均布力偶作用下细长梁力学分析

MECHANICAL ANALYSIS OF UNIFORM SLENDER BEAM ACTED BY UNIFORM COUPLE

通过铁木辛柯梁理论分析了反向均布表面剪应力-等效均匀分布力偶作用下的等截面均质细长梁挠度和应力分布规律,并与有限元法的计算结果对比发现:当边界条件中剪力不为零时,弯曲挠度和正应力分析必须考虑剪力的影响,即Euler梁理论不能满足分析的要求;若存在剪力为零边界时,可使用Euler梁分析弯曲挠度和正应力;剪应力分布和通常规律一样,仍沿高度方向呈抛物线分布,即使对于剪力为零的横截面也可能存在剪应力,这是由于表面剪应力的影响使得梁的上下表面存在剪应力,并且剪应力在横截面内正负可以发生变化.

An interested slender beam with constant section and material is established whose above and bottom surfaces are acted by reversed uniform distributed shear stresses. In engineering beam theory these loads are equivalent with uniform distributed couple. Timoshenko beam theory is used to develop the analytical results of the deflection and stress distribution of this model. And in comparison with the numerical results obtained by finite element method, some useful conclusions can be acquired： （1） when shear force is not equal to zero in boundary conditions,the shear effect need to be taken into account for the analyses of bending deflection and normal stress,i, e. Euler beam theory is not competent. （2） when boundary conditions contain zero shear force, Euler beam theory can be used in the analyses of bending deflection and normal stress. （3） The distribution of the shear stress in the cross-section is parabolic with the height coordinate as usual. When shear force is zero, the shear stress may be zero due to the effect of this surface load. The direction of the shear stress in same cross section can be altered.