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Haddon (1967) / Ling (1948): two equal holes, gap of one radius, tension along the line of centres, K_tg = 2.650

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; Ling, C. B. (1948). "On the Stresses in a Plate Containing Two Circular Holes." Journal of Applied Physics, Vol. 19, pp. 77–82; 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 with centres 0.375 in apart on the x axis sit in a 0.1 in plate that carries 5,000 lb/in in x, along the line of centres. Find the peak hoop stress 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_1 = D_2 = 0.25 in, s = 0.375 in (gap one radius)
  • r = 0.125 in, θ = 0 (the point on the y axis of hole 1)
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Answers

  • K_tg = 2.650 (Haddon 2.650; Ling 2.623)
  • σ_edge,max = 2.650 × 50 = 132.5 ksi
  • Series values along the line for gaps of 1 / 2 / 4 radii: 2.650 / 2.7146 / 2.8272 against Haddon 2.650 / 2.715 / 2.827 (Ling 2.623 / 2.703 / 2.825)

Notes

Enter N_xx = 5000, N_yy = 0 and s = 0.375 in. The neighbouring hole shields the peak below the single-hole value of 3.

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