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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 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 17.1 MPa ; Point D: s x 1 s c 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 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 ± ² R t max ± ² 43.0 MPa ; u s 2 ± ² 45.0° ; Point S2: u s 2 ± 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 Mohr’s 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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