07-03ChapGere.0013

07-03ChapGere.0013 - Solve the preceding problem for a...

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Solution 7.5-3 Plane stress 464 CHAPTER 7 Analysis of Stress and Strain Given: « x , « y , ± (a) N ORMAL STRAIN « z Eq. (7-34c): Eq. (7-36a): Eq. (7-36b): Substitute s x and s y into the first equation and simplify: e z 52 n 1 2 n ( e x 1 e y ) s y 5 E (1 2 n 2 ) ( e y 1 ne x ) s x 5 E (1 2 n 2 ) ( e x 1 ne y ) e z 52 n E ( s x 1 s y ) (b) D ILATATION Eq. (7-47): Substitute s x and s y from above and simplify: e 5 1 2 2 n 1 2 n ( e x 1 e y ) e 5 1 2 2 n E ( s x 1 s y ) Problem 7.5-4 A magnesium plate in biaxial stress is subjected to tensile stresses s x 5 24 MPa and s y 5 12 MPa (see figure). The corresponding strains in the plate are e x 5 440 3 10 2 6 and e y 5 80 3 10 2 6 . Determine Poisson’s ratio n and the modulus of elasticity E for the material. s y s x y x O Solution 7.5-4 Biaxial stress s x 5 24 MPa s y 5 12 MPa « x 5 440 3 10 2 6 « y 5 80 3 10 2 6 P OISSON SRATIO AND MODULUS OF ELASTICITY Eq. (7-39a): Eq. (7-39b): e y 5 1 E ( s y 2 ns x ) e x 5 1 E ( s x 2 ns y ) Substitute numerical values: E (440 3 10 2 6 ) 5 24 MPa 2 ± (12 MPa) E (80 3 10 2 6 ) 5 12 MPa 2 ± (24 MPa) Solve simultaneously: ±5 0.35 E 5 45 GPa Problem 7.5-5
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Unformatted text preview: Solve the preceding problem for a steel plate with s x 5 10,800 psi (tension), s y 5 2 5400 psi (compression), e x 5 420 3 10 2 6 (elongation), and e y 5 2 300 3 10 2 6 (shortening). Solution 7.5-5 Biaxial stress s x 5 10,800 psi s y 5 2 5400 psi « x 5 420 3 10 2 6 « y 5 2 300 3 10 2 6 P OISSON ’ S RATIO AND MODULUS OF ELASTICITY Eq. (7-39a): Eq. (7-39b): e y 5 1 E ( s y 2 ns x ) e x 5 1 E ( s x 2 ns y ) Substitute numerical values: E (420 3 10 2 6 ) 5 10,800 psi 2 ± ( 2 5400 psi) E ( 2 300 3 10 2 6 ) 5 2 5400 psi 2 ± (10,800 psi) Solve simultaneously: ± 5 1/3 E 5 30 3 10 6 psi Probs. 7.5-4 through 7.5-7 A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Tech.

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