Lecture 33

Lecture 33:

Internal Forces

Internal forces are generated within loaded structural elements. These forces are generated within every type of element; if they were not developed, the structure would fail. These are known as Shear, Moment, and Normal Forces . The normal force is found in columns and beams with an axial load. Shear and moment are found in beams and frames. Most of the elements that will be analyzed in this course will be beams, including joists, purlins, girders, decking, planking, etc.

Shear and moment are essential for developing an understanding of how structures behave. Considerable time will be spent on this subject because of its importance now and in the future. The capacity to draw shear and moment diagrams for any designed structure will add to the repertoire of the designer. All of the great Modern architects had this basic skill.

In order to quantify the internal forces of any part of a beam a FBD must be drawn for only that specific part of the beam. If the entire structure is in equilibrium, this part, when isolated from the remainder as a Free Body, must also be in equilibrium. The action of the external forces on that part must be resisted by the internal forces acting at the cut section(s).

Internal Forces

External Moment = Internal Moment
or
External Moment - Internal Moment = 0

Internal resisting forces and moments caused by the loading on a beam usually change along the length of the beam. Let us again examine the internal forces of a weightless beam by means of a FBD:

A beam carrying a load is clearly in equilibrium.

simply supported beam supporting a 600# load at midspan

simply supported beam supporting a 600# load at midspan

If we cut the beam and apply the forces on the cut section which existed internally before the cut, the beam will still be in equilibrium. We can find these forces by applying equations of equilibrium on the ends of the cut sections (as in any FBDs).

The solutions to the equations of equilibrium are the internal normal (N), shear (V) and moment (M) forces at that section. This is then applied to each and every point along the beam.