Tools › Structures › Stress Concentrations › Circular Inclusion › Example
Circular inclusion tool, empty-hole limit: Kirsch general field K_hoop = 3 − S_2/S_1 = 2.737
| Tool | Circular Inclusion |
| Source | Goodier, J. N. (1933). "Concentration of Stress Around Spherical and Cylindrical Inclusions and Flaws." Transactions of the ASME, Journal of Applied Mechanics, Vol. 55, APM-55-7, pp. 39–44 (the cavity limit); Kirsch, G. (1898). "Die Theorie der Elastizität und die Bedürfnisse der Festigkeitslehre." Zeitschrift des Vereines deutscher Ingenieure, Vol. 42, No. 28, pp. 797–807. |
| Level | Graduate |
Problem
The default plate (N_xx = 5,000, N_yy = 15,000, N_xy = 3,000 lb/in, t = 0.1 in, 0.25 in inclusion) has its inclusion removed (empty hole). Find the far-field principal stresses and the hoop-stress concentration factor on the hole edge.
Inputs to Enter
- N_xx = 5000, N_yy = 15000, N_xy = 3000 lb/in, t = 0.1 in
- D = 0.25 in; E_1 = 10 Msi, ν_1 = 0.33; inclusion type: hole
- r = 0.125 in, θ = 90°
Answers
- S_1 = 158.3 ksi at φ_1 = 15.5° from the y axis
- S_2 = 41.7 ksi
- K_hoop = 3 − S_2/S_1 = 2.7367, the Round Hole General Load value for the same state
Notes
Select the hole option; the stresses off the edge equal the Kirsch general field to all digits (build check). The default elastic case (E_2/E_1 = 3) gives f_h = 1.279, f_d = 1.289, K_I = 1.283, K_rad = 1.283.