07-02ChapGere.0013

07-02ChapGere.0013 - 21.801 8 2 R 5 87 MPa R 5 43.5 MPa...

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Problem 7.4-6 An element in biaxial stress is subjected to stresses s x 52 24 MPa and s y 5 63 MPa, as shown in the figure. Using Mohr’s circle, determine (a) the stresses acting on an element oriented at a slope of 1 on 2.5 (see figure) and (b) the maximum shear stresses and associated normal stresses. Show all results on sketches of properly oriented elements. Solution 7.4-6 Biaxial stress SECTION 7.4 Mohr’s Circle for Plane Stress 451 Point D : Point D 9 : t x 1 y 1 5 R sin 60 85 3248 psi s x 1 5 2250 1 R cos 60 85 4125 psi t x 1 y 1 52 R sin 60 852 3248 psi s x 1 5 2250 2 R cos 60 85 375 psi (b) M AXIMUM SHEAR STRESSES Point S 1 : t max 5 R 5 3750 psi Point S 2 : t min 52 R 52 3750 psi s aver 5 2250 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 3250 psi u 5 60 8 4125 psi 375 psi y D D' x O 3750 psi u s 2 5 45 8 2250 psi 2250 psi y S 2 S 1 y x O 63 MPa 24 MPa 1 2.5 s x 52 24 MPa s y 5 63 MPa t xy 5 0 (a) E LEMENT AT A SLOPE OF 1 ON 2.5 (All stresses in MPa) 2 u 5 43.603 8 u 5
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Unformatted text preview: 21.801 8 2 R 5 87 MPa R 5 43.5 MPa Point C : Point D : t x 1 y 1 5 R sin 2 u 5 30 MPa s x 1 5 2 R cos 2 u 1 19.5 5 2 12 MPa s x 1 5 19.5 MPa u 5 arctan 1 2.5 5 21.801 8 Point D 9 : (b) M AXIMUM SHEAR STRESSES Point S 1 : t max 5 R 5 43.5 MPa Point S 2 : t min 5 2 R 5 2 43.5 MPa s aver 5 19.5 MPa u s 2 5 2 45 8 2 u s 2 5 2 90 8 u s 1 5 45 8 2 u s 1 5 90 8 t x 1 y 1 5 2 R sin 2 u 5 2 30 MPa s x 1 5 19.5 1 R cos 2 u 5 51 MPa u 1 2.5 D' D A ( u 5 0) 19.5 43.603 8 2 u C S 1 S 2 R R B ( u 5 90 8 ) ± x 1 t x 1 y 1 63 24 O x O 30 MPa u 5 21.80 8 12 MPa 51 MPa y D D' x O 43.5 MPa u s 1 5 45 8 19.5 MPa 19.5 MPa y S 2 S 1 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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