623_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

623_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 07Ch07.qxd 9/27/08 1:22 PM Page 617 SECTION 7.6 Triaxial Stress 617 Solution 7.6-3 Triaxial stress (cube) âx 225 * 10 6 ây âz 37.5 * 10 6 a E (c) CHANGE IN VOLUME 6 37.5 * 10 V 0.25 (cast iron) 14,000 ksi a (a) NORMAL STRESSES Eq. (7-54a): sx ea 3 0.0192 in.3 ( decrease) ; (d) STRAIN ENERGY 2) )âx + (ây + âz)] [(1 1 (sx âx + sy ây + sz âz) 2 Eq. (7-57a): u ; 4200 psi 0.000300 3 ¢V E (1 + )(1 âx + ây + âz Eq. (7-55): e 4.0 in. 0.55125 psi In a similar manner, Eqs. (7-54 b and c) give 2100 psi sz 2100 psi ; sy U ua 3 35.3 in.-lb ; (b) MAXIMUM SHEAR STRESS 2100 psi s2 s1 s3 2100 psi 4200 psi tmax s3 s1 ; 1050 psi 2 Problem 7.6-4 Solve the preceding problem if the cube is granite (E compressive strains Px 720 * 10 6 and Py Pz 270 * 10 6 60 GPa, 0.25) with dimensions a = 75 mm and . Solution 7.6-4 Triaxial stress (cube) âx 720 * 10 6 ây âz 270 * 10 6 a 0.25 270 * 10 75 mm E 6 sx 64.8 MPa ; (c) CHANGE IN VOLUME Eq. (7-55): e (a) NORMAL STRESSES Eq.(7-54a): E (1 + )(1 10.8 MPa 2 60 GPa (Granite) s3 s1 tmax V ¢V 2) [(1 ea 3 532 mm3 ( decrease) (d) STRAIN ENERGY 64.8 MPa Eq. (7-57 a): u 43.2 MPa 1 (s â + syây + szâz) 2 xx 0.03499 MPa U (b) MAXIMUM SHEAR STESS s3 ; )âx + (âx + âz)] In a similar manner, Eqs. (7-54 b and c) give 43.2 MPa sz 43.2 MPa ; sy 43.2 MPa s2 1260 * 10 a3 ; s1 âx + ây + âz ua 3 14.8 N # m 14.8 J 34.99 kPa ; 6 ...
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