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. It is also useful to label all forces, key dimensions, and angles. This is done by removing everything but the body and drawing in all forces acting on the body. The first step in equilibrium analysis is drawing a free body diagram. In the free body diagram, provide values for any of the know magnitudes or directions for the force vectors and provide variable names for any unknowns (either magnitudes or directions). This diagram should show all the known and unknown force vectors acting on the body. The first step in finding the equilibrium equations is to draw a free body diagram of the body being analyzed. Once we have written out the equilibrium equations, we can solve theĮquations for any unknown forces. We do this by summing up all the x components of the force vectors and setting them equal to zero in our first equation, and summing up all the y components of the force vectors and setting them equal to zero in our second equation. For two dimensional problems, we will split our one vector equation down into two scalar equations. In order to solve for any unknowns in our sum of forces equation, we actually need to turn the one vector equation into a set of scalar equations. This is the basis for equilibrium analysis for a particle. If we know that the body is not accelerating then we know that the sum of the forces acting on that body must be equal to zero. ![]() If a body is in static equilibrium, then by definition that body is not accelerating. ![]() Equilibrium Analysis for Concurrent Force Systems
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