07-02ChapGere.0002

07-02ChapGere.0002 - 8 u p 1 5 117.23 8 Solution 7.3-10...

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Problems 7.3-11 through 7.3-16 An element in plane stress (see figure) is subjected to stresses s x , s y , and t xy . (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. Data for 7.3-11 s x 5 3500 psi, s y 5 1120 psi, t xy 52 1200 psi Solution 7.3-11 Plane stress 440 CHAPTER 7 Analysis of Stress and Strain s x 52 90 MPa s y 5 0 t xy 52 63 MPa (a) P RINCIPAL STRESSES 2 u p 5 54.46 8 and u p 5 27.23 8 2 u p 5 234.46 8 and u p 5 117.23 8 For 2 u p 5 54.46 8 : For 2 u p 5 234.46 8 : s x 1 5 32.4 MPa s x 1 52 122.4 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 1.4000 Therefore, s 1 5 32.4 MPa and s 2 52 122.4 MPa and (b) M AXIMUM SHEAR STRESSES and t 5 77.4 MPa and t 52 77.4 MPa s aver 5 s x 1 s y 2 52 45 MPa u s 2 5 u p 1 1 45 85 162.23 8 u s 1 5 u p 1 2 45 85 72.23 8 t max 5 B ¢ s x 2 s y 2 2 1 t xy 2 5 77.4 MPa u p 2 5 27.23
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Unformatted text preview: 8 u p 1 5 117.23 8 Solution 7.3-10 Propeller shaft } } x O u p 2 5 27.23 8 32.4 MPa 122.4 MPa y x O 77.4 MPa u s 1 5 72.23 8 45 MPa 45 MPa y y x O t xy s x s y s x 5 3500 psi s y 5 1120 psi t xy 5 2 1200 psi (a) P RINCIPAL STRESSES 2 u p 5 2 45.24 8 and u p 5 2 22.62 8 2 u p 5 134.76 8 and u p 5 67.38 8 For 2 u p 5 2 45.24 8 : For 2 u p 5 134.76 8 : s x 1 5 620 psi s x 1 5 4000 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 2 1.0084 Therefore, s 1 5 4000 psi and s 2 5 620 psi and u p 2 5 67.38 8 u p 1 5 2 22.62 8 } x O u p 2 5 67.38 8 4000 psi 620 psi y A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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