634_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

634_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 628 9/27/08 1:24 PM Page 628 CHAPTER 7 Analysis of Stress and Strain Problem 7.7-9 A element of material in plane strain (see figure) is subjected to strains Px 480 * 10 6 6 , Py 70 * 10 and gxy 420 * 10 . Determine the following quantities: (a) the strains for an element oriented at an angle u 75°, (b) the principal strains, and (c) the maximum shear strains. Show the results on sketches of properly oriented element. Solution 7.7-9 Element in plane strain âx 480 * 10 6 gxy 420 * 10 âx + ây âx For up âx1 gx1y1 + 2 2 ây âx 2 2 ây1 For u ây cos 2u + sin 2u + âx + ây 70 * 10 gxy 2 gxy 2 6 22.85°: 6 ây âx + ây âx1 2 sin 2u 2 â1 22.8° ° up2 cos 2u + gxy 2 sin 2u 6 568 * 10 ‹ up1 cos 2u ây âx + 568 * 10 â2 112.8 18 * 10 6 ; 6 ; âx1 75°: âx1 202 * 10 6 ây1 348 * 10 6 gx1y1 569 * 10 6 gmax 2 A gmax 587 * 10 MAXIMUM SHEAR STRAINS us1 PRINCIPAL STRAINS â1,2 âx + ây ; 2 A 275 * 10 â1 tan 2up 6 568 * 10 gxy 6 âx ây a ây âx up1 2 us2 âx â2 1.0244 2up 45.69° and 225.69° up 22.85° and 112.85° âaver 6 18 * 10 6 2 ; 67.8° 587 * 10 âx + ây 2 b 2 293 * 10 22.2° or 157.8° 6 us1 + 90° gmin ây 2 gxy 2 b +a b 2 2 ; 293 * 10 587 * 10 gxy 6 45° gmax a 2 b +a 6 ; 275 * 10 6 6 6 , ...
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