319 final review

319 final review - EM319 Review Spring 2008 Problem 1 The...

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Unformatted text preview: EM319 Review Spring 2008 Problem 1 : The horizontal beam is rigid while the two rods are linearly elastic with axial stiffness AE and coefficient of thermal expansion α . Rod number 1 (and only rod number 1) is subjected to a temperature change Δ T . Determine the force induced in each rod by this temperature change. Solution: FBD EQM ∑ = = 2 1 2 : F F M B (1) Force-displacement relationships h T EA h F Δ + = α δ 1 1 (2 a ) EA h F 2 2 = δ (2 b ) Compatibility (similar triangles, note that cable at point C has a shortening) 2 1 2 δ δ − = (3) h a 2 a 1 2 F 1 F 2 B x B y A B C δ 2 δ 1 Solving (1), (2) and (3) simultaneously gives T EA F Δ − = α 5 4 1 T EA F Δ − = α 5 2 2 . Negative signs mean that they both have opposite directions. Problem 2 : 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 vale and position of maximum shear stress. (c) The value and position of maximum angle of twist. Solution: (a) FBD EQM ∑ + = = L t T T T C A : Internal torques ∑ − = ⇒ = tx T x T T A AB ) ( ∑ − = ⇒ = tL T x T T A AB ) ( Torque-displacement relationship ) 2 ( 1 ) ( 2 tL L T I G I G dx x T A P L P AB AB − = = ∫ φ L L A C B t A C B t T C T A A T A T AB ( x ) x T BC ( x ) A T A L x B P A BC P BC BC BC BC I G L tL T I G L T ) ( , − = = φ Compatibility ) 2 3 2 ( 1 2 = − ⇒ =...
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This note was uploaded on 02/11/2009 for the course EM 319 taught by Professor Kennethm.liechti during the Spring '08 term at University of Texas.

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319 final review - EM319 Review Spring 2008 Problem 1 The...

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