CE 201- Statics Chapter 9 – Lecture 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

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

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