CE 201- Statics

1. CE 201- Statics Chapter 9 – Lecture 2

2. COMPOSITE BODIES • Composite body consists of simpler bodies connected together (triangle, rectangle, ….) • Composite body can be sectioned into its composite parts • Center of gravity of the composite body can be determined without integration, if weight and center of gravity of each part is known • Each part can be treated a discrete particle and use: x = ( x W) /  WR y = ( y W) /  WR z = ( z W) /  WR

3. COMPOSITE BODIES • When the body has a constant density or specific weight, the center of gravity coincides with the centroid of the body • The centroid of line, area, and volume can be found by replacing W with L, A, and V (respectively) in the equations above: x = ( x L) /  L y = ( y L) /  L z = ( z L) /  L x = ( x A) /  A y = ( y A) /  A z = ( z A) /  A x = ( x V) /  V y = ( y V) /  V z = ( z V) /  V

4. Procedure for Analysis • Divide composite body into simpler shapes • If the body has a hole or geometric region having no weight, then consider the body without the hole and the hole as an additional composite part having negative weight or size. • Determine x, y, and z of the center of gravity or centroid of each part • Determine x, y, and z of the whole body