665_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

665_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 08Ch08.qxd 9/18/08 11:03 AM Page 659 659 SECTION 8.3 Cylindrical Pressure Vessels Problem 8.3-6 A circular cylindrical steel tank (see figure) contains a volatile fuel under pressure. A strain gage at point A records the longitudinal strain in the tank and transmits this information to a control room. The ultimate shear stress in the wall of the tank is 84 MPa, and a factor of safety of 2.5 is required. At what value of the strain should the operators take action to reduce the pressure in the tank? (Data for the steel are as follows: modulus of elasticity E 205 GPa and Poisson’s ratio v 0.30.) Pressure relief valve Cylindrical tank A Solution 8.3-6 tULT n 84 MPa E tULT n tmax 2.5 205 GPa tmax v 0.3 33.6 MPa Find maximum allowable strain reading at the gage pr t s1 pr 2t s2 From Eq. (8-11a) â2 â2max âmax From Eq. (8-10) tmax s1 2 pr 2t pr (1 2 tE 2v) pmax r (1 2 tE tmax (1 E 2v) 2v) tmax (1 E 2v) 6.56 max 10 5 2ttmax r Pmax Cylinder Problem 8.3-7 A cylinder filled with oil is under pressure from a piston, as shown in the figure. The diameter d of the piston is 1.80 in. and the compressive force F is 3500 lb. The maximum allowable shear stress tallow in the wall of the cylinder is 5500 psi. What is the minimum permissible thickness tmin of the cylinder wall? (See the figure on the next page.) F p Piston Probs. 8.3-7 and 8.3-8 Solution 8.3-7 Cylinder with internal pressure Maximum shear stress (Eq. 8-10): tmax d 1.80 in. r F 3500 lb tallow 5500 psi Find minimum thickness tmin. Pressure in cylinder: p F 2prt Minimum thickness: 0.90 in. F A pr 2t t min F 2prtallow Substitute numerical values: F pr 2 t min 3500 lb 2p(0.90 in.)(5500 psi) 0.113 in. ; ...
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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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