线性荷载作用下单跨超静定深梁应力计算方法  

Stress Calculation Method for Hyperstatic Deep Beams with Single Span Subjected to Linear Load

作　　者：王正中[1] 刘计良[1,2] 韩彦宝[1] 

机构地区：[1]西北农林科技大学水工程安全与病害防治研究中心,陕西杨凌712100 [2]西北农林科技大学理学院,陕西杨凌712100

出　　处：《北京工业大学学报》2010年第12期1656-1662,共7页Journal of Beijing University of Technology

基　　金：国家'八六三'计划资助项目(2002AA62Z3191);陕西省自然科学基金资助项目(97C19)

摘　　要：为了获得线性荷载作用下工字形截面深梁各应力分量的解析计算方法,以单跨超静定深梁为例,参照以往的研究成果,通过建立合理的力学计算模型,应用弹性力学解法并考虑了弯剪耦合效应,推求出正应力、剪应力和挤压应力的解析计算公式并与材料力学解进行对比.通过对量纲为1翘曲正应力的定义和分析,获得量纲为1翘曲正应力沿梁高和跨度的分布规律,以及随跨高比和翼缘与腹板面积比的变化规律.结果表明剪力使正应力增大,对此类深梁已不能用材料力学中的细长梁纯弯曲理论计算其应力.此结果为线性荷载作用下工字形截面深梁的应力计算提供了一种解析计算方法,为结构设计计算提供了理论方法.To obtain the analytical method for calculating stress components of deep beams with I section subjected to linear loads,by taking a deep beam with a single span as an example,a reasonable mechanical model is built on the basis of previous research results.The analytical formulas for computing the normal stress,shear stress,and extrusion stress are derived by using an elastic mechanics method considering bending-shearing coupling,and the formulas are compared with those obtained by a material mechanics method.By defining and analyzing the dimensionless warping normal stress,the distribution law along the height and span of the beam,and the change law with the span-height ratio and flange-web area ratio are obtained.Results indicate that normal stress of the deep beam increases due to the effect of the shear force and cannot be calculated through the slender beam pure bending theory.The results provide an analytical calculation method for deep beams with I section subjected to linear loads.

关 键 词：单跨超静定深梁 工字形截面 线性荷载 弯应力 

分 类 号：O3[理学—力学]