Efficient geometric nonlinear elastic analysis for design of steel structures: Benchmark studies

Abstract

Most structural design codes require the consideration of geometric nonlinearities or second-order effects. Analysis of second-order forces and moments in structural members requires the solution of a nonlinear system of equilibrium equations. There are many ways to solve such a system, with varying levels of accuracy and computational expense. Numerical solution schemes for the geometric nonlinear analysis of structures have been shown to produce extremely accurate results when applying small load increments and/or implementing multiple linear analyses or iterations per increment. This paper proposes the use of an approximate solution scheme that utilizes two linear analyses within a single load increment, thereby simplifying the second-order elastic analysis to a predictor-corrector type algorithm with improved computational speed. Further contributing to its efficiency is the ability to use the analysis results from within the serviceability design process in the predictor step, thereby requiring only one linear corrector analysis per load combination investigated. The predictor-corrector scheme is proposed as a substitute for either an exact geometric nonlinear elastic analysis or the approximation of second-order results by amplifying first-order results. Twenty-two steel benchmark frames are used to assess the method's accuracy in comparison with a more exact solution scheme. Comparisons are also made, where possible, with interstory drift amplifiers applied to first-order results. The findings demonstrate the method's ability to maintain sufficient accuracy while significantly improving computational efficiency. Use of the method is demonstrated with two illustrative examples, and advantages and limitations are discussed, as well as insights regarding frame sensitivity to second-order effects.