[ 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:

- 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.

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

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.

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 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 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.