Assignment: Pressure Vessels I; 5/11/2007; second year, Mechanical Engineering Department.
Solve the following three problems:
Question One
Hemispherical end caps are welded to a cylindrical main body to form a propane storage tank. The
tank has an inside diameter of di = 750 mm, and is subjected to an internal pressure of p = 750 kPa.
The allowable tensile stress in the wall of the tank is 80 MPa. (a) Determine the minimum wall
thickness tc of the cylindrical part of the tank. (b) Determine the minimum wall thickness ts of the
hemispherical end caps.
Answers: (a) tc = 3.52 mm, and (b) ts = 1.758 mm.
Question Two
The cylindrical tank shown is subjected to an internal pressure p and a distributed loading w. At a
section through the center of the tank, determine the combined normal stresses at the top and bottom of
the tank. Then, determine the maximum in-plane shear stresses at the same locations. Take L = 8 m, D
= 1.8 m, p = 0.4 MPa, w = 15 kN/m, and t = 4 mm.
Answers: at the bottom σlong = 56.79 MPa, σtang = 90, and τmax = 16.61, (b) at the top 33.21, 90, and
28.39 MPa.
Question Three
On the outer surface of a pressure vessel, strains εn = 200 µ and εt = 400 µ are measured along the n and
t directions of the shown figure. (a) Determine the strains εx and εy. (Note: γxy = 0.) (b) Determine the
shear strain γnt. (c) Determine the value of Poisson's ratio ν. (Note: for pressure vessels, σy = 2 σx..) (d)
Express the increase in diameter ∆D in terms of the diameter D.
Answers: (a) εx = 100 µ, εy = 500 µ, γnt = 346 µ (c) ν = 0.33, (d) ∆D = 500 x 10-6 D.
Fig. 1
Fig. 2
Fig. 3