07-03ChapGere.0003

07-03ChapGere.0003 - y 5 11 MPa t xy 5 8 MPa u 5 50 8 (All...

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454 CHAPTER 7 Analysis of Stress and Strain Point D : Point D 9 : t x 1 y 1 52 R sin 16.260 852 1120 psi s x 1 52 R cos 16.260 852 3840 psi t x 1 y 1 5 R sin 16.260 85 1120 psi s x 1 5 R cos 16.260 85 3840 psi (b) P RINCIPAL STRESSES Point P 1 : s 1 5 R 5 4000 psi Point P 2 : s 2 52 R 52 4000 psi u p 2 52 45 8 2 u p 2 52 90 8 u p 1 5 45 8 2 u p 1 5 90 8 x O 1120 psi u 5 36.87 8 3840 psi 3840 psi y D D' x O u p 1 5 45 8 4000 psi 4000 psi y P 2 P 1 Problems 7.4-10 through 7.4-15 An element in plane stress is subjected to stresses s x , s y , and t xy (see figure). 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.) y x O t xy s x s y Solution 7.4-10 Plane stress (angle u ) s x 5 21 MPa s
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Unformatted text preview: y 5 11 MPa t xy 5 8 MPa u 5 50 8 (All stresses in MPa) a 5 arctan 8 5 5 57.99 8 R 5 Ï (5) 2 1 (8) 2 5 9.4340 MPa b 5 2 u 2 a 5 100 8 2 a 5 42.01 8 Point D ( u 5 50 8 ): Point D 9 ( u 5 2 40 8 ): t x 1 y 1 5 R sin b 5 6.31 MPa s x 1 5 16 2 R cos b 5 8.99 MPa t x 1 y 1 5 2 R sin b 5 2 6.31 MPa s x 1 5 16 1 R cos b 5 23.01 MPa Data for 7.4-10 s x 5 21 MPa, s y 5 11 MPa, t xy 5 8 MPa, u 5 50° D' D A ( u 5 0) 2 u 5 100 8 R R R s x 1 ( u 5 90 8 ) ( u 5 50 8 ) t x 1 y 1 8 8 80 8 b B 16 11 21 C 5 O a x O 23.01 MPa u 5 50 8 6.31 MPa 8.99 MPa y D' D 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 Tech.

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