came3pt8 - Q.3.8 The thin cantilever shown in figure is...

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Q.3.8 The thin cantilever shown in figure is subjected to uniform shearing stress t 0 along its upper surface (y = +h) while surfaces y = -h and x = L are free of stress. Determine whether the Airy stress function. Satisfies the required conditions for this problem. Y Fig. t 0 2h X L Solution: First, to evaluate the formulae for stresses, we differentiate stress function with x and y. ) ( 4 2 3 2 0 h y h y y x - - = t f 0 4 4 3 3 2 2 = = = x x x f f f Also, ) 3 2 3 2 ( 4 2 2 2 2 0 h y L h Ly h y x h xy x y + + - - = t f ) h 6Ly h 2L 6xy - . 2 ( 4 2 2 0 2 2 + + - = h h x y t f ) ) ( 6 ( 4 2 0 3 3 h x L y - = t f ) y L. y y x. - y x - (x.y . 4 1 2 3 2 2 3 2 0 h h h h + + = t f
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0 4 4 = y f Now, y x 2 2 = f s ) h 6Ly h 2L 6xy - . 2 .( . 4 1 2 2 0 + + - = h h x x t s x y 2 2 = f s 0 = s y [We note that s y is zero everywhere.] Now, y x xy = . 2 f t ) 3 2 1 ( . 4 1 2 2 0 h y h y xy - - - = t t Now, let us proceed to the upper surface y = + h s y h y = = 0 ) 3 2 1 .( .
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This note was uploaded on 11/22/2011 for the course EML 6653 taught by Professor Law during the Fall '09 term at University of South Florida - Tampa.

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came3pt8 - Q.3.8 The thin cantilever shown in figure is...

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