Tools › Structures › Stress Concentrations › Row of Holes › Example
Infinite row of holes under tension along the row, D/s = 0.5: K_tg 2.139 against the Pilkey fit 2.139
| Tool | Row of Holes |
| Source | Pilkey, W. D. (2005). Formulas for Stress, Strain, and Structural Matrices, 2nd ed. John Wiley and Sons, Hoboken, NJ. Table 6-1, case 5; Pilkey, W. D., and Pilkey, D. F. (2008). Peterson's Stress Concentration Factors, 3rd ed. John Wiley and Sons, Hoboken, NJ. Charts 4.57–4.59. |
| Level | Professional |
Problem
A 0.1 in plate carries 5,000 lb/in in x, parallel to an infinite row of 0.25 in holes at a pitch of 0.5 in. Find the peak hoop stress on the hole edge, its position and the gross stress concentration factor.
Inputs to Enter
- N_xx = 5000 lb/in, N_yy = 0, N_xy = 0, t = 0.1 in (σ_xx∞ = 50 ksi)
- D = 0.25 in, s = 0.5 in (λ = 0.5)
- r = 0.2 in, θ = 30° (probe off the edge)
Answers
- K_tg = 2.1392 at θ = 0 (the point on the y axis, away from the neighbours); Pilkey fit 2.1394
- σ_edge,max = 2.1392 × 50 = 107.0 ksi
- Series K_tg along the row for λ = 0.1 … 0.9: 2.936, 2.768, 2.547, 2.326, 2.139, 1.995, 1.887, 1.802, 1.733 (the cubic fit is 2 % low at λ = 0.1: a first-order neighbour estimate gives 2.934)
Notes
Enter N_xx = 5000, N_yy = 0 and s = 0.5 in; the probe may sit anywhere outside the holes. Pure shear at s = 4a gives ±6.13 at ±40° (single hole 4 at 45°).