Tools › Structures › Stress Concentrations › Two Holes › Example

Ling (1948) / Haddon (1967): two equal holes, gap of two radii, tension across the line of centres, K_tg = 3.066

ToolTwo Holes
SourceLing, C. B. (1948). "On the Stresses in a Plate Containing Two Circular Holes." Journal of Applied Physics, Vol. 19, pp. 77–82; Haddon, 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; 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 1.
LevelGraduate

Problem

A 0.1 in plate carries 5,000 lb/in in y and contains two 0.25 in holes with centres 0.5 in apart on the x axis. Find the peak hoop stress on each hole, where it occurs, the stress at the facing points, the gross and net stress concentration factors and the mid-ligament stresses.

Inputs to Enter

  • N_xx = 0, N_yy = 5000 lb/in, N_xy = 0, t = 0.1 in (σ_yy∞ = 50 ksi)
  • D_1 = 0.25 in, D_2 = 0.25 in, s = 0.5 in (gap = 0.25 in = two radii, λ = 0.5)
  • r = 0.125 in (hole 1 edge), θ = 90°
Open the Two Holes tool (loaded with this example)

Answers

  • σ_edge,max = 153.30 ksi at θ = −90° on both holes (the outer points): K_tg = 3.0660 (Ling / Haddon 3.066)
  • Facing points: 151.01 ksi (3.020 σ∞): for moderate spacing the peak is at the outer points, not the facing points
  • K_tn on Peterson's nominal σ√(1 − λ²)/(1 − λ) = 1.7702 (Pilkey fit 1.7516)
  • Mid-ligament σ_yy = 73.43 ksi (1.469 σ∞), σ_xx = 24.03 ksi; series order 19 per hole

Notes

The tool's default inputs are this case. Series values across the line for gaps of 1 / 2 / 4 radii: 3.2641 / 3.0660 / 3.0201 against Haddon 3.264 / 3.066 / 3.020.

More Examples for This Tool