Tools › Structures › Stress Concentrations › Neuber Hyperbolic Notch › Example
Neuber deep hyperbolic notch in a flat bar, a/ρ = 5 (Noda, Takase and Monda 1996 Table 1)
| 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 (Neuber's exact deep-notch factors). |
| Level | Graduate |
Problem
A flat bar 0.25 in thick has symmetric hyperbolic notches leaving a net width of 1.0 in with a root radius of 0.1 in and a notch depth of 0.25 in. 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 and bending, the shallow-notch factor, the interpolated factors, the nominal and peak stresses.
Inputs to Enter
- Member: flat bar; d = 1.0 in (net width), h = 0.25 in (thickness)
- ρ = 0.1 in (root radius), t = 0.25 in (notch depth, optional)
- P = 10000 lb, M = 2000 lb·in
Answers
- a = d/2 = 0.5 in, a/ρ = 5, t/ρ = 2.5; flank angle 24.1°
- Deep-notch factors (Table 1): K_tP = 2(x+1)√x/[(x+1)atan√x + √x] = 2.937; K_tM = 4x√x/{3[√x + (x−1)atan√x]} = 2.180
- Shallow-notch factor 1 + 2√(t/ρ) = 4.162; Neuber interpolation (m = 2): K_NP = 2.651, K_NM = 2.106 (Noda m = 2.8: 2.786, 2.155)
- σ_nom = P/(dh) = 40 ksi, 6M/(d²h) = 48 ksi; peaks 106.1 ksi (tension), 101.1 ksi (bending); combined root stress 207.1 ksi
Notes
The tool's default inputs are this case. Hand checks recorded at the build: flat bar at a/ρ = 1 gives 1.556 (tension) and 1.333 (bending). The factors are referred to the net section.