146_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

146_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_2.4.qxd 9/25/08 140 11:38 AM Page 140 CHAPTER 2 Axially Loaded Members Problem 2.4-11 A bimetallic bar (or composite bar) of square cross section with dimensions 2b 2b is constructed of two different metals having moduli of elasticity E1 and E2 (see figure). The two parts of the bar have the same cross-sectional dimensions. The bar is compressed by forces P acting through rigid end plates. The line of action of the loads has an eccentricity e of such magnitude that each part of the bar is stressed uniformly in compression. (a) Determine the axial forces P1 and P2 in the two parts of the bar. (b) Determine the eccentricity e of the loads. (c) Determine the ratio 1/ 2 of the stresses in the two parts of the bar. Solution 2.4-11 Bimetallic bar in compression FREE-BODY DIAGRAM (a) AXIAL FORCES (Plate at right-hand end) Solve simultaneously Eqs. (1) and (3): P1 PE1 E1 + E2 P2 PE2 E1 + E2 ; (b ECCENTRICITY OF LOAD P Substitute P1 and P2 into Eq. (2) and solve for e: e EQUATIONS OF EQUILIBRIUM F 0 P1 P2 P b(E2 2(E2 E1) E1) ; (Eq. 1) (c) RATIO OF STRESSES M b Pe + P1 a b 2 0 b P2 a b 2 0 (Eq. 2) EQUATION OF COMPATIBILITY 2 P2L E2A 1 P1L E1A or P2 E2 P1 E1 (Eq. 3) s1 P1 A s2 P2 A s1 s2 P1 P2 E1 E2 ; ...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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