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

p6.10 The mechanism shown in Figure P6.10 is in equilibrium
for an applied load P = 20 kN. Specifications for the mechanism
limit the shear stress in the steel [G = 80 GPa] shaft BC to 70 MPa,
the shear stress in bolt A to 100 MPa, and the vertical deflection of
joint D to a maximum value of 25 mm. Assume that the bearings
allow the shaft to rotate freely. Using L = 1,200 mm, a = 110 mm,
and b = 210 mm, calculate
(a) the minimum diameter required for shaft BC.
(b) the minimum diameter required for bolt A.
a
A
Bolt
was 300 mm. When the applied torque reached 271.4 N ⋅ m, a shear
strain of 2,015 microradians was measured in the specimen. What
was the angle of twist in the specimen?
p6.13 A two-segment shaft is used to transmit power at constant
speed through the pulleys shown in Figure P6.13. Power is input to
the shaft at B through a torque T B = 260 N ⋅ m. A torque T A = 90 N ⋅ m
is removed from the shaft at A, and a torque T C = 170 N ⋅ m is removed
from the shaft at C. The external torques act in the directions indicated
in the figure. Both shaft segments are made of phosphor
bronze [G = 42 GPa], and both segments are solid shafts. Segment
(1) has a diameter d 1 = 25 mm and a length L 1 = 300 mm. Segment
(2) has a diameter d 2 = 30 mm and a length L 2 = 900 mm. Determine
the rotation angle of pulley C relative to pulley A.
Bearings
B
y
T A
T B
D
b
C
L
A
(1)
L 1
B
(2)
L 2
T C
C
x
P
FIGURE p6.10
FIGURE p6.13
p6.11 A simple torsion-bar spring is shown in Figure P6.11.
The shear stress in the steel [G = 11,500 ksi] shaft is not to exceed
10,000 psi, and the vertical deflection of joint D is not to exceed
0.5 in. when a load P = 3,400 lb is applied. Neglect the bending of
the shaft, and assume that the bearing at C allows the shaft to rotate
freely. Determine the minimum diameter required for the shaft. Use
dimensions of a = 72 in., b = 30 in., and c = 18 in.
A
a
B
b
C
p6.14 A compound shaft drives three gears, as shown in Figure
P6.14. Segments (1) and (2) of the shaft are hollow bronze [G =
6,500 ksi] tubes with an outside diameter of 1.75 in. and a wall
thickness of 0.1875 in. Segments (3) and (4) are solid 1.00 in. diameter
steel [G = 11,500 ksi] shafts. The shaft lengths are L 1 = 60 in.,
L 2 = 14 in., L 3 = 20 in., and L 4 = 26 in. The torques applied to the
shafts have magnitudes T B = 960 lb ⋅ ft, T D = 450 lb ⋅ ft, and T E =
130 lb ⋅ ft, acting in the directions shown. The bearings shown allow
the shaft to turn freely. Calculate
(a) the maximum shear stress in the compound shaft.
(b) the rotation angle of flange C with respect to flange A.
(c) the rotation angle of gear E with respect to flange A.
FIGURE p6.11
D
P
p6.12 A rod specimen of ductile cast iron was tested in a torsiontesting
machine. The rod diameter was 22 mm, and the rod length
c
y
(1)
A
L 1
FIGURE p6.14
T B
(2) (3)
C
B
L 2 L 3
T D
D
(4)
L 4
T E
E
x
153