596_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

596_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 07Ch07.qxd 9/27/08 590 1:18 PM Page 590 CHAPTER 7 Analysis of Stress and Strain Solution 7.3-14 sx sy 16.5 MPa txy 91 MPa 39 MPa tmax tmax (a) PRINCIPAL STRESSES 2txy tan(2up) up1 s2 sx up1 sy 2txy sx sy b 90° + up1 sx + sy up2 sy sx + 2 2 sx + sy sy sx + 2 2 9631.7 psi sy sx a 2 2 b + txy2 us1 us1 up1 45° and t1 66.4 MPa 2 17.98° up2 s1 atan a A (b) MAXIMUM SHEAR STRESSES us2 us2 up1 + 45° and t2 66.4 MPa 72.02° cos 12up12 + txy sin 12up12 sx + sy saver ; 27.0° saver 2 ; 63.0° 37.3 MPa cos 12up22 + txy sin 12up22 Therefore, For up1 s1 17.98° For up 2 s2 72.0° Problems 7.3-15 29.2 MPa sx 103.7 MPa 3300 psi, sy 11,000 psi, txy 4500 psi (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. Solution 7.3-15 s sy 3300 psi 11000 psi txy 4500 psi (a) PRINCIPAL STRESSES tan(2up) sx up1 s2 sy 90° + up1 up1 sx sy b 2 For up2 sx + sy up2 sy sx + 2 2 sx + sy sy sx + 2 2 114.73° cos 12up12 + txy sin 12up12 cos 12up22 + txy sin 12up22 s1 A 1228 psi s2 114.7° 13072 psi (b) MAXIMUM SHEAR STRESSES tmax 24.73° up2 s1 atan a 2txy 2txy Therefore, For up1 24.7° tmax a sy sx 2 5922 psi us1 and t1 up1 45° 5922 psi us2 and t2 up1 + 45° 5922 psi saver 2 b + txy2 sx + sy 2 us1 us2 saver ; 20.3° 69.7° ; 7150 psi ...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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