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) / Ly = ( y L) / Lz = ( z L) / L

x = ( x A) / Ay = ( y A) / Az = ( z A) / A

x = ( x V) / Vy = ( y V) / Vz = ( 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