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

### PROBLEM DESCRIPTION

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:

• Conduct a finite element analysis of a one span simply supported composite bridge with cover plate under the girders. The finite element analysis will be simplified by considering only one internal girder of the bridge system;
• Compute the moment envelope diagrams of dead loads and truck loads along the bridge, and influence lines of shear at the end support, and at the bridge mid-span;
• Check that the peak values of deflections, flexural stresses, and shear stresses meet AASHTO Working Stress Design requirements.

### DESCRIPTION OF HIGHWAY BRIDGE

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

#### 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 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.

### FINITE ELEMENT MODELING

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

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.

### WSD RULE CHECKING

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.