2. The AA 2024 ($E = 76$ GPa, $v = 0.34$) torsion shaft (modeled in Figure 2) is composed of 2 pieces of
circular hollow tube welded together, and is subjected to a 300 Nm external torque. The first piece
(AB) has outside and inside diameters of 30 mm and 20 mm, respectively. The wall thickness of
the second piece (BC) is 2.5 mm, and the outside diameter is 25 mm. A fillet of radius $r = 5$ mm is
created at the junction of the two tubes.
(a) With reference to Figure 3, calculate the Safety Factor of the shaft if the maximum allowable
shear stress is 235 MPa. (Note: The chart in Figure 3 is for solid shafts. The chart for hollow
sections is more complex, and it is outside the scope of this course.)
(b) Calculate the total twist angle.
A
B 300 Nm
C
200
100
Figure 2: Shaft for Problem 2 (dimensions in mm)
1.8
1.7
$D/d = 1.111$
$D/d = 1.25$
D
1.6
1.5
$D/d = 1.666$
K 1.4
$D/d = 2$
1.3
$D/d = 2.5$
1.2
1.1
1.0
0 0.05 0.10 0.15 0.20 0.25 0.30
r/d
(Source: W. D. Pilkey and D. F. Pilkey, Peterson's Stress
Concentration Factors, 3rd ed., John Wiley & Sons, New York, 2008.)
Figure 3: Stress Concentration Factor K vs Fillet Radius r
