641_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 641_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 635 SECTION 7.7 Plane Strain Solution 7.7-15 âA 45° strain rosette 6 520 * 10 âC âB 360 * 10 6 ‹ up1 6 80 * 10 up2 âA gxy 520 * 10 2âB âA âx + ây ; 2 A 220 * 10 6 551 * 10 â1 ây âC PRINCIPAL STRAINS â1,2 6 âC 280 * 10 80 * 10 6 6 gmax 2 a ây 6 2 b +a ; 331 * 10 â2 2 gxy 2 b 2 6 111 * 10 6 gmax us1 gmax us2 gmin âaver tan 2up 2up up âx ây ; 6 ; a ây âx 2 gxy 2 b 2 6 662 * 10 2 b +a 6 up1 45° 662 * 10 us1 + 90° 32.5°or 147.5° 6 57.5° 662 * 10 âx + ây 2 ; 6 ; 220 * 10 6 0.4667 25.0° and 205.0° 12.5° and 102.5° For up âx1 gxy A 6 111 * 10 102.5° â2 331 * 10 âx 551 * 10 12.5° â1 MAXIMUM SHEAR STRAINS FROM EQS. (7-77) AND (7-78) OF EXAMPLE 7-8: âx 635 12.5°: âx + ây ây âx + 2 551 * 10 2 cos 2u + gxy 2 sin 2u 6 Problem 7.7-16 A 45°strain rosette (see figure) mounted on the surface of an automobile frame gives the following readings: gage A, 310 * 10 6; gage B, 180 * 10 6; and gage C, 160 * 10 6. Determine the principal strains and maximum shear strains, and show them on sketches of properly oriented elements. ...
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