Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

212.5 MPa
134.4 MPa
145.2 MPa
76.2 MPa
46.9 MPa
+
42.5 MPa
40 mm
+
40 mm
+ =
–
80 mm
–48.8 MPa
80 mm
40 mm
80 mm
+
20.2
MPa
+
89.4 MPa
–78.1 MPa
120 mm
120 mm
120 mm
Tube Jacket
Tube Jacket
Tube
Jacket
Circumferential stresses due
to shrink-fit contact pressure.
Circumferential stresses due
to 170 MPa internal pressure.
FIGURE 14.14 Variation of circumferential stresses in a compound cylinder.
Final circumferential stresses in
compound cylinder as the sum of
contact and internal pressures.
pRoBLEmS
p14.22 A thick-walled cylindrical tank with closed ends, an
inside radius of a = 250 mm, and an outside radius of b = 290 mm is
submerged to a depth of 40 m. Assume that the density of seawater
is 1,100 kg/m 3 . The tank also has an internal pressure of p i = 2 MPa.
Determine the maximum values of σ r , σ θ , and σ long , as well as the
maximum shear stress in the walls of the cylinder remote from its
ends.
p14.23 An open-ended thick-walled cylindrical pressure vessel
with an inside diameter of 250 mm and an outside diameter of
400 mm is subjected to an internal pressure of 75 MPa. Determine
(a) The circumferential stress at a point on the inside surface of
the cylinder.
(b) The circumferential stress at a point on the outside surface of
the cylinder.
(c) The maximum shear stress in the cylinder.
p14.24 A steel cylinder with an inside diameter of 8 in. and an
outside diameter of 14 in. is subjected to an internal pressure of
25,000 psi. Determine
(a) The maximum shear stress in the cylinder.
(b) The radial and circumferential stresses at a point in the
cylinder midway between the inside and outside surfaces.
p14.25 A hydraulic cylinder with an inside diameter of 200 mm
and an outside diameter of 450 mm is made of steel [E = 210 GPa;
ν = 0.30]. For an internal pressure of 125 MPa, determine
(a) The maximum tensile stress in the cylinder.
(b) The change in internal diameter of the cylinder.
p14.26 A closed-ended cylindrical pressure vessel is to be
designed to have an internal diameter of 125 mm and to be subjected
to an internal gage pressure of 10 MPa. The maximum circumferential
normal stress is not to exceed 100 MPa, and the maximum
shear stress is not to exceed 60 MPa. Determine the minimum
external diameter that may be used for the vessel.
p14.27 A cylindrical tank having an external diameter of 16 in.
is to resist an internal pressure of 2,000 psi without the circumferential
stress exceeding 20,000 psi. Determine the minimum wall
thickness required for the tank.
p14.28 A cylindrical steel tank having an internal diameter of
4 ft is submerged in seawater (weight density = 64 lb/ft 3 ) to a depth
of 10,000 ft. The internal gage pressure in the tank is 2,000 psi.
(a) If the allowable stress of the steel is 36 ksi, what is the
minimum allowable outside diameter of the tank?
(b) What is the maximum tensile stress before the tank is
immersed?
p14.29 A thick-walled cylinder with closed ends is subjected
only to internal pressure p i . Let a = 36 in. and b = 40 in., and determine
the maximum permissible internal pressure p i that may be
contained in the cylinder if the allowable tensile stress is 22 ksi and
the allowable shear stress is 12 ksi.
p14.30 A thick-walled cylindrical pressure vessel with an inside
diameter of 200 mm and an outside diameter of 300 mm is
made of a steel that has a yield strength of 430 MPa. Determine the
maximum internal pressure that may be applied to the vessel if a
factor of safety of 3.0 with respect to failure by yielding is required.
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