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

https://doi.org/10.1016/j.jcsr.2010.09.009Get rights and content

Abstract

This paper presents a practical advanced analysis software which can be used for nonlinear inelastic dynamic analysis of space steel structures. The proposed software can predict accurately the nonlinear response of a steel structure by using only one element per member in structural modeling. Three types of element including both geometric and material nonlinearities are implemented in the proposed software: (1) catenary cable element; (2) truss element; and (2) beam–column element. An incremental-iterative solution scheme based on the Newmark method and the Newton–Raphson method is adopted for solving the nonlinear equations of motion. Several numerical examples are presented to verify the accuracy and efficiency of the proposed software in predicting the nonlinear response of steel structures. The proposed program is shown to be an efficient and reliable tool for daily use in design.

Research highlights

► Three elements of cable, truss, and beam-column are implemented in proposed software. ► The proposed software consider both geometric and material nonlinearities. ► It is shown to be an efficient and reliable tool for daily use in design.

Introduction

It is widely recognized that steel structures may exhibit significantly nonlinear behavior prior to achieving their ultimate load-carrying capacity. Thus, advanced analysis is the most appropriate method for assessing the realistic response of a steel structure. Advanced analysis is defined as any analysis method that can efficiently capture the ultimate strength and stability of a whole structural system and its component members so that separate member capacity checks encompassed by specification equations are not required [1]. The advanced analysis method can be generally classified into two categories of plastic zone [2] and plastic hinge types [3] based on the degree of refinement used to represent yielding.

With the rapid development in the finite element technique and computer technology, several computer programs for the nonlinear inelastic dynamic analysis of steel frames have been developed such as DRAIN-3DX [4], OpenSees [5], and FRAME3D [6]. In the DRAIN-3DX program, the geometric nonlinearity caused by the axial force (PΔ effect) is included by adding the geometric stiffness to the tangent stiffness matrix, while the material nonlinearity is considered using the fiber plastic hinge concept. In the OpenSees software, the PΔ effect is captured by using the corotational transformation technique. The inelastic effect is considered using either a concentrated or distributed plasticity model. FRAME3D provides a geometric updating feature to accommodate large translations and rotations of the beam elements and, hence, to capture the PΔ effect automatically. The inelastic effect of the beam–columns can be considered using either the plastic hinge method or the fiber hinge method. However, the three above-mentioned programs are unable to capture accurately the geometric nonlinearity caused by the interaction between the axial force and bending moments (Pδ effect) when one element per member is used in the modeling. Therefore, they overestimate the strength of a member subjected to a significant axial force. Although these programs can accurately capture the Pδ effect by using several elements per member in the modeling, it is generally recognized to be computationally intensive, especially in the time-history analysis. For this reason, they are applicable only for research purposes.

For practical use in design, the advanced analysis software should generate reliable results in a minimal time. Kim et al. [7] developed a Practical Advanced Analysis Program (PAAP) based on the use of stability functions and a refined plastic hinge model for predicting the nonlinear response of a steel frame. They concluded that PAAP is an accurate and time-efficient tool for practical use in the design of steel frames. Since the solution algorithm of PAAP ignores the equilibrium iteration in each time step, it cannot predict accurately the inelastic seismic response of a framed structure which has sustained a very large plastic deformation. This limitation is overcome in the present study by applying the Newton–Raphson iteration in each time step. Recently, Thai and Kim [8] expanded the PAAP program by adding cable elements and truss elements in the element library. The main feature of the PAAP program is to use one element per member to model each structural component and to obtain a realistic representation of the material and geometrical nonlinear effects of the overall structure. However, its application is limited to the steel structures subjected to static loading. Moreover, this software ignores the material nonlinearity of cable and truss elements. Therefore, it should be improved for the nonlinear inelastic dynamic analysis of steel structures.

The purpose of this paper is to extend the capabilities of the PAAP program to the nonlinear inelastic time-history analysis of steel structures. Two modifications of PAAP are made in this research: (1) including the material nonlinearity of cable and truss elements; and (2) extending the application of the PAAP program to the time-history analysis. The material nonlinearity of a cable element is considered using an elastic–plastic hinge model, while the material nonlinearity of a truss element is included by tracing a simple empirical equation of the stress–strain relationship proposed by Hill et al. [9]. In the nonlinear time-history analysis, an incremental-iterative scheme based on the Newmark-β method and the Newton–Raphson method is adopted for solving the nonlinear equations of motion. In comparison with other commercial softwares such as SAP 2000 [10] and ABAQUS [11], the proposed program has the following benefits: (1) it can predict accurately the nonlinear response of a frame by using one beam–column element per member; (2) it can capture the inelastic buckling response of a truss; and (3) it can consider the inelastic response of a cable. The nonlinear dynamic responses of structure in a variety of numerical examples are compared with those generated from finite element commercial packages to show the accuracy and computational efficiency of the present software in applying for practical design purposes.

Section snippets

Element formulation

The element library of the present software includes three basic elements which are usually used in the modeling of steel structures: (1) cable element; (2) truss element; and (3) beam–column element. These elements account for the effects of both geometric and material nonlinearities. Although the stiffness matrix formulation of these elements was given in [8], it is briefly presented here only for the sake of completeness.

Solution algorithm

Newmark’s method [16] has been chosen for the numerical integration of the equation of motion because of its simplicity. The residual forces in each time step can be eliminated by using the Newton–Raphson iterative procedure. The incremental equation of motion of a structure can be written as [M]{ΔD̈}+[C]{ΔḊ}+[K]{ΔD}={ΔF} where [ΔD̈],[ΔḊ], and [ΔD] are the vectors of incremental acceleration, velocity, and displacement, respectively; [M],[C], and [K] are the mass, damping, and tangent

Verification examples

Three numerical examples are presented and discussed to verify the accuracy and efficiency of the proposed program in predicting the nonlinear response of steel structures under earthquake loading. Two earthquake records of the El Centro and the Loma Prieta as shown in Fig. 1 are used as ground excitation. Their peak ground accelerations and time steps are listed in Table 1. The mass- and stiffness-proportional damping factors are chosen based on the first two modes of the structure so that the

Case study

A three-dimensional suspension bridge is used to verify the accuracy and efficiency of the proposed program in predicting the nonlinear inelastic response of a large scale structure. Fig. 12 shows the geometry and sectional properties of the bridge. The Young’s modulus and yield stress of beam–column members are 200 GPa and 248 MPa, respectively, while the Young’s modulus and yield stress of cable members are 165.5 GPa and 1103 MPa, respectively. The weight per unit volume of the cable and

Conclusion

A practical advanced analysis software for the nonlinear dynamic analysis of steel structures considering both geometric and material nonlinearities has been presented. The accuracy andcomputational efficiency of developed software is verified through three numerical examples and one case study of large-scale suspension bridge with two different earthquake loadings. The good results obtained in a short analysis time prove that this software can effectively be used for office design in

Acknowledgement

This research has been supported by the Brain Korea 21 Project of the Korea Research Foundation.

References (18)

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