07-02ChapGere.0010 - s x 1 5 R 2 R cos 2 u 5 13.8 MPa t x 1...

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448 CHAPTER 7 Analysis of Stress and Strain (b) M AXIMUM SHEAR STRESSES Point S 1 : t max 5 R 5 7250 psi Point S 2 : t min 52 R 52 7250 psi s aver 5 R 5 7250 psi u s 2 5 45 8 2 u s 2 5 90 8 u s 1 52 45 8 2 u s 1 52 90 8 x O 7250 psi u s 2 5 45 8 7250 psi 7250 psi y S 2 S 1 Problem 7.4-2 An element in uniaxial stress is subjected to tensile stresses s x 5 55 MPa, as shown in the figure. Using Mohr’s circle, determine (a) the stresses acting on an element oriented at an angle u 52 30° from the x axis (minus means clockwise) and (b) the maximum shear stresses and associated normal stresses. Show all results on sketches of properly oriented elements. Solution 7.4-2 Uniaxial stress y x O 55 MPa s x 5 55 MPa s y 5 0 t xy 5 0 (a) E LEMENT AT u 5 2 30 8 (All stresses in MPa) 2 u 5 2 60 8 u 5 2 30 8 R 5 27.5 MPa Point C : Point D : Point D 9 : t x 1 y 1 52 R sin ƒ 2 u ƒ 52 23.8 MPa
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Unformatted text preview: s x 1 5 R 2 R cos 2 u 5 13.8 MPa t x 1 y 1 5 R sin 2 u 5 R sin 60 8 5 23.8 MPa 5 R (1 1 cos 60 8 ) 5 41.2 MPa s x 1 5 R 1 R cos 2 u s x 1 5 27.5 MPa (b) M AXIMUM SHEAR STRESSES Point S 1 : t max 5 R 5 27.5 MPa Point S 2 : t min 5 2 R 5 2 27.5 MPa s aver 5 R 5 27.5 MPa u s 2 5 45 8 2 u s 2 5 90 8 u s 1 5 2 45 8 2 u s 1 5 2 90 8 D' D ( u 5 ] 30 8 ) A ( u 5 0) 55 MPa 2 u = ] 60 8 C S 1 S 2 R R O x 1 t x 1 y 1 B ( u 5 90 8 ) x O 41.2 MPa u 5 30 8 13.8 MPa 23.8 MPa y D D' x O 27.5 MPa u s 2 5 45 8 27.5 MPa 27.5 MPa y S 1 S 2 A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Institute of Technology.

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