07-01ChapGere.0011 - t xy 5 48 MPa (see the figure for...

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Principal Stresses and Maximum Shear Stresses When solving the problems for Section 7.3, consider only the in-plane stresses (the stresses in the xy plane). Problem 7.3-1 An element in plane stress is subjected to stresses s x 5 6500 psi, s y 5 1700 psi, and t xy 5 2750 psi (see the figure for Problem 7.2-1). Determine the principal stresses and show them on a sketch of a properly oriented element. Solution 7.3-1 Principal stresses SECTION 7.3 Principal Stresses and Maximum Shear Stresses 435 s x 5 6500 psi s y 5 1700 psi t xy 5 2750 psi P RINCIPAL STRESSES 2 u p 5 48.89 8 and u p 5 24.44 8 2 u p 5 228.89 8 and u p 5 114.44 8 For 2 u p 5 48.89 8 : For 2 u p 5 228.89 8 : s x 1 5 450 psi s x 1 5 7750 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 1.1458 Therefore, s 1 5 7750 psi and s 2 5 450 psi and } u p 2 5 114.44 8 u p 1 5 24.44 8 Problem 7.3-2 An element in plane stress is subjected to stresses s x 5 80 MPa, s y 5 52 MPa, and
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Unformatted text preview: t xy 5 48 MPa (see the figure for Problem 7.2-2). Determine the principal stresses and show them on a sketch of a properly oriented element. Solution 7.3-2 Principal stresses s x 5 80 MPa s y 5 52 MPa t xy 5 48 MPa P RINCIPAL STRESSES 2 u p 5 73.74 8 and u p 5 36.87 8 2 u p 5 253.74 8 and u p 5 126.87 8 For 2 u p 5 73.74 8 : For 2 u p 5 253.74 8 : s x 1 5 16 MPa s x 1 5 116 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 3.429 Therefore, s 1 5 116 MPa and s 2 5 16 MPa and } u p 2 5 126.87 8 u p 1 5 36.87 8 x O u p 1 5 24.44 8 450 psi y 7750 psi x O u p 1 5 36.87 8 16 MPa y 116 MPa A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Institute of Technology.

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