639_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

639_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 633 SECTION 7.7 Plane Strain MAXIMUM SHEAR STRAINS ây 2 âx gxy 2 gmax b +a b a 2 A 2 2 6 671 * 10 gmax 6 1342 * 10 us1 up1 gmax 45° 54.8° 6 1342 * 10 us2 us1 + 90° gmin ; 144.8° 6 1342 * 10 âx + ây âaver ; 245 * 10 2 6 Problem 7.7-14 Solve the preceding problem for the following data: sx txy 16 MPa, and u 50°. The material is brass with E 150 MPa, sy 0.34. 100 GPa and 210 MPa, Solution 7.7-14 Element in plane strain sx 150 MPa sy txy 16 MPa E 210 MPa 100 GPa 0.34 HOOKE’S LAW (EQS. 7-34 AND 7-35) âx 1 (s Ex sy) 786 * 10 ây 1 (s Ey sx) 1590 * 10 gxy FOR u âx1 txy 2txy(1 + ) G E âx + ây ây âx + 2 2 ây âx 2 ây1 429 * 10 6 2 sin 2u + 717 * 10 âx + ây cos 2u + gxy 2 sin 2u PRINCIPAL STRAINS ây 2 âx + ây âx gxy 2 ; b +a b â1,2 a 2 A 2 2 âx1 gxy 2 â1 cos 2u 6 tan 2up 2up 6 907 * 10 6 6 1188 * 10 6 358.5 * 10 gx1y1 6 50°: 1469 * 10 gx1y1 6 up 732 * 10 gxy âx 6 ây ; 456 * 10 â2 0.5333 151.9° and 331.9° 76.0° and 166.0° 6 1644 * 10 6 633 ...
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