CFRP加固负载混凝土梁抗弯承载力及可靠度研究
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摘要
碳纤维复合材料(CFRP)由于具有强度高、模量高、耐腐蚀和施工简便等突出优点,已经成为混凝土结构加固的主要材料,其加固计算理论研究和设计方法完善一直是人们关注的热点问题。本文结合钢筋混凝土梁在不同受荷状态下加固前以及碳纤维布加固后的受弯承载力试验,寻找滞后应变随受荷状态的变化规律,以及对抗弯加固效果的影响,建立更加符合工程实际的滞后应变简化公式,并从可靠度角度出发,建立以界限配布率控制材料用量的碳纤维布加固混凝土梁受弯承载力的实用设计公式,达到延性设计和可靠设计的目的,主要研究成果如下：
(1)滞后应变值与受荷状态有关,卸载前承担的荷载越大,卸载后滞后应变值越高。根据钢筋混凝土梁在不同荷载历史条件下卸载至不同程度时的混凝土和钢筋的应变变化规律,得到卸载时截面应变仍服从平截面假定,受压区混凝土和受拉钢筋的应力-应变关系服从卸载定理,裂缝在卸载的过程中逐渐闭合,可以认为卸载过程中中和轴位置不变。
(2)建立滞后应变简化公式。首先根据卸载前钢筋混凝土梁受压区混凝土和受拉钢筋所处的4种不同弹塑性状态,分别建立了相应的4个卸载后的碳纤维片材滞后应变理论公式。然后对此4个理论公式进行影响因素分析,得出配筋率和相对卸载量是影响滞后应变的重要因素,据此经过一系列回归并结合试验结果得到考虑受荷状态的滞后应变简化公式。
(3)钢筋的屈服是加固梁发生延性破坏的有利条件。从不同损伤程度的钢筋混凝土梁抗弯加固试验结果中得出：当碳纤维布与混凝土粘贴牢固时,只有在钢筋屈服之后,应力才会发生重分布,应力的增长将由碳纤维布来承担,说明只有利用钢筋的屈服性质,才能充分发挥碳纤维布的作用。因此,加固设计需保证加固梁破坏之前钢筋已经屈服。
(4)采用满足延性要求的界限配布率控制碳纤维布用量。由于滞后应变的存在,为充分发挥材料作用以及避免脆性破坏的发生,与传统的界限破坏条件不同,结合试验重新确定界限破坏条件,据此确定最小配布率和最大配布率,达到经济合理的设计目的。
(5)确定滞后应变为随机变量的碳纤维布加固混凝土梁抗弯承载力的统计参数和概率分布模型。首先在碳纤维布力学性能指标测试试验的基础上,采用数理统计方法得到了碳纤维布拉伸强和弹性模量的统计参数和概率分布模型,然后利用Matlab优化统计工具箱结合Monte-Carlo法对工程常用材料强度、截面尺寸的碳纤维布加固梁按本文建议公式进行抗弯承载力模拟,在考虑滞后应变为随机变量的情况下,对发生规范所允许的受压破坏时的抗力进行了统计分析,得到抗力比值的统计参数和概率分布模型。
(6)基于可靠度的碳纤维布加固混凝土梁抗弯承载力界限配布率优化。对于常见的三种荷载组合工况,采用JC法分别计算了不同荷载效应比值情况下按照本文建议公式进行碳纤维布加固混凝土梁抗弯承载力设计的可靠指标,得出受压破坏的可靠指标平均值满足二级结构延性破坏的目标可靠指标要求,并从满足目标可靠指标的角度优化界限配布率,验证了本文提出的配布率界限值具有较好的可靠指标一致性。
CFRP have become the major materials for strengthened concrete structures because of their advantage of high strength, high elastic modulus, excellent anticorrosion and simple construction. Based on flexural capacity experiment of reinforced concrete beams under different loading history before and after strengthened by carbon fiber reinforced plastic (CFRP), the variation of hysteretic strain with loading history and the influence on the reinforcement effect are found, a revised formula for hysteretic strain is proposed to accord with engineering practice. From the view of reliability, the practicable formula with material requirement controlled by limit ratio of CFRP is presented for flexural capacity of strengthened concrete beams satisfying ductile and reliable design. The following are the main research results:
(1) The hysteretic strain is relevant to loading history, which is higher after unloading with the higher load before unloading. According to the variation of strain of concrete and of steel bars after unloading to varying level under different loading history, cross-sectional strain is still subject to the plane section assumption, the stress-strain relationship of compressed concrete and of tensile steel bars obey the offloading theorem, and then location of the neutral axis remains the same because of cracks closing gradually during unloading.
(2) A revised formula for hysteretic strain is presented. In accordance with four elastoplastic states of compressed concrete and of tensile steel bars, the corresponding theoretical formulas are established especially. The reinforcement ratio and the relative amount of unloading are the important influential factors, so the simplified formula for hysteretic strain associated with above-mentioned influential factors and the experiment results are obtained after a series of regression analysis, which considers the load history.
(3) The steel yielding is advantageous to the ductile failure for CFRP-strengthened beams. On the basis of the experimental results under different damage degree, the redistribution of stress will occur only after the steel yielding with firm interface bond, and the growing stress is born by CFRP. That is CFRP would play a greater role after steel yielding. Therefore, the steel must be yielded before ductile failure in the design.
(4) Material requirement is controlled by limit ratio of CFRP satisfying ductility. Because of hysteretic strain, the critical failure condition, different from ordinary critical failure basis, are reconsidered upon experiments in order to achieve economical design, for the sake of functioning adequately and avoiding brittle failure.
(5) Statistical parameters and the probability distribution model with hysteretic strain as a random variable for flexural capacity of CFRP-strengthened concrete beams are obtained. Based on the mechanical property tests of CFRP, statistical characteristics of tensile strength and elastic modulus are acquired by mathematical statistics. Then, the flexural capacity suggested in this paper are simulated for engineering material strength, and cross-sectional dimensions commonly used, using optimized statistical tool-box in Matlab and Monte-Carlo method. So in the case of hysteretic strain as a random variable, statistical characteristics of resistance ratio for compression failure are given.
(6) The limit ratios of CFRP are optimized on the basis of reliability. Reliability indexes of flexural capacity suggested in this paper meet the object reliability index for ductile failure of secondary structures, using JC method under different load effect ratios for usual three load combinations respectively. The limit ratios of CFRP are optimized from the point of reliability, which achieve better consistency of reliability index.
(1)滞后应变值与受荷状态有关,卸载前承担的荷载越大,卸载后滞后应变值越高。根据钢筋混凝土梁在不同荷载历史条件下卸载至不同程度时的混凝土和钢筋的应变变化规律,得到卸载时截面应变仍服从平截面假定,受压区混凝土和受拉钢筋的应力-应变关系服从卸载定理,裂缝在卸载的过程中逐渐闭合,可以认为卸载过程中中和轴位置不变。
(2)建立滞后应变简化公式。首先根据卸载前钢筋混凝土梁受压区混凝土和受拉钢筋所处的4种不同弹塑性状态,分别建立了相应的4个卸载后的碳纤维片材滞后应变理论公式。然后对此4个理论公式进行影响因素分析,得出配筋率和相对卸载量是影响滞后应变的重要因素,据此经过一系列回归并结合试验结果得到考虑受荷状态的滞后应变简化公式。
(3)钢筋的屈服是加固梁发生延性破坏的有利条件。从不同损伤程度的钢筋混凝土梁抗弯加固试验结果中得出：当碳纤维布与混凝土粘贴牢固时,只有在钢筋屈服之后,应力才会发生重分布,应力的增长将由碳纤维布来承担,说明只有利用钢筋的屈服性质,才能充分发挥碳纤维布的作用。因此,加固设计需保证加固梁破坏之前钢筋已经屈服。
(4)采用满足延性要求的界限配布率控制碳纤维布用量。由于滞后应变的存在,为充分发挥材料作用以及避免脆性破坏的发生,与传统的界限破坏条件不同,结合试验重新确定界限破坏条件,据此确定最小配布率和最大配布率,达到经济合理的设计目的。
(5)确定滞后应变为随机变量的碳纤维布加固混凝土梁抗弯承载力的统计参数和概率分布模型。首先在碳纤维布力学性能指标测试试验的基础上,采用数理统计方法得到了碳纤维布拉伸强和弹性模量的统计参数和概率分布模型,然后利用Matlab优化统计工具箱结合Monte-Carlo法对工程常用材料强度、截面尺寸的碳纤维布加固梁按本文建议公式进行抗弯承载力模拟,在考虑滞后应变为随机变量的情况下,对发生规范所允许的受压破坏时的抗力进行了统计分析,得到抗力比值的统计参数和概率分布模型。
(6)基于可靠度的碳纤维布加固混凝土梁抗弯承载力界限配布率优化。对于常见的三种荷载组合工况,采用JC法分别计算了不同荷载效应比值情况下按照本文建议公式进行碳纤维布加固混凝土梁抗弯承载力设计的可靠指标,得出受压破坏的可靠指标平均值满足二级结构延性破坏的目标可靠指标要求,并从满足目标可靠指标的角度优化界限配布率,验证了本文提出的配布率界限值具有较好的可靠指标一致性。
CFRP have become the major materials for strengthened concrete structures because of their advantage of high strength, high elastic modulus, excellent anticorrosion and simple construction. Based on flexural capacity experiment of reinforced concrete beams under different loading history before and after strengthened by carbon fiber reinforced plastic (CFRP), the variation of hysteretic strain with loading history and the influence on the reinforcement effect are found, a revised formula for hysteretic strain is proposed to accord with engineering practice. From the view of reliability, the practicable formula with material requirement controlled by limit ratio of CFRP is presented for flexural capacity of strengthened concrete beams satisfying ductile and reliable design. The following are the main research results:
(1) The hysteretic strain is relevant to loading history, which is higher after unloading with the higher load before unloading. According to the variation of strain of concrete and of steel bars after unloading to varying level under different loading history, cross-sectional strain is still subject to the plane section assumption, the stress-strain relationship of compressed concrete and of tensile steel bars obey the offloading theorem, and then location of the neutral axis remains the same because of cracks closing gradually during unloading.
(2) A revised formula for hysteretic strain is presented. In accordance with four elastoplastic states of compressed concrete and of tensile steel bars, the corresponding theoretical formulas are established especially. The reinforcement ratio and the relative amount of unloading are the important influential factors, so the simplified formula for hysteretic strain associated with above-mentioned influential factors and the experiment results are obtained after a series of regression analysis, which considers the load history.
(3) The steel yielding is advantageous to the ductile failure for CFRP-strengthened beams. On the basis of the experimental results under different damage degree, the redistribution of stress will occur only after the steel yielding with firm interface bond, and the growing stress is born by CFRP. That is CFRP would play a greater role after steel yielding. Therefore, the steel must be yielded before ductile failure in the design.
(4) Material requirement is controlled by limit ratio of CFRP satisfying ductility. Because of hysteretic strain, the critical failure condition, different from ordinary critical failure basis, are reconsidered upon experiments in order to achieve economical design, for the sake of functioning adequately and avoiding brittle failure.
(5) Statistical parameters and the probability distribution model with hysteretic strain as a random variable for flexural capacity of CFRP-strengthened concrete beams are obtained. Based on the mechanical property tests of CFRP, statistical characteristics of tensile strength and elastic modulus are acquired by mathematical statistics. Then, the flexural capacity suggested in this paper are simulated for engineering material strength, and cross-sectional dimensions commonly used, using optimized statistical tool-box in Matlab and Monte-Carlo method. So in the case of hysteretic strain as a random variable, statistical characteristics of resistance ratio for compression failure are given.
(6) The limit ratios of CFRP are optimized on the basis of reliability. Reliability indexes of flexural capacity suggested in this paper meet the object reliability index for ductile failure of secondary structures, using JC method under different load effect ratios for usual three load combinations respectively. The limit ratios of CFRP are optimized from the point of reliability, which achieve better consistency of reliability index.
引文
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