equilibrium%2010%20class[1]

equilibrium%2010%20class[1] - Topics Equilibrium Eqs in 3-D...

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Topics Equilibrium Eqs in 3-D and 2-D Reaction Forces Free Body Diagrams Book Sections 3/1-3/4
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Equilibrium A system of forces and couples acting on a body is said to be in equilibrium if the resultant of the force system is zero. For a general system of forces and couples equilibrium implies which is equivalent to six scalar equations where x y z e x e y e z 0 0 i i i j = = = × + = R F M r F C 0 0 0 ix iy iz F F F = = = ( 29 ( 29 ( 29 0 0 0 i i jx x i i jy y i i jz z C C C × + = × + = × + = r F r F r F ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 i i i i x x i i i i y y i i i i z z × = × × × = × × × = × × r F r F e r F r F e r F r F e
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2-D Equilibrium For 2-D force-couple systems the only non-zero equilibrium equations are the three scalar equations x y Note that the point we take moments about for either 2-D or 3-D systems is arbitrary. If we satisfy equilibrium where moments are taken about a point P, then it is easy to show that equilibrium is satisfied for moments taken about any other point Q: ( 29 0 0 0 ix iy i i jz z F F C = = × + = r F 0 0 i P = = F M 0 0 i Q = = F M
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Equilibrium Equations In applying these equations we must include all forces and couples acting on a body. These are usually of two types: (1) applied forces or couples , some or all of which may be known
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This note was uploaded on 10/17/2011 for the course EM 274 taught by Professor Boylan during the Fall '08 term at Iowa State.

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equilibrium%2010%20class[1] - Topics Equilibrium Eqs in 3-D...

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