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

m14.5 A cylindrical steel [E = 200 GPa; ν = 0.3] tank contains
a fluid under pressure. The ultimate shear strength of the
steel is 300 MPa, and a factor of safety of 4 is required. The
fluid pressure must be carefully controlled to ensure that
the shear stress in the cylinder does not exceed the allowable
shear stress limit. To monitor the tank, a strain gage records
the longitudinal strain in the tank. Determine the critical
strain gage reading that must not be exceeded for safe operation
of the tank.
ExERcISES
m14.3 For an indicated internal gage pressure, determine the
normal stress perpendicular to a weld and the shear stress parallel
to a weld.
m14.4 The strain gage shown is
used to determine the gage pressure
in the cylindrical steel [E = 200 GPa;
ν = 0.32] tank. The tank has a specified
outside diameter and wall thickness.
Determine the strain gage reading
for a specified internal tank
pressure.
m14.5 A strain gage is used to monitor the strain in a spherical
steel [E = 210 GPa; ν = 0.32] tank, that contains a fluid under pressure.
The ultimate shear strength of the steel is 560 MPa. Determine
the factor of safety with respect to the ultimate shear strength
if the strain gage reading is a specified value.
FIGURE m14.4
FIGURE m14.5
pRoBLEmS
p14.1 Determine the normal stress in a ball
(Figure P14.1) that has an outside diameter of
185 mm and a wall thickness of 3 mm when
the ball is inflated to a gage pressure of 80 kPa.
FIGURE p14.1
p14.3 A spherical pressure vessel has an inside diameter of
3.25 m and a wall thickness of 8 mm. The tank will be
constructed from structural steel that has a yield strength of
370 MPa. If a factor of safety of 3.0 with respect to the yield
strength is required, determine the maximum allowable internal
pressure.
p14.2 A spherical gas-storage tank with an inside diameter of
21 ft is being constructed to store gas under an internal pressure of
160 psi. The tank will be constructed from steel that has a yield
strength of 50 ksi. If a factor of safety of 3.0 with respect to the
yield strength is required, determine the minimum wall thickness
required for the spherical tank.
p14.4 A spherical pressure vessel has an inside diameter of 6 m
and a wall thickness of 15 mm. The vessel will be constructed from
steel [E = 200 GPa; ν = 0.29] that has a yield strength of 340 MPa.
If the internal pressure in the vessel is 1,750 kPa, determine (a) the
normal stress in the vessel wall, (b) the factor of safety with respect
to the yield strength, (c) the normal strain in the sphere, and (d) the
increase in the outside diameter of the vessel.
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