612_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

612_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 07Ch07.qxd 9/27/08 606 1:19 PM Page 606 CHAPTER 7 Analysis of Stress and Strain Problems 7.4-21 sx 11,500 psi, sy 18,250 psi, txy 7200 psi Using Mohr’s circle, determine (a) the principal stresses and (b) the maximum shear stresses and associated normal stresses. Show all results on sketches of properly oriented elements. Solution 7.4-21 sx txy sy 11500 psi 7200 psi saver R 2(sx saver 2 txy saver `b R s2 a 2 up2 180° 2 R + saver 64.89° a us1 up2 90° + us1 us1 us2 Point S1: saver ; 32.4° 270° 2 us2 a ; 22827 psi (b) MAXIMUM SHEAR STRESSES a up1 ; 6923 psi 7952 psi (a) PRINCIPAL STRESSES up1 R + saver Point P2: s2 14875 psi saver)2 + txy2 sx Point P1: s1 s1 sx + sy atan a ` a 18250 psi tmax 192.6° ; 14875 psi R ; 102.6° tmax 7952 psi ; 57.6° Problems 7.4-22 sx 3.3 MPa, sy 8.9 MPa, txy 14.1 MPa Using Mohr’s circle, determine (a) the principal stresses and (b) the maximum shear stresses and associated normal stresses. Show all results on sketches of properly oriented elements. Solution 7.4-22 sy sx 3.3 MPa txy (a) PRINCIPAL STRESSES 14.1 MPa saver R a 2(sx up1 saver 2 2 saver) + txy sx saver a 2 2.8 MPa txy2 `b a + 180° 2 up2 sx + sy atan a ` 8.9 MPa R a 15.4 MPa 66.6° up2 up1 123.3° 33.3° Point P1: s1 R + saver s1 18.2 MPa Point P2: s2 R + saver ; ; ; ...
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