Tools › Structures › Stress Concentrations › Two Holes › Example

Haddon (1967): two equal holes, gap of one radius, tension across the line of centres, K_tg = 3.264

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; 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 1.
LevelGraduate

Problem

Two 0.25 in holes in a 0.1 in plate have their centres 0.375 in apart (a gap of one radius) on the x axis; the plate carries 5,000 lb/in in y. Find the peak hoop stress and the gross stress concentration factor.

Inputs to Enter

  • N_xx = 0, N_yy = 5000 lb/in, N_xy = 0, t = 0.1 in
  • D_1 = D_2 = 0.25 in, s = 0.375 in (gap 0.125 in = one radius)
  • r = 0.125 in, θ = 90°
Open the Two Holes tool

Answers

  • K_tg = 3.2641 (Haddon 3.264)
  • σ_edge,max = 3.2641 × 50 = 163.2 ksi
  • At this spacing (D/s = 0.667) the peak sits at the facing points, which take over from the outer points for D/s above about 0.55

Notes

Change the default centre distance to 0.375 in. The tool's gap limit is 0.2 × the larger diameter (0.05 in here). The Drawn Cutout tool's boundary-element solution of the same geometry gives 3.266.

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