1/4/2024 0 Comments Static equilibrium 3d![]() Next you will need to choose the x, y, z axes. In the free body diagram, provide values for any of the known magnitudes, directions, and points of application for the force vectors and provide variable names for any unknowns (either magnitudes, directions, or distances). ![]() This diagram should show all the force vectors acting on the body. \Īs with particles, the first step in finding the equilibrium equations is to draw a free body diagram of the body being analyzed. ![]() 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 an 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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