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643_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 643_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 637 637 SECTION 7.7 Plane Strain Problem 7.7-17 A solid circular bar of diameter d 1.5 in. is subjected to an axial force P and a torque T (see figure). Strain gages A and B mounted on the surface of the bar give reading Pa 100 * 10 6 and Pb 55 * 10 6. The bar is made of steel 0.29. having E 30 * 106 psi and d T P C (a) Determine the axial force P and the torque T. (b) Determine the maximum shear strain gmax and the maximum shear stress tmax in the bar. B 45∞ A C Solution 7.7-17 Circular bar (plane stress) Bar is subjected to a torque T and an axial force P. E 6 30 * 10 psi Diameter d STRAIN AT u 0.29 âx1 1.5 in. âx1 STRAIN GAGES At u 0°: âA At u âx 45°: âB 100 * 10 âx + ây ây âx + 2 2 âB 55 * 10 gxy cos 2u + 6 2u sin 2u 2 (1) 90° Substitute numerical values into Eq. (1): 6 6 55 * 10 6 55 * 10 45° Solve for T: 35.5 * 10 T 6 6 (0.0649 * 10 )T ; 1390 lb-in ELEMENT IN PLANE STRESS 4P sx P A âx 100 * 10 sy pd 2 6 txy 0 ây MAXIMUM SHEAR STRAIN AND MAXIMUM SHEAR STRESS 16T gxy pd 3 âx 29 * 10 6 Eq. (7-75): gmax 2 AXIAL FORCE P âx sx E 4P pd 2E a )T P 6 5300 lb 32T(1 + ) )T (T pd 3E lb-in.) ; 6 180.4 * 10 ây âx 2 2 b +a 111 * 10 pd 2Eâx 4 SHEAR STRAIN txy 2txy(1 + ) gxy G E (0.1298 * 10 A 6 (0.1298 * 10 6 gmax 222 * 10 rad tmax Ggmax 2 b 2 rad 6 gxy rad 2580 psi ; ; ...
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