Tools › Structures › Stress Concentrations › Semicircular Edge Notch › Example
Ling (1947) / Maunsell (1936): semicircular edge notch in a semi-infinite plate under tension parallel to the edge, K_t = 3.065
| Tool | Semicircular Edge Notch |
| Source | Ling, C. B. (1947). "On the Stresses in a Notched Strip." Journal of Applied Mechanics, Vol. 14, pp. A275–A280 (as quoted in Pilkey and Pilkey 2008, Chart 2.2); Maunsell, F. G. (1936). "Stresses in a Notched Plate under Tension." Philosophical Magazine, Series 7, Vol. 21, pp. 765–773. |
| Level | Graduate |
Problem
A semi-infinite plate 0.1 in thick carries 5,000 lb/in parallel to its straight free edge, which has a semicircular notch of 0.125 in radius. Find the applied stress, the hoop stress at the notch root and the stress concentration factor, the hoop stress at 45° round the notch, the lowest stress on the notch and on the free edge, and the stresses on the root line at twice the radius.
Inputs to Enter
- N_yy = 5000 lb/in (along the edge), t = 0.1 in (σ = 50 ksi)
- ρ = 0.125 in
- r = 0.125 in (notch surface), θ = 90° (the root)
Answers
- Root hoop stress 153.27 ksi: K_t = 3.0653 (Ling 3.065; Maunsell 3.05; Hasebe's semi-elliptic table 3.065)
- Hoop at θ = 45°: 62.96 ksi; minimum −2.39 ksi at θ = 170.5°; the free 90° corners carry zero stress
- Root line x = 2ρ: σ_yy = 62.18 ksi, σ_xx = 17.11 ksi; free edge at y = 2ρ: σ_yy = 18.37 ksi, edge minimum −2.04 ksi at y = 1.18 ρ
Notes
The tool's default inputs are this case (series of 60 terms, residual 1.3e-4; the root value converges 3.0413 / 3.0622 / 3.0657 / 3.0653 for N = 10 / 20 / 40 / 60). Only tension parallel to the edge is admissible.