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

Note: Only the magnitude of the torque is needed in this instance; consequently, the absolute
value of T 2 is computed here.
The torque available at gear D in this system is therefore T D = 340 N · m. Ans.
Shear Stresses
The polar moment of inertia for the solid 25 mm diameter shafts is
π
4 4
J = (25 mm) = 38,349.5 mm
32
The maximum shear stress magnitudes in each segment can be calculated by the elastic
torsion formula:
Tc 1 1
(212.2066 Nm)(25 ⋅ mm/2)(1, 000 mm/m)
τ 1 = =
= 69.2 MPa Ans.
4
J
38,349.5 mm
1
Tc 2 2
τ 2 = =
J
2
(339.5306 Nm)(25 ⋅ mm/2)(1, 000 mm/m)
38,349.5 mm
4
= 110.7 MPa Ans.
mecmovies
ExERcISES
m6.14 Six basic calculations involving power transmission in
two shafts connected by gears.
m6.15 Six basic calculations involving power transmission in
three shafts connected by gears.
FIGURE m6.14
problems
p6.24 A solid 40 mm diameter shaft is rotating at a speed of
560 rpm with a maximum shear stress of 85 MPa. Determine the
power in kW being delivered by the shaft.
p6.25 A solid 1.50 in. diameter shaft is used to synchronize
multiple mechanisms in a manufacturing plant. The torque delivered
by the shaft is 3,100 lb ⋅ in. What horsepower must be delivered
to the shaft to maintain a shaft speed of 600 rpm? What is the maximum
shear stress developed in the shaft?
p6.26 A solid steel [G = 11,500 ksi] shaft that has a diameter of
2.00 in. and a length of 30 ft transmits 14 hp while rotating at 90 rpm.
What is the angle of twist in the shaft?
p6.27 A solid stainless steel [G = 86 GPa] shaft with a diameter
of 30 mm and a length of 900 mm transmits 42 kW from an electric
motor to a compressor. If the allowable shear stress is 50 MPa and
the allowable angle of twist is 1.5°, what is the minimum allowable
speed of rotation?
FIGURE m6.15
p6.28 A hollow aluminum alloy [G = 3,800 ksi] shaft having a
length of 12 ft, an outside diameter of 4.50 in., and a wall thickness
of 0.50 in. rotates at 3 Hz. The allowable shear stress is 6 ksi, and
the allowable angle of twist is 5°. What horsepower may the shaft
transmit?
p6.29 The impeller shaft of a fluid agitator transmits 28 kW at
440 rpm. If the allowable shear stress in the shaft must be limited to
80 MPa, determine
(a) the minimum diameter required for a solid impeller shaft.
(b) the maximum inside diameter permitted for a hollow impeller
shaft if the outside diameter is 40 mm.
(c) the percent savings in weight realized if the hollow shaft is
used instead of the solid shaft. (Hint: The weight of a shaft is
proportional to its cross-sectional area.)
p6.30 A pulley with a diameter D = 8 in. is mounted on a shaft
with a diameter d = 1.25 in. as shown in Figure P6.30. Around the
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