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Two unequal holes (radius ratio 2, gap one small radius) under tension across the line: 4.051 on the small hole

ToolTwo Holes
SourceHaddon, R. A. W. (1967). "Stresses in an Infinite Plate with Two Unequal Circular Holes." Quarterly Journal of Mechanics and Applied Mathematics, Vol. 20, No. 3, pp. 277–291; Chiang's values as collected in Badiger, S. M., and Ramakrishna, D. S. (2024). "Interaction of Two Circular Holes in an Infinite Plate by Body Force Method." Materials Physics and Mechanics, Vol. 52, No. 3, pp. 96–107. Table 2.
LevelGraduate

Problem

A 0.1 in plate carries 5,000 lb/in in y and contains a 0.25 in hole and a 0.5 in hole whose edges are 0.125 in apart (one radius of the small hole). Find the peak hoop stress on each hole and the gross stress concentration factor of the pair.

Inputs to Enter

  • N_xx = 0, N_yy = 5000 lb/in, N_xy = 0, t = 0.1 in
  • D_1 = 0.25 in (hole 1 at the origin), D_2 = 0.5 in, s = 0.5 in (gap 0.125 in)
  • r = 0.125 in, θ = 90°
Open the Two Holes tool

Answers

  • Peak on the small hole: K_tg = 4.0508 (Chiang 4.051); σ_edge,max = 202.5 ksi
  • Radius ratios 2 / 3 / 4 at the same gap give 4.0508 / 4.8544 / 5.5449 against Chiang 4.051 / 4.854 / 5.537
  • Tension along the line instead: peak on the large hole 2.9251 / 2.9817 / 2.9957 against 2.924 / 2.982 / 2.993

Notes

Change the defaults to D_2 = 0.5 in (s stays 0.5 in). The Pilkey Table 6-1 case 4 fits are for equal holes only.

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