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

p15.54 A thin-walled cylindrical pressure vessel of inside
diameter d = 36 in. is fabricated from a material with a tensile yield
strength of 40 ksi. The internal pressure in the cylinder is 1,600 psi.
Assuming that the material obeys the von Mises criterion of yielding,
and that there is to be a safety factor of 3.0 against yielding,
determine the necessary wall thickness remote from the ends of the
vessel.
p15.55 A thin-walled cylindrical pressure vessel of inside
diameter d = 500 mm and wall thickness t = 5 mm is fabricated
from a material with a tensile yield strength of 280 MPa. Determine
the maximum internal pressure p that may be used in the cylinder
according to
(a) the maximum-shear-stress theory.
(b) the maximum-distortion-energy theory.
p15.56 A solid 80 mm diameter circular shaft made of coldrolled
steel is subjected to the simultaneous action of a torque T =
19 kN · m, a bending moment M = 8.5 kN · m, and a compressive
axial force P = 250 kN. The cold-rolled steel has a yield strength of
s Y = 420 MPa, in both tension and compression. On the basis of
(a) the maximum-shear-stress theory and
(b) the maximum-distortion-energy theory,
is the shaft overstressed?
p15.57 A 75 mm diameter solid circular shaft rotating at 800 rpm
transmits 400 kW and carries a tensile axial force P = 140 kN. The
material that makes up the shaft has a tensile yield strength of s Y =
110 MPa. On the basis of
(a) the maximum-shear-stress theory and
(b) the maximum-distortion-energy theory,
is the shaft overstressed? State the factors of safety for each theory.
p15.58 A hollow circular shaft made of an aluminum alloy is
subjected to a bending moment M = 1.2 kN · m and a torque T. The
shaft has an outside diameter of 60 mm and an inside diameter of
40 mm. Assume that the aluminum alloy has a yield strength
s Y = 275 MPa. Use
(a) the maximum-shear-stress theory and
(b) the maximum-distortion-energy theory
to determine the value of the torque T so that the shaft does not fail
by yielding.
p15.59 A 3 in. diameter solid circular shaft made of stainless
steel is subjected to the simultaneous action of a torque T = 6.0 kip · ft,
a tensile axial force P = 55 kips, and a bending moment M. The
stainless steel has a yield strength of s Y = 36 ksi, in both tension
and compression. Use
(a) the maximum-shear-stress theory and
(b) the maximum-distortion-energy theory
to determine the value of the moment M so that the shaft does not
fail by yielding.
p15.60 A solid circular shaft made of steel is subjected to a
torque T = 780 lb · ft and a tensile axial force P = 13,500 lb. Assume
that the steel has a yield strength s Y = 30,000 psi. Use
(a) the maximum-shear-stress theory and
(b) the maximum-distortion-energy theory
to determine the required diameter of the shaft so that the shaft does
not fail by yielding.
p15.61 The stresses on the surface of a machine component will
be in a state of plane stress with s x = s y = −40 ksi and τ xy = 85 ksi.
The ultimate failure strengths for the material that the component is
made of are 100 ksi in tension and 190 ksi in compression. Use the
Mohr failure criterion to determine whether this component is safe
for the state of stress given. Support your answer with appropriate
documentation.
p15.62 The stresses on the surface of a machine component
will be in a state of plane stress with s x = 510 MPa, s y = −140 MPa,
and τ xy = 375 MPa. The ultimate failure strengths for the material
that the component is made of are 700 MPa in tension and 420 MPa
in compression. Use the Mohr failure criterion to determine
whether this component is safe for the state of stress given. Support
your answer with appropriate documentation.
p15.63 The state of stress at a point in a cast iron [s UT = 290 MPa; s
UC = 650 MPa] component is s x = 0, s y = −180 MPa, and τ xy = 200
MPa. Determine whether failure occurs at the point according to (a)
the maximum-normal-stress theory and (b) the Mohr failure criterion.
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