604_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

604_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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598 CHAPTER 7 Analysis of Stress and Strain Problem 7.4-6 An element in biaxial stress is subjected to stresses s x ±² 29 MPa and s y ± 57 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). (b) The maximum shear stresses and associated normal stresses. Show all results on sketches of properly oriented elements. y x O 57 MPa 29 MPa 1 2.5 Solution 7.4-6 (a) E LEMENT AT A SLOPE OF 1 ON 2.5 s y 1 ± 45.1 MPa Point D œ : s y 1 ± s c + R cos (2 u ) ; t x 1 y 1 ± R sin (2 u ) t x 1 y 1 ± 29.7 MPa s x 1 ±² 17.1 MPa ; Point D: s x 1 ± s c ² R cos (2 u ) Point C: s c ± s x + R s c ± 14.0 MPa 2 u ± 43.603° R ± | s x | + | s y | 2 R ± 43.0 MPa ; u ± atan a 1 2.5 b u ± 21.801° s x ±² 29 MPa s y ± 57 MPa t xy ± 0 MPa (b) M AXIMUM SHEAR STRESSES
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Unformatted text preview: s aver s c s aver 14.0 MPa ; t max R t max 43.0 MPa ; u s 2 45.0 ; Point S2: u s 2 90 2 t max R t max 43.0 MPa ; Point S1: u s 1 90 2 u s 1 45.0 ; Problem 7.4-7 An element in pure shear is subjected to stresses t xy 2700 psi, as shown in the figure. Using Mohrs circle, determine: (a) The stresses acting on an element oriented at a counterclockwise angle u 52 from the x axis. (b) The principal stresses. Show all results on sketches of properly oriented elements. y x O 2700 psi 07Ch07.qxd 9/27/08 1:19 PM Page 598...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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