STRESS CONCENTRATION FACTORS FOR A SINGLE ELLIPTICAL HOLE IN A FINITEWIDTH
PLATE
Theoretical stress concentration factors (K_{t}) of single elliptical hole in finite width plate
can be
calculated by this calculator for tension and inplane 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:
Note: Use dot "." as decimal separator.
RESULTS 
LOADING TYPE  TENSION 

Parameter 
Symbol 
Value 
Unit 
Stress concentration factor at point A * 
K_{t} 


 
Nominal tension stress ^{
o} 
σ_{nom
} 



Maximum tension stress at Point  A 
σ_{max
} 


LOADING TYPE  INPLANE BENDING 

Parameter 
Symbol 
Value 
Unit 
Stress concentration factor at point  A * 
K_{tA} 


 
Nominal tension stress^{ +} 
σ_{nom}




Maximum tension stress at Point  A 
σ_{max }



Note 1: * Geometry rises σ_{nom} by a factor of K_{t} . (K_{t }= σ_{max}/σ_{nom})
Note 2: ^{o} σ_{nom}= P/[(12a/D)Dt] (Nominal tension stress at
the plate cross section due to tension load)
Note 3: ^{+} σ_{nom} = 12Ma/[t(D^{3}8a^{3})]
(Nominal tension stress)
Note 4: K_{tA } = (σ_{nom}/σ_{max}) 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.
K_{t}: Theoretical stress
concentration factor in elastic range = (σ_{max}/σ_{nom})
List of Equations:
Reference:

Young, W. C., Budynas, R. G.(2002). Roark’s Formulas for Stress and Strain .7nd
Edition McGrawHill