The case of a long-span roof structure of an airplane hangar serves as a classic example. The structure consists of a post-tensioned concrete folded plate, 14 feet deep, spanning 270 feet. Several months after construction was completed, the roof exhibited creep deflections that were greater than anticipated, such that the 40-foot-high hangar doors could not open and close without binding. As a result, the hangar doors were taken down, trimmed to make them shorter, and reinstalled — all at great expense. Unfortunately, the roof continued to creep and, after another several months, the hangar doors again had to be taken down, trimmed, and reinstalled. The structural engineer of record scrutinized his piles of computer output, but couldn't find any glitch in the computer program that would cause the results to be erroneous.

At the start of the ensuing lawsuit, my firm was called in to investigate the problem and determine its cause. While we were preparing our own computer model, we were puzzled to see that the design drawings called for a relatively large number of tendons in the web of the end plate (folded plate element located over the hangar doors). To get a sense of the structural behavior and order-of-magnitude stresses and deflections under dead and live loads, we performed a quick wL²/8 hand calculation. We were now even more puzzled, since our hand calculation indicated that the number of tendons required in the bottom flange of the end plate was about twice the amount called for on the design drawings. Since the roof structure was essentially a simple span, our subsequent computer analysis agreed very closely with our hand calculation.

During the litigation discovery period we were able to obtain a copy of the EOR's computer model and analysis results, and we were then able to solve the tendon mysteries. For the end plate, the dead weight had been incorrectly entered as a lateral load, rather than a vertical load. This resulted in a large number of tendons in the web and not enough tendons in the bottom flange. Clearly, the problems with this roof structure could have been completely avoided by just performing a simple hand calculation to check the computer results.

The lesson to be learned here is that — at the risk of using an obvious cliché — the computer is just a tool. Indeed, it is a remarkable tool. We can now design complex structures more efficiently, examining hundreds of loading combinations and foregoing the overdesign that was necessary in the past, when the only tools we had were slide rules, conjugate beams, moment distribution, slope deflection, etc. But because we no longer have that built-in overdesign and gratuitously added safety margin, we need to be sure that our computer model is correct and that all of the loadings and load combinations have been accounted for. Of no lesser importance is the need to perform hand calculations (preferably before the computer analysis is performed), to get an approximation of stresses, deflections, direction of reactions, etc. that can be compared with the computer output. Even the most complicated structure can be idealized to enable a hand calculation that will give results that are "in the ballpark."

The other lesson to be learned is that, after all these years, wL²/8 still works — it has not been modified due to the advent of more powerful computers and software, or due to inflation!

Daniel A. Cuoco, P.E., F.ASCE,
dcuoco@zweigwhite.com