632_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

632_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 07Ch07.qxd 9/27/08 626 1:24 PM Page 626 CHAPTER 7 Analysis of Stress and Strain Solution 7.7-6 Element in plane strain âx 420 * 10 6 gxy 310 * 10 6 âx + ây âx1 ây ây âx cos 2u + + 2 gx1y1 2 ây âx 2 ây1 âx + ây For u gxy sin 2u + 2 6 170 * 10 2 gxy 2 sin 2u cos 2u 37.5°: âx1 âx1 6 351 * 10 ây1 101 * 10 gx1y1 490 * 10 6 6 480 * 10 6, 140 * 10 6, and gxy 350 * 10 6. Determine the principal strains and maximum shear strains, and show these strains on sketches of properly oriented elements. Problem 7.7-7 The strains for an element of material in plane strain (see figure) are as follows: Px Py Solution 7.7-7 Element in plane strain âx 480 * 10 gxy 6 ây 6 350 * 10 PRINCIPAL STRAINS â1, 2 âx + ây ; 2 A 310 * 10 â1 tan 2up 6 554 * 10 gxy a âx 6 âx 6 140 * 10 ây 2 gxy 2 b +a b 2 2 ; 244 * 10 â2 6 66 * 10 6 1.0294 ây 2up 45.8° and 22.9° and gmax 2 134.2° up 67.1° For up âx1 + 2 2 554 * 10 ‹ up1 up2 ây âx gmax 67.1° cos 2u + gxy 2 us1 â1 â2 554 * 10 66 * 10 ây âx 2 2 b +a 6 6 ; ; 488 * 10 up1 45° 488 * 10 2 67.9° or 112.1° 6 us1 + 90° âaver 2 b 6 gmax gmin gxy 6 us2 sin 2u 6 22.9° a 244 * 10 22.9°: âx + ây A MAXIMUM SHEAR STRAINS 488 * 10 âx + ây 2 ; 22.1° 6 ; 310 * 10 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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