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N_-_Rigid_Body_Equilibrium_2-D

N_-_Rigid_Body_Equilibrium_2-D - RIGID BODY EQUILIBRIUM...

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RIGID BODY RIGID BODY EQUILIBRIUM EQUILIBRIUM Rigid Body Equilibrium 2-D Rigid Body Equilibrium 2-D
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LEARNING OBJECTIVES LEARNING OBJECTIVES Be able to recognize two-force Be able to recognize two-force members members Be able to apply equations of Be able to apply equations of equilibrium to solve for unknowns equilibrium to solve for unknowns
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PRE-REQUISITE KNOWLEDGE PRE-REQUISITE KNOWLEDGE Units of measurement Units of measurement Trigonometry concepts Trigonometry concepts Vector concepts Vector concepts Rectangular component concepts Rectangular component concepts
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RIGID BODY EQUILIBRIUM 2 - D RIGID BODY EQUILIBRIUM 2 - D In 2-D, a body is in equilibrium if and only if the sum of In 2-D, a body is in equilibrium if and only if the sum of the forces in each direction is equal to zero and the sum the forces in each direction is equal to zero and the sum of the moment at any point is equal to zero. of the moment at any point is equal to zero. = = = 0 . 0 M F F Y X
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STEPS FOR SOLVING 2-D EQUILIBRIUM PROBLEMS 1. Establish a suitable x-y 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.
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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 solve for the horizontal force first using F X = 0. 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.
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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?
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TWO-FORCE 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). Applying the equations of equilibrium to such member one can determine the resultant forces at A and B. These resultants must be equal in magnitude and act in the opposite directions along the line joining points A and B.
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EXAMPLE Two-force Members In the above figures, since the directions of the resultant forces at A and B are known (along the line joining points A and B), all AB members can be considered two-force members if their weights are neglected. This simplifies the equilibrium analysis of some rigid bodies.
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