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

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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 : 0 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
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