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Unformatted text preview: RIGID BODY RIGID BODY EQUILIBRIUM EQUILIBRIUM Rigid Body Equilibrium 2D Rigid Body Equilibrium 2D LEARNING OBJECTIVES LEARNING OBJECTIVES Be able to recognize twoforce Be able to recognize twoforce members members Be able to apply equations of Be able to apply equations of equilibrium to solve for unknowns equilibrium to solve for unknowns PREREQUISITE KNOWLEDGE PREREQUISITE KNOWLEDGE Units of measurement Units of measurement Trigonometry concepts Trigonometry concepts Vector concepts Vector concepts Rectangular component concepts Rectangular component concepts STEPS FOR SOLVING 2D EQUILIBRIUM PROBLEMS 1. Establish a suitable xy coordinate system (if not given). 2. Draw a free body diagram (FBD) of the object under analysis. 3. Apply the three equations of equilibrium to solve for the unknowns. IMPORTANT NOTES 1. If we have more unknowns than the number of independent equations then the problem is a statically indeterminate. We cannot solve this problem using just static. 2. The order in which we apply equations may affect the simplicity of the solution. For example, if we have two unknown vertical forces and one unknown horizontal force, then solving ∑ F X = 0 first allows us to find the horizontal unknown quickly. 3. If the answer for an unknown comes out as negative number then the direction of the unknown force is opposite to that drawn on the FBD. APPLICATIONS For a given load on the platform, how can we determine the forces at joint A and the force in the link (cylinder) BC? A steel beam is used to support roof joists. How can we determine the support reactions at each end of the beam? TWOFORCE MEMBERS The solution of some equilibrium problems can be simplified if we can recognize members that are subjected to forces at only two points (e.g., at points A and B). If we apply the equations of equilibrium to such member then we can easily determine the resultant forces at points A and B that must be equal in magnitude and act in the opposite directions along the line joining points A and B. EXAMPLE Twoforce Members In the above case, members AB can be considered as twoforce members such that its weight is neglected. This fact simplifies the equilibrium analysis of some rigid bodies since the directions of the resultant forces at A and B are known (along the line joining points A and B). EQUATIONS OF EQUILIBRIUM A body is subjected to a system of forces lie in the xy plane....
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This note was uploaded on 07/26/2009 for the course CE 221 taught by Professor Buch during the Spring '08 term at Michigan State University.
 Spring '08
 Buch

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