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Unformatted text preview: Topics Equilibrium –Multiple Free Body Diagrams MATLAB solution Book Sections 3/13/4 (look ahead in chapter 4) Since in the most general case we have six equations of equilibrium, that must be satisfied for a body it would appear that we could at most solve for six unknown forces or couples. However, these six equations of equilibrium must apply also to every part of the body . Thus, in fact we can solve for many more than six unknowns. ix iy iz F F F = = = ∑ ∑ ∑ ( 29 ( 29 ( 29 Px i i jx x Py i i jy y Pz i i jz z M C M C M C = × + = = × + = = × + = ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ r F r F r F Example: consider a coplanar force system where there are only three nonzero equilibrium equations Consider the following structure, where there are two bars, each weighing 100 lb, and an applied force of 200 lb acting on the pin at B. The bars are attached to each other and to the floor via smooth pins 200 lb A B C 6' 8' ix iy Pz F F M = = = ∑ ∑ ∑ If we look just at the entire structure it would appear we cannot solve for all the unknown reaction forces since there are four of them 200 lb Ax A y Cx Cy x y However, now break the system up into parts 100 lb 100 lb 200 lb Ax A y Cx Cy 100 lb 100 lb Bx B y Bx B y B'x B' y B'x B' y There now are eight unknown reaction forces. How many nonzero equilibrium equations are there?...
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 Fall '08
 Boylan
 Equations, Force, Elementary algebra, lb, bx

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