8 - Equilibrium of forces and plane frameworks

Abstract

This chapter discusses equilibrium of forces and plane frameworks. Equilibrium means a state of balance. When a rigid body is at rest, under the action of a number of external forces all of which are acting in one plane, there is no tendency for the body to move in a straight line in any direction, and there is no tendency for the body to rotate. Surfaces are stated in mechanics to be either smooth or rough. In practice, all surfaces have some degree of roughness. From the condition for equilibrium of three forces, their lines of action must meet in a single point. This point must be the intersection of the lines of action of the weight and the normal reaction to the wall. If a force is applied through a hinged joint the reaction is not normal to the fixed surface. When the lines of action of a number of forces lie in one plane and pass through a common point they are termed coplanar concurrent forces. If a system of forces is in equilibrium—as at a joint in a structural framework—then the force diagram must be a closed figure. This is the basis for the graphical analysis of frames.