# RECTANGULAR HOLE IN AN INFINITE PLATE

Rectangular hole with round corners in an infinite plate. Stress concentration factors (Kt) calculator for tension loads.

 INPUT PARAMETERS Parameter Value Rectangle height [2a] mm cm m inch ft Rectangle width [2b] Corner radius [r] Axial stress [σ1] MPa psi ksi

Note: Use dot "." as decimal separator.

 RESULTS LOADING TYPE - AXIAL STRESS Parameter Value TENSION STRESS Stress concentration factor [Kt] * --- --- Maximum tension stress [σmax] --- MPa psi ksi

Note 1: * Geometry rises σnom by a factor of Kt . (Kt = σmaxnom)

### 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)

### Formulas:

 Tension $$0.2\le r/b\le 1.0$$ and $$0.3\le b/a\le 1.0$$ $${ C }_{ 1 }=14.815-15.774\sqrt { r/b } +8.149r/b$$ $${ C }_{ 2 }=-11.201-9.750\sqrt { r/b } +9.600r/b$$ $${ C }_{ 3 }=0.202+38.662\sqrt { r/b } -27.374r/b$$ $${ C }_{ 4 }=3.232-23.002\sqrt { r/b } +15.482r/b$$ $${ K }_{ t }={ C }_{ 1 }+{ C }_{ 2 }\frac { b }{ a } +{ C }_{ 3 }{ (\frac { b }{ a } ) }^{ 2 }+{ C }_{ 4 }{ (\frac { b }{ a } ) }^{ 3 }$$ $${ \sigma }_{ max }={ K }_{ t }{ \sigma }_{ 1 }$$