![]() We break the moments into three component equations We break the forces into three component equations The second set of three equilibrium equations states that the sum of the moment components about the x, y, and z axes must also be equal to zero. The body may also have moments about each of the three axes. There are three equilibrium equations for force, where the sum of the components in the x, y, and z direction must be equal to zero. If we look at a three dimensional problem we will increase the number of possible equilibrium equations to six. The one moment vector equation becomes a single moment scalar equation. The sum of each of these will be equal to zero.įor a two dimensional problem, we break our one vector force equation into two scalar component equations. This means that a rigid body in a two dimensional problem has three possible equilibrium equations that is, the sum of force components in the x and y directions, and the moments about the z axis. ![]() In a two dimensional problem, the body can only have clockwise or counter clockwise rotation (corresponding to rotations about the z axis). This means that our vector equation needs to be broken down into scalar components before we can solve the equilibrium equations. ![]() The addition of moments (as opposed to particles where we only looked at the forces) adds another set of possible equilibrium equations, allowing us to solve for more unknowns as compared to particle problems. For a rigid body in static equilibrium, that is a non-deformable body where forces are not concurrent, the sum of both the forces and the moments acting on the body must be equal to zero.
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