07-01ChapGere.0014

07-01ChapGere.0014 - Solution 7.3-8 Maximum shear stresses...

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Problem 7.3-7 An element in plane stress is subjected to stresses s x 52 11,000 psi, s y 52 3,000 psi, and t xy 52 4200 psi (see the figure for Problem 7.2-7). Determine the maximum shear stresses and associated normal stresses and show them on a sketch of a properly oriented element. Solution 7.3-7 Maximum shear stresses 438 CHAPTER 7 Analysis of Stress and Strain s x 52 11,000 psi s y 52 3,000 psi t xy 52 4,200 psi P RINCIPAL ANGLES 2 u p 5 46.40 8 and u p 5 23.20 8 2 u p 5 226.40 8 and u p 5 113.20 8 For 2 u p 5 46.40 8 : For 2 u p 5 226.40 8 : Therefore, u p 1 5 113.20 8 s x 1 52 1,200 psi s x 1 52 12,800 psi 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 1.0500 M AXIMUM SHEAR STRESSES and t 5 5,800 psi and t 52 5,800 psi s aver 5 s x 1 s y 2 52 7,000 psi u s 2 5 u p 1 1 45 85 158.20 8 u s 1 5 u p 1 2 45 85 68.20 8 t max 5 B ¢ s x 2 s y 2 2 1 t xy 2 5 5,800 psi } Problem 7.3-8 An element in plane stress is subjected to stresses s x 52 54 MPa, s y 52 12 MPa, and t xy 5 20 MPa (see the figure for Problem 7.2-8). Determine the maximum shear stresses and associated normal stresses and show them on a sketch of a properly oriented element.
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Unformatted text preview: Solution 7.3-8 Maximum shear stresses s x 5 2 54 MPa s y 5 2 12 MPa t xy 5 20 MPa P RINCIPAL ANGLES 2 u p 5 2 43.60 8 and u p 5 2 21.80 8 2 u p 5 136.40 8 and u p 5 68.20 8 For 2 u p 5 2 43.60 8 : For 2 u p 5 136.40 8 : Therefore, u p 1 5 68.20 8 s x 1 5 2 4.0 MPa s x 1 5 2 62 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 2 0.9524 M AXIMUM SHEAR STRESSES and t 5 29.0 MPa and t 5 2 29.0 MPa s aver 5 s x 1 s y 2 5 2 33.0 MPa u s 2 5 u p 1 1 45 8 5 113.20 8 u s 1 5 u p 1 2 45 8 5 23.20 8 t max 5 B s x 2 s y 2 2 1 t xy 2 5 29.0 MPa x O 29.0 MPa u s 1 5 23.20 8 33.0 MPa 33.0 MPa y } x O 5,800 psi u s 1 5 68.20 8 7,000 psi 7,000 psi y A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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