595_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

595_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 07Ch07.qxd 9/27/08 1:18 PM Page 589 SECTION 7.3 Principal Stresses and Maximum Shear Stresses Therefore, tmax For up1 For up2 s1 76.3° A 2262 kPa s2 13.70° 263 kPa ; us1 us1 up1 45° and t1 1000 kPa ; Problems 7.3-13 a sy sx 2 sx 2 b + txy2 14,500 psi, sy 58.7° ; us 2 up1 + 45° us 2 31.3° ; 1000 kPa and t2 sx + sy saver saver 1263 kPa 2 (b) MAXIMUM SHEAR STRESSES tmax 145 psi 1070 psi, txy 1900 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 7.3-13 sx sy 14500 psi txy 1070 psi Therefore, 1900 psi For up1 atan a sx up1 sy up1 90° + up1 sx sy s1 s2 sx + sy up2 sy sx + 2 2 sx + sy sy sx + 2 14764 psi ; 97.9° s2 806 psi ; 2 A tmax 6979 psi (b) MAXIMUM SHEAR STRESSES 2 7.90° up2 b s1 tmax 2txy tan(2up) 2txy 7.90° For up2 (a) PRINCIPAL STRESSES 97.90° cos 12up12 + txy sin 12up12 cos 12up22 + txy sin 12up22 sx 16.5 MPa, sv 91 MPa, txy sy sx 2 us1 u p1 45° and t1 6979 psi 2 b + txy2 us1 us2 us2 up1 + 45° and t2 6979 psi saver Problems 7.3-14 a sx + sy 2 saver ; 37.1° 52.9° ; 7785 psi 39 MPa (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. 589 ...
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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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