Tools › Structures › Stress Concentrations › Round Hole General Load › Example
Round hole under pure shear: ±4τ at ±45° from the load axes
| 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" (pure shear as tension plus compression at 45°). |
| Level | Undergraduate |
Problem
A 0.1 in thick plate carries a pure shear resultant of 5,000 lb/in and contains a 0.25 in round hole. Find the far-field principal stresses, the extreme hoop stresses on the hole edge, where they occur, and the stress concentration factor referred to the maximum far-field principal stress.
Inputs to Enter
- N_xx = 0, N_yy = 0, N_xy = 5000 lb/in
- t = 0.1 in, D = 0.25 in
- r = 0.125 in (hole edge), θ = −45° (the peak)
Answers
- τ∞ = 50 ksi; S_1 = +50 ksi, S_2 = −50 ksi at 45° to the axes
- σ_edge,max = 3S_1 − S_2 = 200 ksi = 4τ at θ = −45°; σ_edge,min = 3S_2 − S_1 = −200 ksi at θ = +45°
- K_t = 4 referred to S_1
Notes
Enter N_xx = N_yy = 0 and N_xy = 5000; set the probe angle to −45° to land on the peak (θ is measured from +y towards +x). The uniaxial tool cannot show this case.