STRESS CONCENTRATION FACTORS FOR A SINGLE ELLIPTICAL HOLE IN A FINITE-WIDTH PLATE


Theoretical stress concentration factors (Kt) of single elliptical hole in finite width plate can be calculated by this calculator for tension and in-plane bending loads. In addition to stress concentration factor calculation, the calculator can be used to find maximum stress values at the edge of plate and hole if loading parameters are known. See footnotes of the "Results" table for the necessary equations for the stress calculations.

There exist some validity conditions for the equations which are used in the calculations. If input parameters don't satisfy validity conditions of equations, a warning message is given by the calculator.

The formulas and parameters used in the calculator are given in " List of Equations " section of this page.


Calculator:
 
Single elliptical hole in finite-width plate
 INPUT PARAMETERS
Parameter Symbol Value Unit
Plate width D
Semi-major axis 2a
Semi-minor axis 2b
Plate thickness t
Tension force P
In-plane bending moment M

Note: Use dot "." as decimal separator.

 


 RESULTS
LOADING TYPE - TENSION
Stress concentration factor for single elliptical hole in finite-width plate under tension
Parameter Symbol Value Unit
Stress concentration factor at point A * Kt --- ---
Nominal tension stress o σnom ---
Maximum tension stress at Point - A σmax ---
LOADING TYPE - IN-PLANE BENDING
Stress concentration factor for single elliptical hole in finite-width plate under in-plane bending
Parameter Symbol Value Unit
Stress concentration factor at point - A * KtA --- ---
Nominal tension stress + σnom ---
Maximum tension stress at Point - A σmax ---

Note 1: * Geometry rises σnom by a factor of Kt . (Kt = σmaxnom)
Note 2: o σnom= P/[(1-2a/D)Dt] (Nominal tension stress at the plate cross section due to tension load)
Note 3: + σnom  = 12Ma/[t(D3-8a3)] (Nominal tension stress)
Note 4: KtA  = (σnommax) Theoretical stress concentration factor at point A in elastic range

Definitions:

Stress Concentration Factor: Dimensional changes and discontinuities of a member in a loaded structure causes variations of stress and high stresses concentrate near these dimensional changes. This situation of high stresses near dimensional changes and discontinuities of a member (holes, sharp corners, cracks etc.) is called stress concentration. The ratio of peak stress near stress riser to average stress over the member is called stress concentration factor.

Kt: Theoretical stress concentration factor in elastic range = (σmaxnom)

List of Equations:

Single elliptical hole in finite-width plate
Tension Formulas for stress concentration factor for single elliptical hole in finite-width plate under tension
Stress concentration factor for single elliptical hole in finite-width plate under tension
In-Plane Bending Formulas for stress concentration factor for single elliptical hole in finite-width plate under in-plane bending
Stress concentration factor for single elliptical hole in finite-width plate under in-plane bending

Reference:
  • Young, W. C., Budynas, R. G.(2002). Roark’s Formulas for Stress and Strain .7nd Edition McGraw-Hill