249_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

249_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_2.8-2.12.qxd 9/25/08 11:44 AM Page 243 243 SECTION 2.12 Elastoplastic Analysis Problem 2.12-9 The structure shown in the figure consists of a horizontal rigid bar ABCD supported by two steel wires, one of length L and the other of length 3L/4. Both wires have cross-sectional area A and are made of elastoplastic material with yield stress Y and modulus of elasticity E. A vertical load P acts at end D of the bar. L A (a) Determine the yield load PY and the corresponding yield displacement Y at point D. (b) Determine the plastic load PP and the corresponding displacement P at point D when the load just reaches the value PP. (c) Draw a load-displacement diagram with the load P as ordinate and the displacement D of point D as abscissa. 3L 4 B C D P 2b b b Solution 2.12-9 Rigid bar supported by two wires FREE-BODY DIAGRAM A Y E cross-sectional area EQUILIBRIUM: yield stress MA modulus of elasticity 0 FB(2b) 2FB FC(3b) P(4b) 3FC 4P (3) DISPLACEMENT DIAGRAM FORCE-DISPLACEMENT RELATIONS FBL dC EA dB D 3 dB 2 (1) 3FCL 4EA 2 (2) FC B EA (4, 5) Substitute into Eq. (1): COMPATIBILITY: dC 3 FC a L b 4 3FBL 2EA 2FB (6) ...
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