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609_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 609_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 7.4 Mohr’s Circle 603 Solution 7.4-15 b 180° 2 u + a b 82.28° a atan a | t xy | | s x s aver | b a 32.28° R 2 ( s x s aver ) 2 + t xy 2 R 3933 psi s aver s x + s y 2 s aver 2375 psi u 65° s x 5700 psi s y 950 psi t xy 2100 psi s y 1 2904 psi ; Point D œ : s y 1 s aver R cos ( b ) t x 1 y 1 R sin ( b ) t x 1 y 1 3897 psi ; s x 1 1846 psi ; Point D: s x 1 s aver + R cos ( b ) Problems 7.4-16 s x 29.5 MPa, s y 29.5 MPa, t xy 27 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. y x O t xy s x s y Solution 7.4-16 (a) P RINCIPAL STRESSES u p 2 u p 1 90° u p 2 21.2° ; u p 1 180° a 2 u p

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609_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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