stat indeterm_supports

stat indeterm_supports - y y y y y B L C L wL L A B C wL...

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Static Determinant and Indeterminant Systems w lb/ft L/2 L/2 wL/2 A y A x B y 3L/4 + + + this problem is statically determinant ( 29 ( 29 0 0 0 / 2 3 / 4 0 3 / 8 0 / 2 0 / 8 x x A y y y y y y F A M B L wL L B wL F A B wL A wL = = = - = = = + - = =
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L/2 L/2 wL/2 A y A x B y 3L/4 C y + + + 2 equations in 3 unknowns statically indeterminant ( 29 ( 29 ( 29 0 0 0 / 2 / 2 3 / 4 0 0 / 2 0 x x A y y y y y y F A M B L C L wL L F A B C wL = = = + - = = + + - =
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To remove this indeterminancy we need to bring in deformations, either of the beam or the supports. Let us assume the roller supports are linear springs and the beam is rigid and the springs are unstretched when the beam is horizontal. L/2 L/2 k k Cy = k dc By = kdb d c L/2 L/2 db so and now gives and 2 b c d d = 2 y y B C = ( 29 ( 29 ( 29 / 2 / 2 3 / 4 0 / 2
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Unformatted text preview: y y y y y B L C L wL L A B C wL +-= + +-= 3 / 20 / 20 y y C wL A wL = = 2 3 /10 y y B C wL = = L/2 L/2 k k k If we had assumed all the supports act like springs Cy = k dc By = kdb d c L/2 L/2 db Ay =k da da / 2 2 2 b a b c b c a y y y d d d d L L d d d B C A--= =-=-which gives Compare to our previous values ( 29 ( 29 ( 29 / 2 / 2 3 / 4 / 2 y y y y y B L C L wL L A B C wL +-= + +-= 2 y y y B C A =-24 4 24 7 24 y y y wL A wL C wL B = = = 20 3 20 6 20 y y y wL A wL C wL B = = =...
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stat indeterm_supports - y y y y y B L C L wL L A B C wL...

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