602_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

602_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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596 CHAPTER 7 Analysis of Stress and Strain (b) M AXIMUM SHEAR STRESSES Point S1: t max ± R t max ± 24.5 MPa ; ; u s 1 ±² 45.0° u s 1 ± ² 90° 2 Point S2: s aver ± R s aver ± 24.5 MPa ; t max ±² R t max ±² 24.5 MPa ; u s 2 ± 90° 2 u s 2 ± 45.0° ; Problem 7.4-3 An element in uniaxial stress is subjected to compressive stresses of magnitude 6100 psi, 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 (see figure). (b) The maximum shear stresses and associated normal stresses. Show all results on sketches of properly oriented elements. y x O 6100 psi 1 2 Solution 7.4-3 (a) E LEMENT AT A SLOPE OF 1 ON 2 Point C: Point D: t x 1 y 1 ±² R sin (2 u ) t x 1 y 1 ± 2440 psi ; s x 1 ±² 4880 psi ; s x 1 ± R + R cos (2 u ) s c ± R s c ±² 3050 psi 2 u ± 53.130° R ± s x 2 R ±² 3050 psi ; u ± atan a 1 2 b u ± 26.565° s x ±² 6100 psi s y ± 0 psi t xy ± 0 psi Point (b) M AXIMUM SHEAR STRESSES
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Unformatted text preview: Point S1: Point S2: s aver ± R s aver ± ² 3050 psi ; t max ± R t max ± ² 3050 psi ; u s 2 ± ² 45° ; u s 2 ± ² 90° 2 t max ± ² R t max ± 3050 psi ; u s 1 ± 90° 2 u s 1 ± 45° ; s y 1 ± ² 1220 psi D œ : s y 1 ± R ² R cos (2 u ) Problem 7.4-4 An element in biaxial stress is subjected to stresses s x ± ² 48 MPa and s y ± 19 MPa, as shown in the figure. Using Mohr’s circle, determine: (a) The stresses acting on an element oriented at a counterclockwise angle u ± 25° from the x axis. (b) The maximum shear stresses and associated normal stresses. Show all results on sketches of properly oriented elements. y x O 19 MPa 48 MPa 07Ch07.qxd 9/27/08 1:19 PM Page 596...
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