考虑双重剪切的弹性地基梁分析

Analysis for Elastic Foundation Beam with Double Shear Effect

考虑地基的抗剪能力和梁的剪切变形影响,建立了双参数地基Timoshenko梁的平衡方程,导出了初参数解和传递矩阵法,利用初参数解建立了有限元列式.当地基的抗剪劲度为0时,双参数地基可退化成Winkler地基,当梁的抗剪劲度无穷大时,Timoshenko梁可退化成Euler梁.利用本文有限元法分析了双参数地基倒T形Timoshenko梁在两端集中荷载作用、双参数地基变截面阶梯形Timoshenko梁在集中力、集中力偶和均布荷载作用下的受力问题.算例结果表明,本文计算结果与其他方法结果完全一致,证明所推导的初参数解、传递矩阵法和有限元刚度的正确性.

Considering the shear capacity of elastic foundation and the shear deformation effect of beam,the equilibrium equation for Timoshenko beam resting on two-parameter foundation was derived.The initial parameter solution and transfer matrix method were presented.Using the initial parameter solutions,the finite element formulation and equivalent nodal forces of distributing load were deduced.When the shear rigidity of foundation was zero,the two-parameter foundation could be degenerated into Winkler foundation.When the shear rigidity was infinite,Timoshenko beam could be degenerated into Euler beam.Using the present finite element method,we analyzed inverse T type Timoshenko beam on two-parameter foundation under the concentrated loads on ends and stepped Timoshenko beam on two-parameter foundation under concentrated load,concentrated moment and distributing load.Results have shown that the present results are identical with others,which validate initial parameter solutions,transfer matrix and finite element method.