Working Stress Design (WSD) of a Single Span Highway Bridge

[ Problem Description ] [ Description of Highway Bridge ]
[ Finite Element Model ] [ WSD Code Checking ] [ Input and Output Files ]


In this example, we use ALADDIN for the AASHTO Working Stress Design of a single-span highway bridge structure, with design rule checking. We will:


A plan and cross sectional view of a typical bridge system is shown in Figures 1 and 2.

Figure 1 : Plan of Highway Bridge

Figure 2 : Typical Cross Section

The bridge girders are made of rolled beam W33x130 with a 14" X 3/4" steel cover plate. An elevation view of the bridge and the position of the steel cover plate is shown. The material properties are Fy = 50 ksi, and Es = 29000 ksi. The effective cross sectional properties of the composite steel/concrete girder (with and without the cover plate) are computed with n = Es/Ec = 10. The section properties are also shown.

Figure 3 : Elevation of Beam

Figure 4 : Section Properties (n = 10)

The bridge is subjected to dead and live external loadings. The design dead load includes 7 inches concrete slab, steel girder, and superimposed load. The design live load consists of a 72 kips HS-20 truck, which will be modeled as a single concentrated load moving load along the girder nodes.


The single-span bridge girder is modeled with 10 two-dimensional beam/column finite elements along the bridge length.

Figure 5 : Moment Diagram due to Dead Loads and Truck Loads

Figure 5 shows the Bending Moment Diagram due to Dead Loads and Truck Loads. Because this is a simply supported bridge, the maximum deflections and bending moment will occur at the mid-span.

Figure 6 : Influence line of bending moment at mid-span

Figure 6 shows the influence line for bending moment at the bridge mid-span.


With the bending moment and influence lines diagrams known, ALADDIN can check that the peak displacements, flexural stresses, and shear stresses, meet AASHTO WSD requirements. The ALADDIN statements:

 *  =========================================================
 *  WSD Code Checking for Deflections and Stress Requirements  
 *  =========================================================

   print "\n\nSTART ASD CODE CHECKING::\n";

/* Check computed deflections against allowable values */

   if( -impact*max_displ_live[1][2] > (1/800)*length ) then {
       print "\n\tWarning : (LL+I) deflection exceeds 1/800 span\n";
   } else {
       print "\n\tOK : (LL+I) deflection less than 1/800 span\n";

show, for example, how the maximum computed displacements are compared against AASHTO WSD requirements. A full listing of ALADDIN statements for design rule checking may be found at the end of the input file.


  1. Click here to visit the input file.
  2. Click here to visit the output file.

Developed in April 1996 by Mark Austin and Wane-Jang Lin
Last Modified June 27, 1996
Copyright © 1996, Mark Austin and Wane-Jang Lin, Department of Civil Engineering, University of Maryland