中文摘要：

建立Winkler地基上Timoshenko深梁的初参数解和有限元列式,导出单元刚度矩阵和均布荷载、集中力、集中力偶等非结点荷载的等效公式。根据《材料力学》剪应力分布假定,提出截面剪切修正系数的梯形分块算法,计算T形截面的剪切修正系数。运用建立的有限元对弹性地基上变截面阶梯梁、等截面倒T梁的弯曲问题进行计算。分析剪切变形对两端固支弹性地基梁的地基沉降影响。研究结果表明：考虑剪切变形影响与不考虑剪切变形影响计算的悬空长度、最大挠度、最大转角、最大剪力和最大弯矩分别相差48.88%,4.61%,67.17%,43.59%和59.26%,证明剪切变形对弹性地基梁有重要影响。

英文摘要：

Initial parameter solution and finite element formulation of Timoshenko beam on elastic foundation were presented.Element stiffness and equivalent nodal forces of distributing load,concentrating load and concentrating moment were deduced.Based on the shear stress distribution assumption of material mechanics,trapezium-meshed arithmetic method for shear correction factor was proposed.Shear correction factors of T-type cross-sections were calculated.Stepped T-beam of variable cross-section and inverse T-beam were analyzed.Local hanging beam on elastic foundation was studied with and without shear deformation.The results show that the hanging length,maximum deformation,slope,shear force and moment differ at 48.88%,4.61%,67.17%,43.59%,59.26%,which verifies the importance effect of shear deformation for beam on elastic foundation.