635_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

635_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 07Ch07.qxd 9/27/08 1:24 PM Page 629 629 SECTION 7.7 Plane Strain Problem 7.7-10 Solve the preceding problem for the following data: Px gxy 780 * 10 6 , and u 6 1120 * 10 6 430 * 10 , Py , 45°. Solution 7.7-10 Element in plane strain âx gxy âx1 gx1y1 780 * 10 ây âx 2 2 ây âx âx + ây 430 * 10 6 ‹ up1 up2 + 2 For u ây 6 âx + ây 2 ây1 6 1120 * 10 sin 2u + cos 2u + gxy 2 gxy 2 â1 65.7° 254 * 10 â2 155.7° 1296 * 10 sin 2u cos 2u âx1 45°: âx1 385 * 10 ây1 6 1165 * 10 gx1y1 690 * 10 6 6 A MAXIMUM SHEAR STRAINS gmax 2 a ây âx 2 521 * 10 gmax us1 PRINCIPAL STRAINS ây 2 âx + ây âx gxy 2 â1, 2 ; a b +a b 2 A 2 2 775 * 10 254 * 10 gxy â1 tan 2up 6 6 âx ; 521 * 10 â2 gmax u s2 gmin 6 1296 * 10 6 1.1304 ây 2up 131.5° and 311.5° up 65.7° and 155.7° For up âx1 65.7°: âx + ây ây âx + 2 254 * 10 2 6 cos 2u + gxy 2 sin 2u âaver 1041 * 10 up1 2 b +a us1 + 90° 2 2 6 20.7° 6 ; 110.7° 1041 * 10 âx + ây 2 b 6 45° 1041 * 10 gxy 6 ; 775 * 10 6 6 ; 6 ; ...
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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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