Elastic Nonlinear Analysis of Plane Truss Bridges

Abstract

There are, enormous number of, steel truss bridges in the U.S. and around the world. Elementary theory of structural analysis or linear elastic small displacement finite element method is typically used for analysis and design of these bridges. However, steel bridges may face large deflections and inelastic displacements due to unexpected live loads and/or unfavorable environmental conditions. Therefore, there is a need for the second- or higher-order elastic and/or inelastic analysis of these bridges. This article presents a methodology for the elastic large displacement analysis of plane trusses that are novel in bridge engineering practice. Higher-order stiffness matrices and finite element procedure is used for the elastic nonlinear analysis of plane truss structures. The higher-order stiffness matrices are derived and formatted by using the updated Lagrangian description and the finite element concept. Then a numerical method, a modified Riks-Wempner approach, is used for the solution of geometric nonlinear plane truss problems. First, background on nonlinear truss analysis, the scope of this work, and the assumptions pertinent to this research are given. Second, the stiffness matrices, for nonlinear elastic plane truss analysis, are presented by using the incremental equation of equilibrium that is derived from first variation of increment of total potential energy. Third, a modified Riks-Wempner method is used for programming and software development. Numerical examples and results are presented next. The accuracy of the software developed is checked by comparing the results of numerical examples with theoretical results and examples published by other authors. In this research, the concept of Object-Oriented technology and C++ programming language are used for coding and software developed.