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

p15.5 A solid 1.50 in. diameter shaft is used in an aircraft
engine to transmit 160 hp at 2,800 rpm to a propeller that develops
a thrust of 1,800 lb. Determine the magnitudes of the principal
stresses and the maximum shear stress at any point on the outside
surface of the shaft.
p15.6 A short cast iron shaft 2 in. in diameter is subjected to a
tensile force of 22,000 lb combined with a torque T. Find the torque
T that the shaft can resist (a) if the allowable shear stress is 6,000 psi
and (b) if the allowable tensile stress is 3,000 psi.
p15.7 A compound shaft consists of two tube segments. Segment
(1) has an outside diameter of 40 mm and a wall thickness of
3.2 mm. Segment (2) has an outside diameter of 70 mm and a wall
thickness of 4.0 mm. The shaft is subjected to a tensile load P = 15 kN
and torques T A = 350 N · m and T B = 900 N · m, which act in the
directions shown in Figure P15.7/8.
(a) Determine the principal stresses and the maximum shear
stress at point K on the surface of the shaft.
(b) Show these stresses on an appropriate sketch.
FIGURE p15.9
p15.10 A hollow shaft is subjected to an axial load P and a
torque T, acting in the directions shown in Figure P15.10. The shaft
is made of bronze [E = 15,200 ksi; ν = 0.34], and it has an outside
diameter of 2.50 in. and an inside diameter of 2.00 in. Strain gages
a and b are mounted on the shaft at the orientations shown in the
figure, where θ has a magnitude of 25°.
(a) If P = 6 kips and T = 17 kip · in., determine the strain readings
that would be expected from the gages.
(b) If the strain gage readings are e a = −1,100 me and e b = 720 me,
determine the axial force P and the torque T applied to the shaft.
θ
T
P
y
Gage b
Gage a
90°– θ
θ
T
P
z
P
A
T A
FIGURE p15.7/8
(1)
H
B
p15.8 A compound shaft consists of two stainless steel tube segments.
Segment (1) has an outside diameter of 1.5 in. and a wall
thickness of 0.120 in. Segment (2) has an outside diameter of 3.0 in.
and a wall thickness of 0.120 in. The shaft is subjected to a tensile
load P = 6,200 lb and torques T A = 420 lb · ft and T B = 1,060 lb · ft,
which act in the directions shown in Figure P15.7/8. Determine the
maximum compressive normal stress in the tube wall at (a) point H
and (b) point K.
p15.9 A hollow shaft is subjected to an axial load P and a torque
T, acting in the directions shown in Figure P15.9. The shaft is made
of bronze [E = 105 GPa; ν = 0.34], and it has an outside diameter
of 55 mm and an inside diameter of 45 mm. A strain gage is
mounted at an angle θ = 40° with respect to the longitudinal axis of
the shaft, as shown in the figure.
(a) If P = 13,000 N and T = 260 N · m, what is the strain reading
that would be expected from the gage?
(b) If the strain gage gives a reading of −195 me when the axial
load has a magnitude of P = 6,200 N, what is the magnitude
of the torque T applied to the shaft?
T B
(2)
K
C
x
FIGURE p15.10
p15.11 The cylinder in Figure P15.11 is fabricated from spirally
wrapped steel plates that are welded at the seams in the orientation
shown. The cylinder has an inside diameter of 1,060 mm and
a wall thickness of 10 mm. The cylinder is subjected to a compressive
load P = 2,200 kN and a torque T = 850 kN · m, which acts in
the direction shown. For a seam angle β = 30°, determine
(a) the normal stress perpendicular to the weld seams.
(b) the shear stress parallel to the weld seams.
(c) the principal stresses and the maximum shear stress on the
outside surface of the cylinder.
β
y
P
T
FIGURE p15.11
x
620