HW_13 Solutions - 002 . 6 012 . = = in in Z e Since the...

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Unformatted text preview: 002 . 6 012 . = = in in Z e Since the Material is Confined = = Y X e e Using Generalized Hookes Law with thermal strains [ ] ( 29 [ ] ( 29 [ ] ( 29 [ ] ( 29 [ ] ( 29 [ ] ( 29 20 . 6 35 . 200 ) 1 10 ( 1 . 13 35 . ) 10 ( 10 1 002 . 1 2 . 26 35 . 200 ) 1 10 ( 1 . 13 35 . ) 10 ( 10 1 1 2 . 26 35 . 200 ) 1 10 ( 1 . 13 35 . ) 10 ( 10 1 1 6 6 6 6 6 6 + +- = + +- = +-- = + +- = + +- = +-- = + +- = + +- = +-- =--- Y X Z Y X Z Y X Z Z Z X Y Z X Y Z X Y Y Z Y X Z Y X Z Y X X F F psi T E F F psi T E F F psi T E s s s s s s a us us s e s s s s s s a us us s e s s s s s s a us us s e Solving the three equations simultaneously yields the solution ksi ksi Z X Y 2 . 55 70- =- = = s s s First Determine Normal Stress ( 29 ( 29 [ ] ksi psi in in lb A P N 694 . 5 . 694 25 . 1 5 . 1 1500 2 2 = =- = = p s Now find Shear Stress ( 29 ( 29 [ ] ksi psi in in in ft in lbft J Tc XY 4977 . 3 7 . 3497 25 . 1 5 . 1 2 ) 5 . 1 )( / 12 ( 800 4 4 = =- = = p t Now determine average and Radius: Element shown to right ksi R R ksi ksi XY Y X Y X Avg 51 . 3 ) 4977 . 3 ( 2 ) 694 . ( 2 347 . 2 ) 694 . ( 2 2 2 2 2 = + -- = + - =- =- + = + = t s s s s s Using Mohrs circle find Principal Stresses and Orientation ksi ksi ksi R ksi ksi ksi R Avg Avg 86 . 3 51 . 3 347 ....
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HW_13 Solutions - 002 . 6 012 . = = in in Z e Since the...

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