2.2 A small closed cylinder has dimensions 50 mm external diameter by 160 mm long with 0.25 mm wall thickness. (a) What is the allowable internal pressure if the safe tensile stress for the material is 250 MPa? (b) What change in length and diameter occurs in the cylinder if it is pressurised to this value? Take E200 GPa, and 0.3. [2.53 MPa, 0.0400 mm, 0.0531 mm] V 2.3 A hydraulic ram with an internal diamter of 50.5 mm and external diameter of 55 mm carries an internal pressure of 15 MPa. Before the piston reaches the end of its travel, the cylinder can be treated as an 'open' thin-walled cylindrical pressure vessel. The Modulus of Elasticity and the Poisson's ratio are respectively 200 GPa and 0.3. Consider the case that the piston has not reached the end of its travel. (a) Determine the hoop and longitudinal stress in the cylinder. (b) Determine the strains within the cylinder wall in the three axis directions: the hoop, the longitudinal, and in the out-of-plane direction. [168.3 MPa, 0 MPa; 841.7, -252.5 -252.5] 2.4 A pressure vessel with an outside diameter of 1300 mm and wall thickness of 12 mm is made of steel with E200 GPa and 0.3. Strains measured on the vessel at a particular condition were 621.6 x 10 and y 146.3 x 10-6 (a) Determine the stresses in the x- and y-directions. (b) Specify the type of the vessel: closed cylinder, open cylinder, or sphere. (c) Calculate the internal pressure. [146.3 MPa, 73.1 MPa; closed cylinder; 2.7 MPa] 2.5 A spherical pressure vessel of 500 mm inside diameter is to be fabricated from a steel with a 400 MPa ultimate strength in tension. Knowing that the maximum gage pressure is to be 8 MPa and that a factor of safety of 3.00 is desired, determine the smallest wall thickness which may be used. [7.5 mm] 2.6 A spherical pressure vessel is of 450 mm inside diameter with a wall thickness of 6 mm. It is constructed by welding together two aluminium hemispheres. The ultimate and yield stresses in tension of the weld are 168 MPa and 112 MPa respectively. If the tank must have a factor of safety of 2.1 with respect to the ultimate strength and 1.5 with respect to the yield strength, what is the maximum allowable pressure in the tank? [3.98 MPa)