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

z
D
(3)
A
y
(1)
L1,
L3
N B
B
L 2
(a) Determine the temporary installation torque T′ B that must be
applied at B to align the bolt holes at A.
(b) Determine the maximum shear stress τ initial in the pipe after
the bolts are connected and the temporary installation torque
at B is removed.
(c) Determine the magnitude of the maximum shear stress in
segments (1) and (2) if an external torque T B = 150 kip ⋅ in. is
applied at B after the bolts are connected.
(2)
T C
FIGURE p6.47
N E
E
x'
C
x
y
L 1
L 2
p6.48 The aluminum alloy [G = 4,000 ksi] pipe shown in Figure
P6.48 is fixed to the wall support at C. The bolt holes in the flange at
A were supposed to align with mating holes in the wall support; however,
an angular misalignment of 4° was found to exist. To connect
the pipe to its supports, a temporary installation torque T′ B must be
applied at B to align flange A with the mating holes in the wall
support. The outside diameter of the pipe is 5.5625 in. and its wall
thickness is 0.258 in. The segment lengths are L 1 = 16 ft and L 2 = 24 ft.
z
A
FIGURE p6.48
(1)
T B
B
(2)
C
x
6.10 Stress concentrations in circular Shafts
Under Torsional Loadings
In Section 5.7, it was shown that the introduction of a circular hole or other geometric discontinuity
into an axially loaded member causes a significant increase in the magnitude of
the stress in the immediate vicinity of the discontinuity. This phenomenon, called stress
concentration, also occurs for circular shafts under torsional forms of loading.
Previously in this chapter, the maximum shear stress in a circular shaft of uniform
cross section and made of a linearly elastic material was given by Equation (6.5):
τ max =
In the context of stress concentrations in circular shafts, this stress is considered a nominal
stress, meaning that it gives the shear stress in regions of the shaft that are sufficiently
removed from discontinuities. Shear stresses become much more intense near abrupt
changes in shaft diameter, and Equation (6.5) does not predict the maximum stresses near
discontinuities such as grooves or fillets. The maximum shear stress at discontinuities is
expressed in terms of a stress-concentration factor
K
τ
Tc
J
max
= (6.21)
τ nom
In this equation, τ nom is the stress given by Tc/J for the minimum diameter of the shaft
(termed the minor diameter) at the discontinuity.
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