集中力作用下深梁弯剪耦合变形应力计算方法

THE STRESS CACULATION METHOD FOR DEEP BEAMS WITH SHEAR-BENDING COUPLING DISTORTION UNDER CONCENTRATED LOAD

深梁受力机理及影响因素之多决定了深梁计算的复杂性。由于存在纵向纤维挤压和截面的翘曲,深梁不能简单的应用材料力学细长梁的纯弯应力计算公式。虽然,深梁计算理论中已经有了各种各样的方法,包括级数解法及差分法、有限元法,但应用上,这些理论过于复杂。从弹性力学半平面体受集中荷载作用的计算理论出发,将深梁跨中及支座处的局部看作是一半平面体受集中力作用,并考虑到集中力产生的弯曲应力的影响,应用迭加原理推导出了深梁的应力计算公式,为工程设计提供简单正确且易于实现的计算方式。

For deep beams, the complexity of stress mechanism and the variety of the influence factors complicate its calculation. Due to the existence of the extrusion of longitudinal fiber and the warping of the beam section, the classical bending stress calculation formula can not be adopted simply for deep beam problems. Although that there exist various calculation methods for deep beams, such as series solution method, finite difference method and finite element method, they are too complicated to adopt, Starting from the problem of a half-plane continuum with a concentrated load in elastic mechanics, this article considers the middle of the deep beam and the local part of the support as a half-plane continuum with a concentrated load. The influence of bending stress caused by the concentrated load is also taken into consideration. The stress calculation formula for deep beams is deducted, which provides a simple and precise calculation method that can be easily achieved in engineering design.