601_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

601_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 7.4 Mohr’s Circle 595 Mohr’s Circle 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 ± 11,375 psi, as shown in the figure. Using Mohr’s circle, determine: (a) The stresses acting on an element oriented at a counterclockwise angle u ± 24° 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 11,375 psi Solution 7.4-1 (a) E LEMENT AT PointD œ : s y 1 ± R ² R cos (2 u ) t x 1 y 1 ±² 4227 psi ; t x 1 y 1 ±² R sin (2 u ) s x 1 ± 9493 psi ; Point D: s x 1 ± R + R cos(2 u ) Point C: s c ± R s c ± 5688 psi 2 u ± 48° R ± s x 2 R ± 5688 psi ; u ± 24° s x ± 11375 psi s y ± 0 psi t xy ± 0 psi (b) M AXIMUM SHEAR STRESSES s aver ± R s aver ± 5688 psi ; t max ±² R t max ±² 5688 psi ; Point S2: u s 2 ± 90° 2 u s 2 ± 45° ; t max ± R t max ± 5688 psi ; Point S1: u s 1 ± ² 90° 2 u s 1 ±² 45° ; s y 1 ± 1882 psi
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Unformatted text preview: ; Problem 7.4-2 An element in uniaxial stress is subjected to tensile stresses s x ± 49 MPa, as shown in the figure Using Mohr’s circle, determine: (a) The stresses acting on an element oriented at an angle u ± ² 27° from the x axis (minus means clockwise). (b) The maximum shear stresses and associated normal stresses. Show all results on sketches of properly oriented elements. y x O 49 MPa Solution 7.4-2 (a) E LEMENT AT Point C: s c ± R s c ± 24.5 MPa 2 u ± ² 54.0° R ± s x 2 R ± 24.5 MPa u ± ² 27° s x ± 49 MPa s y ± 0 MPa t xy ± 0 MPa Point D: Point s y 1 ± 10.1 MPa ; D œ s y1 ± R ² R cos ( |2 u | ) t x 1 y 1 ± 19.8 MPa ; t x 1 y 1 ± ² R sin (2 u ) s x 1 ± 38.9 MPa ; s x 1 ± R + R cos ( | 2 u | ) 07Ch07.qxd 9/27/08 1:19 PM Page 595...
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