248_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

248_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_2.8-2.12.qxd 242 9/25/08 11:44 AM Page 242 CHAPTER 2 Axially Loaded Members Problem 2.12-8 A rigid bar ACB is supported on a fulcrum at C and loaded by a force P at end B (see figure). Three identical wires made of an elastoplastic material (yield stress Y and modulus of elasticity E) resist the load P. Each wire has cross-sectional area A and length L. (a) Determine the yield load PY and the corresponding yield displacement Y at point B. (b) Determine the plastic load PP and the corresponding displacement P at point B when the load just reaches the value PP. (c) Draw a load-displacement diagram with the load P as ordinate and the displacement B of point B as abscissa. L A C B P L a a a a Solution 2.12-8 Rigid bar supported by wires (b) PLASTIC LOAD PP (a) YIELD LOAD PY Yielding occurs when the most highly stressed wire reaches the yield stress Y At the plastic load, all wires reach the yield stress. MC PP 0 4sYA 3 ; At point A: dA (sYA) a L b EA sYL E At point B: MC PY YA At point A: dA dB 0 sYA L a ba b 2 EA 3dA dY dP 3sYL E ; (c) LOAD-DISPLACEMENT DIAGRAM ; sYL 2E At point B: dB 3dA 3sYL 2E ; PP dP 4 P 3Y 2dY ...
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