基于多薄壁圆管套装假设的圆轴扭转切应力-变形量分析

Shear stress-deformation analysis of torsional circular shaft based on the assumption of multiple thin-walled circular tubes set

针对材料力学、工程力学等教材中圆轴扭转章节的切应力-变形量公式,提出了一种基于多个薄壁圆管套装假设的新推理方法,导出了厚壁圆管及实心圆轴的切应力公式、单位长度扭转角公式等.提出用薄壁圆管扭转实验测量切应变和切应力参数,并验证两者之间的正比例关系即剪切胡克定律的正确性,从而测量材料切变模量G.提出用受扭薄壁圆管实例辅助证明切应力互等定理.研究结果有助于提高教学质量.

In the report,aimed at the shear stress-deformation formulas in the circular shaft torsion chapter of mechanics textbook,a new derivation method based on the hypothesis of multiple thin-walled circular tubes was proposed,and the strength and stiffness formulas of thick-walled circular tubes and solid circular shafts were derived.The torsion experiment of thin-walled circular tubes was performed to determine the shear strain and shear stress parameters,the correctness of the proportional relationship between them,the shear Hooke's law,were verified.So,the shear modulus G was obtained,the example of twisted thin-walled circular tube was used to prove the reciprocal theorem of shear stress.Our data are helpful for improving the teaching effects.