One of the greatest sources of confusion in this course involves the use of the word “moment”. The word is used in two different ways.
Applied Moments
When the line of action of an external force is offset some perpendicular distance from a point on a structure, the force causes a moment about that point. The magnitude of the moment equals the force times the perpendicular distance. Because the moment is applied to the beam by a force external to the beam, it is described as an external applied moment.
Throughout these notes this will be referred to as an applied moment. An applied moment will cause a structure to twist if the axis about which the applied moment acts is parallel to the structure. This type of applied moment is called a torque. An applied moment will cause a structure to bend or curve if the axis about which the applied moment acts is perpendicular to the structure.
So, an applied moment is due to an external force is at some perpendicular distance from a point on a structure. An applied moment can cause either twisting (when it is called a torque), or it can cause bending.
Bending Moments
When an applied moment causes a structure to bend or curve, the amount of curving varies at different points in the structure. For example, a person sitting on a plank causes high curvature in the center, but no curvature or bending at the ends.
To describe the amount of bending that is occurring within the plank, we determine the internal bending moment in the plank. The internal bending moment describes a situation inside the structure. In practice we drop the word “internal”, and just call this the bending moment. Much more about bending moments later.
- Required Reading (40 minutes):
- Hibbeler, R.C., Statics and mechanics of Materials, Section 4.2 and 4.3.