圆弧拱平面外弹性弯扭屈曲临界荷载分析.pdfVIP

第 29 卷第 3 期 Vol.29 No.3 工 程 力 学 2012 年 3 月 Mar. 2012 ENGINEERING MECHANICS 83 文章编号：1000-4750(2012)03-0083-07 圆弧拱平面外弹性弯扭屈曲临界荷载分析 窦 超，郭彦林 (清华大学土木工程系，北京 100084) 摘 要：该文从采用经典平衡理论推导了双轴对称纯压、纯弯圆弧拱的平面外弯扭屈曲方程，给出了两铰圆弧拱 的平面外屈曲荷载解析解，其中考虑了截面翘曲刚度、荷载作用位置等参数的影响。推导中进行适当的近似，使 过程更加简化和直观。对 3 种不同形式均布径向荷载的情况进行了讨论，并与有限元结果进行了对比。研究表明， 3 种均布径向荷载中以静水压力作用下屈曲荷载最高，该文提出的双轴对称截面纯压、纯弯两铰圆弧拱的平面外 屈曲荷载解析解与有限元数值解吻合良好。 关键词：弯扭屈曲；平衡理论；屈曲方程；翘曲；纯压拱；纯弯拱 中图分类号：TU32 文献标志码：A STUDY ON FLEXURAL-TORSIONAL BUCKLING LOAD OF CIRCULAR ARCHES DOU Chao , GUO Yan-lin (Department of Civil Engineering, Tsinghua University, Beijing 100084, China) Abstract: In this paper the stability equations are obtained according to the classical equilibrium theory, and the out-of-plane elastic flexural-torsional buckling loads of a two-hinged circular arch under uniform compression and uniform bending are studied accordingly. The parameters such as the warping stiffness and loading position are involved in the derivation and analysis. In the derivation proper approximations are adopted and make the process more explicit and compact. Buckling loads for a pure compressive arch under three different forms of uniform radial loads are discussed; meanwhile theoretical solutions are compared with FEA results. It indicates that the buckling load of a pure compressive arch under hydrostatic load is the highest of the three, and the solutions for two-hinged circular arches developed in this paper are close to the numerical ones of FEA. Key words: flexural-torsional buckling; equilibrium theory; stability equation; warping;