![]() ![]() Thus ΣFx = 0, but the remaining two force–equilibrium equations are satisfied because all other acceleration components are zero. For example, for a car which accelerates on a straight and level road in the x-direction, Newton’s second law tells us that the resultant force on the car equals its mass times its acceleration. ![]() ![]() 3/3 are independent conditions because any of them can be valid without the others. The reference axes may be chosen arbitrarily as a matter of convenience, the only restriction being that a right-handed coordinate system should be chosen when vector notation is used. These six equations are both necessary and sufficient conditions for complete equilibrium. The second three scalar equations express the further equilibrium requirement that there be no resultant moment acting on the body about any of the coordinate axes or about axes parallel to the coordinate axes. The first three scalar equations state that there is no resultant force acting on a body in equilibrium in any of the three coordinate directions. These two vector equations of equilibrium and their scalar components may be written as 3/1, which require that the resultant force and resultant couple on a body in equilibrium be zero. ![]() 3/1 the general conditions for the equilibrium of a body were stated in Eqs. 3.46).We now extend our principles and methods developed for two dimensional equilibrium to the case of three-dimensional equilibrium. In these cases, the equations of equilibrium should be defined according to the deformed geometry of the structure ( Art. For some structures, however, such changes in dimensions may not be negligible. It is assumed that no appreciable changes in dimensions occur because of applied loading. Furthermore, in statics, a structure is usually considered rigid or nondeformable, since the forces acting on it cause very small deformations. Moment equations state that for a body in equilibrium there is no resultant moment producing rotation about any axes parallel to any of the three coordinate axes. Resultant force producing a translation in any of the three principal directions. The three force equations state that for a body in equilibrium there is no įor three-dimensional structures, the equations of equilibrium may be written The internal forces in the truss members cut by the section must balance the external force and reaction on that part of the truss i.e., all forces acting on the free body must satisfy the three equations of equilibrium. (Since only vertical forces are involved, the equilibrium equation for horizontal forces does not apply.)Ī free-body diagram of a portion of the truss to the left of section AA is shown in Fig.ģ.7b). For instance, the moment of the forces about the right support reaction RR is 3.29.) The sum of the moments of all external forces about any point is zero. (The process of determining these reactions is presented in Art. (3.11), the sum of the reactions, or forces RL and RR, needed to support the truss, is 20 kips. Where /x and /y are the sum of the components of the forces in the direction of the perpendicular axes x and y, respectively, and M is the sum of the moments of all forces about any point in the plane of the forces.įigure 3.7a shows a truss that is in equilibrium under a 20-kip (20,000-lb) load. In a two-dimensional space, these conditions can be written: Since there is no rotation, the sum of the moments about any point must be zero. Since there is no translation, the sum of the forces acting on the body must be zero. When a body is in static equilibrium, no translation or rotation occurs in any direction (neglecting cases of constant velocity). ![]()
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