WORLD FOR CIVIL

Topic 1.2 - Translational Equilibrium

The topic of statics deal with objects or structures which are in equilibrium, that is structures that are at rest or in uniform, (non-accelerated) motion. We will be normally looking at structures which are at rest. For these structures we will be interested in determining the forces (loads and support reactions) acting on the structure and forces acting within members of the structure (internal forces). To determine forces on and in structures we will proceed carefully, using a well defined methodology. This is important as most problems in statics and strength of materials are not the kind of problem in which we can easily see the answer, but rather we must relay on our problem solving techniques.

For static equilibrium problems, we will be able to apply the Conditions of Equilibrium to help us solve for the force in and on the structures. There are two general equilibrium conditions: Translational Equilibrium, and Rotational Equilibrium.

The Translational Equilibrium condition states that for an object or a structure to be in translational equilibrium (which means that the structure as a whole will not experience linear acceleration) the vector sum of all the external forces acting on the structure must be zero. Mathematically this may be expressed as:
or, in 3-dimensions:, ,
That is, forces in the x-direction must sum to zero, for translational equilibrium in the x-direction, and, the forces in the y-direction must sum to zero, for translational equilibrium in the y-direction, and, the forces in the z-direction must sum to zero, for translational equilibrium in the z-direction.

To see the application of the first condition of equilibrium and also the application of a standard problem solving technique, let's look carefully at introductory examples. Select: Example 1- Concurrent Forces.
Select: Example 2- Concurrent Forces