Derivation of Polynomial Functions for The Prediction of Critical Axial Forces in Bridge Trusses.

ABSTRACT This study presents the derivation of polynomial functions for the prediction of critical axial forces in bridge trusses. Four different bridge trusses were considered in this study, three of which are statically determinate while one is statically indeterminate. These trusses at different height to span (aspect) ratios were tested for critical axial forces under the same conditions. The graphs of their critical axial forces against aspect ratios were plotted and this led to the findings that these axial forces fit into certain polynomial behavior (equations). This study was designed by first writing a computer program with the visual basic platform that can return the axial forces for all the members in each of these selected trusses for any number of spans. These data from the program were what we took as the theoretical solutions of the truss. This study was conducted by applying a vertical point load of 100KN at the nodes of the bottom chord and obtaining results for each of the truss types as the number of their bays were progressively increased from four to ten as the aspect ratios varied between 0.3 and 1.2. The maximum axial loads recorded for each of the trusses were plotted against their aspect ratios and a series of plots with polynomial behavior were established. These polynomials were then modified to suit any point load values initially applied at the same position and are regarded as the models. These models were used to predict the maximum axial forces in each of the trusses. For an aspect ratio of 1 and for six spans when initially loaded with a 100KN point load at each node the theoretical data gave 2250KN, 450KN, 450KN and 434KN. Whereas the model prediction gave 2246KN, 448KN, 448KN and 434KN for truss types A, B, C and D respectively. The percentage closeness of the theoretical data and the models are 99.822%, 99.556%, 99.556% and 99.770% respectively. The percentage closeness suggests that the models can be used as an approximation of the theoretical methods and can be safely applied for limit state truss analysis.