Q. An air vessel, which is made of steel in 2m long. It has an external diameter 40 cm and is 2cm thick. 1. Calculate the permissible pressure allowed if the longitudinal stress in the wall must not exceed 18MPA. 2. Determine longitudinal and hoop strains. 3. Calculate the change in diameter and change in volume. Take E= 200 GPa and v 0.3
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- The stresses on an element are sx= 1000 Psi. sy= 500 psi, and txy= 350 psi. Find the stresses acting on an element oriented at an angle 0 = 250. Show these stresses on the rotated element.A rubber ball (sec figure) is inflated to a pressure of 65 kPa. At that pressure, the diameter of the ball is 240 mm and the wall thickness is 1.25 mm. The rubber has a modulus of elasticity E = 3,7 MPa and Poisson's ratio v = 0.48. (a) Determine the maximum stress and strain in the ball, (b) If the strain must be limited to 0.425, Find the minimum required wall thickness of the ball.A hollow, circular, cast-iron pipe (Ec =12,000 ksi) supports a brass rod (Ec= 14,000 ksi} and weight W — 2 kips, as shown. The outside diameter of the pipe is dc= 6 in. (a) If the allowable compressive stress in the pipe is S00O psi and the allowable shortening of the pipe is 0.02 in., what is the minimum required wall thickness trmm? (Include the weights of the rod and steel cap in your calculations.) (b) What is the elongation of the brass rod Srdue to both load Wand its own weight? (c) What is the minimum required clearance h?
- (a) Solve part (a) of the preceding problem if the pressure is 8.5 psi, the diameter is 10 in., the wall thickness is 0,05 in., the modulus of elasticity is 200 psi, and Poisson's ratio is 0.48. (b) If the strain must be limited to 1.01, find the maximum acceptable inflation pressureA spherical balloon is filled with a gas. The outer diameter of the balloon is 20 in. and the thickness is 0,012 in. Calculate the maximum permissible pressure in the balloon if the allowable tensile stress and the allowable shear stress in the balloon are 1 ksi and 0.3 ksi, respectively.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 98 MPa, and a factor of safety of 2,8 is required. (a) At what value of the strain should the operators take action to reduce the pressure in the tank? (Data for the steel are modulus of elasticity E = 210 GPa and Poisson's ratio v = 0.30.) (b) What is the associated strain in the radial direction
- An element of aluminum is subjected to tri-axial stresses. Calculate the strains in the element in x, y, and z directions lithe stresses axayand az are -2000 psi, 3500 psi, and 2700 psi, respectively. Assume E = 10,000 ksi and v = 0.33. Also, find the unit volume change of the element.A large spherical tank (see figure) contains gas at a pressure of 420 psi. The tank is 45 ft in diameter and is constructed of high-strength steel having a yield stress in tension of 80 ksi. (a) Determine the required thickness (to the nearest 1/4 inch) of the wall of the tank if a factor of safety of 3,5 with respect to yielding is required. (b) If the tank wall thickness is 2.25 in., what is the maximum permissible internal pressure?A spherical steel pressure vessel (diameter 500 mm, thickness 10 mm) is coated with brittle lacquer that cracks when the strain reaches 150 X 10~ (see figure). (a) What internal pressure p will cause the lacquer to develop cracks? (Assume E = 205 GPa and v = 0.30.) (b) If the strain is measured at 125 x 10-6, what is the internal pressure at that point?
- - A specimen used in a coupon test has norm al stress ??. = 15 MPa (see figure). Using Mohr’s circle, find the state of stress on the element oriented at angle ? = 20° and show the full stress state on a sketch of a properly oriented element.An element of aluminum is subjected to tri- axial stresses. Calculate the strains in the element in and directions if the stresses are -20 MPa, 28 MPa, and -18 MPa. respectively. Assume E = 70 GPa and v = 0.33. Also, find the strain energy density of the element.An aluminum tube is required to transmit an axial tensile force P = 33 k (sec figure part a). The thickness of the wall of the tube is 0.25 in. (a) What is the minimum required outer diameter d minif the allowable tensile stress is 12.000 psi? (b) Repeat part (a) if the tube has a hole of a diameter J/10 at mid-length (see figure parts b and C).