均布荷载作用下悬臂深梁应力计算方法

Stress calculation method for a cantilever deep beam subjected to a uniform load

通过建立力学模型,应用弹性力学中的半逆解法对均布荷载作用下工字形截面悬臂深梁的应力进行计算。考虑了弯剪耦合效应和剪力对弯应力的影响推导出工字形截面悬臂深梁的各应力分量的解析计算公式。结果表明:剪力使正应力增大,当跨高比减小或翼缘与腹板面积比增大时,剪力对弯应力的影响随之增大,并且这种影响沿跨长随剪力与弯矩之比同步变化,沿梁高与剪应力分布规律一致;悬臂深梁的剪力对弯应力的影响小于简支深梁的剪力对弯应力的影响,均布荷载作用下悬臂深梁的剪力对弯应力的影响小于线性荷载作用下悬臂深梁的剪力对弯应力的影响。该结果可为悬臂深梁的设计提供有理论基础的计算方法。

The stresses in an I section cantilever deep beam with uniform loads are predicted using a mechanical model with a semi-inverse method from elastic mechanics for the solution. Analytical formulas for the stress components were derived by considering the shea^bending coupling and the effect of the shear force on the normal stress. The results show that the normal stress is increased by the shear force with the effect increasing as the span-height ratio decreases and as the flangerweb area ratio increases. The effect changes in synchronization with the ratio of the shear force and bending moment along the span. The effect distribution along the height is the same as the shear stress distribution. The effect of the shear force on the normal stress in the cantilever deep beam is less than that of a simply-supported deep beam subjected to a uniform load. The effect of the shear force on the normal stress in the cantilever deep beam is less for a uniform load than that for a linear load. The results provide an analysis with a theoretical basis for the design of cantilever deep beams.