Practical advanced analysis software for nonlinear inelastic analysis of space steel structures

Abstract

This paper presents a practical advanced analysis software which can be used for nonlinear inelastic analysis of space steel structures. The software employs the stability functions and the refined plastic hinge model to minimize modeling and computational time. The generalized displacement control method is adopted to solve the nonlinear equilibrium equations. This algorithm can accurately trace the equilibrium path of the nonlinear problem with multiple limit points and snap-back points. A user-friendly graphic interface of the software is developed to facilitate the modeling process and result interpretation of the problem. Several numerical examples are presented to verify the accuracy and computational efficiency of the proposed software by comparing the results predicted by the present software with those given by the ABAQUS and other available results.

Introduction

The advanced analysis or the nonlinear inelastic analysis, which can assess the limit state strength and stability of a structural system and its individual members without requiring the separate member capacity checks, can generally be classified into two categories of the finite element and beam–column types. In the finite element method, the interpolation functions are usually used to represent the second-order effects, and the fiber approach is adopted to capture the spread of plasticity. This method has been presented by Pi and Trahair [1], Izzuddin and Smith [2], Teh and Clark [3], Torkamani and Sonmez [4] and Jiang et al. [5]. Although the solution of this method can be considered to be relatively accurate, it requires a very refined discretisation of the structures. For this reason, it is applicable only for research purpose because of its highly computational cost. In the beam–column approach, the stability functions derived from the differential equilibrium equation are employed to capture the second-order effects, and the refined plastic hinge model proposed by Liew et al. [6] and Kim et al. [7], [8], [9] is adopted to account for the material nonlinearity. The benefit of this method is that it enables only one or two elements per member to accurately predict the nonlinear response of structures and, hence, to save computational time.

Several computer programs for nonlinear inelastic analysis of three-dimensional steel frames have been developed using various types of beam and column elements. These include the DRAIN-3DX [10], OpenSees [11] and FRAME3D [12]. In the DRAIN-3DX program, the geometric nonlinearity caused by the axial force (P − Δ effect) is included by adding the geometric stiffness to the tangent stiffness matrix, while the material nonlinearity is considered using the fiber hinge method. OpenSees includes beam–column elements with both concentrated and distributed plasticity using the numerical integration method. The P − Δ effect is considered using corotational transformation technique. FRAME3D provides a geometric updating feature to accommodate large translations and rotations of the beam elements and, hence, to capture the P − Δ effect automatically. The inelastic effect is considered using the fiber hinge method. However, the above-mentioned programs ignore the geometric nonlinearity caused by the interaction between the axial force and bending moments (P − δ effect). Therefore, they overestimate strength of a member subjected to significant axial force.

The Practical Advanced Analysis Program (PAAP) using the beam–column approach is developed in this paper for predicting the nonlinear inelastic behavior of space steel structures. The second-order effects are captured by the use of stability functions to minimize modeling and solution time, while the material nonlinearity is implemented using the refined plastic hinge concept. The Generalized Displacement Control (GDC) method proposed by Yang and Shieh [13] is adopted for solving the nonlinear equilibrium equations. This algorithm can accurately trace the equilibrium path of the nonlinear problem with multiple limit points and snap-back points. For ease of use in design, a user-friendly graphic interface of the present software is also developed to facilitate the modeling process and result interpretation of the problem. The pre-processor of the software is reasonably designed following the sequence of modeling for the users’ convenience. The results can be displayed graphically in the post-processor of the software to help the users quickly visualize and understand the response of structure under applied loads. Some graphical representations are shown to illustrate the efficient features of the software. The present software PAAP is verified for the accuracy and computational efficiency through several numerical examples. The obtained results are compared with those from the commercial finite element package ABAQUS and the other results reported in the literature.