![]() Remember that any force vector that travels through a given point will exert no moment about that point. Any point should work, but it is usually advantageous to choose a point that will decrease the number of unknowns in the equation. To do this you will need to choose a point to take the moments about. Next you will need to come up with the the moment equations. Your first equation will be the sum of the magnitudes of the components in the \(x\) direction being equal to zero, the second equation will be the sum of the magnitudes of the components in the \(y\) direction being equal to zero, and the third (if you have a 3D problem) will be the sum of the magnitudes in the \(z\) direction being equal to zero. Once you have chosen axes, you need to break down all of the force vectors into components along the \(x\), \(y\) and \(z\) directions (see the vectors page in Appendix 1 page for more details on this process). ![]() If you choose coordinate axes that line up with some of your force vectors you will simplify later analysis. These axes do need to be perpendicular to one another, but they do not necessarily have to be horizontal or vertical. Next you will need to choose the \(x\), \(y\), and \(z\) 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.
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