Tools › Structures › Stress Concentrations › Neuber Hyperbolic Notch › Example
Neuber deep hyperbolic groove in a round bar, a/ρ = 5, ν = 0.3: tension, bending and torsion
| Tool | Neuber Hyperbolic Notch |
| Source | Noda, N.-A., Takase, Y., and Monda, K. (1996). "Formula of Stress Concentration Factors for Round and Flat Bars with Notches." Localized Damage IV (Transactions on Engineering Sciences, Vol. 13), WIT Press, pp. 317–324. Table 1. |
| Level | Graduate |
Problem
A round bar with a hyperbolic circumferential groove has a net diameter of 1.0 in, a root radius of 0.1 in and a groove depth of 0.25 in; Poisson's ratio is 0.3. It carries an axial force of 10,000 lb and a bending moment of 2,000 lb·in. Find Neuber's deep-notch factors in tension, bending and torsion and the peak stresses.
Inputs to Enter
- Member: round bar; d = 1.0 in (net diameter), ν = 0.3
- ρ = 0.1 in (root radius), t = 0.25 in (groove depth)
- P = 10000 lb, M = 2000 lb·in, T = 0
Answers
- a/ρ = 5: K_tP = 2.448, K_tM = 1.994, K_tT = 1.513 (hand values from Table 1 at the build: 2.448 / 1.994 / 1.513)
- Shallow factors 4.162 (tension, bending) and 1 + √(t/ρ) = 2.581 (torsion); interpolated K_NP = 2.316, K_NM = 1.949, K_NT = 1.488
- σ_nom = 4P/(πd²) = 12.73 ksi, 32M/(πd³) = 20.37 ksi; peaks 29.49 ksi and 39.70 ksi; root stress 69.19 ksi
- At a/ρ = 3 (ρ = 0.1667 in) the factors are 1.984 / 1.671 / 1.350
Notes
Select the round bar in the Member Type dropdown and keep the other defaults. In SI (same geometry in mm) the build recorded K_tP = 2.448 and a von Mises root stress of 905.7 MPa for its SI load set.