EM 319 - 1st Midterm Solutions

EM 319 - 1st Midterm Solutions - Assume the pile has...

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Exercise 3 (40 points) During the construction of a bridge pier, a solid circular pile is driven into the earth by a torque T o . A distributed torque is induced during this process. The distributed torque varies linearly in intensity from zero at end D to t o at point C as in the figure below (observe that t o is the intensity of the external distributed torque at C , not the internal torque there! ). As an engineer, you are asked to analyze the following: (a) Write an expression of t o (in terms of T o and L ). (Hint: state the equilibrium of the pile.) (b) Find the value and location of maximum shear stress of the pile. (Hint: find the distribution of the internal torque in the pile. Use a coordinate system with origin at D .) (c) Find the total angle of twist of the entire pile.
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Unformatted text preview: Assume the pile has diameter d and is made of steel with shear modulus G . Solution: (a) Considering the pile is in equilibrium, we have ( ) L T t T L t T O o O o 2 2 1 = = = t o T o A B D L L 2 L C 10 (b) Define an origin at D , y positive upward FBD EQM ( ) = = L y t y T T 4 2 o Maximum torque is found between B and C . The value is -T o , 3 o max max 16 d T I r T P = = (c) Total angle of twist P P P L P P L P P L P P CD BC AB GI L T GI L t GI L T y L GI t GI L T dy L y t GI GI L T dy GI y T GI L T 3 5 3 2 3 4 4 1 ) ( O 2 o O 2 3 o O 2 2 o O 2 O Total = = = = + + = + + = T ( y ) L y t 2 o y 10 8 2 8 2...
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EM 319 - 1st Midterm Solutions - Assume the pile has...

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