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K.A.S. Susantha £¬ Hanbin Ge, Tsutomu Usami*
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Uniaxial stress¨Cstrain relationship of concrete confined by various shaped steel tubes
K.A.S. Susantha, Hanbin Ge, Tsutomu Usami *
Department of Civil Engineering, Nagoya University, Chikusa-ku, Nagoya 464-8603, Japan
Received 31 May 2000; received in revised form 19 December 2000; accepted 14 February 2001
Abstract
A method is presented to predict the complete stress¨Cstrain curve of concrete subjected to triaxial compressive stresses caused by axial load plus lateral pressure due to the confinement action in circular, box and octagonal shaped concrete-filled steel tubes. Available empirical formulas are adopted to
determine the lateral pressure exerted on concrete in circular concrete-filled steel columns. To evaluate the lateral pressure exerted on the concrete in box and octagonal shaped columns, FEM analysis is adopted with the help of a concrete¨Csteel interaction model. Subsequently, an extensive parametric study is conducted to propose an empirical
equation for the maximum average lateral pressure, which depends on the material and geometric properties of the columns. Lateral pressure so
calculated is correlated to confined concrete strength through a well known empirical formula. For determination of the post-peak stress¨Cstrain relation, available experimental results are used. Based on the test results,
approximated expressions to predict the slope of the descending branch and the strain at sustained concrete strength are derived for the confined concrete in columns having each type of sectional shapes. The predicted concrete strength and post-peak behavior are found to exhibit good
2001 Elsevier Science Ltd. All rights reserved.??agreement with the test results within the accepted limits. The proposed model is intended to be used in fiber analysis involving beam¨Ccolumn elements in order to establish an ultimate state prediction criterion for concrete-filled steel columns designed as earthquake resisting structures. ?
Keywords: Concrete-filled tubes; Confinement; Concrete strength; Ductility; Stress¨Cstrain relation; Fiber analysis
1. Introduction
Concrete-filled steel tubes (CFT) are becoming increasingly popular in recent decades due to their excellent earthquake resisting characteristics such as high ductility and improved strength. As a result, numerous experimental investigations have been carried out in recent years to examine the overall performance of CFT columns [1¨C11]. Although the behavior of CFT columns has been extensively examined, the concrete core confinement is not yet well understood. Many of the previous research works have been mainly focused on investigating the performance of CFT columns with various limitations. The main variables subjected to such limitations were the concrete strength, plate width-to- thickness (or radius-to-thickness) ratios and shapes of the sections. Steel strength, column slenderness ratio and rate of loading were also
additionally considered. It is understandable that examination of the effects of all the above factors on performances of CFTs in a wider range, exclusively on
experimental manner, is difficult and costly. This can be overcome by following a suitable numerical theoretical approach which is capable of handling many experimentally unmanageable situations. At present, finite element analysis (FEM) is considered as the most powerful and accurate tool to simulate the actual behavior of structures. The accurate constitutive relationships for
materials are essential for reliable results when such analysis procedures are involved. For example, CFT behavior may well be investigated through a
suitable FEM analysis procedure, provided that appropriate steel and concrete material models are available. One of the simplest yet powerful techniques for the examination of CFTs is fiber analysis. In this procedure the cross section is discretized into many small regions where a uniaxial constitutive relationship of either concrete or steel is assigned. This type of analysis can be employed to predict the load¨Cdisplacement relationships of CFT columns designed as earthquake resisting structures. The accuracy involved with the fiber analysis is found to be quite satisfactory with respect to the practical design purposes.
At present, an accurate stress¨Cstrain relationship for steel, which is readily applicable in the fiber analysis, is currently available [12]. However, in the case of concrete, only a few models that are suited for such analysis can be found [3,8,9]. Among them, in Tomii and Sakino¡¯s model [3], which is applicable to square shaped columns, the strength improvement due to confinement has been neglected. Tang et al. [8] developed a model for circular tubes by taking into account the effect of geometry and material properties on strength enhancement as well as the post-peak behavior. Watanabe et al. [9]
conducted model tests to determine a stress¨Cstrain relationship for confined concrete and subsequently proposed a method to analyze the ultimate behavior of concrete-filled box columns considering local buckling of component plates and initial imperfections. Among the other recent
investigations, the work done by Schneider [10] investigated the effect of steel tube shape and wall thickness on the ultimate strength of the composite columns. El-Tawil and Deierlein [11] reviewed and evaluated the concrete
encased composite design provisions of the American Concrete Institute Code (ACI 318) [13], the AISC-LRFD Specifications [14] and the AISC Seismic Provisions [15], based on fiber section analyses considering the inelastic behavior of steel and concrete.
In this study, an analytical approach based on the existing experimental results is attempted to determine a complete uniaxial stress¨Cstrain law for confined concrete in relatively thick-walled CFT columns. The primary objective of the proposed stress¨Cstrain model is its application in fiber analysis to investigate the inelastic behavior of CFT columns in compression or combined
compression and bending. Such analyses are useful in establishing rational