659_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

659_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 8.2 Spherical Pressure Vessels 653 Problem 8.2-8 Solve the preceding problem for the following data: diameter 1.0 m, thickness 48 mm, pressure 22 MPa, modulus 210 GPa, and Poisson’s ratio 0.29. Solution 8.2-8 r ± 0.5 m E ± 210 GPa t ± 48 mm v ± 0.29 (steel) (a) T ENSILE LOAD CARRIED BY WELD T ± Total load f ± load per inch T ± pA ± p p r 2 c ± Circumference of tank ± 2 p r ± 5.5 MN/m ; f ± T c ± p 1 p r 2 2 2 p r ± pr 2 ± (22 MPa)(0.5 m) 2 (b) M AXIMUM SHEAR STRESS IN WALL ( EQ . 8-3) (c) M AXIMUM NORMAL STRAIN IN WALL ( EQ . 8-4) ± 3.87 * 10 ² 4 ; â max ± pr (1 ² v ) 2 tE ± (22 MPa)(0.5 m) 0.71 2(48 mm)(210 GPa) ± 57.3 MPa ; t max ± pr 4 t ± (22 MPa)(0.5 m) 4(48 mm) Problem 8.2-9 A spherical stainless-steel tank having a diameter of 22 in. is used to store propane gas at a pressure of 2450 psi. The properties of the steel are as follows: yield stress in tension, 140,000 psi; yield stress in shear, 65,000 psi; modulus of elasticity, 30 ³ 10 6 psi; and Poisson’s ratio, 0.28. The desired factor of safety with respect to yielding is 2.8.
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Unformatted text preview: Also, the normal strain must not exceed 1100 10 6 . Determine the minimum permissible thickness t min of the tank. Solution 8.2-9 r 11 in. E 30 10 6 psi p 2450 psi v 0.28 (steel) s Y 140000 psi n 2.8 t Y 65000 psi max 1100 10 6 M IMIMUM WALL THICKNESS t (1) T ENSION ( EQ . 8-1) (2450 psi) (11 in.) 2 140000 psi 2.8 0.269 in. t 1 pr 2 s max pr 2 a s Y n b s max pr 2 t 1 (2) S HEAR ( EQ . 8-3) (3) S TRAIN ( EQ . 8-4) t 3 t 2 t 1 Thus, t min 0.294 in. ; 0.294 in. (2450 psi)(11 in.) 2 1 1100 * 10 6 21 30 * 10 6 psi 2 0.72 t 3 pr 2 max E (1 v ) max pr 2 t 3 E (1 v ) t 2 pr 4 t Y n (2450 psi)(11 in.) 4 65000 psi 2.8 0.29 in. t max pr 4 t 2 08Ch08.qxd 9/18/08 11:03 AM Page 653...
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