Page 160 - Shigley's Mechanical Engineering Design

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Load and Stress Analysis 135
3–51 Consider a 1-in-square steel thin-walled tube loaded in torsion. The tube has a wall thickness
1
t = in, is 36 in long, and has a maximum allowable shear stress of 12 kpsi. Determine the max-
16
imum torque that can be applied and the corresponding angle of twist of the tube.
(a) Assume that the internal radius at the corners r i = 0.
1
(b) Assume that the internal radius at the corners is more realistically r i = in.
8
r i r m

1 in t
Problem 3–51

1 in
3–52 The thin-walled open cross-section shown is transmitting torque T. The angle of twist per unit
length of each leg can be determined separately using Eq. (3–47) and is given by

3T i
θ 1 = 3
GL i c
i
where for this case, i = 1, 2, 3, and T i represents the torque in leg i. Assuming that the angle of
twist per unit length for each leg is the same, show that
Gθ 1 3 3
T = L i c i and τ max = Gθ 1 c max
3
i=1
c
1
c 3

T
Problem 3–52 L 1
L 3
c
2

L 2
3–53 to Using the results from Prob. 3–52, consider a steel section with τ allow = 12 kpsi.
3–55 (a) Determine the torque transmitted by each leg and the torque transmitted by the entire section.
(b) Determine the angle of twist per unit length.
Problem
Number c 1 L 1 c 2 L 2 c 3 L 3
3–53 2 mm 20 mm 3 mm 30 mm 0 0
1 3 1 1 5
3–54 in in in 1 in in in
16 4 8 16 8
3–55 2 mm 20 mm 3 mm 30 mm 2 mm 25 mm
3–56 Two 300-mm-long rectangular steel strips are placed together as shown. Using a maximum allow-
able shear stress of 80 MPa, determine the maximum torque and angular twist, and the torsional