07-02ChapGere.0009 - stresses Show all results on sketches of properly oriented elements Solution 7.4-1 Uniaxial stress y x O 14,500 psi s x 5

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SECTION 7.4 Mohr’s Circle for Plane Stress 447 (b) P RINCIPAL STRESSES 2 u p 5 2 44.93 8 and u p 5 2 22.46 8 2 u p 5 135.07 8 and u p 5 67.54 8 For 2 u p 5 2 44.93 8 : For 2 u p 5 135.07 8 : Therefore, s 1 5 26.3 MPa and s 2 52 84.7 MPa and u p 2 52 22.46 8 u p 1 5 67.54 8 s x 1 5 26.3 MPa s x 1 52 84.7 MPa s x 1 5 s x 1 s y 2 1 s x 2 s y 2 cos 2 u 1 t xy sin 2 u tan 2 u p 5 2 t xy s x 2 s y 52 0.99746 x O u p 1 5 67.54 8 84.7 MPa 26.3 MPa y Mohr’s Circle for Plane Stress The problems for Section 7.4 are to be solved using Mohr’s circle. Consider only the in-plane stresses (the stresses in the xy plane). Problem 7.4-1 An element in uniaxial stress is subjected to tensile stresses s x 5 14,500 psi, as shown in the figure. Using Mohr’s circle, determine (a) the stresses acting on an element oriented at a counterclockwise angle u 5 24° from the x axis and (b) the maximum shear stresses and associated normal
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Unformatted text preview: stresses. Show all results on sketches of properly oriented elements. Solution 7.4-1 Uniaxial stress y x O 14,500 psi s x 5 14,500 psi s y 5 t xy 5 (a) E LEMENT AT u 5 24 8 (All stresses in psi) 2 u 5 48 8 u 5 24 8 R 5 7250 psi Point C : s x 1 5 7250 psi Point D : Point D 9 : t x 1 y 1 5 5390 psi s x 1 5 R 2 R cos 2 u 5 2400 psi t x 1 y 1 5 R sin 2 u 5 2 5390 psi s x 1 5 R 1 R cos 2 u 5 12,100 psi D' D ( u 5 24 8 ) A ( u 5 0) 14,500 2 u 2 u s 2 2 u s 1 = ] 90 8 C S 1 S 2 R R O B ( u 5 90 8 ) s x 1 t x 1 y 1 x O 5390 psi u 5 24 8 2400 psi 12,100 psi 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 Institute of Technology.

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