599_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 599_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 7.3 Principal Stresses and Maximum Shear Stresses 593 35 MPa 18.7 MPa 65.3 MPa t max ( σ y1 ) σ y 1 Problem 7.3-19 An element in plane stress is subjected to stresses s x ± 5700 psi and t xy ±² 2300 psi (see figure). It is known that one of the principal stresses equals 6700 psi in tension. (a) Determine the stress s y . (b) Determine the other principal stress and the orientation of the principal planes, then show the principal stresses on a sketch of a properly oriented element. y x O 5700 psi s y 2300 psi Solve for Therefore, 18.7 MPa s y 65.3 MPa s y ± a 65.3 18.7 b MPa s y ± s x ³ J 2 2 t max 2 ² t xy 2 ² a 2 2 t max 2 ² t xy 2 b K s y From Eq. (1): t max ( s y
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Unformatted text preview: 1 ) ± A a s x ² s y 1 2 b 2 + t xy 2 Solution 7.3-19 (a) S TRESS Because is smaller than a given principal stress, we know that the given stress is the larger principal stress. s 1 ± s x + s y 2 + A a s x ² s y 2 b 2 + t xy 2 s 1 ± 6700 psi s y s y s x ± 5700 psi s y unknown t xy ±² 2300 psi Solve for (b) P RINCIPAL STRESSES u p 2 ± 90° + u p 1 u p 2 ± 66.50° u p 1 ± ² 23.50° 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 y s y ± 1410 psi ; 07Ch07.qxd 9/27/08 1:18 PM Page 593...
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