603_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

603_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 597 597 SECTION 7.4 Mohr’s Circle Solution 7.4-4 sx sy 48 MPa (a) ELEMENT AT 2u u Point C: sx sc (b) MAXIMUM SHEAR STRESSES Point S1: us1 |sx| + |sy| R 2 sc sx + R Point D: sx1 0 MPa ; 25° 50.0 deg R txy 19 MPa us1 33.5 MPa tmax 14.5 MPa tx1y1 R sin(2u) tx1y1 tmax 90° 2 sc ; 45.0° tmax R saver saver ; 33.5 MPa 14.5 MPa ; sc + R cos(2u) sy1 7.0 MPa Problem 7.4-5 An element in biaxial stress is subjected to stresses sx and sy ; 33.5 MPa us2 ; 25.7 MPa Point D œ : sy1 tmax R ; 36.0 MPa ; 45.0° Point S2: us2 R cos(2u) sx1 90° 2 6250 psi 1750 psi, as shown in the figure. Using Mohr’s circle, determine: y (a) The stresses acting on an element oriented at a counterclockwise angle u 55° from the x axis. (b) The maximum shear stresses and associated normal stresses. Show all results on sketches of properly oriented elements. 1750 psi 6250 psi O x Solution 7.4-5 sx sy 6250 psi (a) ELEMENT AT 2u u Point D: sx1 sx1 0 psi |sx| + |sy| 2 sx R R sc tx1y1 sc 45° R Point S2: us2 ; 3464 psi Point D œ : sy1 us1 tmax 2250 psi R cos(2u) tmax 90° 2 ; ; 4000 psi us2 ; 45° tmax ; sy1 4250 psi R tmax 4000 psi ; saver R sin (2u) tx1y1 90° 2 4000 psi sc + R cos(2u) 250 psi (b) MAXIMUM SHEAR STRESSES Point S1: us1 60° 120° R Point C: sc txy 1750 psi sc saver 2250 psi ; ...
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