590_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

590_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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584 CHAPTER 7 Analysis of Stress and Strain Problem 7.3-5 The normal and shear stresses acting on element A are 6500 psi, 18,500 psi, and 3800 psi (in the directions shown in the figure) (see the figure for Problem 7.2-5). Determine the maximum shear stresses and associated normal stresses and show them on a sketch of a properly oriented element. Solution 7.3-4 P RINCIPAL STRESSES u p 2 ± u p 1 + 90° u p 2 ± 75.8° u p 1 ±² 14.2° u p 1 ± atan a 2 t xy s x ² s y b 2 s x ± 40 MPa s y ±² 160 MPa t xy ±² 54 MPa s 2 ±² 173.6 MPa ; s 1 ± 53.6 MPa ; s 2 ± s x + s y 2 + s x ² s y 2 cos 1 2 u p 2 2 + t xy sin 1 2 u p 2 2 s 1 ± s x + s y 2 + s x ² s y 2 cos 1 2 u p 1 2 + t xy sin 1 2 u p 1 2 Solution 7.3-5 P RINCIPAL ANGLES s 2 ± s x + s y 2 + s x ² s y 2 cos 1 2 u p 2 2 + t xy sin 1 2 u p 2 2 s 1 ± s x + s y 2 + s x ² s y 2 cos 1 2 u p 1 2 + t xy sin 1 2 u p 1 2 u p 2 ± u p 1 + 90° u p 2 ± 81.55° u p 1 ±² 8.45° u p 1 ± atan a 2 t xy s x ² s y b 2 s x ± 6500 psi s y ±² 18500 psi t xy ±² 3800 psi M AXIMUM SHEAR STRESSES s aver ± s x + s y 2 s aver ±² 6000 psi ; u s 1 ± u p 1 ² 45° u s 1 ±²
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Unformatted text preview: 53.4 ; t max A a s x s y 2 b 2 + t xy 2 t max 13065 psi ; s 2 19065 psi s 1 7065 psi Problem 7.3-6 An element in plane stress from the fuselage of an airplane is subjected to compressive stresses of magnitude 27 MPa in the horizontal direction and tensile stresses of magnitude 5.5 MPa in the vertical direction. Also, shear stresses of magnitude 10.5 MPa act in the directions shown (see the figure for Problem 7.2-6). Determine the maximum shear stresses and associated normal stresses and show them on a sketch of a properly oriented element. 07Ch07.qxd 9/27/08 1:18 PM Page 584...
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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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