集中力下的Winkler地基上双层弹塑性梁  

Elastic-plastic bi-layer beams on Winkler foundation under a concentrated load

作　　者：成林燕 谈至明[1] Cheng Linyan;Tan Zhiming(Key Laboratory of Road and Traffic Engineering of Ministry of Education,Tongji University,Shanghai 201804,China)

机构地区：[1]同济大学道路与交通工程教育部重点实验室,上海201804

出　　处：《东南大学学报（自然科学版）》2024年第4期894-901,共8页Journal of Southeast University：Natural Science Edition

基　　金：国家自然科学基金资助项目(51778479)。

摘　　要：为了完善弹性地基上弹塑性梁的理论基础,假设梁弯曲符合理想弹塑性模型,双层梁层间为竖向弹簧连接,根据受力平衡和本构关系建立Winkler地基上双层弹塑性梁的微分方程并给出通解.以无限长双层梁中心处作用集中荷载为例,研究同质同宽双层梁的加载全过程,分析梁厚、层间竖向模量等参数对梁极限承载力的影响.结果表明:当上、下层梁厚度相同或下层梁更薄时,不论层间竖向模量取多大都是上层梁先屈服;层间竖向模量趋近于无穷时,上下层梁的挠曲线相同,极限承载力趋近于双层叠合梁的极限承载力,此时结构退化成双层叠合梁;当层间竖向模量与地基反应模量之比大于5000时,上、下层梁竖向拉压变形对梁极限承载力的影响超过3%,应予以考虑,宜采用广义模量计入梁截面竖向拉压变形的影响.To improve the theoretical basis of elastic-plastic beams on elastic foundations,assuming that the beams are ideal elastic-plastic and the bi-layer beams are connected by vertical springs between the layers,the differential equations of the bi-layer elastic-plastic beams on Winkler foundation were formulated based on force equilibrium and constitutive relationships,and generalized solutions were given.Subsequently,an analysis was conducted on the bi-layer beams with an infinite length and a centralized load at its center.The entire loading process of the bi-layer beams with uniform quality and width was investigated,and the effects of parameters such as beam thickness and interlayer vertical modulus on the beam's maximum load-bearing capacity were analyzed.The results indicate that if the upper and lower beams have same thickness or the lower beam is thinner,the upper beam will give first,independent of the interlayer vertical modulus.As the interlayer vertical modulus approaches infinity,the deflection curves of the upper and lower beams become identical,and the ultimate load carrying capacity approaches that of the bi-layer stacked beams.Then,the structure transforms into bi-layer stacked beams.When the ratio of the interlayer's vertical modulus to the reactive modulus of the foundation is greater than 5000,the effect of the vertical tensile and compressive deformation of the upper and lower beams on the ultimate bearing capacity of the beams exceeds 3%and should be considered.It is appropriate to employ the generalized modulus to account for the effect of vertical tensile and compressive deformation of the beam section.

关 键 词：弹塑性地基梁 极限承载力 双层梁 WINKLER地基 解析解 

分 类 号：U416.216[交通运输工程—道路与铁道工程]