611_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

611_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 07Ch07.qxd 9/27/08 1:19 PM Page 605 SECTION 7.4 Mohr’s Circle 605 Problems 7.4-19 sx 2050 psi, sy 6100 psi, txy 2750 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 7.4-19 sx 2050 psi sy saver R 2(sx sx + sy atan a ` a 6100 psi txy saver 2 2 saver) + txy sx saver 2750 psi R `b a 3415 psi 53.63° up2 up1 us2 90° + a 2 ; 26.8° tmax us1 90° + us1 Point S1: saver up2 ; 660 psi (b) MAXIMUM SHEAR STRESSES ; 63.2° R + saver s2 us1 a 180° 2 a 2 ; 7490 psi Point P2: s2 (a) PRINCIPAL STRESSES up1 R + saver s1 4075 psi txy2 Point P1: s1 us2 71.8° ; 4075 psi tmax R ; 18.2° ; 3415 psi Problems 7.4-20 sx 2900 kPa, sy 9100 kPa, txy 3750 kPa 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 7.4-20 sx 2900 kPa sy saver R a 2(sx sx + sy atan a ` 9100 kPa txy saver 2 sx saver `b R a Point P1: s1 s1 6000 kPa saver)2 + txy2 txy 3750 kPa R + saver R + saver Point P2: s2 s2 4865.4393 kPa (b) MAXIMUM SHEAR STRESSES 50.42° 90° + a 2 us2 90° + us1 (a) PRINCIPAL STRESSES a + 180° 2 up2 a 2 up2 up1 25.2° 115.2° ; ; 1135 kPa us1 up1 ; 10865 KPa ; Point S1: saver tmax us1 us2 160.2° 6000 kPa R ; 70.2° tmax ; ; 4865 kPa ; ...
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