607_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

607_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 601 SECTION 7.4 Mohr’s Circle 601 Solution 7.4-10 sx u sy 27 MPa txy 40° saver R a 6 MPa b 2u 2(sx saver 2 saver)2 + txy 2 txy sx saver sx1 20.50 MPa R b a Point D: sx1 sx + sy atan a 14 MPa saver + R cos ( b ) a ; 27.5 MPa tx1y1 tx1y1 8.8459 MPa R sin ( b ) 5.36 MPa Point D œ : sy1 b 37.29° 42.71° saver sy1 ; R cos ( b ) ; 13.46 MPa Problem 7.4-11 sx 3500 psi, sy 12,200 psi, txy 3300 psi, u 51° Using Mohr’s circle, determine the stresses acting on an element oriented at an angle u from the x axis. Show these stresses on a sketch of an element oriented at the angle u. (Note: The angle u is positive when counterclockwise and negative when clockwise.) Solution 7.4-11 sx u saver R a sy 3500 psi 3300 psi ; 51° 2(sx b 180° + 2u Point D: sx1 sx + sy atan a txy 12200 psi saver 2 sx1 7850 psi b a saver + R cos ( b ) saver) + txy txy sx saver 2 R R sin ( b ) tx1y1 5460 psi 3569 psi Point D sy1 œ: b a 37.18° ; 11982 psi tx1y1 2 40.82° sy1 saver ; R cos ( b ) ; 3718 psi Problem 7.4-12 sx 47 MPa, sy 186 MPa, txy 29 MPa, u 33° Using Mohr’s circle, determine the stresses acting on an element oriented at an angle u from the x axis. Show these stresses on a sketch of an element oriented at the angle u. (Note: The angle u is positive when counterclockwise and negative when clockwise.) Solution 7.4-12 sx 47MPa u 33° saver R a b 2(sx sy 2u txy 29MPa Point D: sx1 sx1 sx + sy atan a ` 186MPa 2 saver) + txy txy sx a saver b `b 61.7 MPa 116.50 MPa 2 R a 43.35° 75.3077 MPa 22.65° tx1y1 51.7 MPa ; R sin ( b ) tx1y1 saver 2 saver + R cos ( b ) Point D œ : sy1 sy1 saver ; R cos ( b ) 171.3 MPa ; ...
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