Crash testing an upcoming model of a Big Three automobile manufacturer's pickup truck revealed a weakness in the side rail. The problem was that post-buckling stress rendered a certain portion of the rail cross-section ineffectual. Normally, this problem would have to be addressed with a tedious series of iterative hand calculations or a lengthy and expensive finite element analysis. In this case, the GAS (Geometric Analysis of Sections) module of AISI/CARS software developed by Desktop Engineering Int'l Inc., Woodcliff Lake, New Jersey, for the Auto/Steel Partnership (A/SP) and The American Iron and Steel Institute (AISI), Southfield, Michigan, was used to automatically calculate effective section properties. This package guided engineers to properly position a panel that made the cross-section fully effective without increasing the gauge of the side rail. Using this approach, the problem was solved in two hours thus avoiding days of tedious hand calculations and the possibility of extra crash simulation and physical testing iterations.

In 35 mph barrier crash tests on an early prototype, the side rail behind the cab collapsed to the point that the box moved forward against the rear of the cab. Obviously, this had to be fixed. It should be noted that the 35 mph barrier test generates 36 percent more energy than the 30 mph test, which is all that is mandated by current government standards. Despite this fact, the 35 mph barrier test is used by all major U.S. vehicle producers as a corporate standard.

The crash vehicle was equipped with cameras but this area of the vehicle was not visible during crash tests, so it was impossible to determine exactly what happened. Originally, engineers guessed that the problem involved top flange instability. So they increased the gauge of the sheet metal in this area and modeled it on the manufacturer's in-house crash analysis software running on a Cray computer. Analysis showed that even with the increased gauge and yield strength the area would still collapse.

To help solve this problem, the manufacturer asked for assistance from a consultant who specialzes in the strength and durability of vehicle frames. The work of Gerford Carver, president of Gerford Carver Consulting (Milwaukee, WI), has been focused on this issue since he joined the automobile industry in 1952. Since 1987, he has had his own consulting practice. Carver knew that the crux of this and many other similar problems is the "effective width concept" that accounts for the post-buckling strength of a thin walled section. The post-buckling strength is the additional load carried by elements of the cross section, after they have buckled locally, by means of a redistribution of stress. Under the effective width concept, only certain portions of the plate width are considered to be effective in carrying loads after exceeding the local buckling stress. The nonuniformity of stress distribution in each element is accounted for by replacing the actual plate width by a reduced effective width so that the total area under the stress distribution curve is the same.

The effective width of a cross section element is a function of a number of parameters such as boundary condition, stress condition, material and width to thickness ratio, etc. The stress distribution cannot be computed until the cross section property is calculated. Therefore, it is necessary to assume a certain stress distribution and compute the associated effective property.

Generally, stress distribution is obtained first, based on the assumption that the whole cross section is effective. Accordingly, effective width of each segment in the cross section is computed. If the results indicate that any element is not fully effective, the calculation becomes iterative. The stress distribution in the subsequent calculation is obtained by moving the principal axis. For cross sections with arbitrary shape, flanges and webs are difficult to identify and stress distribution can be very complicated.

The iterative nature of the effective property calculation makes the manual calculation very time consuming. In the past, a spreadsheet was used that calculates section properties based on a manually-entered estimate of how much material is effective. This program performed most of the manual calculations automatically but still took a very long time because of the many iterations that were required to determine the effectiveness of the section.

To facilitate the effective property calculation for cold formed steel cross sections, AISI and A/SP sponsored the development of GAS and its integration into the Computerized Application and Reference System (CARS), a computerized version of the Automotive Steel Design Manual. The following procedure was developed and implemented in GAS to compute the effective cross section properties: 1) Compute the normal stress distribution assuming all the segments are fully effective. 2) Calculate the effective width of each segment. 3) Calculate the cross section properties of the section based on the effective portion of each segment. 4) Compute the stress distribution using the calculated effective section. 5) Calculate the effective width of each segment based on the revised stress distribution. 6) Calculate the cross section properties of the section based on the effective portion of each segment. 7) Repeat Steps 4 and 6 until the area and moments of inertia of the effective section converge.

Carver used GAS to analyze the section properties of the side rail by entering the geometry of the rail, the yield strength of the material and the type of loading. The program determined the effective properties of each section. Viewing the effective properties made it readily apparent to the consultant that a side panel needed to be added to the rail to make it into a fully effective section. The panel was positioned 1/3 of the way from each end of the web. The program showed that the first iteration was fully effective and provided the properties needed to withstand the crash. The results were given to the auto manufacturer and they confirmed them in their crash analysis program. Prototypes were built and tested and these further confirmed the GAS results.

In the past, stiffening the web would have required a lengthy trial and error process that could only have been addressed with tedious hand calculations that would have taken several days at a minimum. It would have been necessary to calculate the properties of each section, then from empirical formulas determine how much of the section was effective, then recalculate and so on until a section that was fully effective was created.

The problem also could have been solved with finite element analysis but it would have taken several days to model the component and iterate to a solution. The component would have to be remodeled for each different configuration that was tried. With GAS, the problem was solved in only two hours.

The auto manufacturer was very pleased with the results and informed Carver that the company had saved a considerable amount of time both in crash analysis and in prototype build and testing.