Abbreviated Output File

The opening sections of the following output file contain details of the 11 node, 10 element mesh. The left-hand side of the girder is modeled as a pin fixed against translation. The right-hand side of the girder is supported on a roller.

The latter components of the output file contain summaries of the shear and moment envelopes, together with maximum values of response quantities.

START OF ABBREVIATED OUTPUT FILE

===========================================================================
Title : DESCRIPTION OF FINITE ELEMENT MESH          
                       
===========================================================================

 Problem_Type:  Static Analysis

=======================
Profile of Problem Size
=======================

   Dimension of Problem        =      2

   Number Nodes                =     11
   Degrees of Freedom per node =      3
   Max No Nodes Per Element    =      2

   Number Elements             =     10
   Number Element Attributes   =      2
   Number Loaded Nodes         =      0
   Number Loaded Elements      =      0


------------------------------------------------------------------------------
Node#      X_coord           Y_coord          Tx    Ty    Rz  
------------------------------------------------------------------------------

    1    0.0000e+00 ft    0.0000e+00 ft    -1    -2     1 
    2    5.6700e+00 ft    0.0000e+00 ft     2     3     4 
    3    1.1340e+01 ft    0.0000e+00 ft     5     6     7 
    4    1.7010e+01 ft    0.0000e+00 ft     8     9    10 
    5    2.2680e+01 ft    0.0000e+00 ft    11    12    13 
    6    2.8350e+01 ft    0.0000e+00 ft    14    15    16 
    7    3.4020e+01 ft    0.0000e+00 ft    17    18    19 
    8    3.9690e+01 ft    0.0000e+00 ft    20    21    22 
    9    4.5360e+01 ft    0.0000e+00 ft    23    24    25 
   10    5.1030e+01 ft    0.0000e+00 ft    26    27    28 
   11    5.6700e+01 ft    0.0000e+00 ft    29    -3    30 


--------------------------------------------------------------------
Element#     Type         node[1]   node[2]      Element_Attr_Name
----------------------------------------------------------------------

       1   FRAME_2D             1         2      girder1
       2   FRAME_2D             2         3      girder1
       3   FRAME_2D             3         4      girder2
       4   FRAME_2D             4         5      girder2       5   FRAME_2D             5         6      girder2
       6   FRAME_2D             6         7      girder2
       7   FRAME_2D             7         8      girder2
       8   FRAME_2D             8         9      girder2
       9   FRAME_2D             9        10      girder1
      10   FRAME_2D            10        11      girder1

--------------------- 
Element Attribute Data :        
--------------------- 


ELEMENT_ATTR No.   1  : name = "girder1" 
                      : section = "no_cover" 
                      : material = "steel" 
                      : type = FRAME_2D
                      : gdof [0] =    1 : gdof[1] =    2 : gdof[2] =    3
                      : Young's Modulus =  E =        2.900e+04 ksi
                      : Yielding Stress = fy =        5.000e+01 ksi
                      : Poisson's ratio = nu =        3.000e-01   
                      : Density         =        0.000e+00 (null)
                      : Inertia Izz     =        1.727e+04 in^4
                      : Area            =        3.809e+02 in^2



ELEMENT_ATTR No.   2  : name = "girder2" 
                      : section = "cover" 
                      : material = "steel" 
                      : type = FRAME_2D
                      : gdof [0] =    1 : gdof[1] =    2 : gdof[2] =    3
                      : Young's Modulus =  E =        2.900e+04 ksi
                      : Yielding Stress = fy =        5.000e+01 ksi
                      : Poisson's ratio = nu =        3.000e-01   
                      : Density         =        0.000e+00 (null)
                      : Inertia Izz     =        2.570e+04 in^4
                      : Area            =        3.809e+02 in^2

============= End of Finite Element Mesh Description ==============


MATRIX : "max_displ_dead"

row/col                  1            2            3   
        units           in           in          rad   
   1            0.00000e+00 -3.44203e-01  5.69206e-18

MATRIX : "max_mom_dead"

row/col                  1            2            3   
        units          lbf          lbf       lbf.in   
   1           -0.00000e+00  3.02494e+03 -4.93961e+06
   2            0.00000e+00 -3.02494e+03  5.14543e+06

MATRIX : "max_sh_dead"

row/col                  1            2            3   
        units          lbf          lbf       lbf.in   
   1           -0.00000e+00  2.72245e+04 -8.24290e-09
   2            0.00000e+00 -2.72245e+04  1.85236e+06

MATRIX : "cover_mom_dead"

row/col                  1            2            3   
        units          lbf          lbf       lbf.in   
   1           -0.00000e+00  2.11746e+04 -1.85236e+06
   2            0.00000e+00 -2.11746e+04  3.29308e+06

MATRIX : "moment_dead"

row/col                  1   
        units                
   1   lbf.in  -8.24290e-09
   2   lbf.in   1.85236e+06
   3   lbf.in   3.29308e+06
   4   lbf.in   4.32216e+06
   5   lbf.in   4.93961e+06
   6   lbf.in   5.14543e+06
   7   lbf.in   4.93961e+06
   8   lbf.in   4.32216e+06
   9   lbf.in   3.29308e+06
  10   lbf.in   1.85236e+06
  11   lbf.in   8.24290e-09

MATRIX : "max_displ_live"

row/col                  1            2            3   
        units           in           in          rad   
   1            0.00000e+00 -6.53755e-01  1.06252e-17

MATRIX : "max_mom_live"

row/col                  1            2            3   
        units          lbf          lbf       lbf.in   
   1           -0.00000e+00  3.60000e+04 -9.79776e+06
   2            0.00000e+00 -3.60000e+04  1.22472e+07

MATRIX : "max_sh_live"

row/col                  1            2            3   
        units          lbf          lbf       lbf.in   
   1           -0.00000e+00  7.20000e+04  0.00000e+00
   2            0.00000e+00 -0.00000e+00  0.00000e+00

MATRIX : "cover_mom_live"

row/col                  1            2            3   
        units          lbf          lbf       lbf.in   
   1           -0.00000e+00  5.76000e+04 -3.91910e+06
   2            0.00000e+00 -5.76000e+04  7.83821e+06

MATRIX : "influ_mid_mom"

row/col                  1   
        units                   1   lbf.in   0.00000e+00
   2   lbf.in   2.44944e+06
   3   lbf.in   4.89888e+06
   4   lbf.in   7.34832e+06
   5   lbf.in   9.79776e+06
   6   lbf.in   1.22472e+07
   7   lbf.in   9.79776e+06
   8   lbf.in   7.34832e+06
   9   lbf.in   4.89888e+06
  10   lbf.in   2.44944e+06
  11   lbf.in   0.00000e+00

MATRIX : "influ_end_sh"

row/col                  1   
        units                
   1      lbf   7.20000e+04
   2      lbf   6.48000e+04
   3      lbf   5.76000e+04
   4      lbf   5.04000e+04
   5      lbf   4.32000e+04
   6      lbf   3.60000e+04
   7      lbf   2.88000e+04
   8      lbf   2.16000e+04
   9      lbf   1.44000e+04
  10      lbf   7.20000e+03
  11      lbf   0.00000e+00

MATRIX : "envelop_mom_live"

row/col                  1   
        units                
   1   lbf.in   0.00000e+00
   2   lbf.in   4.40899e+06
   3   lbf.in   7.83821e+06
   4   lbf.in   1.02876e+07
   5   lbf.in   1.17573e+07
   6   lbf.in   1.22472e+07
   7   lbf.in   1.17573e+07
   8   lbf.in   1.02876e+07
   9   lbf.in   7.83821e+06
  10   lbf.in   4.40899e+06
  11   lbf.in   0.00000e+00

impact factor =      1.275 


MATRIX : "max_displ"

row/col                  1            2            3   
        units           in           in          rad   
   1            0.00000e+00 -1.17786e+00  1.92411e-17

MATRIX : "max_mom"

row/col                  1            2            3   
        units          lbf          lbf       lbf.in   
   1           -0.00000e+00  4.89314e+04 -1.74335e+07
   2            0.00000e+00 -4.89314e+04  2.07628e+07

MATRIX : "max_sh"

row/col                  1            2            3   
        units          lbf          lbf       lbf.in   
   1           -0.00000e+00  1.19037e+05 -8.24290e-09
   2            0.00000e+00 -2.72245e+04  1.85236e+06

MATRIX : "cover_mom"

row/col                  1            2            3   
        units          lbf          lbf       lbf.in   
   1           -0.00000e+00  9.46249e+04 -6.84991e+06
   2            0.00000e+00 -9.46249e+04  1.32882e+07


START ASD CODE CHECKING::

   OK : (LL+I) deflection less than 1/800 span

   OK : moment stress less than 0.55*Fy
 
   OK : shear stress less than 0.33*Fy

A summary of the bridge response is contained in the moment and influence line graphs.

The following points are noted:

Since this is a simple-supported bridge, the maximum displacement and maximum bending moment will occur at the middle of the span. The maximum shear force will occur at the end support.

The final results of moment, shear and displacement are calculated according to AASHTO ASD request: Total = DL + impact * LL.

The stress due to bending is given by ; Moment stress = (M * y)/I.

Because there are two different section properties, we have to calculate not only the maximum moment stress in the middle of the span (stress2), but also the moment stress of where the section changed (stress1).

Shear stress = V /(tw * d.

We assume that the shear force is carried by the girder web alone, and therefore, we only check for maximum shear at the end support.

The influence line for the bending moment at the middle of the span -- details are shown in Figure 2 -- is obtained by iteratively positioning one truck load at a finite element node, then solving for the reaction forces. A similar procedure is employed to compute the influence line of shear force at the end support -- see Figure 3.

Figure 1 shows the distribution of bending moments due to truck loadings (we note in passing that the bending momend diagram corresponds to an envelope of the moment influence lines of the truck load).

The follow array elements are used in the generation of program output:

    max_displ[1][2] = the maximum displacement of the beam.
    max_mom[2][3]   = the maximum moment.
    max_sh[1][2]    = the maximum shear force.
    cover_mom[2][3] = the moment at where the bridge section changed.

Figure 2 : Influence Line of Moment at Mid-Span