Tools › Structures › Stress Concentrations › Round Hole General Load › Example
Round hole under a general in-plane state: σ_max = 3S_1 − S_2 on the S_2 axis
| 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"; Pilkey, W. D., and Pilkey, D. F. (2008). Peterson's Stress Concentration Factors, 3rd ed. John Wiley and Sons, Hoboken, NJ. Chapter 4, circular hole under biaxial stress. |
| Level | Undergraduate |
Problem
A 0.1 in thick plate carries N_xx = 5,000, N_yy = 15,000 and N_xy = 3,000 lb/in and contains a 0.25 in round hole. Find the far-field principal stresses and their direction, the peak hoop stress on the hole edge and the stress concentration factor referred to the maximum far-field principal stress.
Inputs to Enter
- N_xx = 5000 lb/in, N_yy = 15000 lb/in, N_xy = 3000 lb/in
- t = 0.1 in, D = 0.25 in
- r = 0.125 in, θ = 90°
Answers
- σ_xx∞ = 50, σ_yy∞ = 150, τ_xy∞ = 30 ksi; S_1 = 158.3 ksi at φ_1 = 15.5° from the y axis, S_2 = 41.7 ksi
- σ_edge,max = 3S_1 − S_2 = 433.2 ksi on the S_2 axis
- K_t = σ_edge,max / S_1 = 2.737 = 3 − S_2/S_1
Notes
The tool's default inputs are this case. K_t is referred to S_1 (the tool's convention); the same loads on the Circular Inclusion tool with the empty-hole option give K_hoop = 2.7367.