摘要
根据以前的有限元分析结果,本文对吊车梁腹板在轮压作用下的局部承压应力,采用半无限平面上无限长梁作用法向集中力的问题的模型进行求解。这个问题早在70多年前已由前苏联学者获得了级数形式的解,并由级数解反推出闭合解,解答过程非常复杂繁冗。本文介绍了一个新的简单解法,直接利用Flamant解,建立无限长梁的平衡微分方程和梁与半无限平面的变形协调方程,进行Fourier变换,联立Fourier变换后的方程求解,然后进行Fourier逆变换,方便地求出半平面体上表面的位移和应力以及无限长梁的剪力和弯矩的积分表达式。理论解与前人结果一致,应用于吊车梁所求出的等效承压长度,与有限元分析结果接近。本文提出了修改等效承压长度的计算公式的建议。
Based on previous finite element （FE） analysis, this paper uses the model of ＂an infinite beam on a semi-infinite plane＂ to solve the local bearing stress in the web of beams supporting overhead cranes. The solutions of an infinite beam on a semi- infinite plane, subjected to a concentrated force have already been achieved by Former Soviet Union scholars in 1930s, but their solutions were very complicated and cumbersome. This paper introduces a new and simple method, in which the Fourier transform （FT） is applied to the equilibrium equations of the beam and the compatibility conditions between the beam and the semi-infinite plane to find the their FT forms. The inverse Fourier transform is then carried out to find the final analytical solutions to the problem. Expressions for the beam deflection, bending moment and shear force on the cross-section of the beam are formulated; the stresses in the semi-infinite plane are also presented. Equivalent bearing length is compared with previous results based on FE analysis and approximate model, and good correlation between both is found. Suggestions for revising the code for design of steel structures are proposed.
出处
《建筑钢结构进展》
2010年第4期24-27,共4页
Progress in Steel Building Structures
