07-01ChapGere.0009

07-01ChapGere.0009 - s y 5 t xy 5 At u 5 40 8 and u 5 80...

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Problem 7.2-16 Solve the preceding problem for the element shown in the figure. Solution 7.2-16 Plane stress SECTION 7.2 Plane Stress 433 26.7 MPa 66.7 MPa 25.0 MPa y x O u = 60 ° Transform from u 5 60 8 to u 5 0 8 . Let: s x 52 26.7 MPa, s y 5 66.7 MPa, t xy 52 25.0 MPa, and u 5 2 60 8 . s y 1 5 s x 1 s y 2 s x 1 52 25 MPa t x 1 y 1 52 s x 2 s y 2 sin 2 u 1 t xy cos 2 u 52 28 MPa 5 65 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 F OR u 5 0: t xy 5 t x 1 y 1 52 28 MPa s y 5 s y 1 52 25 MPa s x 5 s x 1 5 65 MPa Problem 7.2-17 A plate in plane stress is subjected to normal stresses s x and s y and shear stress t xy , as shown in the figure. At counterclockwise angles u 5 40° and u 5 80° from the x axis the normal stress is 5000 psi tension. If the stress s x equals 2000 psi tension, what are the stresses s y and t xy ? Solution 7.2-17 Plane stress y x O t xy s y s x = 2000 psi s x 5 2000 psi
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Unformatted text preview: s y 5 ? t xy 5 ? At u 5 40 8 and u 5 80 8 ; (tension) Find s y and t xy . F OR u 5 40 8 : or 0.41318 s y 1 0.98481 t xy 5 3826.4 psi (1) 5 2000 1 s y 2 1 2000 2 s y 2 cos 80 8 1 t xy sin 80 8 s x 1 5 5000 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 s x 1 5 5000 psi F OR u 5 80 8 : or 0.96985 s y 1 0.34202 t xy 5 4939.7 psi (2) S OLVE E QS . (1) AND (2): s y 5 4370 psi t xy 5 2050 psi 5 2000 1 s y 2 1 2000 2 s y 2 cos 160 8 1 t xy sin 160 8 s x 1 5 5000 O y x 65 MPa 25 MPa 28 MPa A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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