came2pt24 - Add(3 and(1 we get e e y 1200 = ∴ x...

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Q.2.24 The following state of strain has been measured at a point on the surface of a crane hook. The readings are 75 , 30 , 15 , 200 , 250 , 1000 0 c 0 b 0 a = = - = = - = = q q q e e e m m m c b a . Determine strain components e g e xy and , y , x . Solution . We first write the formula for strain at any angle “ θ ”, q q q q g e e e q cos . sin . sin . cos . xy 2 y 2 + + = x Now, for 15 0 - = q a ) 15 cos( ). 15 sin( . ) 15 ( sin . ) 15 ( cos . 1000 xy 2 y 2 - - + - + - = g e e x . 25 . 0 . 0.066 . 933 . 0 1000 xy y g e e - + = x ………………………………….(1) Similarly, for 30 0 = q b ) 30 cos( ). 30 sin( . ) 30 ( sin . ) 30 ( cos . 250 xy 2 y 2 g e e + + = - x . 433 . 0 . 25 . 0 . 75 . 0 250 xy y g e e + + = - x ………………………………….(2) Similarly, for 75 0 = q c ) 75 cos( ). 75 sin( . ) 75 ( sin . ) 75 ( cos . 200 xy 2 y 2 g e e + + = x . 25 . 0 . 0.933 . 066 . 0 200 xy y g e e + + = x ………………………………….(3) Now, we solve these three equations simultaneously, . 25 . 0 . 0.066 . 933 . 0 1000 xy y g e e - + = x ……………….(1) . 25 . 0 . 0.933 . 066 . 0 200 xy y g e e - + = x ……………….(3)
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Unformatted text preview: Add (3) and (1), we get: e e y . 1200 + = ∴ x ……………(4) And, substitute the value of γ xy from (1) into (2), we get: ). 1000 066 . 933 . ( 4 433 . . 25 . . 75 . 250 y-+ × × + + =-∴ e e e e y x x 1482 . . 0.3643 . 3659 . 2 y-+ = ∴ e e x …………(5) From (4), we get, e e x 1200 .-= y . )-0.364(1200 . 366 . 2 1482 x e e + = ∴ x Which gives: m e 522 = ∴ x This when substituted back in (4) gives: m e 678 = ∴ y Also, re-substituting we get: m g 1873-= ∴ xy Final Answer : m e 522 = x m e 678 = y m g 1873-= xy...
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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.

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came2pt24 - Add(3 and(1 we get e e y 1200 = ∴ x...

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