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07-01ChapGere.0013 - Solution 7.3-6 Maximum shear stresses...

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Problem 7.3-5 An element in plane stress is subjected to stresses x 7,500 psi, y 20,500 psi, and xy 4,800 psi (see the figure for Problem 7.2-5). Determine the maximum shear stresses and associated normal stresses and show them on a sketch of a properly oriented element. Solution 7.3-5 Maximum shear stresses SECTION 7.3 Principal Stresses and Maximum Shear Stresses 437 x 7,500 psi y 20,500 psi xy 4,800 psi P RINCIPAL ANGLES 2 p 18.92 and p 9.46 2 p 161.08 and p 80.54 For 2 p 18.92 : For 2 p 161.08 : Therefore, u p 1 9.46 s x 1 21,300 psi s x 1 8,300 psi s x 1 s x s y 2 s x s y 2 cos 2 u t xy sin 2 u tan 2 u p 2 t xy s x s y 0.3429 M AXIMUM SHEAR STRESSES and 14,800 psi and 14,800 psi } s aver s x s y 2 6,500 psi u s 2 u p 1 45 35.54 u s 1 u p 1 45 54.46 t max B ¢ s x s y 2 2 t xy 2 14,800 psi Problem 7.3-6 An element in plane stress is subjected to stresses x 25.5 MPa, y 6.5 MPa, and xy 12.0 MPa (see the figure for Problem 7.2-6). Determine the maximum shear stresses and associated normal stresses and show
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Unformatted text preview: Solution 7.3-6 Maximum shear stresses s x 5 2 25.5 MPa s y 5 6.5 MPa t xy 5 2 12.0 MPa P RINCIPAL ANGLES 2 u p 5 36.87 8 and u p 5 18.43 8 2 u p 5 216.87 8 and u p 5 108.43 8 For 2 u p 5 36.87 8 : For 2 u p 5 216.87 8 : Therefore, u p 1 5 108.4 8 s x 1 5 10.5 MPa s x 1 5 2 29.5 MPa s x 1 5 s x 1 s y 2 1 s x 2 s y 2 cos 2 u 1 t xy sin 2 u tan 2 u p 5 2 t xy s x 2 s y 5 0.7500 M AXIMUM SHEAR STRESSES and t 5 20.0 MPa and t 5 2 20.0 MPa s aver 5 s x 1 s y 2 5 2 9.5 MPa u s 2 5 u p 1 1 45 8 5 153.43 8 u s 1 5 u p 1 2 45 8 5 63.48 8 t max 5 B ¢ s x 2 s y 2 ≤ 2 1 t xy 2 5 20.0 MPa } x O 14,800 psi u s 2 5 35.54 8 6,500 psi y 6,500 psi x O 20.0 MPa u s 1 5 63.43 8 9.5 MPa 9.5 MPa y A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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