Engineering Applications

3Equilibrium of Structures

The mechanical engineering principles described in this chapter can be applied to framework structures to determine the internal forces in the members due to externally applied loads.

Frame structures are typically:

1. – Frames that are usually indeterminate and composed of straight members with hinges or rigid connections.
2. – Trusses that are usually arranged in a triangular fashion and composed of straight members pinned to the ground or to the rest of the frame at both end points (Figures 3.1 and 3.2).

When the members of a framework structure, e.g, frame or truss, are constructed in a plane, the framework structure is called a plane structure while a space structure is three dimensional. The members – considered to have a negligible weight – are assumed to carry loads only in the longitudinal direction.

A framework structure is called statically indeterminate if more links that are needed to prevent collapse are present. Additional links or supports that are not necessary for maintaining the equilibrium configuration are called redundant. Statically determinate plane structures do not have more supporting constraints than are necessary to maintain equilibrium.

3.1 Equilibrium Equations

A mechanical system (framework structure made of several members) is in equilibrium if and only if all of its subsystems (member) are in equilibrium, that is, each subsystem is stationary. For a system to remain stationary (be in equilibrium) it is necessary that ...