Modeling Cyclic Behavior of Reinforcing Steel: Relevance in Seismic Response Analysis of Reinforced Concrete Structures

In nonlinear dynamic analyses of RC structures based on fiber-based discretization of member cross-sections, the constitutive model used to represent the cyclic behavior of reinforcing steel typically plays a significant role in controlling the structural response especially for nonductile systems. The accuracy of a fiber-section model is almost entirely dependent on the ability of both the concrete and reinforcing steel constitutive material models to represent the overall inelastic behavior of the member. This paper describes observations related to the fundamental properties of reinforcing steel such as buckling, hardening, diminishing yield plateau and growth of curvature, Bauschinger effect, and low-cycle fatigue and strength degradation that are relevant to the overall task of developing an accurate material model for use in seismic response analysis of reinforced concrete structures. Background and Introduction Advanced research on modeling inelastic behavior of reinforced concrete (RC) components have been conducted in an effort to improve the accuracy in predicting the nonlinear response of RC structures for performance-based seismic evaluation. The use of a fiber model-based discretization of an RC section is currently the most advanced approach in nonlinear frame analysis. In such cases, the proper modeling of nonlinear material behavior is crucial in the overall analysis framework. A simple bilinear model, however, is still commonly adopted as the constitutive model of reinforcing steel in nonlinear analysis for RC structures while confined concrete properties are modeled using confined models proposed by Mander et al [1], Hoshikuma et al [2], etc. As shown in Fig. 1, the seismic response of an RC frame structure can be considerably different when different steel models are utilized to represent the cyclic behavior of reinforcing steel bars in the RC section. Shown in the figure are the inter story drifts of a 12 story moment resistant RC frame. Solid black lines represent the response using a bilinear steel model while the grey lines represent the response of the same frame when a different and more sophisticated reinforcing steel model is used. Also, the responses are found to vary when the concrete constitutive model is changed as shown in Fig. 1 (a) and (b). These observations justify the development of rational and accurate constitutive models to characterize the cyclic response of reinforcing steel and confined concrete. Key Engineering Materials Vols. 400-402 (2009) pp 301-309 online at http://www.scientific.net © (2009) Trans Tech Publications, Switzerland Online available since 2008/Oct/21 All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of the publisher: Trans Tech Publications Ltd, Switzerland, www.ttp.net. (ID: 76.105.5.249-11/11/08,20:03:41) (a) (b) Figure 1: Comparison of interstory drift demands in a moment frame building subjected to a strong ground motion – (a) Different models of reinforcing steel and Mander model for confined concrete; (b) Different models of reinforcing steel and Hoshikuma model for confined concrete Although there certainly are other important factors affecting seismic structural response such as concrete confinement, non-stationary characteristics of earthquakes, beam-column joint properties, etc., this paper, however, only focuses on thoroughly investigating and describing the main features of reinforcing steel, which need to be incorporated in a robust constitutive model of reinforcing steel. Some essential features of a cyclic model for reinforcing steel have earlier been examined by Restrepo-Posada et al. [3]. The key features of reinforcing steel are illustrated in this paper through conceptual diagrams and experimental data. The concepts described here are expected to contribute to future research on improving the modeling of reinforcing steel as well as to comprehend essential and critical properties of reinforcing steel bars observed during both monotonic and cyclic tests. Experimental Observations A series of experiments were carried out by the writers at the Structural Test Facility at the University of Southern California to investigate the cyclic and fatigue characteristics of reinforcing steel bars. To enable cyclic testing of steel reinforcing bars, the following test setup characteristics were identified: tensile and compressive loading; accommodate reinforcing bar sizes typically used for longitudinal reinforcement up to #18 (56 mm diameter); no physical alteration of the specimen over a given test length (six times the bar diameter, db or L/d =6); ability to apply constant and variable amplitude strain histories to the specimen; and the need for a re-usable gripping mechanism for transferring force to the reinforcing bar. A special-purpose grip was designed and fabricated to satisfy the above requirements. A view of the complete grip system is shown in Figure 2. As is evident from the figure, the gripping mechanism consists of four sets of tapered steel blocks with holes in orthogonal directions to accommodate post-tensioning rods. Also shown in the figure are dimensional details of a typical gripping block. 302 Advances in Concrete and Structures