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quiz%203%20w08%20solution - ENFD 375 BASIC STRENGTH OF...

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ENFD 375 – BASIC STRENGTH OF MATERIALS QUIZ #3 Given: A steel column is fixed at the top and bottom and has a 30k force applied 10 ft from the top. It has an area of 10 in 2 and an elastic modulus of 30000 ksi. Find the reactions, R A and R C . DO NOT ASSUME the arrows are correct. Remove the support from point A: Now, how much does R A need to pull UP? (The arrow is wrong is the diagram.) Now by equilibrium, R C = 10 k PL AE δ = ( )( ) ( ) ( ) 2 30 20 0.002 10 30000 PL AE k ft ft in ksi δ δ = = = ( )( ) ( ) ( ) 2 30 0.002 10 30000 20 A A PL AE R ft ft in ksi R k δ δ = = = = 0 30 20 10 y c c F k k R R k + ↑ Σ = = − + + =
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This makes sense. Stiffness = AE/L. The column has a uniform EA, thus the only difference in stiffness is the length L.
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