# SINGLE ELLIPTICAL HOLE IN A FINITE-WIDTH PLATE

Single elliptical hole in a finite width plate. Theoretical stress concentration factors (Kt)calculator for tension and in-plane bending loads.

 INPUT PARAMETERS Parameter Value Plate width [D] mm cm m inch ft Semi-major axis [2a] Semi-minor axis [2b] Plate thickness [t] Tension force [P] N kN lbf In-plane bending moment [M] N*m lbf*in lbf*ft

Note: Use dot "." as decimal separator.

 RESULTS LOADING TYPE - TENSION Parameter Value Stress concentration factor at point A [Kt] * --- --- Nominal tension stress [σnom ] o --- MPa psi ksi Maximum tension stress at Point - A [σmax ] --- LOADING TYPE - IN-PLANE BENDING Parameter Value Stress concentration factor at point - A [KtA] * --- --- Nominal tension stress [σnom ] + --- MPa psi ksi 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)

### Formulas:

 Tension For 0.5 ≤ a/b ≤ 10.0 $${ C }_{ 1 }=1.000-0.000\sqrt { a/b } +2.000a/b$$ $${ C }_{ 2 }=-0.351-0.021\sqrt { a/b } -2.483a/b$$ $${ C }_{ 3 }=3.621-5.183\sqrt { a/b } +4.494a/b$$ $${ C }_{ 4 }=-2.270+5.204\sqrt { a/b } -4.011a/b$$ $${ K }_{ tA }={ C }_{ 1 }+{ C }_{ 2 }\frac { 2a }{ D } +{ C }_{ 3 }{ (\frac { 2a }{ D } ) }^{ 2 }+{ C }_{ 4 }{ (\frac { 2a }{ D } ) }^{ 3 }$$ $${ \sigma }_{ nom }=P/[(D-2a)t]$$ $${ \sigma }_{ A }={ K }_{ tA }{ \sigma }_{ nom }$$ In-Plane Bending 0.4 ≤ 2a/D ≤ 1.0,  1.0 ≤ a/b ≤ 2.0 $${ C }_{ 1 }=3.465-3.739\sqrt { a/b } +2.274a/b$$ $${ C }_{ 2 }=-3.841+5.582\sqrt { a/b } -1.741a/b$$ $${ C }_{ 3 }=2.376-1.843\sqrt { a/b } -0.534a/b$$ $${ K }_{ tA }={ C }_{ 1 }+{ C }_{ 2 }\frac { 2a }{ D } +{ C }_{ 3 }{ (\frac { 2a }{ D } ) }^{ 2 }$$ $${ \sigma }_{ nom }=12Ma/([{ D }^{ 3 }-8{ a }^{ 3 }]t)$$ $${ \sigma }_{ max }={ \sigma }_{ A }={ K }_{ tA }{ \sigma }_{ nom }$$