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Unformatted text preview: Home Work # 4 (a) Consider the stress function, 3 xy = . (1) Compute the corresponding stresses. (2) Show on the sketch the sense and magnitude of the boundary forces at point A and along the edge BC . (3) Compute the displacements u and v of point C relative to point o . Assume no rigid body motion. (b) Compute Airys stress function, , and plot the boundary values for the following loadings: 10" 10" A 12" C 45 o o B x y 1 h = ( 29 2 x y p p 2 b 2 a ( 29 ( 29 ( 29 3 1 2 + M M ( 29 1 ( 29 4 1 Solution (a) (1) Compute the stresses 2 2 6 x xy y = = , 2 y x = = , 2 3 xy y x y =  =  (2) Sketch boundary forces at A and along BC. from Eq. (311) 2 2 2 2 2 2 dy dx x y ds x y ds dx dy y x ds x y ds = + =  2 2 2 2 10 10 for A , , third quadrant , 2 2 1 1 10 10 1 10 1 6 3 6 3 75 2 2 2 2 2 2 2 2 1 10 1 3 3 75 2 2 2 2 A A dx dy x y ds ds x xy y y y =  =  +  = + = + =  =  =  = ( 29 ( 29 ( 29 2 for BC / 0, / 1 6 3 1 300 B C B C dy ds dx ds x xy y y = = = + = = (3) ( 29 ( 29 2 1 2 2 6 6     (a) 6 6    (b) from (a), 3 from (b), 3 y x x y x y u xy u E xy x E E E x v xy v E xy y E E E y Eu x y g y Ev x y g x = = = = = = =  =  = + =  + 2 ( 29 ( 29 2 2 1 2 1 3 3    (c) xy u v x...
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This note was uploaded on 09/24/2011 for the course CIVL 7690 taught by Professor Staff during the Summer '10 term at Auburn University.
 Summer '10
 Staff

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