07-01ChapGere.0012

# 07-01ChapGere.0012 - properly oriented element Solution...

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Problem 7.3-3 An element in plane stress is subjected to stresses s x 52 9,900 psi, s y 52 3,400 psi, and t xy 5 3,600 psi (see the figure for Problem 7.2-3). Determine the principal stresses and show them on a sketch of a properly oriented element. Solution 7.3-3 Principal stresses 436 CHAPTER 7 Analysis of Stress and Strain s x 52 9900 psi s y 52 3400 psi t xy 5 3600 psi P RINCIPAL STRESSES 2 u p 5 2 47.92 8 and u p 5 2 23.96 8 2 u p 5 132.08 8 and u p 5 66.04 8 For 2 u p 5 2 47.92 8 : For 2 u p 5 132.08 8 : s x 1 52 1,800 psi s x 1 52 11,500 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 52 1.1077 Therefore, s 1 52 1,800 psi and s 2 52 11,500 psi and } u p 2 52 23.96 8 u p 1 5 66.04 8 Problem 7.3-4 An element in plane stress is subjected to stresses s x 5 42 MPa, s y 52 140 MPa, and t xy 52 60 MPa (see the figure for Problem 7.2-4). Determine the principal stresses and show them on a sketch of a
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Unformatted text preview: properly oriented element. Solution 7.3-4 Principal stresses s x 5 42 MPa s y 5 2 140 MPa t xy 5 2 60 MPa P RINCIPAL STRESSES 2 u p 5 2 33.40 8 and u p 5 2 16.70 8 2 u p 5 146.60 8 and u p 5 73.30 8 For 2 u p 5 2 33.40 8 : For 2 u p 5 146.60 8 : s x 1 5 2 158 MPa s x 1 5 60 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 0.6593 Therefore, s 1 5 60 MPa and s 2 5 2 158 MPa and } u p 2 5 73.30 8 u p 1 5 2 16.70 8 x O u p 1 5 66.04 8 11,500 psi y 1,800 psi x O u p 2 5 73.30 8 60 MPa y 158 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 Tech.

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