Tools › Structures › Stress Concentrations › Elliptic Hole General Load › Example

Elliptic hole under equal biaxial tension: 2S·a/b at the ends of the major axis

ToolElliptic Hole General Load
SourceInglis, C. E. (1913). "Stresses in a Plate Due to the Presence of Cracks and Sharp Corners." Transactions of the Institution of Naval Architects, Vol. 55, pp. 219–241 (all-round tension case).
LevelUndergraduate

Problem

A 0.1 in thick plate under equal normal resultants of 10,000 lb/in in x and y contains an elliptic hole with semi-axes 0.25 in along x and 0.125 in along y. Find the hoop stress at the ends of each axis and the stress concentration factor.

Inputs to Enter

  • N_xx = 10000 lb/in, N_yy = 10000 lb/in, N_xy = 0, t = 0.1 in (S = 100 ksi)
  • a = 0.25 in (along x), b = 0.125 in (along y), β = 0
  • r = 0.25 in (end of a), θ = 90°
Open the Elliptic Hole General Load tool

Answers

  • Ends of a: σ_hoop = 2S·a/b = 400 ksi, K_t = 4
  • Ends of b: σ_hoop = 2S·b/a = 100 ksi
  • Round-hole limit a = b under the same state: 2S = 200 ksi all round, K_t = 2

Notes

Change the defaults to N_xx = N_yy = 10000 and N_xy = 0. With N_yy alone the tool returns the Inglis uniaxial values (K_t = 5 aligned, 4.329 at θ = 66.1° for β = 30°); with a = b and pure shear it returns 4.