591_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

591_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 7.3 Principal Stresses and Maximum Shear Stresses 585 Problem 7.3-7 The stresses acting on element B in the web of a wide-flange beam are found to be 14,000 psi compression in the horizontal direction and 2600 psi compression in the vertical direction. Also, shear stresses of magnitude 3800 psi act in the directions shown (see the figure for Problem 7.2-7). Determine the maximum shear stresses and associated normal stresses and show them on a sketch of a properly oriented element. Solution 7.3-6 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 1 ± u p 2 + 90° u p 1 ± 106.43° u p 2 ± 16.43° u p 2 ± atan a 2 t xy s x ² s y b 2 s x ±² 27 MPa s y ± 5.5 MPa t xy ±² 10.5 MPa M AXIMUM SHEAR STRESSES s aver ± s x + s y 2 s aver ±² 10.8 MPa ; u s 1 ± u p 1 ² 45° u s 1 ± 61.4° t max ± 19.3 MPa ; t max ± A a s x ² s y 2 b 2 + t xy 2 s 2 ±² 30.1 MPa s 1 ± 8.6 MPa Solution 7.3-7 P RINCIPAL ANGLES 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 1 ± u p 2 + 90° u p 1 ± 106.85° u p 2 ±
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Unformatted text preview: 16.85° u p 2 ± atan a 2 t xy s x ² s y b 2 t xy ±² 3800 psi s x ± ² 14000 psi s y ± ² 2600 psi M AXIMUM SHEAR STRESSES s aver ± s x + s y 2 s aver ± ² 8300 psi ; u s 1 ± u p 1 ² 45° u s 1 ± 61.8° ; t max ± A a s x ² s y 2 b 2 + t xy 2 t max ± 6851 psi ; s 2 ±² 15151 psi s 1 ± ² 1449 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 Problem 7.3-8 The normal and shear stresses acting on element B are s x ±² 46 MPa, s y ±² 13 MPa, and t xy ± 21 MPa (see figure for Problem 7.2-8). 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 585...
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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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