A Practical Method to Determine Critical Moments of Bridge Decks Using the Method of Least Squares and Spreadsheets

In this paper, a simple yet practical and direct method is presented for the determination of critical bending moments of bridge decks subject to traffic loads by taking the advantages of the concept of influence surfaces and the versatility of commercial FE software. The influence surfaces are obtained by putting unit loads across the region concerned and the corresponding computed results are exported to a spreadsheet. A least square fit to the classical thin-plate solution, based on the computed results can be easily obtained. Based on such a least-square solution, the locations and the corresponding critical moments for different types of designed loads can be calculated exactly by using a simple and readily available optimization tools in Excel. Comparing with conventional approaches in determining critical moments, the method is simple yet versatile and reliable, and it does not require any complicated mathematics or special software for practicing engineers to implement. Such an approach would lead to a more reasonable estimation of stresses in bridge decks or other plate-type structures which are subject to various moving loads with different arrangements.