.110   1.325   1.540   1.715
     b        0.410    0.475    0.575    0.705   0.865   1.090   1.370   1.715   1.075
    q         0.500
                                                   K0
    Ref. Pt
                -b     -3b/4     -b/2     -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000        0.550    0.790    1.000   1.210    1.320   1.210   1.000   0.790   0.550
    b/4        0.000    0.300    0.630   0.960    1.210   1.400   1.440   1.400   1.400
    b/2       -0.540   -0.170    0.220   0.630    1.000   1.400   1.800   2.080   2.300
   3b/4       -0.960   -0.540   -0.170   0.300    0.790   1.400   2.080   2.840   3.500
     b        -1.430   -0.960   -0.540   0.000    0.550   1.400   2.300   3.500   4.800

                                                   K1
    Ref. Pt
                -b     -3b/4     -b/2     -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000       0.850    0.920    1.000    1.070    1.130   1.070   1.000   0.920   0.850
    b/4       0.680    0.760    0.860    0.960    1.070   1.160   1.150   1.120   1.090
    b/2       0.550    0.630    0.730    0.860    1.000   1.150   1.300   1.350   1.390
   3b/4       0.450    0.530    0.630    0.760    0.920   1.120   1.350   1.580   1.760
     b        0.380    0.450    0.550    0.680    0.850   1.090   1.390   1.760   2.150

    q         0.525
                                                   K0
    Ref. Pt
                -b     -3b/4     -b/2     -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000        0.485    0.765    1.010    1.240   1.360   1.240   1.010   0.765   0.485
    b/4       -0.050    0.275    0.630    0.970   1.240   1.425   1.450   1.375   1.330
    b/2       -0.535   -0.175    0.215    0.630   1.010   1.415   1.820   2.075   2.275
   3b/4       -0.925   -0.520   -0.175    0.275   0.765   1.375   2.075   2.855   3.600
     b        -1.365   -0.925   -0.535   -0.050   0.485   1.330   2.275   3.600   4.950

                                                   K1
    Ref. Pt
                -b     -3b/4     -b/2     -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000       0.830    0.910    1.000    1.080    1.140   1.080   1.000   0.910   0.830
    b/4       0.665    0.735    0.850    0.960    1.080   1.170   1.160   1.130   1.090
    b/2       0.525    0.605    0.710    0.850    1.000   1.160   1.325   1.375   1.415
   3b/4       0.425    0.505    0.605    0.735    0.910   1.130   1.375   1.615   1.815
     b        0.355    0.425    0.525    0.665    0.830   1.090   1.415   1.815   2.240

    q         0.550
                                                   K0
    Ref. Pt
                -b     -3b/4     -b/2     -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000        0.420    0.740    1.020    1.270   1.400   1.270   1.020   0.740   0.420
    b/4       -0.100    0.250    0.630    0.980   1.270   1.450   1.460   1.350   1.260
    b/2       -0.530   -0.180    0.210    0.630   1.020   1.430   1.840   2.070   2.250
   3b/4       -0.890   -0.500   -0.180    0.250   0.740   1.350   2.070   2.870   3.700
     b        -1.300   -0.890   -0.530   -0.100   0.420   1.260   2.250   3.700   5.100
                                                       K1
    Ref. Pt
                    -b     -3b/4     -b/2     -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000           0.810    0.900    1.000    1.090    1.150   1.090   1.000   0.900   0.810
    b/4           0.650    0.710    0.840    0.960    1.090   1.180   1.170   1.140   1.090
    b/2           0.500    0.580    0.690    0.840    1.000   1.170   1.350   1.400   1.440
   3b/4           0.400    0.480    0.580    0.710    0.900   1.140   1.400   1.650   1.870
     b            0.330    0.400    0.500    0.650    0.810   1.090   1.440   1.870   2.330

    q             0.575
                                                       K0
    Ref. Pt
                    -b     -3b/4     -b/2     -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000            0.350    0.700    1.020   1.330    1.460   1.330   1.020   0.700   0.350
    b/4           -0.130    0.220    0.620   1.000    1.330   1.500   1.480   1.340   1.100
    b/2           -0.530   -0.180    0.210   0.620    1.020   1.480   1.860   2.080   2.260
   3b/4           -0.840   -0.490   -0.180   0.220    0.700   1.340   2.080   2.900   3.800
     b            -1.160   -0.840    0.530   0.130    0.350   1.100   2.220   3.800   5.300

                                                       K1
    Ref. Pt
                    -b     -3b/4     -b/2     -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000           0.800    0.890    1.000    1.110    1.170   1.110   1.000   0.890   0.800
    b/4           0.600    0.700    0.810    0.950    1.110   1.210   1.200   1.140   1.080
    b/2           0.470    0.550    0.660    0.810    1.000   1.200   1.380   1.440   1.450
   3b/4           0.370    0.450    0.550    0.700    0.890   1.140   1.440   1.720   1.920
     b            0.300    0.370    0.470    0.600    0.800   1.080   1.450   1.920   2.420

    q             0.600
                                                       K0
    Ref. Pt
                    -b     -3b/4     -b/2     -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000            0.310    0.660    1.020    1.350   1.500   1.350   1.020   0.660   0.310
    b/4           -0.170    0.210    0.620    1.020   1.350   1.530   1.470   1.310   1.030
    b/2           -0.520   -0.180    0.200    0.620   1.020   1.470   1.870   2.060   2.190
   3b/4           -0.800   -0.470   -0.180    0.210   0.660   1.310   2.060   2.920   3.080
     b            -1.050   -0.800   -0.520   -0.200   0.310   1.100   2.190   3.080   5.450
              .
                                                       K1
    Ref. Pt
                    -b     -3b/4     -b/2     -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000           0.800    0.890    1.000    1.120    1.190   1.120   1.000   0.890   0.800
    b/4           0.580    0.670    0.800    0.950    1.120   1.230   1.200   1.150   1.080
    b/2           0.440    0.520    0.660    0.800    1.000   1.200   1.400   1.450   1.460
   3b/4           0.340    0.410    0.520    0.670    0.890   1.150   1.450   1.750   1.960
     b            0.280    0.340    0.440    0.580    0.800   1.080   1.460   1.960   2.500
    q             0.625
                                                       K0
    Ref. Pt
                    -b     -3b/4     -b/2     -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000            0.230    0.635    1.023    1.390   1.540   1.390   1.023   0.630   0.230
    b/4           -0.220    0.180    0.615    1.030   1.390   1.570   1.490   1.290   0.965
    b/2           -0.520   -0.180    0.200    0.615   1.023   1.490   1.890   2.060   2.160
   3b/4           -0.755   -0.455   -0.180    0.180   0.635   1.290   2.060   2.935   3.045
     b            -0.920   -0.755   -0.520   -0.235   0.230   1.010   2.160   3.045   5.250
              .
                                                       K1
    Ref. Pt
                    -b     -3b/4     -b/2     -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000           0.775    0.870    0.990    1.013    1.210   1.130   0.990   0.870   0.775
    b/4           0.515    0.655    0.785    0.950    1.130   1.250   1.220   1.150   1.070
    b/2           0.420    0.495    0.615    0.785    0.990   1.220   1.425   1.480   1.480
   3b/4           0.320    0.385    0.495    0.655    0.870   1.150   1.480   1.845   2.010
     b            0.260    0.320    0.420    0.555    0.775   1.070   1.480   2.010   2.775

    q             0.650
                                                       K0
    Ref. Pt
                    -b     -3b/4     -b/2     -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000            0.150    0.610    1.025    1.420   1.580   1.420   1.025   0.610   0.150
    b/4           -0.260    0.150    0.610    1.040   1.420   1.600   1.510   1.260   0.900
    b/2           -0.520   -0.180    0.200    0.610   1.025   1.510   1.910   2.060   2.130
   3b/4           -0.710   -0.440   -0.180   -0.150   0.610   1.260   2.060   2.950   3.010
     b            -0.800   -0.710   -0.520   -0.270   0.150   0.920   2.130   3.010   5.070
              .
                                                       K1
    Ref. Pt
                    -b     -3b/4     -b/2     -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000           0.750    0.850    0.980    1.140    0.980   0.850   0.750   0.870   0.775
    b/4           0.550    0.640    0.770    0.950    1.140   1.270   1.240   1.150   1.060
    b/2           0.400    0.470    0.600    0.770    0.980   1.240   1.450   1.500   1.500
   3b/4           0.300    0.360    0.470    0.640    0.850   1.150   1.500   1.840   2.060
     b            0.240    0.300    0.400    0.530    0.750   1.060   1.500   2.060   2.650

    q             0.675
                                                       K0
    Ref. Pt
                    -b     -3b/4     -b/2     -b/4    0.000    b/4     b/2    3b/4     b
Load at
  0.000            0.055    0.570    1.027    1.470   1.630   1.465   1.027   0.570   0.055
    b/4           -0.315    0.130    0.605    1.050   1.470   1.650   1.530   1.235   0.785
    b/2           -0.510   -0.185    0.190    0.605   1.027   1.530   1.935   2.055   2.080
   3b/4           -0.640   -0.420   -0.185    0.130   0.570   1.235   2.055   2.975   3.150
     b            -0.640   -0.640   -0.510   -0.320   0.055   0.825   2.080   3.510   5.500
              .
                                                       K1
    Ref. Pt
                    -b     -3b/4     -b/2     -b/4    0.000     b/4     b/2    3b/4      b
Load at
  0.000           0.730    0.842    0.980    1.155    1.255    1.155   0.980   0.842   0.730
    b/4           0.525    0.615    0.755    0.945    1.155    1.300   1.250   1.150   1.050
    b/2           0.365    0.450    0.575    0.755    0.980    1.250   1.480   1.525   1.510
   3b/4           0.270    0.370    0.450    0.615    0.842    1.150   1.525   1.385   2.110
     b            0.200    0.270    0.365    0.510    0.730    1.050   1.510   2.110   2.750

    q             0.700
                                                       K0
    Ref. Pt
                    -b     -3b/4     -b/2     -b/4    0.000     b/4     b/2    3b/4      b
Load at
  0.000           -0.040    0.530    1.030    1.520    1.680   1.510   1.030   0.530   -0.040
    b/4           -0.370    0.110    0.000    1.060    1.510   1.700   1.550   1.210    0.670
    b/2           -0.500   -0.190    0.180    0.600    1.030   1.550   1.960   2.050    2.030
   3b/4           -0.570   -0.400   -0.190    0.110    0.530   1.210   2.050   3.000    4.010
     b            -0.480   -0.570   -0.500   -0.370   -0.040   0.730   2.030   4.010    6.030
              .
                                                       K1
    Ref. Pt
                    -b     -3b/4     -b/2     -b/4    0.000     b/4     b/2    3b/4      b
Load at
  0.000           0.710    0.835    0.980    1.170    1.280    1.170   0.980   0.835   0.710
    b/4           0.500    0.590    0.740    0.940    1.170    1.330   1.270   1.150   1.040
    b/2           0.330    0.430    0.550    0.740    0.980    1.270   1.510   1.550   1.520
   3b/4           0.240    0.320    0.430    0.590    0.835    1.150   1.550   1.930   2.160
     b            0.180    0.240    0.330    0.490    0.710    1.040   1.520   2.160   2.850

    q             0.725
                                                       K0
    Ref. Pt
                    -b     -3b/4     -b/2     -b/4    0.000     b/4     b/2    3b/4      b
Load at
  0.000           -0.125    0.495    1.025    1.550   1.725    1.550   1.025   0.495   -0.125
    b/4           -0.400    0.080    0.585    1.070   1.550    1.735   1.570   1.180    0.585
    b/2           -0.495   -0.185    0.175    0.585   1.025    1.570   1.980   2.040    1.990
   3b/4           -0.505   -0.375   -0.185    0.080   0.495    1.180   2.040   3.025    3.600
     b            -0.390   -0.505   -0.495   -0.400   0.125    0.645   1.990   3.600    6.365
              .
                                                       K1
    Ref. Pt
                    -b     -3b/4     -b/2     -b/4    0.000     b/4     b/2    3b/4      b
Load at
  0.000           0.685    0.817    0.980    1.185    1.305    1.185   0.980   0.817   0.685
    b/4           0.475    0.570    0.730    0.940    1.185    1.350   1.285   1.150   1.030
    b/2           0.315    0.410    0.530    0.730    0.980    1.285   1.540   1.575   1.535
   3b/4           0.225    0.300    0.410    0.570    0.817    1.150   1.575   1.920   2.205
     b            0.165    0.225    0.315    0.470    0.685    1.030   1.535   2.205   2.925
    q             0.750
                                                       K0
    Ref. Pt
                    -b     -3b/4     -b/2     -b/4    0.000     b/4     b/2    3b/4      b
Load at
  0.000           -0.210    0.460    1.020    1.580    1.770   1.580   1.020   0.460   -0.210
    b/4           -0.430    0.050    0.570    1.080    1.580   1.770   1.590   1.150    0.500
    b/2           -0.490   -0.180    0.170    0.570    1.020   1.590   2.000   2.040    1.950
   3b/4           -0.440   -0.350   -0.180    0.050    0.460   1.150   2.040   3.050    3.200
     b            -0.300   -0.440   -0.490   -0.430   -0.210   0.560   1.950   3.200    6.700
              .
                                                       K1
    Ref. Pt
                    -b     -3b/4     -b/2     -b/4    0.000     b/4     b/2    3b/4      b
Load at
  0.000           0.660    0.800    0.980    1.200    1.330    1.200   0.980   0.800   0.660
    b/4           0.450    0.550    0.720    0.940    1.200    1.370   1.300   1.150   1.020
    b/2           0.300    0.390    0.510    0.720    0.980    1.300   1.570   1.600   1.550
   3b/4           0.210    0.280    0.390    0.550    0.500    1.150   1.600   2.010   2.250
     b            0.150    0.210    0.300    0.450    0.660    1.020   1.550   2.250   3.000

    q             0.775
                                                       K0
    Ref. Pt
                    -b     -3b/4     -b/2     -b/4    0.000     b/4     b/2    3b/4      b
Load at
  0.000           -0.280    0.425    1.020    1.620    1.825   1.620   1.020   0.425   -0.280
    b/4           -0.460    0.035    0.560    1.090    1.620   1.825   1.607   1.125    0.415
    b/2           -0.485   -0.180    0.160    0.560    1.020   1.607   2.030   2.030    1.885
   3b/4           -0.390   -0.325   -0.180    0.350    0.425   1.125   2.030   3.075    3.610
     b            -0.230   -0.390   -0.485   -0.455   -0.280   0.475   1.885   3.610    6.860
              .
                                                       K1
    Ref. Pt
                    -b     -3b/4     -b/2     -b/4    0.000     b/4     b/2    3b/4      b
Load at
  0.000           0.645    0.790    0.980    1.210    1.355    1.210   0.980   0.790   0.645
    b/4           0.425    0.530    0.700    0.935    1.210    1.400   1.320   1.145   1.010
    b/2           0.275    0.365    0.490    0.700    0.980    1.320   1.600   1.620   1.550
   3b/4           0.185    0.255    0.365    0.530    0.790    1.145   1.620   2.055   2.290
     b            0.135    0.185    0.275    0.425    0.645    1.000   0.155   2.290   3.100
    q             0.800
                                                       K0
    Ref. Pt
                    -b     -3b/4     -b/2     -b/4    0.000     b/4     b/2    3b/4      b
Load at
  0.000           -0.350    0.390    1.025    1.660    1.880   1.660   1.025   0.390   -0.350
    b/4           -0.490    0.020    0.550    1.100    1.660   1.880   1.640   1.100    0.330
    b/2           -0.480   -0.180    0.150    0.550    1.025   1.640   2.060   2.030    1.820
   3b/4           -0.340   -0.300   -0.180    0.020    0.390   1.100   2.030   3.100    4.020
     b            -0.160   -0.340   -0.480   -0.480   -0.350   0.390   1.820   4.020    7.020
              .
                                                       K1
    Ref. Pt
                    -b     -3b/4     -b/2     -b/4    0.000     b/4     b/2    3b/4      b
Load at
  0.000           0.630    0.780    0.980    1.220    1.380    1.220   0.980   0.780   0.630
    b/4           0.400    0.510    0.680    0.930    1.220    1.430   1.340   1.140   1.000
    b/2           0.250    0.340    0.470    0.680    0.980    1.340   1.630   1.640   1.550
   3b/4           0.160    0.230    0.340    0.510    0.780    1.140   1.640   2.100   2.330
     b            0.120    0.160    0.250    0.400    0.630    0.980   1.550   2.330   3.200
Unit load distribution coefficient.
                                                                                                    RUN
    q       0.503
For no torsion grillage a = 0                          K0
    Ref. Pt                                                                                           Row
                  -b       -3b/4     -b/2     -b/4     0       b/4        b/2     3b/4       b
Load at                                                                                             integral
      0         0.541      0.787     1.001    1.214   1.325   1.214      1.001    0.787    0.541      7.87
     b/4       -0.007      0.297     0.630    0.961   1.214   1.403      1.441    1.397    1.391      8.04
     b/2       -0.539     -0.171     0.219    0.630   1.001   1.402      1.803    2.079    2.297      7.84
    3b/4       -0.955     -0.537    -0.171    0.297   0.787   1.397      2.079    2.842    3.513      7.97
      b        -1.421     -0.955    -0.539   -0.007   0.541   1.391      2.297    3.513    4.820      7.94

For full torsion grillage a = 1                        K1
    Ref. Pt                                                                                           Row
                  -b        -3b/4    -b/2     -b/4     0       b/4        b/2     3b/4       b
Load at                                                                                             integral
      0         0.847      0.919    1.000    1.071    1.131   1.071      1.000    0.919    0.847      7.96
     b/4        0.678      0.757    0.859    0.960    1.071   1.161      1.151    1.121    1.090      7.96
     b/2        0.547      0.627    0.727    0.859    1.000   1.151      1.303    1.353    1.393      7.99
    3b/4        0.447      0.527    0.627    0.757    0.919   1.121      1.353    1.585    1.767      8.00
      b         0.377      0.447    0.547    0.678    0.847   1.090      1.393    1.767    2.162      8.04

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

    Ref. Pt                                                                                           Row
                 -b        -3b/4     -b/2     -b/4     0       b/4        b/2     3b/4       b
Load at                                                                                             integral
     -b         4.300      3.172     2.120   1.332    0.601   0.127      -0.327   -0.681   -1.070     7.96
   -3b/4        3.172      2.596     1.937   1.343    0.812   0.387      -0.015   -0.329   -0.681     7.98
    -b/2        2.120      1.937     1.705   1.353    1.001   0.675       0.319   -0.015   -0.327     7.87
    -b/4        1.332      1.343     1.385   1.356    1.186   0.961       0.675    0.387    0.127     8.02
      0         0.601      0.812     1.001   1.186    1.287   1.186       1.001    0.812    0.601     7.89
     b/4        0.127      0.387     0.675   0.961    1.186   1.356       1.385    1.343    1.332     8.02
     b/2       -0.327     -0.015     0.319   0.675    1.001   1.353       1.705    1.937    2.120     7.87
    3b/4       -0.681     -0.329    -0.015   0.387    0.812   1.343       1.937    2.596    3.172     7.98
      b        -1.070     -0.681    -0.327   0.127    0.601   1.332       2.120    3.172    4.300     7.96
Distribution coefficient K' for SIDL

-b             -3b/4         -b/2             -b/4              0        b/4           b/2               3b/4               b
     0.5 t/m                                                                                                        0.5 t/m



      2.075                         2.650                     2.65               2.65                       2.075

                       G1                        G2                     G3                          G4

                                                                       lwKa
                Load
   Ref. Pt      factor       -b       -3b/4           -b/2      -b/4    0       b/4           b/2         3b/4          b
Load at
                (lw )
     -b          0.43        1.87      1.38            0.92     0.58   0.26    0.06          -0.14        -0.30       -0.46
   -3b/4         0.07        0.21      0.17            0.13     0.09   0.05    0.03           0.00        -0.02       -0.05
    -b/2         0.00        0.00      0.00            0.00     0.00   0.00    0.00           0.00         0.00        0.00
    -b/4         0.00        0.00      0.00            0.00     0.00   0.00    0.00           0.00         0.00        0.00
      0          0.00        0.00      0.00            0.00     0.00   0.00    0.00           0.00         0.00        0.00
     b/4         0.00        0.00      0.00            0.00     0.00   0.00    0.00           0.00         0.00        0.00
     b/2         0.00        0.00      0.00            0.00     0.00   0.00    0.00           0.00         0.00        0.00
    3b/4         0.07       -0.05     -0.02            0.00     0.03   0.05    0.09           0.13         0.17        0.21
      b          0.43       -0.46     -0.30           -0.14     0.06   0.26    0.58           0.92         1.38        1.87
   Slw           1.00
  SlwKa                     1.57      1.23             0.91     0.75    0.63   0.75          0.91         1.23         1.57
  K' = SlwKa/Slw            1.566     1.231           0.905    0.747   0.629   0.747         0.905        1.231       1.566

Distribution coefficient K' at girder location

 Girder Nr.     G1        G2         G3       G4
     K'        1.221     0.806      0.774    1.221
Note : Coefficients have been increased by 10% to take into account the effect of higher harmonics.
Distribution coefficient K' for live load (3 lane class A)

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

                 Class A                               Class A                          Class A
      0.95m           1.8m            1.7m                1.8m            1.7m               1.8m


              2.075                   2.65                       2.65                   2.65                       2.075

                        G1                       G2                         G3                              G4


                                                                          lwKa
               Load
   Ref. Pt
               factor         -b        -3b/4          -b/2        -b/4     0          b/4           b/2          3b/4      b
Load at
               (lw )
     -b         2.12          9.11      6.72        4.49           2.82   1.27        0.27          -0.69         -1.44    -2.27
   -3b/4        4.62         14.65     11.99        8.95           6.20   3.75        1.79          -0.07         -1.52    -3.15
    -b/2        4.99         10.58      9.67        8.51           6.75   5.00        3.37           1.59         -0.07    -1.63
    -b/4        5.37          7.15      7.21        7.44           7.28   6.37        5.16           3.62          2.08     0.68
      0         4.95          2.97      4.02        4.95           5.87   6.37        5.87           4.95          4.02     2.97
     b/4        4.99          0.63      1.93        3.37           4.80   5.92        6.77           6.91          6.70     6.65
     b/2        4.62         -1.51     -0.07        1.47           3.12   4.62        6.25           7.87          8.95     9.79
    3b/4        2.54         -1.73     -0.84       -0.04           0.98   2.07        3.42           4.93          6.60     8.07
      b         0.00          0.00      0.00        0.00           0.00   0.00        0.00           0.00          0.00     0.00
   Slw         34.20
  SlwKa                      41.86     40.64       39.14          37.82   35.37       32.88         29.12        25.31     21.12
  K' = SlwKa/Slw             1.224     1.188       1.145          1.106   1.034       0.962         0.851        0.740     0.617

Distribution coefficient K' at girder location

 Girder Nr.     G1        G2         G3       G4
     K'        1.289     1.207      1.087    0.860
Note : Coefficients have been increased by 10% to take into account the effect of higher harmonics.
Distribution coefficient K' for live load (70 - R)
  -b          -3b/4            -b/2              -b/4           0               b/4           b/2                3b/4            b

                                   70 - R
           2.18m                     1.93m


             2.075                    2.65                          2.65                2.65                       2.075

                        G1                        G2                         G3                             G4


                                                                           lwKa
               Load
   Ref. Pt     factor         -b         -3b/4          -b/2   -b/4         0          b/4           b/2          3b/4       b
Load at
               (lw )
     -b         0.00         0.00       0.00         0.00      0.00        0.00       0.00           0.00         0.00      0.00
   -3b/4        4.75         15.06      12.33        9.20      6.38        3.86       1.84          -0.07        -1.56     -3.23
    -b/2        6.15         13.05      11.92       10.49      8.33        6.16       4.15           1.96        -0.09     -2.01
    -b/4        6.10         8.12       8.19         8.44      8.27        7.23       5.86           4.11         2.36      0.78
      0         0.00         0.00       0.00         0.00      0.00        0.00       0.00           0.00         0.00      0.00
     b/4        0.00         0.00       0.00         0.00      0.00        0.00       0.00           0.00         0.00      0.00
     b/2        0.00         0.00       0.00         0.00      0.00        0.00       0.00           0.00         0.00      0.00
    3b/4        0.00         0.00       0.00         0.00      0.00        0.00       0.00           0.00         0.00      0.00
      b         0.00         0.00       0.00         0.00      0.00        0.00       0.00           0.00         0.00      0.00
   Slw         17.00
  SlwKa                      36.23      32.44       28.14      22.97       17.25      11.85         6.01         0.70       -4.47
  K' = SlwKa/Slw             2.131      1.908       1.655      1.351       1.015      0.697         0.353        0.041     -0.263

Distribution coefficient K' at girder location

 Girder Nr.     G1        G2         G3       G4
     K'        1.995     1.440      0.897    0.173
Note : Coefficients have been increased by 10% to take into account the effect of higher harmonics.
Distribution coefficient K' for live load (1lane class A + 70 - R)
 -b          -3b/4           -b/2              -b/4             0              b/4           b/2               3b/4           b

                                 70 - R                              Class A
          2.18m                    1.93m                               1.8m


             2.075                   2.65                     2.65                     2.65                      2.075

                     G1                          G2                            G3                         G4


                                                                          lwKa
               Load
   Ref. Pt
               factor       -b         -3b/4          -b/2      -b/4           0      b/4           b/2         3b/4      b
Load at
               (lw )
     -b         0.00        0.00        0.00           0.00     0.00       0.00      0.00           0.00         0.00     0.00
   -3b/4        4.75       15.07       12.33           9.20     6.38       3.86      1.84          -0.07        -1.56    -3.24
    -b/2        6.15       13.04       11.91          10.49     8.32       6.16      4.15           1.96        -0.09    -2.01
    -b/4        6.33        8.43        8.50           8.76     8.58       7.51      6.08           4.27         2.45     0.80
      0         5.47        3.29        4.44           5.48     6.49       7.04      6.49           5.48         4.44     3.29
     b/4        4.84        0.62        1.87           3.27     4.65       5.74      6.56           6.70         6.50     6.45
     b/2        0.86       -0.28       -0.01           0.27     0.58       0.86      1.16           1.47         1.67     1.82
    3b/4        0.00        0.00        0.00           0.00     0.00       0.00      0.00           0.00         0.00     0.00
      b         0.00        0.00        0.00           0.00     0.00       0.00      0.00           0.00         0.00     0.00
   Slw         28.40
  SlwKa                    40.16       39.05          37.47    35.00      31.17      26.28         19.80        13.40     7.12
  K' = SlwKa/Slw           1.414       1.375          1.319    1.233      1.097      0.926         0.697        0.472    0.251

Distribution coefficient K' at girder location

 Girder Nr.     G1        G2         G3       G4
     K'        1.490     1.337      1.088    0.611
Note : Coefficients have been increased by 10% to take into account the effect of higher harmonics.
DESIGN OF MAIN GIRDER

Calculation of dead load
Inner girder

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

      Running weight                                                     =    3.30   t/m

  1   Weight of cross girder             =((2.65-0.325)*1.5*2.4-0.108-   =    2.67   t
                                         0.054)*0.325)
      Web thickening at near ends
  1   Wt due to extra widening (uni) =2*0.5*(2*2-2*0.25-2*0.25-          =   0.97 t/m
  2   Wt due to extra widening (vary) 0.15-0.15)*(0.625-0.325)*2.4       = 0.97 to 0 t/m


                                                   Main girder


                                  0.6       0.9

                               Extra widening at support
Outer girder

  1   Weight of web                      =(2-0.25-0.25)*0.325*2.4        =    1.17   t/m
  2   Weight of top haunch               =2*0.5*0.3*0.15*2.4             =    0.11   t/m
  3   Weight of bottom haunch            =2*0.5*0.15*0.15*2.4            =    0.05   t/m
  4   Weight of bulb                     =0.625*0.25*2.4                 =    0.38   t/m
  5   Weight of deck slab                =((0.5*2.65*0.25)+0.5*(0.3+     =    1.94   t/m
                                         0.2)*(2.075-0.325*0.5))*2.4
      Running weight                                                     =    3.65   t/m

  1   Weight of cross girder             =((2.65-0.325)*1.5*2.4-0.108-   =    1.33   t
                                         0.054)*0.325)*0.5
      Web thickening at near ends
                                      =(0.5*(2*2-2*0.25 -2*0.25-0.15-
  1   Wt due to extra widening (uni)
                                      0.15)*(0.625-0.325) +           =   0.98 t/m
  2   Wt due to extra widening (vary) (0.5*(2*2-2*0.3-2*0.25-
                                      0.15)*(0.625-0.325))*0.5*2.4    = 0.98 to 0 t/m
Calculation of SIDL (uniform)
Inner girder
  1       Weight of wearing coat                                    =     0.53      t/m

Outer girder
  1       Weight of wearing coat                                    =     0.57      t/m

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

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

          2.67 t                            2.67 t                         2.67 t
                        9.75                                 9.75

                                           3.83t/m                                  0.97t/m

                                                                    0.9    0.6
                                            19.5 m
          A                                                                         B

Support reaction at A                                               =     42.34     t

                                      Location
Sl. Nr.       Item      Deff       Span      Span    Span
                      from sup     (L/8)     (L/4)   (L/2)
  1       BM (t-m)      70.2       83.4     143.5    195.5

  2       SF (t)        31.0       29.3      20.0     0.0


Outer girder

          1.33 t                            1.33 t                         1.33 t
                        9.75                                 9.75

                                           4.22t/m                                  0.98t/m

                                                                    0.9    0.6
                                            19.5 m
          A                                                                         B
Support reaction at A                                                      =   44.17   t

                                          Location
Sl. Nr.       Item         Deff        Span      Span      Span
                         from sup      (L/8)     (L/4)     (L/2)
  1       BM (t-m)            75.7     89.9     154.2      207.6

  2       SF (t)              33.4     31.5      21.2          0.0

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

                                                2.00t/m


                                                19.5 m
          A                                                                            B

Support reaction at A                                                      =   19.50   t

                                          Location
Sl. Nr.       Item         Deff        Span      Span      Span
                         from sup      (L/8)     (L/4)     (L/2)
  1       BM (t-m)            35.0     41.6      71.3      95.1

  2       SF (t)              15.5     14.6       9.8          0.0

Calculation of short term deflection due to dead load & sidl

                         D2                D1             D2

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

          D1 =    =(5*19.5/16)*(2*(2*(195.5+207.6)+95.1)*0.5*19.5/3        =    9      mm
                      )/ (31220.186*100*2*(0.296+0.338))*1000
      D2 =        =D1/(2)0.5 (considering parabolic profile)               =    6      mm
Calculation of bending moment and shear force (Live load)

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

                                                                                               Design live load B M ( t-m)
                             BM (t-m)             Total BM Total BM Total BM Total BM                                          Max
SL.  Section    Girder                BM (t-m)                                                                                        Design
                              (dl+uni            for 1L Cl A for 1L Cl A for 70 - R for 70 - R 3 Lane     70 - R 1L Cl A      design
Nr. considered location               (con sidl)                                                                                     BM (t-m)
                                sidl)             (Reverse) (Forward) (Reverse) (Forward) Class A (wheel) + 70 - R            LL BM

       At Deff      Inner       70.2       7.1        56.6         44.7       110.1      118.8       54.4     50.5    59.2     59.2    136.5
 1      from
       support      Outer       75.7       10.7       56.6         44.7       110.1      118.8       58.1     70.0    65.9     70.0    156.4

       At 1/8th     Inner       83.4       8.4        70.9         55.8       138.3      149.2       68.2     63.4    74.3     74.3    166.1
 2
      span (L/8)    Outer       89.9       12.7       70.9         55.8       138.3      149.2       72.8     87.8    82.8     87.8    190.5

      At quarter    Inner      143.5       14.4       116.0        97.1       237.3      248.5      111.5     105.6   125.4   125.4    283.3
 3
      span (L/4)    Outer      154.2       21.8       116.0        97.1       237.3      248.5      119.1     146.3   139.7   146.3    322.3

      At middle     Inner      195.5       19.2       144.1       144.1       325.3      325.3      138.5     138.2   166.7   166.7    381.3
 4
      span (L/2)    Outer      207.6       29.0       144.1       144.1       325.3      325.3      148.0     191.5   185.7   191.5    428.1

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

Calculation of impact factor for live load.

 1   For class A = 1+ 4.5/(6+L)            1.18
 2   For 70 R (Wheeled)                    1.18    From curve IRC 6 1966 Cl. 211.3
Design of section for flexure

Inner girder                                             Outer girder
               Deff from    L/8 of    L/4 of    L/2 of   Deff from    L/8 of    L/4 of    L/2 of
 SECTION
                support      span      span      span     support      span      span      span
    DATA
 M (t.m)     136.5          166.1     283.3     381.3      156.4      190.5     322.3     428.1
 h    (m)    2.000          2.000     2.000     2.000      2.000      2.000     2.000     2.000
bf (m)       2.650          2.650     2.650     2.650      3.400      3.400     3.400     3.400
df (m)       0.250          0.250     0.250     0.250      0.250      0.250     0.250     0.250
bw (m)       0.325          0.325     0.325     0.325      0.325      0.325     0.325     0.325
Ast (m^2)  0.00482         0.00482   0.00804   0.01126    0.00563    0.00563   0.00965   0.01286
c    (m)     0.115          0.115     0.124     0.132      0.109      0.109     0.120     0.148
Asc (m^2)  0.00080         0.00040   0.00040   0.00040    0.00080    0.00040   0.00040   0.00040
dc (m)       0.064          0.064     0.064     0.064      0.064      0.064     0.064     0.064
 m            10.0           10.0      10.0      10.0       10.0       10.0      10.0      10.0
  RESULTS
   d   (m)   1.885           1.885     1.876     1.868      1.891      1.891     1.880     1.852
 Asf (m^2) 0.00515         0.00511   0.00513   0.00516    0.00656    0.00652   0.00656   0.00667
 AA (m^2)   0.0000          0.0000    0.5813    0.5813     0.0000     0.0000    0.7688    0.7688
   A (m)    2.6500          2.6500    0.3250    0.3250     3.4000     3.4000    0.3250    0.3250
 B (m^2) 0.1110             0.1037    1.3305    1.3949     0.1270     0.1198    1.7377    1.8020
 C (m^3) -0.1828           -0.1823   -0.4474   -0.5663    -0.2138    -0.2133   -0.5554   -0.6691
   n   (m)   0.243           0.243     0.312     0.373      0.233      0.233     0.303     0.349
 CC (m^2) 0.0332            0.0336    0.0635    0.0902     0.0388     0.0391    0.0783    0.1053
   jd (m)    1.804           1.804     1.778     1.761      1.814      1.813     1.784     1.749
fc (t/m^2)    231             283       396       481        215        263       359       442
fs (t/m^2) -15677          -19083    -19815    -19232     -15321     -18665    -18723    -19030

Cracked moment of inertia Ir (m4)   0.224    0.296                              0.272     0.338
 d=h-c
 Asf=(bf*df^2+2*(m-1)*Asc*(df-dc))/(2*m*(d-df))
 AA=(bf-bw)*df for As<Asf , else 0
 A=bw for As<Asf , else bf
 B=2*(AA+(m-1)*Asc+m*As)
 C=-(AA*df+2*(m-1)*Asc*dc+2*m*As*d)
 n=(-B-sqrt(B^2-4*A*C))/(2*A)
 CC=(bf-bw)*(min(df,n))^2*(3*n-2*min(df,n))
 jd=d-(CC+bw*n^3+6*(m-1)*Asc*(n-dc)*dc)/(6*m*As*(d-n))
 fs=-M/(As*jd)
 fc=-(fs/m)*n/(d-n)
Calculation of shear force (Live load)

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

a) For loads at within 5.5m : Greater of the followings.
          i) Assuming the deck slab continuous with supports being assumed as unyielding.
         ii) By distribution coefficient ie. Morice-Little as used for calculation of bending moments.

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

At Deff from support

For class A (Forward train)

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

For 70 - R (wheel) (Forward train)

Total shear force (from computer print out on previous sheets)                               = 64.2 t
Component of shear force due to loads within 5.5 m from support.                             = 31.3 t
Component of shear force due to loads beyond 5.5 m from support.                             = 32.9 t

Distribution of shear force for 70 - R (wheel)

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

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

                        15.66 t      15.66 t

                1.63m        1.93m



             1.525                2.65                     2.65                   2.65

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

Simple SF             18.674             12.646
Elastic SF            -1.388              1.388 1.659             -1.659 -0.271          0.271
Reaction           17.29                      15.69                   -1.93                  0.27
    1        For inner girder =      (32.92*1.440/4+15.69)*1.18                                 = 32.5 t
    2        For outer girder =      (32.92*1.995/4+17.29)*1.18                                 = 39.8 t

Design Shear force =Average SF x IF x DF

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

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

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

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

                         15.66 t        15.66 t               5.97 t        5.97 t

                 1.63m          1.93m             1.88m             1.8m



               1.525               2.65                     2.65                     2.65

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

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

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

Design Shear force =Average SF x IF x DF
Reduced the SF by 10% for each additional loaded traffic lane in excess of 2 lanes.
[As per clause 208.2 IRC 6, 1966]

    1        For inner girder                                                                   = 36. t
    2        For outer girder                                                                   = 35.8 t
At 1/8th span (L/8)

For class A (Forward train)

Total shear force (from computer print out on previous sheets)                                = 22.9 t
Component of shear force due to loads within 5.5 m from support.                              = 12.2 t
Component of shear force due to loads beyond 5.5 m from support.                              = 10.7 t

For 70 - R (wheel) (Forward train)

Total shear force (from computer print out on previous sheets)                                = 61.2 t
Component of shear force due to loads within 5.5 m from support.                              = 30.1 t
Component of shear force due to loads beyond 5.5 m from support.                              = 31.1 t

Distribution of shear force for 70 - R (wheel)

A. By Morrice - Little's method
    1    For inner girder       =1.440*61.2*1.18/4                                            = 26.0 t
    2    For outer girder       =1.995*61.2*1.18/4                                            = 36.0 t

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

                         15.05 t        15.05 t

                 1.63m          1.93m



               1.525               2.65                     2.65                   2.65

FEM                      -3.107           5.518
Balance                  3.107            -2.759   -2.759
Carryover                -1.380            1.554   0.000           -1.380
Balance                  1.380            -0.777   -0.777           0.690 0.690
Total M                  0.000             3.536   -3.536          -0.690 0.690

Simple SF              17.946             12.154
Elastic SF             -1.334              1.334 1.595             -1.595 -0.260          0.260
Reaction            16.61                      15.08                   -1.85                  0.26

    1        For inner girder =      (31.1*1.440/4+15.08)*1.18                                = 31.0 t
    2        For outer girder =      (31.1*1.995/4+16.61)*1.18                                = 37.9 t

Design Shear force =Average SF x IF x DF

    1        For inner girder                                                                 = 31.0 t
    2        For outer girder                                                                 = 37.9 t
Distribution of shear force for 1 L Class A + 70 - R (wheel)

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

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

                         15.05 t        15.05 t               6.1 t          6.1 t

                 1.63m          1.93m             1.88m               1.8m



               1.525               2.65                     2.65                      2.65

FEM                      -3.107           5.518    -2.108           1.925    -1.801           0.334
Balance                  3.107            -1.705   -1.705          -0.062    -0.062          -0.334
Carryover                -0.853            1.554   -0.031          -0.853    -0.167          -0.031
Balance                  0.853            -0.761   -0.761           0.510    0.510            0.031
Total M                  0.000             4.605   -4.605           1.520    -1.520           0.000

Simple SF              17.946             12.154 3.188              2.912 5.145               0.955
Elastic SF             -1.738              1.738 1.164             -1.164 0.574              -0.574
Reaction            16.21                      18.24                    7.47                      0.38

    1        For inner girder =      ((10.7+31.1)*1.34/4+18.24)*1.18*0.9                         = 34.2 t
    2        For outer girder =      ((10.7+31.1)*1.49/4+16.21)*1.18*0.9                         = 33.7 t

Design Shear force =Average SF x IF x DF
Reduced the SF by 10% for each additional loaded traffic lane in excess of 2 lanes.
[As per clause 208.2 IRC 6, 1966]

    1        For inner girder                                                                    = 34.2 t
    2        For outer girder                                                                    = 33.7 t
At quarter span (L/4)

For class A (Forward train)

Total shear force (from computer print out on previous sheets)                                 = 18.8 t
Component of shear force due to loads within 5.5 m from support.                               = 3.1 t
Component of shear force due to loads beyond 5.5 m from support.                               = 15.7 t

For 70 - R (wheel) (Forward train)

Total shear force (from computer print out on previous sheets)                                 = 48.7 t
Component of shear force due to loads within 5.5 m from support.                               = 16.4 t
Component of shear force due to loads beyond 5.5 m from support.                               = 32.3 t

Distribution of shear force for 70 - R (wheel)

A. By Morrice - Little's method
    1    For inner girder       =1.440*48.7*1.18/4                                             = 20.7 t
    2    For outer girder       =1.995*48.7*1.18/4                                             = 28.7 t

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

                         8.20 t           8.20 t

                 1.63m          1.93m



               1.525               2.65                      2.65                   2.65

FEM                      -1.693            3.007
Balance                  1.693             -1.503   -1.503
Carryover                -0.752             0.846   0.000           -0.752
Balance                  0.752             -0.423   -0.423           0.376 0.376
Total M                  0.000              1.927   -1.927          -0.376 0.376

Simple SF                 9.778            6.622
Elastic SF                -0.727           0.727 0.869              -0.869 -0.142          0.142
Reaction               9.05                    8.22                     -1.01                  0.14

    1        For inner girder =      (32.3*1.440/4+8.22)*1.18                                  = 23.4 t
    2        For outer girder =      (32.3*1.995/4+9.05)*1.18                                  = 29.7 t

Design Shear force =Average SF x IF x DF

    1        For inner girder                                                                  = 23.4 t
    2        For outer girder                                                                  = 29.7 t
Distribution of shear force for 1 L Class A + 70 - R (wheel)

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

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

                         8.20 t           8.20 t               1.55 t        1.55 t

                 1.63m          1.93m              1.88m             1.8m



               1.525               2.65                      2.65                     2.65

FEM                      -1.693            3.007    -0.536           0.489   -0.458           0.085
Balance                  1.693             -1.236   -1.236          -0.016   -0.016          -0.085
Carryover                -0.618             0.846   -0.008          -0.618   -0.042          -0.008
Balance                  0.618             -0.419   -0.419           0.330   0.330            0.008
Total M                  0.000              2.198   -2.198           0.186   -0.186           0.000

Simple SF                 9.778            6.622 0.810               0.740 1.307              0.243
Elastic SF                -0.830           0.830 0.759              -0.759 0.070             -0.070
Reaction               8.95                    9.02                      1.36                     0.17

    1        For inner girder =      ((15.7+32.3)*1.34/4+9.02)*1.18*0.9                          = 26.6 t
    2        For outer girder =      ((15.7+32.3)*1.49/4+8.95)*1.18*0.9                          = 28.5 t

Design Shear force =Average SF x IF x DF
Reduced the SF by 10% for each additional loaded traffic lane in excess of 2 lanes.
[As per clause 208.2 IRC 6, 1966]

    1        For inner girder                                                                    = 26.6 t
    2        For outer girder                                                                    = 28.5 t
Summary of shear force
          Section                    SF (t)                      1Lane
                                                        70 - R           Design           Design
 SL. Nr. considere Girder           (dl+uni   SF (t)           class A +
                                                       (wheel)           LL SF           SF (t-m)
             d     location           sidl) (con sidl)           70 - R
           Deff      Inner            31.0     3.1       32.5     36.0    36.0             70.1
   1
         from sup Outer               33.4     4.7       39.8     35.8    39.8             77.9
           Span      Inner            29.3     2.9       31.0     34.2    34.2             66.5
   2
           (L/8)    Outer             31.5     4.5       37.9     33.7    37.9             73.9
           Span      Inner            20.0     2.0       23.4     26.6    26.6             48.6
   3
           (L/4)    Outer             21.2     3.0       29.7     28.5    29.7             53.9

Shear stress   tv   (N/mm )
                             2
                                 < tmax      =   2.1       N/mm
                                                                 2


   tc    = K1 x K2 x   tco       [ Cl. 304.7.3 IRC - 21 1987 ]
Where
 K1   =              1.14 - 0.7 d            >= 0.5
 K2   =              0.5 + 0.25 r            >= 1.0
 tco =                   0.45

          Section
         considere Girder           Design       tv        r%          K1         K2        tc
                                                       2                                          2
 SL. Nr.     d     location         SF (t)   (N/mm )                                     (N/mm )
           Deff      Inner           70.1      1.14        0.787       0.5       1.00      0.23
    1
         from sup Outer              77.9      1.27        0.916       0.5       1.00      0.23
           Span      Inner           66.5      1.09        0.787       0.5       1.00      0.23
    2
           (L/8)    Outer            73.9      1.20        0.916       0.5       1.00      0.23
           Span      Inner           48.6      0.80        1.319       0.5       1.00      0.23
    3
           (L/4)    Outer            53.9      0.88        1.579       0.5       1.00      0.23
           Span      Inner            0.0      0.00        1.854       0.5       1.00      0.23
    4
           (L/2)    Outer             0.0      0.00        2.137       0.5       1.03      0.23


                                                           Reinf provided
                                     Reinf required                    2
          Section                                            (Asv) (cm /m)      Spacing Spacing
                                                  2
         considere Girder           (Asv / Sv) (cm /m)     No of      Bar dia   required Provided
 SL. Nr.     d     location                                 legs       (mm)       (mm)    (mm)
           Deff      Inner                18.6               2         16          216     210
    1
         from sup Outer                   20.6               2         16          195     190
           Span      Inner                17.6               2         16          228     220
    2
           (L/8)    Outer                 19.5               2         16          206     200
           Span      Inner                12.9               2         12          175     170
    3
           (L/4)    Outer                 14.3               2         12          158     150
           Span      Inner                 9.1               2         12          248     170
    4
           (L/2)    Outer                  9.0               2         12          251     150
DESIGN OF CROSS GIRDER

End cross girder

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

          50.12 t                     46.26 t                              46.11 t                         50.12 t

                         2.650                              2.650                                2.650


              0.65        1.35         0.65     0.65            1.35        0.65     0.65        1.350      0.65

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

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

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

For span AB                    L=     2.65      D = 1.75
                              L/D = 1.514       >= 1 for contineous beam
Lever arm Z =        0.2*(2.65+1.5*1.75)                                                = 1.055 m

For span CD                    L=     2.65      D = 1.75
                              L/D = 1.514       >= 1 for contineous beam
Lever arm Z =        0.2*(2.65+1.5*1.75)                                                = 1.055 m
                                   =M/sst*Z
                                                                                  2
Required Ast for max span M                        =10.682/1.055*20000   = 5.06 cm
                                                                                     2
Minimum Ast at bottom              =0.2%bd       =0.002*32.5*175         =   11   cm
Provide 3 nos       16 f       +    2 nos 16 f     +     2 nos 12 f
at bottom within a depth of (0.25D - 0.05L)                              = 0.305 m
from bottom face with a development length of (0.8*35*dia of bar)        = 448 mm
Provided Ast                                                             = 12.3 cm2

Required Ast for max support M =M/sst*Z
                                                                                   2
                                                 =32.579/1.055*20000     = 15.44 cm
Provide 3 nos        20 f      +      2 nos 16 f   +     2 nos 12 f
Distributed as per clause 28.3.2 (b) IS 456-1978
                                                                                     2
Provided Ast                                                             = 15.7 cm

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

Total shear                        =50.121+46.107+46.264+50.121          = 192.6 t
Required Ast as hanging R/F        =192.6*10000/20000                    = 96.3 cm2
Required Ast per m length         =96.3/7.95                             = 12.1 cm2/m
Provide   2L       12 f       @ 180 c/c as vertical reinforcement
Provided Ast                                                             = 12.6 cm2/m

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

0.1 % of web area on either face with spacing not more then 450 mm.
                                                                                     2
Required Ast     =0.001 *175*32.5                                        = 5.69 cm

				
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