02-02ChapGere.0019

02-02ChapGere.0019 - P 1 E 1 E 2 E 1 E 2 F REE-BODY DIAGRAM...

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Problem 2.4-11 A bimetallic bar (or composite bar) of square cross section with dimensions 2 b 3 2 b is constructed of two different metals having moduli of elasticity E 1 and E 2 (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 P 1 and P 2 in the two parts of the bar. (b) Determine the eccentricity e of the loads. (c) Determine the ratio s 1 / s 2 of the stresses in the two parts of the bar. Solution 2.4-11 Bimetallic bar in compression 98 CHAPTER 2 Axially Loaded Members 2 b P e b b b b P e E 1 E 2 2 b b 2 b b P 2 P 1 P 2
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Unformatted text preview: P 1 E 1 E 2 E 1 E 2 F REE-BODY DIAGRAM (Plate at right-hand end) E QUATIONS OF EQUILIBRIUM F 5 P 1 1 P 2 5 P (Eq. 1) (Eq. 2) E QUATION OF COMPATIBILITY d 2 5 d 1 (Eq. 3) P 2 L E 2 A 5 P 1 L E 1 A or P 2 E 2 5 P 1 E 1 M 5 0 ` ~ Pe 1 P 1 b 2 2 P 2 b 2 5 (a) A XIAL FORCES Solve simultaneously Eqs. (1) and (3): (b E CCENTRICITY OF LOAD P Substitute P 1 and P 2 into Eq. (2) and solve for e : (c) R ATIO OF STRESSES s 1 5 P 1 A s 2 5 P 2 A s 1 s 2 5 P 1 P 2 5 E 1 E 2 e 5 b ( E 2 2 E 1 ) 2( E 2 1 E 1 ) P 1 5 PE 1 E 1 1 E 2 P 2 5 PE 2 E 1 1 E 2 P 2 P 1 e P b 2 b 2 A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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