637_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

637_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 631 SECTION 7.7 Plane Strain Problem 7.7-12 Solve the preceding problem if the plate is made of aluminum with E sx is 86.4 MPa, the angle f is 21° , and the strain P is 946 * 10 6 72 GPa and 631 1/3, the stress . Solution 7.7-12 Aluminum plate in biaxial stress sx E gxy 86.4 MPa 0 72 GPa sy MAXIMUM IN-PLANE SHEAR STRESS ? Strain gage: f â 21° (tmax) xy 6 946 * 10 âx STRAIN IN BIAXIAL STRESS (EQS. 7-39) âx ây 1 (sy E âz E (sx sy) 1 (86.4 72,000 sx) 1 (sy 72,000 STRAINS AT ANGLE f âx1 âx + ây ây + 946 * 10 2 6 cos 2u + sy) gxy 2 sy 500 * 10 6 ây 6 101 * 10 6 A MAXIMUM SHEAR STRAINS (EQ. 7-75) (2) xy plane: (gmax) xy 2 gxy (3) xz plane: sin 2u yz plane: (gmax)xz 2 (4) 0 (gmax) yz 2 gyz A a ây âx 2 0 (gmax) xy gxz 4 s b cos 42° 3y 21.55 MPa 1100 * 10 (1) 1 1 2 a ba b a 57.6 + sy b 2 72,000 3 1 1 b a 115.2 + a ba 2 72,000 Solve for sy: 28.8) âz 21° (EQ. 7-71a) âx 2 1 s) 3y 1/ 3 (86.4 72,000 sy) ; 32.4 MPa 2 STRAINS FROM EQS. (1), (2), AND (3) UNITS: All stresses in MPa. 1 (s Ex sy sx 1/3 0 A a gxy âx âz 2 2 b +a 2 (gmax) yz gxz 2 b +a 2 6 b ; 2 6 1600 * 10 âz 2 ây b 2 1200 * 10 (gmax) xz a 2 b +a ; gyz 2 2 399 * 10 b 6 ; ...
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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.

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