4 Equilibrium of Rigid Bodies

Eighth Edition

CHAPTER

4

VECTOR MECHANICS FOR
ENGINEERS: STATICS
Ferdinand P. Beer
E. Russell Johnston, Jr.

Equilibrium of Rigid Bodies

Lecture Notes:
J. Walt Oler
Texas Tech University

© 2007 The McGraw-Hill Companies, Inc. All rights

Eight h Vector Mechanics for Engineers: Statics
Contents
Introduction
Free-Body Diagram
Reactions at Supports and Connections for a Two-Dimensional
StructurReactions at Supports and
Connections for a Two-Dimensional
Structure

Equilibrium of a Rigid Body in Three
Dimensions
Reactions at Supports and Connections for a
Three-Dimensional Structure
Sample Problem 4.8

Equilibrium of a Rigid Body in Two
Dimensions
Statically Indeterminate Reactions
Sample Problem 4.1
Sample Problem 4.3
Sample Problem 4.4
Equilibrium of a Two-Force Body
Equilibrium of a Three-Force Body
Sample Problem 4.6
© 2007 The McGraw-Hill Companies, Inc. All rights

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Eight h Vector Mechanics for Engineers: Statics
Introduction
• For a rigid body in static equilibrium, the external forces and moments are balanced and will impart no translational or rotational motion to the body.
• The necessary and sufficient condition for the static equilibrium of a body are that the resultant force and couple from all external forces form a system equivalent to zero,

• Resolving each force and moment into its rectangular components leads to 6 scalar equations which also express the conditions for static equilibrium, © 2007 The McGraw-Hill Companies, Inc. All rights

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Eight h Vector Mechanics for Engineers: Statics
Free-Body Diagram
First step in the static equilibrium analysis of a rigid body is identification of all forces acting on the body with a free-body diagram.
• Select the extent of the free-body and detach it from the ground and all other bodies.
• Indicate point of application, magnitude, and direction of external forces, including the rigid body weight.
• Indicate point of application and assumed direction of unknown applied forces. These
usually