中国石油大学工程力学课件tm4a1mat45.ppt

* Kylinsoft MOM-A-* Homework P230-A.1(a)*、 P230-A.6(a)*、 P230-A.7 * Kylinsoft MOM-A-* 制作群 素材收集 海盗船长 多媒体制作 海盗船长 总编辑 海盗船长 审核 海盗船长 总策划 海盗船长 赞助 海盗船长 Kylinsoft * Kylinsoft MOM-A-* 附录A 平面图形的几何性质Appendix A Properties of Plane Areas(Centroids and Moments of Inertia) 海盗船长 * Kylinsoft MOM-A-* 1. Centroids (形心) of Plane Areas (1) Area (面积) y z O y z yC zC C dA (2) First moments (静矩) of the area with respect to the y and z axes * Kylinsoft MOM-A-* If an area is symmetric about an axis, the centroid must lie on that axis because the first moment about an axis of symmetry equals zero. C z y Area with one axis of symmetry Area with two axes of symmetry C z y * Kylinsoft MOM-A-* (3) Centroids of Composite Areas Example Problem A-1 Determine the distances to the centroids of the L-shaped area (or angle section) shown in Fig. The area and first moments of composite area: The coordinates of the centroid of the composite area: zC1 yC1 yC2 zC2 y z 80 10 O 120 10 C(yC,zC) I II Solution * Kylinsoft MOM-A-* rectangleⅠ：A1=1200mm2 yC1=5mm， zC1=60mm rectangle II ：A2=700mm2 yC2=45mm， zC1=5mm The area can be divided into two rectangles of areas Al and, A2 with centroids C1 and C2, respectively: yC2 zC2 zC1 yC1 y z 80 10 O 120 10 C(y,z) I II the coordinates yC and zC of the centroid C of the composite area: * Kylinsoft MOM-A-* 2. Moments of Inertia (惯性矩) and Products of Inertia (惯性积) of Plane Areas The polar moment of inertia (极惯性矩) of a plane area with respect to an axis through perpendicular to the plane is defined by the integral y z O y z r dA The moments of inertia (惯性矩) of a plane area with respect to the y and z axes, respectively, are defined by the integrals * Kylinsoft MOM-A-* the product of inertia (惯性积) of a plane area with respect to the y and z axes is defined by the integral the product of inertia of an area is zero with respect to any pair of axis in which at least one axis is an axis of symmetry of the area. y z y