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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):
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
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
E2A 1 P1L
E1A or P2
E1 (Eq. 3) s1 P1
A s2 P2
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.
- Fall '11