考虑剪切变形效应的受竖向集中荷载作用的单跨斜梁研究  

Mechanical analysis of single-span skewed beam with considering shear deformation effect under vertical concentrated load

作　　者：夏桂云[1,2] 郭德群[1,3] 谭俊[1] 

机构地区：[1]长沙理工大学土木与建筑学院,长沙410004 [2]中南大学土木工程学院,长沙410075 [3]茂名市交通设计院,茂名525000

出　　处：《应用力学学报》2016年第5期852-858,938,共7页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(51278072);湖南省科技计划项目(2012FJ4125);长沙理工大学土木工程重点学科创新项目(16ZDXK09)

摘　　要：为解决中、小跨径斜梁结构分析中采用初等梁理论而不考虑剪切变形的影响而导致计算挠度偏小的问题,基于Timoshenko深梁理论的力法及图乘法,推导了考虑剪切变形影响的单跨斜深梁在竖向集中荷载作用下的内力和变形计算公式,并用有限元软件对所推导的计算公式进行了验证。结果表明:本文理论解析结果与有限元结果吻合较好,证明了本文理论公式的正确性。通过对标准A型单跨斜箱梁桥的跨径比、斜交角、平面形状等参数进行分析得到跨径越小、斜交角越大,剪切效应对斜梁挠度的影响越大;剪切效应对平行四边形斜梁的挠度影响最大,对等腰梯形斜梁的挠度影响最小;中、小跨径斜梁桥挠度计算时应采用考虑剪切变形影响的Timoshenko深梁理论,否则会低估挠度结果;所推导的斜深梁桥内力与变形计算公式能方便设计人员的使用,有助于推动斜梁桥计算理论的深化和拓展,丰富了斜梁桥的计算方法。Euler beam theory is often used to analyze short span and middle span skewed beams without considering shear deformation effect, which leads to underestimate deflections. To overcome this shortcoming, based on the force method and graphic multiplication method of Timoshenko deep beam theory, a calculating method with considering shearing deformation effect is established for single span skewed beam. The internal forces and deformation formulae of single span skewed deep beam under vertical concentrated load are deduced. These derived formulas are verified by finite element method. The results show that results of theoretical analyses are consistent with those of finite element method, which approves the correctness of these theoretical formulas. Through the parameter analyses of span, skew angle and planar configuration of standard A-type single-span box girder, it concludes that, the smaller the span, the greater the skew angle, the greater the influence of shear deformation effects on the deflection of skewed beam bridges. Shear deformation effect has the biggest influence on the deflection for parallelogram skewed beam, and has the smallest influence for isosceles trapezoid skewed beam. The deflection calculations for skewed bridges with medium and small spans should adopt Timoshenko deep beam theory with considering shear deformation affect, otherwise it would underestimate the deflection results. The calculating formulas derived in this paper are convenient to design, and enrich the calculating methods for skewed girder bridge.

关 键 词：斜梁 Timoshenko深梁理论 剪切变形 力法 解析解 挠度 

分 类 号：U445.47[建筑科学—桥梁与隧道工程]