597_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

597_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 7.3 Principal Stresses and Maximum Shear Stresses 591 Problems 7.3-16 s x ±² 108 MPa, s y ± 58 MPa, t xy ±² 58 MPa (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. Solution 7.3-16 (a) P RINCIPAL S TRESSES Therefore, For For ; s 2 ±² 126.3 MPa u p 2 ± 17.47° ; u p 1 ± 107.47° s 1 ± 76.3 MPa 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 1 ± 90° + u p 2 u p 1 ± 107.47° u p 2 ± 17.47° tan(2 u p ) ± 2 t xy s x ² s y u p 2 ± atan a 2 t xy s x ² s y b 2 s x ±² 108 MPa s y ± 58 MPa t xy ±² 58 MPa (b) M AXIMUM S HEAR S TRESSES s aver ± s x + s y 2 s aver ±² 25.0 MPa and t 2 ±² 101.3 MPa
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Unformatted text preview: ; u s 2 u p 1 + 45 u s 2 152.47 and t 1 101.3 MPa ; u s 1 u p 1 45 u s 1 62.47 t max 14686.1 psi t max A a s x s y 2 b 2 + t xy 2 Problem 7.3-17 At a point on the surface of a machine component, the stresses acting on the x face of a stress element are s x 5900 psi and t xy 1950 psi (see figure). What is the allowable range of values for the stress s y if the maximum shear stress is limited to t 2500 psi? y x O t xy = 1950 psi s y s x = 5900 psi 07Ch07.qxd 9/27/08 1:18 PM Page 591...
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