07-01ChapGere.0008

07-01ChapGere.0008 - , and t xy . Show the results on a...

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432 CHAPTER 7 Analysis of Stress and Strain Problem 7.2-14 Solve the preceding problem for s x 5 32 MPa and s y 52 50 MPa (see figure). Solution 7.2-14 Biaxial stress y x a a O 50 MPa 32 MPa u s x 5 32 MPa s y 52 50 MPa t xy 5 0 Find angles u for s 5 0. s 5 normal stress on plane a-a 5 2 9 1 41 cos 2 u (MPa) For we obtain [ 2 u 5 77.32 8 and u 5 38.66 8 cos 2 u 5 9 41 s x 1 5 0, 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 TRESS ELEMENT u 5 38.66 8 5 2 40 MPa t x 1 y 1 52 s x 2 s y 2 sin 2 u 1 t xy cos 2 u s y 1 5 s x 1 s y 2 s x 1 52 18 MPa s x 1 5 0 a a u s x O 40 MPa u 5 38.66 8 18 MPa y Problem 7.2-15 An element in plane stress from the frame of a racing car is oriented at a known angle u (see figure). On this inclined element, the normal and shear stresses have the magnitudes and directions shown in the figure. Determine the normal and shear stresses acting on an element whose sides are parallel to the xy axes; that is, determine s x , s y
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Unformatted text preview: , and t xy . Show the results on a sketch of an element oriented at u 5 0. Solution 7.2-15 Plane stress 2,360 psi 4,180 psi 15,220 psi y x O u = 30 Transform from u 5 30 8 to u 5 8 . Let: s x 5 2 15,220 psi, s y 5 2 4,180 psi, t xy 5 2,360 psi, and u 5 2 30 8 . 5 2 14,500 psi s y 1 5 s x 1 s y 2 s x 1 5 2 4,900 psi t x 1 y 1 5 2 s x 2 s y 2 sin 2 u 1 t xy cos 2 u 5 2 3,600 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 F OR u 5 0: t xy 5 t x 1 y 1 5 2 3,600 psi s y 5 s y 1 5 2 4,900 psi s x 5 s x 1 5 2 14,500 psi y x O 4,900 psi 14,500 psi 3,600 psi A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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