646_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

646_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 07Ch07.qxd 9/27/08 640 1:24 PM Page 640 CHAPTER 7 Analysis of Stress and Strain FOR u âx1 âC âC SOLVE EQS. (1) AND (2): 120°: âx + ây ây âx + 2 âA + ây 2 gxy 13 ây âA + 2 2 3ây âA + 4 4 cos 2u + gxy (cos 240°) 2 gxy sin 2u ây (sin 240°) gxy 2 1 (2âB + 2âC 3 2 (âB 13 âA) âC) ; ; (2) 4 Problem 7.7-21 On the surface of a structural component in a space vehicle, the y strainsare monitored by means of three strain gages arranged as shown in the figure. During a certain maneuver, the following strains were recorded: Pa 1100 * 10 6, Pb 200 * 10 6, and Pc 200 * 10 6. Determine the principal strains and principal stresses in the material, which is a magnesium alloy for which E 6000 ksi and 0.35. (Show the principal strains and principal stresses on sketches of properly oriented element.) C B 30° O Solution 7.7-21 Magnesium alloy: E 6000 ksi 0.35 tan 2up STRAIN GAGES Gage A at u 0° Gage B at u 90° Gage C at u 1100 * 10 6 âB âC 150° âx âA FOR u 90°: ây âB 200 * 10 FOR u 150°: âx + ây 6 1100 * 10 200 * 10 ây âx 2 6 2 650 * 10 6 cos 2u + + 225 * 10 gxy 2 6 0.43301gxy Solve for gxy: gxy 6 1558.9 * 10 PRINCIPAL STRAINS ây 2 âx + ây âx gxy 2 â1,2 ; a b +a b 2 A 2 2 650 * 10 â1 1550 * 10 6 ; 900 * 10 6 â2 6 250 * 10 âx ây 60° 1550 * 10 6 ‹ up1 + gxy up 1.7321 30° FOR up 30°: ây âx + ây âx gxy âx1 + cos 2u + sin 2u 2 2 2 6 200 * 10 0°: âC 2up 6 200 * 10 PA FOR u âx1 13 30-60-90° strain rosette x A 6 up2 sin 2u 30° 120° 6 â1 â2 1550 * 10 6 250 * 10 ; 6 ; ...
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