SolutionEquilibrium for the Ring: From the FBD What is the pressure the hoop exerts on the cylinder, and the tensile stress in the ring when it cools back down to 65 F?Īns:T1 = 128F, s1 = 12.1 ksi, p = 252 psi If it and the 24-in.-diameter rigid cylinder have a temperature of 65 F, determine the temperature to which the hoop should be heated in order for it to just slip over the cylinder. If the vessel sustains an internal pressure of 450 kPa, determine the average shear stress in the weld and the state of stress in the wall of the vessel.Īns:tavg = 5.06 MPa,s1 = 5.06 MPa,s2 = 2.53 MPa Solution+cFy = 0 p(0.225)2450(103) - tavg (2p)(0.225)(0.01) = 0 Ī pressure-vessel head is fabricated by welding the circular plate to the end of the vessel as shown. The gas within the pipe is at a pressure of 600 lb> in2. If there are rigid retainers at the piers that hold the pipe fixed, determine the longitudinal and hoop stress in the pipe if the temperature rises 60 F from the temperature at which it was installed. The gas pipe line is supported every 20 ft by concrete piers and also lays on the ground. If the bolts are tightened so that the tension in them is 400 lb, determine the normal stress in the band, the pressure exerted on the cylinder, and the distance half the band stretches.Īns:s1 = 1.60 ksi, p = 25 psi, d = 0.00140 in. wide and is secured around the smooth rigid cylinder.
Draw the state of stress on a volume element located on the wall.ĭ = P1L = 55.1724(10- 6)(p)a8 + 116 b = 0.00140 in. If the valve A is closed and the water pressure is 300 psi, determine the longitudinal and hoop stress developed in the wall of the pipe at point B. The steel water pipe has an inner diameter of 12 in. The state of stress on an element in the pipe wall is shown in Fig. If the valve A is opened and the flowing water has a pressure of 250 psi as it passes point B, determine the longitudinal and hoop stress developed in the wall of the pipe at point B. = 24 7 10, thin-wall analysis can be used. SolutionNormal Stress: Since the pipe has two open ends, If the steam pressure in the boiler is 1.35 MPa, determine (a) the circumferential stress in the boilers plate away from the seam, (b) the circumferential stress in the outer cover plate along the rivet line aa, and (c) the shear stress in the rivets.Īns:(a) s1 = 127 MPa,(b) s1 = 79.1 MPa,(c) (tavg)b = 322 MPa + cFy = 0 Fb - 79.1(106) = 0Ī boiler is constructed of 8-mm-thick steel plates that are fastened together at their ends using a butt joint consisting of two 8-mm cover plates and rivets having a diameter of 10 mm and spaced 50 mm apart as shown. Each piston has a radius of 45 mm and the cylinder has a wall thickness of 2 mm. The pressure P is supported by the surface of the pistons in the longitudinal direction.ĭetermine the maximum force P that can be exerted on each of the two pistons so that the circumferential stress in the cylinder does not exceed 3 MPa. If the cylinder has a wall thickness of 2 mm, determine the state of stress in the wall of the cylinder. 82Īir pressure in the cylinder is increased by exerting forces P = 2 kN on the two pistons, each having a radius of 45 mm. Longitudinal Stress for Cylindrical Vessels: Applying Eq. Hoop Stress for Cylindrical Vessels: Since rt= Draw a volume element of the material at this point, and show the results on the element. If the inner diameter of the tank is 22 in., and the wall thickness is 0.25 in., determine the stress components acting at point A. The tank of the air compressor is subjected to an internal pressure of 90 psi. and the inner diameter of the cylinder is 8 in.Īns:(a) s1 = 1.04 ksi, s2 = 0, (b) s1 = 1.04 ksi, s2 = 520 psi
Determine the state of stress in the wall of the cylinder for both cases if the piston P causes the internal pressure to be 65 psi. The thin-walled cylinder can be supported in one of two ways as shown. If it is subjected to an internal pressure of p = 200 psi, determine its outer radius if the maximum normal stress is not to exceed 15 ksi.
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If it is subjected to an internal pressure of p = 300 kPa, determine its required thickness if the maximum normal stress is not to exceed 12 MPa.Ĭlick here to Purchase full Solution Manual at Ī pressurized spherical tank is made of 0.5-in.-thick steel. A spherical gas tank has an inner radius of r = 1.5 m.
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