K.A.S. Susantha ， Hanbin Ge, Tsutomu Usami*
土木工程学院，名古屋大学, Chikusa-ku ，名古屋 464-8603, 日本
收讫于2000年5月31日 ; 正式校定于2000年12月19日; 被认可于2001年2月14日
一种预测受三轴压应力混凝土的完全应力-应变曲线的方法被提出，这种三轴压应力是由环形、箱形和八角形的钢管混凝土中的限制作用导致的轴向荷载加测向压力所产生的。有效的经验公式被用来确定施加于环形钢管混凝土柱内混凝土的侧向压力。FEM（有限元）分析法和混凝土-钢箍交互作用模型已被用来估计施加于箱形和八角形柱的混凝土侧向压力。接着，进行了广泛的参数研究，旨在提出一个经验公式，确定不同的筒材料和结构特性下的最大平均侧向压力。如此计算出的侧向压力通过一个著名经验公式确定出侧向受限混凝土强度。对于高峰之后的应力-应变关系的确定，使用了有效的试验结果。基于这些测试结果，和近似表达式来推算下降段的斜度和各种断面形状的筒内侧向受限混凝土在确认的混凝土强度下的应变。推算出的混凝土强度和后峰值性能在允许的界限内与测试结果吻合得非常好。所提出的模型可用于包括梁柱构件在内的纤维分析，以确定抗震结构设计中混凝土填充钢柱筒的极限状态的推算标准。 •版权所有2001 Elsevier科学技术有限公司。
Uniaxial stress–strain 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
A method is presented to predict the complete stress–strain curve of concrete subjected to triaxial compressive stresses caused by axial load plus lateral pressure e 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–steel interaction model. Subsequently, an extensive parametric study is concted 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–strain 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
agreement with the test results within the accepted limits. The proposed model is intended to be used in fiber analysis involving beam–column elements in order to establish an ultimate state prediction criterion for concrete-filled steel columns designed as earthquake resisting structures. •2001 Elsevier Science Ltd. All rights reserved.
Keywords: Concrete-filled tubes; Confinement; Concrete strength; Ductility; Stress–strain relation; Fiber analysis
Concrete-filled steel tubes (CFT) are becoming increasingly popular in recent decades e to their excellent earthquake resisting characteristics such as high ctility and improved strength. As a result, numerous experimental investigations have been carried out in recent years to examine the overall performance of CFT columns [1–11]. 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 proceres are involved. For example, CFT behavior may well be investigated through a suitable FEM analysis procere, 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 procere 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–displacement 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–strain relationship for steel, which is readily applicable in the fiber analysis, is currently available . 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 , which is applicable to square shaped columns, the strength improvement e to confinement has been neglected. Tang et al.  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.  concted model tests to determine a stress–strain 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  investigated the effect of steel tube shape and wall thickness on the ultimate strength of the composite columns. El-Tawil and Deierlein  reviewed and evaluated the concrete encased composite design provisions of the American Concrete Institute Code (ACI 318) , the AISC-LRFD Specifications  and the AISC Seismic Provisions , 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–strain law for confined concrete in relatively thick-walled CFT columns. The primary objective of the proposed stress–strain 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 strength and ctility prediction proceres of seismic resisting structures. Three types of sectional shapes such as circular, box and octagonal are considered. A concrete–steel interaction model is employed to estimate the lateral pressure on concrete. Then, the maximum lateral pressure is correlated to the strength of confined concrete through an empirical formula. A method based on the results of fiber analysis using assumed concrete models is adopted to calibrate the post-peak behavior of the proposed model. Finally, the complete axial load–average axial strain curves obtained through the fiber analysis using the newly proposed material model are compared with the test results. It should be noted that a similar type of interaction model as used in this study has been adopted by Nishiyama et al. , which has been combined with a so called peak load condition line in order to determine the maximum lateral pressure on reinforced concrete columns.
Meanwhile, previous researches [17,18] indicate that the stress–strain relationship of concrete under compressive load histories proces an envelope curve identical to the stress–strain curve obtained under monotonic loading. Therefore, in further studies, the proposed confined uniaxial stress–strain law can be extended to a cyclic stress–strain relationship of confined concrete by including a suitable unloading/reloading stress–strain rule.
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