EM 319 - 5th Quiz

EM 319 - 5th Quiz - A solid circular bar is fixed between...

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Unformatted text preview: A solid circular bar is fixed between rigid wall at points A and C . A uniformly distributed torque t is then applied to the bar over the region AB (see figure). Assume that the bar has shear modulus G and diameter d . Find: (a) The reaction torques at two supports. (b) The value and position of maximum shear stress. (c) The value and position of maximum angle of twist. The answers should be in terms of t , L , G , d only. Solution: FBD EQM L t T T T C A + = = ∑ (1) internal torques x t T x T T A AB − = = ∑ ) ( : ∑ = = C BC T T T : Load/displacement relations P A L P AB AB I G tL L T I G dx x T 2 2 1 ) ( − = = ∫ φ P C BC I G L T = φ Compatibility = + BC AB φ φ L L A C B t t T A T C T A A T AB ( x ) T BC C T C 2 1 2 = + − P C P A I G L T I G tL L T or L t T T C A 2 1 = + (2) solving (1) and (2) simultaneously (a) L t T L t T C A 4 1 ; 4 3 − = = . (b) To find maximum shear stress, have to find maximum internal torque first. Draw internal torque as a function of x as follow...
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This note was uploaded on 09/18/2011 for the course EM 319 taught by Professor Staff during the Spring '11 term at Oklahoma State.

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EM 319 - 5th Quiz - A solid circular bar is fixed between...

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