Tools › Structures › Stress Concentrations › Round Hole Finite Strip › Example
Howland (1930): round hole in a finite strip, D/W = 0.5, K_tg = 4.348
| Tool | Round Hole Finite Strip |
| Source | Howland, R. C. J. (1930). "On the Stresses in the Neighbourhood of a Circular Hole in a Strip under Tension." Philosophical Transactions of the Royal Society of London, Series A, Vol. 229, pp. 49–86; Pilkey, W. D., and Pilkey, D. F. (2008). Peterson's Stress Concentration Factors, 3rd ed. John Wiley and Sons, Hoboken, NJ. Chart 4.1; Deghboudj, S., Satha, H., and Boukhedena, W. (2016). "Effect of Shape Factor upon Stress Concentration Factor in Isotropic/Orthotropic Plates with Central Hole Subjected to Tension Load." U.P.B. Scientific Bulletin, Series D, Vol. 78, No. 4, pp. 143–154. Table 1. |
| Level | Graduate |
Problem
A long strip 1 in wide and 0.1 in thick with a central 0.5 in hole carries an axial load of 5,000 lb. Find the gross and net nominal stresses, the peak stress at the hole edge and the gross and net stress concentration factors.
Inputs to Enter
- P = 5000 lb, t = 0.1 in
- W = 1 in, D = 0.5 in (D/W = 0.5)
- r = 0.25 in (hole edge), θ = 90° (the strip's transverse axis)
Answers
- σ_g = P/(Wt) = 50 ksi, σ_n = P/((W − D)t) = 100 ksi
- K_tg = 4.348 (series converged to 1e-13); Howland's own table 4.32, Pilkey Chart 4.1 fit 4.314, Deghboudj FE 4.366
- K_tn = K_tg (1 − D/W) = 2.174; σ_max = 217.4 ksi
- Series values at other ratios: D/W 0.1 3.036, 0.2 3.153, 0.3 3.374, 0.4 3.747, 0.6 5.318, 0.8 10.350; D/W = 0.02 gives 3.0014 (Kirsch)
Notes
Change the default hole diameter to 0.5 in. The converged series lies between the Pilkey fit to Howland's hand table (0 to 1.4 % lower) and the finite-element values (0.1 to 0.6 % higher) at every ratio; do not expect 4.32 exactly.