惯性矩转轴公式的几何法研究

Research on Transformation Equations of Moments and Products of inertia with Geometry

截面的惯性矩(积)是重要的截面参数,是进行工程构件设计的依据。惯性矩(积)转轴公式常用于计算当坐标轴发生旋转时截面的惯性矩(积)、计算主惯性矩,是材料力学的重要知识点。但转轴公式并没有指出最大主惯性矩和最小主惯性矩对应的轴的位置。定义了广义惯性积,重新研究了转轴公式,得出更为直观的转轴公式的惯性矩圆表示方法,该方法简单、概念明确,不失为转轴公式的重要补充。

The moments and products of inertia of a plane area are important parameters for section and the section designing basis.The transformation equations of moments and product are used to determine the new values of the moments and products of inertia and the Principal axis of inertia when the axises are rotated,but the maximum and minimum principal axis of inertia are not definite.This article defines the generalized products of inertia and derives a new type of transformation equations,and it appears that Us...