HW2 Solutions - EM 319 Mechanics of Solids Fall 2010...

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EM 319 Mechanics of Solids Fall 2010 Homework #2 Due: 9/9/2010 1. Find the change of length of the entire structure, given that: E AB = 2 E , E BC = E , E CD = 3 E , A AB = A , A BD = 2 A . Solution: FBDs EQM P P P P P P F ED CE BC AB x 2 0 Change of length EA PL A E L P A E L P A E L P A E L P A E L P A E L P A E L P A E L P ED ED ED ED CE CE CE CE BC BC BC BC AB AB AB AB ED CE BC AB 2 ) 2 )( 3 ( ) 2 ( ) 2 )( 3 ( ) 2 )( ( ) 2 ( ) 2 ( ) ( ) 2 ( ) ( total (negative sign means the whole structure gets shorter) 2 P L P A B D 1/2 L 3 P C 1/2 L L E P AB P A A B P BC P A B P CE C P P ED 2 P
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2. The structure ABC is subjected to the loads shown in the figure. The member has constant thickness t (out-of plane direction) and Young’s modulus of the material is E . Find the change of length of the structure. Solution: First find the reaction at support A FBD EQM 0 0 A x R F FBDs EQM P P P P P F EC BE AB x 3 0 0 Change of length Ebt Pa bt E Pa bt E a P A E L P A E L P EC EC EC EC EB EB BE BE EC BE AB 4 ) ( ) ( ) 3 ( 0 0 total P 3 P 2 P 2 a a A B C b 2 b a P 3 P 2 P A B C R A E P 2 P P BE C E A P AB P P EC C R A
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3. A bar is subjected to linearly distributed load which has intensity o q at the support O and zero at the free end B . The bar has constant Young’s modulus E and cross sectional area A . (a) Calculate the elongation of the entire bar.
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HW2 Solutions - EM 319 Mechanics of Solids Fall 2010...

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