605_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

605_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 599 599 SECTION 7.4 Mohr’s Circle Solution 7.4-7 sx sy 0 psi u (a) ELEMENT AT 2u txy 0 psi 104.0° R 2700 psi (b) PRINCIPAL STRESSES Point P1: up1 52° txy R 2700 psi Point D: sx1 R cos (2u 2620 psi ; s1 Point P2: up2 tx1y1 R sin (2u 653 psi up2 R ; 2700 psi 45° s2 ; 45° 90° 2 90°) tx1y1 ; Dœ : sy1 R cos (2u 90°) sy1 Point up1 R 90°) sx1 s1 90° 2 2620 psi ; s2 ; 2700 psi ; Problem 7.4-8 An element in pure shear is subjected to stresses txy shown in the figure. Using Mohr’s circle, determine: y 14.5 MPa, as (a) The stresses acting on an element oriented at a counterclockwise angle u from the x axis (b) The principal stresses. Show all results on sketches of properly oriented elements. 22.5° O x 14.5 MPa Solution 7.4-8 sx sy 0 MPa (a) ELEMENT AT 2u R 0 MPa u txy 22.5° 14.5 MPa Point P1: up1 45.00° |txy| R Point D: sx1 sx1 tx1y1 tx1y1 Point D œ : sy1 sy1 s1 14.50 MPa R cos (2u 90°) ; 10.25 MPa R sin (2u 10.25 MPa Point P2: up2 270° u 2 p1 s1 R ; 90°) ; ; 135.0° 14.50 MPa 270° 2 up2 135.0° s2 90°) 10.25 MPa R cos (2u (b) PRINCIPAL STRESSES R s2 14.50 MPa ; ; ; ...
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