![]() Two-dimensional rigid bodies have only one degree of rotational freedom, so they can be solved using just one moment equilibrium equation, but to solve three-dimensional rigid bodies, which have six degrees of freedom, all three moment equations and all three force equations are required. ![]() To analyze rigid bodies, which can rotate as well as translate, the moment equations are needed to address the additional degrees of freedom. These two vector equations can be written as six scalar equations of equilibrium (E-of-E). We saw in Chapter 3 that particle equilibrium problems can be solved using the force equilibrium equation alone, because particles have, at most, three degrees of freedom and are not subject to any rotation. These models enable us to write the appropriate equations of equilibrium, which can then be analyzed. EQUATIONS OF EQUILIBRIUM (Section 5.6) As stated earlier, when a body is in equilibrium, the net force and the net moment equal zero, i.e., F 0 and MO 0. ![]() Normally this will be a system with the origin at the particle and a horizontal x axis and a vertical. The particle will be the object or point where the lines of action of all the forces intersect. In many cases we do not need all six equations. In this video, we go from 2D particles to looking at 3D force systems and how to solve for them when they are in equilibrium. 5.6 EQUATIONS OF EQUILIBRIUM As stated earlier, when a body is in equilibrium, the net force and the net moment equal zero, i.e., F 0 and M O 0. The general procedure for solving equilibrium of a particle problems in two dimensions is to: Identify the particle. Working with these scalar equations is often easier than using their vector equivalents, particularly in two-dimensional problems.
0 Comments
Leave a Reply. |