Tools › Structures › Stress Concentrations › Round Hole General Load › Example
Round hole under equal biaxial tension: hoop stress 2S all round the edge
| Tool | Round Hole General Load |
| Source | Timoshenko, S. P., and Goodier, J. N. (1970). Theory of Elasticity, 3rd ed. McGraw-Hill, New York. Chapter 4, "The Effect of Circular Holes on Stress Distributions in Plates" (superposition of the Kirsch solution). |
| Level | Undergraduate |
Problem
A 0.1 in thick plate carries equal normal resultants of 5,000 lb/in in x and y and no shear. It has a 0.25 in round hole. Find the far-field stress, the hoop stress on the hole edge and the stress concentration factor.
Inputs to Enter
- N_xx = 5000 lb/in, N_yy = 5000 lb/in, N_xy = 0
- t = 0.1 in, D = 0.25 in
- r = 0.125 in (hole edge), θ = 90°
Answers
- σ∞ = N/t = 50 ksi in both directions, S_1 = S_2 = 50 ksi
- σ_θθ = 2S = 100 ksi at every point of the edge, σ_rr = 0
- K_t = σ_edge,max / S_1 = 2 (the closed form 3S_1 − S_2 with S_1 = S_2)
Notes
Change the default N_yy to 5000 and N_xy to 0. The tool prints the general Kirsch field with D(θ) = 0 for an isotropic far field.