WORLD FOR CIVIL

Topic 2.1: Frames (non-truss, rigid body structures)

We are now ready to begin looking at somewhat more involved problems in statics. As we do so there will be a number of concepts we need to keep in mind (and apply) as we approach these problems. We will begin by looking at problems involving rigid bodies. This simply means that at this point we will not be concerned with the fact that a body (or member of a structure) may actually bend or deform (change length) length under the applied loads. Bending and deformation effects will be considered in later materials. At this point in the course we will also ignore the weight of the members, which are often small compared to the loads applied to the structures.

As we begin to analyze structures there are two important considerations to keep in mind, especially as we draw our free body diagrams. The first concern will be Structure Supports. Different types of supports will result in different types of support forces (reactions) acting on the structure. For example, a roller or bearing can only be placed in compression, thus the force it will exert on a structure will be a normal or perpendicular force only, while a hinged or pinned support point may exert both a horizontal and vertical force. [Or to be more specific, a hinged or pinned support (or joint) will exert a support force acting at a particular angle, this force may then always be broke into an x and y-component. The net effect is that a hinged or pinned support may be replaced by x and y support forces.] See Diagram 1 below.

In Diagram 1 we have shown a horizontal beam supported at point A by a roller and at point C by a pinned support. Diagram 1a is the Free Body Diagram of the beam with the roller and the pinned joint now replaced by the support forces which they apply on the beam. The roller applies the vertical force A_y and the pinned support applies the forces C_x and C_y. If we knew the value of the load, we could apply statics principles to find the actual value of the support forces. We shall do this process in great detail later for a somewhat more complex example.

Diagram 2 below shows examples of supports and the types of forces and/or torque which they may exert on a structure.

The second important concept to keep in mind as we begin looking at our structure is the type of members the structure is composed of - Axial or Non-Axial Members. (The importance of this will be seen in more detail when we look at our first extended example.)

In equilibrium or statics problems, an Axial Member is a member which is only in simple tension or compression. The internal force in the member is constant and acts only along the axis of the member. A simple way to tell if a member is an axial member is by the number of Points at which forces act on a member. If forces (no matter how many) act at only Two Points on the member - it is an axial member. That is, the resultant of the forces must be two single equal forces acting in opposite directions along axis of the member. See Diagram 3.

A Non-Axial Member is a member which is not simply in tension or compression. It may have shear forces acting perpendicular to the member and/or there may be different values of tension and compression forces in different parts of the member. A member with forces acting at More Than Two Points (locations) on the member is a non-axial member. See Diagram 4.

EXAMPLES: To show the application of the concepts discussed above and of our general statics problem-solving technique, we will now look in careful detail at several statics problems.
In Example 1 we will concentrate on finding the values of the external support forces acting on the structure. Select Example 1
In Example 2, we will examine a relatively straight forward problem which points out several features concerning torques and beam loading. Select Example 2
In Example 3, we will see how both the external support reactions and also the internal forces in a member of the structure may be found. Select Example 3
In Example 4, we will look at a problem which seems to be a statically indeterminate problem. Select Example 4

Additional Examples: The following additional examples all demonstrate different aspects and features of a variety of non-truss, or frame problems.