Let the shaft of Problem 14.4 be subjected simultaneously to a bending moment M = 15.0 kN • m and torsional moment T = 30.0 kN • m. With the stress concentration factors determined in Problem 14.4, compute the following stress quantities that occur in the shaft at the root of the groove:
a. the maximum principal stress
b. the maximum shear stress
c. the octahedral shear stress
Problem 14.4
A cylindrical shaft has a circular groove, the depth of the groove is t = 6.00 mm, and the radius at the root of the groove is ρ = 2.20 mm. (See Figure D, Table 14.3.) The radius of the cross section at the root of the groove is b = 60 mm. By Neuber’s nomograph (Figure 14.10), determine the value of Scc for the cases where the shaft is subjected to
a. axial tensile load
b. bending
c. torsion
Figure D of Table 14.3:
TABLE 14.3 Directions for Use of Figure 14.10 (Neuber) in Finding Calculated Stress Concentration Factor Scc in Bars
Type of notch | Type of load | Formula for nominal stress | Scale for | Curve for finding Scc |
Tension | f | 6 | ||
Bending | f | 7 |
FIGURE 14.10 Neuber's diagram (nomog raph) for a calculated stress concentration factor at the root of a notch.
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