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# chap54-7 - 5.4 Two and Three Force Members The solution to...

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5.4 Two and Three Force Members The solution to some problems can be made easier if you recognize members that are subjected to only 2 forces. Two force members - only 2 forces applied at 2 points on the member. - no moments. - line of action of both forces must lie along a line connecting the 2 points of applications. Three force members- just read about. Equilibrium in Three dimensions 5.5 Free Body diagrams Reactions-3-D supports, Table 5-2, Pg. 217 5.6 Equations of Equilibrium 0 0 0 0 = Σ = Σ = Σ = Σ z y x F F F F y 0 0 0 0 ) ( = Σ = Σ = Σ = × Σ = Σ z y x M M M F r M y y y We have 6 equations => 6 unknowns 5.7 Constraints for a Rigid Body Redundant constraints- There are more constraints than necessary to hold a body in equilibrium. More unknowns than equations of equilibrium. -statically indeteminant For example: P Q S P Q S C D A B X A X B Y A Y B 4 unknowns Statically

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3 equations Indeterminant Partial constraints- There are fewer reactive forces than E.O.E. For example: P Q S P Q S C D FBD A B Y A Y B 2 unknowns partial 3 equations constraint
1). Given: FBD z Z M 20,601N Z A Y M Y A X A G C x X M B y 45,000N 8,000N 0 0 = + + + = Σ A L T W F y y y y y i T k W ˆ 000 , 8 ˆ 601 , 20 = - = k A j A i A A k L Z y ˆ ˆ ˆ ˆ 000 , 45 + + = = 0 ˆ

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