606_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

606_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Problem 7.4-10 s x ± 27 MPa, s y ± 14 MPa, t xy ± 6 MPa, u ± 40° Using Mohr’s circle, determine the stresses acting on an element oriented at an angle u from the x axis. Show these stresses on a sketch of an element oriented at the angle u .( Note: The angle u is positive when counterclockwise and negative when clockwise.) y x O t xy s x s y 600 CHAPTER 7 Analysis of Stress and Strain Problem 7.4-9 An element in pure shear is subjected to stresses t xy ± 3750 psi, as shown in the figure. Using Mohr’s circle, determine: (a) The stresses acting on an element oriented at a slope of 3 on 4 (see figure). (b) The principal stresses. Show all results on sketches of properly oriented elements.
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Unformatted text preview: O 3 4 y x 3750 psi Solution 7.4-9 (a) E LEMENT AT A SLOPE OF 3 ON 4 s y 1 ±² 3600 psi ; Point D œ : s y 1 ±² R cos (2 u ² 90°) t x 1 y 1 ± 1050 psi ; t x 1 y 1 ± ² R sin (2 u ² 90°) s x 1 ± 3600 psi ; Point D: s x 1 ± R cos (2 u ² 90°) 2 u ± 73.740° R ± t xy R ± 3750 psi u ± atan a 3 4 b u ± 36.870° s x ± 0 psi s y ± 0 psi t xy ± 3750 psi (b) P RINCIPAL STRESSES s 2 ± ² R s 2 ± ² 3750 psi ; u p 2 ± ² 45° ; Point P2: u p 2 ± ² 90° 2 s 1 ± R s 1 ± 3750 psi ; Poin P1: u p 1 ± 90° 2 u p 1 ± 45° ; Probs. 7.4-10 through 7.4-15 07Ch07.qxd 9/27/08 1:19 PM Page 600...
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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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