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589_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

589_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 7.3 Principal Stresses and Maximum Shear Stresses 583 Problem 7.3-2 An element in plane stress is subjected to stresses s x 100 MPa, s y 80 MPa, and t xy 28 MPa (see the figure for Problem 7.2-2). Determine the principal stresses and show them on a sketch of a properly oriented element. Solution 7.3-2 P RINCIPAL STRESSES u p 2 u p 1 + 90° u p 2 125.17° u p 1 35.2° u p 1 atan a 2 t xy s x s y b 2 s x 100 MPa s y 80 MPa t xy 28 MPa s 2 60 MPa ; s 1 120 MPa ; s 2 s x + s y 2 + s x 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 s y 2 cos 1 2 u p 1 2 + t xy sin 1 2 u p 1 2 Problem 7.3-3 An element in plane stress is subjected to stresses s x 5700 psi, s y 2300 psi, and t xy 2500 psi (see the figure for Problem 7.2-3). Determine the principal stresses and show them on a sketch of a properly oriented element. Solution 7.3-3 P RINCIPAL STRESSES u p 1 u p 2 + 90° u p 1 62.1° u p 2 27.89° u p 2 atan a 2 t xy s x s y b 2 s x 5700 psi
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Unformatted text preview: s y ±² 2300 psi t xy ± 2500 psi s 2 ± ² 7023 psi ; s 1 ± ² 977 psi ; 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 Problem 7.3-4 The stresses acting on element A in the web of a train rail are found to be 40 MPa tension in the horizontal direction and 160 MPa compression in the vertical direction (see figure). Also, shear stresses of magnitude 54 MPa act in the directions shown (see the figure for Problem 7.2-4). Determine the principal stresses and show them on a sketch of a properly oriented element. 07Ch07.qxd 9/27/08 1:18 PM Page 583...
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