钢筋混凝土柱的“强剪弱弯”可靠性区间分析  

INTERVAL ANALYSIS FOR STRONG SHEAR WEAK BENDING RELIABILITY OF REINFORCED CONCRETE COLUMN

作　　者：易伟建[1] 李浩[1] 

机构地区：[1]湖南大学土木工程学院,湖南长沙410082

出　　处：《工程力学》2007年第9期72-79,共8页Engineering Mechanics

基　　金：国家自然科学基金项目(50678064);湖南省科技计划重点项目(06FJ3003)资助

摘　　要：在钢筋混凝土结构抗震设计中,"强剪弱弯"是保证结构延性的一个重要设计概念。引进区间变量表达认知不确定性,对钢筋混凝土框架柱进行失效概率区间分析。通过结合代表认知不确定性的区间变量与代表偶遇不确定性的随机变量完成了对不确定性的数学描述。在此基础上,根据对基本事件的包含关系建立"强剪弱弯"区间可靠性概率模型,并从证据理论出发论证了该失效概率区间的上下界实质上等价于证据理论中的信任与似然函数。对于含有区间值不确定性参数的结构承载力计算,将Berz-Taylor模型引进计算过程中,减少由于区间扩张而导致的误差。在数值模拟计算中,运用模拟退火遗传算法(SAGA)确定了"强剪弱弯"的大致设计区间。根据该设计区间构造了特殊的采样函数进行重要性采样模拟从而得到了失效概率区间。误差分析表明该方法具有较好的精度。最后通过算例分析了各设计因素对"强剪弱弯"可靠性的影响,并提出了相应的设计建议。In aseismic design of reinforced concrete structures, ＂strong shear weak bending＂ is an important design conception to guarantee the ductibility of the structure. The interval variable is introduced to express the epistemic uncertainty and the failure probability interval of reinforced concrete column is analyzed. The mathematic description of uncertainty is fulfilled by integration of the interval variable and random variable that represents the epistemic and aleatory uncertainty, respectively. The interval-valued probabilistic reliability model for ＂strong shear weak bending＂ is formulated according to the inclusion relation of the element events and the failure event. The equivalence relation between the belief-plausibility function and the upper-lower boundaries of failure probability interval is verified by the evidence theory as well. For the computation of the resistance capability involving interval-valued uncertain parameters, Berz-Taylor model is introduced to reduce the error induced by interval inflation. The simulated annealing genetic algorithm （SAGA） is applied to determine the approximate design interval of the ＂strong shear weak bending＂ in numerical simulation. A specific sampling function constructed by such design interval is adopted to gain the failure probability interval; error analysis indicates that the precision of the method is acceptable. Finally, simulated data analysis is carded out on the different design parameters affecting the reliability and corresponding design suggestions are proposed.

关 键 词：钢筋混凝土柱 可靠性 强剪弱弯 区间分析 证据理论 模拟退火遗传算法 重要性采样 

分 类 号：TU375.3[建筑科学—结构工程] TB114.3[理学—概率论与数理统计]