643_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

643_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ; ; ...
View Full Document

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.

Ask a homework question - tutors are online