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

ExAmpLE 6.13
A rectangular box section of aluminum alloy has
outside dimensions of 100 mm by 50 mm. The plate
thickness is 2 mm for the 50 mm sides and 3 mm for
the 100 mm sides. If the maximum shear stress must
be limited to 95 MPa, determine the maximum
torque T that can be applied to the section.
3 mm
50 mm 2 mm
100 mm
Plan the Solution
The maximum shear stress will occur in the Cross-sectional dimensions.
thinnest plate. From the allowable shear stress,
the shear flow in the thinnest plate will be calculated. Next, the area A enclosed by the
median line (see Figure 6.22) of the section wall will be calculated. Finally, the maximum
torque will be computed from Equation (6.27).
T
SolutioN
The maximum shear stress will occur in the thinnest plate; therefore, the critical shear
flow q is
The area enclosed by the median line is
q = τt = (95 N/mm 2 )(2 mm) = 190 N/mm
A = (100 mm − 2mm)(50 mm − 3 mm) = 4,606 mm
m
Finally, the torque that can be transmitted by the section is computed from
Equation (6.27):
2
T = q(2 A ) = (190 N/mm)(2)(4,606 mm ) = 1,750,280 Nmm ⋅ = 1,750 Nm ⋅ Ans.
m
2
pRoBLEmS
p6.55 A solid 1.50 in. × 1.50 in. square shaft is made of steel
[G = 11,500 ksi] that has an allowable shear stress of 16 ksi. The
shaft is used to transmit power from a tractor to farm implements,
and it has a length of 6 ft. Determine
(a) the largest torque T that may be transmitted by the shaft.
(b) the angle of twist in the shaft at the torque found in part (a).
p6.56 The allowable shear stress for each bar shown in Figure
P6.56/57 is 50 ksi. Assume that a = 0.5 in. and determine
(a) the largest torque T that may be applied to each bar.
(b) the corresponding rotation angle at the free end if each bar
has a length of 48 in. Assume that G = 12,500 ksi.
p6.57 The bars shown in Figure P6.56/57 have equal crosssectional
areas, and they are each subjected to a torque T = 550 N ⋅ m.
Using a = 10 mm, determine
(a) the maximum shear stress in each bar.
(b) the rotation angle at the free end if each bar has a length of
900 mm. Assume that G = 28 GPa.
1.5a
(1)
8a
T
FIGURE p6.56/57
3a
p6.58 The steel [G = 11,200 ksi] angle shape shown in Figure
P6.58 is subjected to twisting moments of T = 400 lb ⋅ ft about its
longitudinal axis (i.e., the x axis) at its ends. The angle shape is
4a
(2)
T
6a
2a
(3)
T
191