EM 319 - Review for 1st Midterm Exam

EM 319 - Review for 1st Midterm Exam - Review 1 Fall 08 1 A...

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Review 1 Fall 08 1. A solid circular bar is fixed against rotation at the ends and loaded by a distributed torque t ( x ) that varies linearly in intensity from zero at end A to t o at end B (see figure). Assume that the bar has shear modulus G and diameter d . Find: (a) The reaction torques at two supports. (b) The vale and position of maximum shear stress. (c) The value and position of maximum angle of twist. Solution: FBD EQM L t T T T C A o 2 1 0 + = = (1) internal torque L x t T x T T A AB 2 ) ( : 0 2 o = = Load/displacement relations ( ) 6 1 2 1 ) ( 2 o 0 2 o 0 L t L T GI dx L x t T I G I G dx x T A P L A P L P AB AB = = = φ A B t o L t ( x ) T A T C t o T A A T AB ( x ) x t o x/L
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