02-02ChapGere.0017

02-02ChapGere.0017 - (Eqs. 3, 4)) d AC 5 R A L E s A s d BC...

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Problem 2.4-9 The aluminum and steel pipes shown in the figure are fastened to rigid supports at ends A and B and to a rigid plate C at their junction. The aluminum pipe is twice as long as the steel pipe. Two equal and symmetrically placed loads P act on the plate at C . (a) Obtain formulas for the axial stresses s a and s s in the aluminum and steel pipes, respectively. (b) Calculate the stresses for the following data: P 5 12 k, cross-sectional area of aluminum pipe A a 5 8.92 in. 2 , cross-sectional area of steel pipe A s 5 1.03 in. 2 , modulus of elasticity of aluminum E a 5 10 3 10 6 psi, and modulus of elasticity of steel E s 5 29 3 10 6 psi. Solution 2.4-9 Pipes with intermediate loads 96 CHAPTER 2 Axially Loaded Members P C P B A Steel pipe Aluminum pipe 2 L L Pipe 1 is steel. Pipe 2 is aluminum. E QUATION OF EQUILIBRIUM © F vert 5 0 R A 1 R B 5 2 P (Eq. 1) E QUATION OF COMPATIBILITY d AB 5 d AC 1 d CB 5 0 (Eq. 2) (A positive value of d means elongation.) F ORCE - DISPLACEMENT RELATIONS
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Unformatted text preview: (Eqs. 3, 4)) d AC 5 R A L E s A s d BC 5 2 R B (2 L ) E a A a S OLUTION OF EQUATIONS Substitute Eqs. (3) and (4) into Eq. (2): (Eq. 5) Solve simultaneously Eqs. (1) and (5): (Eqs. 6, 7) (a) A XIAL STRESSES (Eq. 8) (compression) (Eq. 9) (tension) (b) N UMERICAL RESULTS P 5 12 k A a 5 8.92 in. 2 A s 5 1.03 in. 2 E a 5 10 3 10 6 psi E s 5 29 3 10 6 psi Substitute into Eqs. (8) and (9): s s 5 9,350 psi (tension) s a 5 1,610 psi (compression) Steel: s s 5 R A A s 5 4 E s P E a A a 1 2 E s A s Aluminum: s a 5 R B A a 5 2 E a P E a A a 1 2 E s A s R A 5 4 E s A s P E a A a 1 2 E s A s R B 5 2 E a A a P E a A a 1 2 E s A s R A L E s A s 2 R B (2 L ) E a A a 5 P C P B A 2 L L 1 2 P C P B A R A R B E s A s E a A a A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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