Technical Mathematics, Sixth Edition

3.6. Statics Applications

The following section should be of great interest to students who expect to be involved in structures of any kind, buildings, bridges, trusses, and so forth.

3.6.1. Moments

The moment of a force about some point a (written M_a) is the product of the force F and the perpendicular distance d from the force to the point. The moment of a force is also referred to as torque. In Fig. 3-9 it is

NOTE

Figure 3.9. FIGURE 3-9

Example 36: The moment of the force in Fig. 3-10 about point a is Ma = 275 lb(1.45 ft) = 399 ft–lb

Figure 3.10. Moment of a force.

3.6.2. Equations of Equilibrium

If the wagon, Fig. 3-11a, is pushed from the left, it will, of course, move to the right. If it does not move, it means there must be an equal force pushing it to the left, Fig. 3-11b. In other words if the wagon does not move, the sum of the horizontal forces acting on the wagon must be zero. When a body is at rest (or moving with a constant velocity) we say that it is in equilibrium.

What we said about horizontal forces also applies to vertical forces, and to moments tending to rotate the body. These are formally stated as the equations of equilibrium. For a body in equilibrium, ...