594_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

594_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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588 CHAPTER 7 Analysis of Stress and Strain Problems 7.3-11 s x ± 2500 psi, s y ± 1020 psi, t xy ±² 900 psi (a) Determine the principal stresses and show them on a sketch of a properly oriented element. (b) Determine the maximum shear stresses and associated normal stresses and show them on a sketch of a properly oriented element. y x O t xy s x s y Solution 7.3-11 (a) P RINCIPAL STRESSES s 2 ± s x + s y 2 + s x ² s y 2 cos 1 2 u p 2 2 + t xy sin 1 2 u p 2 2 s 1 ± s x + s y 2 + s x ² s y 2 cos 1 2 u p 1 2 + t xy sin 1 2 u p 1 2 u p 2 ± 90 ° + u p 1 u p 2 ± 64.71° u p 1 ± 25.29° tan(2 u p ) ± 2 t xy s x ² s y u p 1 ± atan a 2 t xy s x ² s y b 2 s x ± 2500 psi s y ± 1020 psi t xy ±² 900 psi Therefore, (b) M AXIMUM S HEAR S TRESSES s aver ± s x + s y 2 s aver ± 1760 psi ; t 2 ±² 1165 psi ; u s 2 ± u p 1 ² 45° u s 2 ± 19.71° and t 1 ± 1165 psi ; u s 1 ± u p 1 ² 45° u s 1 ±² 70.3° and t max ± 1165 psi t max ± A a s x ² s y 2 b 2 + t xy 2 s 2 ± 595 psi ; For u p 2 ± 64.7°: For u p 1 ±² 25.3°: s 1 ± 2925 psi ; Problems 7.3-12 s x ± 2150 kPa, s y ± 375 kPa, t xy ±² 460 kPa (a) Determine the principal stresses and show them on a sketch of a properly oriented element.
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Unformatted text preview: (b) Determine the maximum shear stresses and associated normal stresses and show them on a sketch of a properly oriented element. Solution 7.3-12 (a) P RINCIPAL S TRESSES tan(2 u p ) 2 t xy s x s y u p 1 atan a 2 t xy s x s y b 2 s x 2150 kPa s y 375 kPa t xy 460 kPa s 2 s x + s y 2 + s x s y 2 cos 1 2 u p 2 2 + t xy sin 1 2 u p 2 2 s 1 s x + s y 2 + s x s y 2 cos 1 2 u p 1 2 + t xy sin 1 2 u p 1 2 u p 2 90 + u p 1 u p 2 76.30 u p 1 13.70 Probs. 7.3-11 through 7.3-16 07Ch07.qxd 9/27/08 1:18 PM Page 588...
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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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