solution2 - x ) 180 0.5404 2 sin( 2 200 ) 180 0.5404 2 cos(...

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Question 2.9 : A thin rectangular plate a=20 mm and b=12 mm is acted upon by a stress distribution resulting in the uniform strains, m g m e m e 200 , 500 , 300 xy y = = = x . Determine the changes in length of diagonals QB and AC. Solution: Y A B b Q C a Since the diagonals are in a direction different from the X, Y-axes, We will have to first evaluate the strains in those directions which when multiplied with the original length of the diagonal will give us the change in the length of the diagonal. From the equations of stress transformation as given by eq.(2.11a) and (2.10b) ) 2 sin( 2 ) 2 cos( 2 2 ' q g q e e e e e × + × - + + = xy y x y x x ) sin - cos ( cos . sin ) - ( 2 2 2 xy x y ' q q g q q e e g + = xy Now, for diagonal QB : b a QB AC 2 2 + = = mm QB AC 32 . 23 ) 12 ( ) 20 ( 2 2 = + = = = = = - - ) 20 12 ( tan ) ( tan 1 1 a b q 0.5404 m e 17 . 441 ' =
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Unformatted text preview: x ) 180 0.5404 2 sin( 2 200 ) 180 0.5404 2 cos( 2 500 300 2 500 300 ' p p e × × × + × × ×-+ + = x Hence, the change in length of diagonal QB is QB x QB × = ∆ e ' mm QB 0102 . 32 . 23 10 17 . 441 6 = × × = ∆ ∴-Now, for diagonal AC : 6011 . 2 ) 12 20 ( tan 57 . 1 ) ( tan 2 1 1 = + = + =--b a p q m e 7 . 264 ' = ∴ x Hence, the change in length of diagonal AC is AC x AC × = ∆ e ' mm AC 0061 . 32 . 23 10 7 . 264 6 = × × = ∆ ∴-Final Answer: mm mm AC QB 0061 . and 0102 . = ∆ = ∆ ) 180 2.6011 2 sin( 2 200 ) 180 2.6011 2 cos( 2 500 300 2 500 300 ' p p e × × × + × × ×-+ + = x...
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solution2 - x ) 180 0.5404 2 sin( 2 200 ) 180 0.5404 2 cos(...

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