Tools › Structures › Stress Concentrations › Rounded Square Hole › Example
Savin's rounded square hole (m = −1/6) under uniaxial tension parallel to a side
| Tool | Rounded Square Hole |
| Source | Savin, G. N. (1961). Stress Concentration Around Holes, translated by E. Gros. Pergamon Press, Oxford. Chapter III, square hole with rounded corners, one-term map z = R(ζ + m/ζ³). |
| Level | Graduate |
Problem
A 0.1 in thick plate under a normal resultant of 10,000 lb/in in y contains a square hole of 0.25 in across flats with 0.015 in corner radii (Savin's proportions, ρ/c = 0.12). Find the peak hoop stress and its position, and the hoop stress at the middle of the loaded and the parallel sides.
Inputs to Enter
- N_xx = 0, N_yy = 10000 lb/in, N_xy = 0, t = 0.1 in (S = 100 ksi)
- W = 0.25 in across flats, ρ = 0.015 in (ρ/c = 0.12, Savin's m = −1/6), β = 0
- r = 0.125 in, θ = 90°
Answers
- K_t = 3.857 just off the corners (r = 0.1738 in of the 0.175 in corner distance): σ_edge,max = 385.7 ksi
- Middle of the loaded side: σ_hoop = −0.857 S = −85.7 ksi
- Middle of the side parallel to the load: σ_hoop = 1.476 S = 147.6 ksi
Notes
Change the default loads to N_yy only and the corner radius to 0.015 in. The 3.857 is the tool's converged value on Savin's one-term map; the explanation page notes the sides bulge by about 2 % of c. ρ = W/2 recovers the round hole.