张磊, 童根树. 工字形截面悬臂钢梁的稳定性研究[J]. 工程力学, 2003, 20(4): 176-182.
引用本文: 张磊, 童根树. 工字形截面悬臂钢梁的稳定性研究[J]. 工程力学, 2003, 20(4): 176-182.
ZHANG Lei, TONG Gen-shu. ON STABILITY OF I-SECTION STEEL CANTILEVERS[J]. Engineering Mechanics, 2003, 20(4): 176-182.
Citation: ZHANG Lei, TONG Gen-shu. ON STABILITY OF I-SECTION STEEL CANTILEVERS[J]. Engineering Mechanics, 2003, 20(4): 176-182.

工字形截面悬臂钢梁的稳定性研究

ON STABILITY OF I-SECTION STEEL CANTILEVERS

  • 摘要: 在钢梁的稳定问题上近年来存在着两种不同的理论,对这两种理论应用于悬臂梁的情况进行了比较。应用非线性力学对稳定问题的变分原理,提出了考虑钢梁内各种应力的非线性应变能的新的总势能公式。对纯弯下单轴对称工字形截面的钢梁进行了研究,将以往两种理论及本文提出的理论在这个问题上存在的问题进行了讨论。对单轴对称截面悬臂梁作用于端部集中荷载的情况,从两种不同的总势能出发,编制了有限元程序,结果与文献的试验结果进行了比较。还提出了受横向荷载的双轴对称截面梁的新的临界弯矩计算公式,与文献公式和有限元结果进行了比较,结果说明本文的公式更精确,在形式上更加简单。

     

    Abstract: This paper investigates the buckling of thin-walled cantilevers. Two different theories available in the literature are discussed, and a new one is presented which takes into account the nonlinear shear strain energy and the nonlinear transverse normal strain energy. The latter strain energy term has been ignored by previous researchers Comparison is made in this paper between the results of the present theory and those of previous experimental results for cantilevers with monosymmetrical sections. It is found that the results of the present theory is in a good agreement with experimental ones, and great discrepances are found between the theory neglecting the nonlinear transverse normal strain energy and the experimental results. Cantilevers with doubly symmetrical sections under uniform moment, uniformly transverse distributed load and concentrated load at free end are analyzed, respectively. Accurate and simple formulae for predicting the critical moments are proposed in which the effects of the load acting position are included.

     

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