# STRESS CONCENTRATION FACTORS FOR ECCENTRIC SINGLE CIRCULAR HOLE IN FINITE-WIDTH PLATE

Theoretical stress concentration factors (Kt) of eccentric single circular hole in finite width plate can be calculated by this calculator for tension and bending loads. The maximum stress values at the edge of plate and hole are calculated if the loading parameters known. See footnotes of the "Results" table for the formulas 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.

### Eccentric Single Circular Hole in Finite Width Plate :

 INPUT PARAMETERS Parameter Value Plate width [D] mm cm m inch ft Hole diameter [d] Plate thickness [t] Edge distance [c] Distributed tension force [P] N kN lbf Bending moment [M] N*m lbf*in lbf*ft

Note: Use dot "." as decimal separator.

 RESULTS LOADING TYPE - TENSION Parameter Value Stress concentration factor [Kt] * --- --- Nominal tension stress [σnom] o --- MPa psi ksi Maximum tension stress (at Point-B) [σmax] --- LOADING TYPE - BENDING Parameter Value At Edge of Plate Stress concentration factor at point - A  [KtA] * --- --- Nominal tension stress [σnom ] + --- MPa psi ksi Maximum tension stress (at Point-A) [σmax ] --- At Edge of Hole Stress concentration factor at point - B [KtB] * --- --- Nominal tension stress [σnom] x --- MPa psi ksi Maximum tension stress (at Point-B) [σmax ] ---

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

Note 2: o For the formula, check List of Equation section.

Note 3: + σnom  = 6M/[tD2] (Nominal tension stress at the edge of plate due to bending)

Note 4: x σnom = 6M/[tD2] (Nominal tension stress at the edge of hole due to bending)

Note 5: KtA  = (σmaxnom) Theoretical stress concentration factor at point A in elastic range

Note 6: KtB  = (σmaxnom) Theoretical stress concentration factor at point B 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)

### Supplements:

 Link Usage Central Single Circular Hole in Finite Width Plate Stress concentration factors (Kt) of central single circular hole in finite width plate.

### List of Equations:

 Tension $${ K }_{ t }=3.000-3.140\frac { d }{ 2c } +3.667{ \left( \frac { d }{ 2c } \right) }^{ 2 }-1.527{ \left( \frac { d }{ 2c } \right) }^{ 3 }$$ $${ \sigma }_{ nom }=\frac { P\sqrt { 1-{ \left( d/2c \right) }^{ 2 } } }{ Dt(1-d/2c) } \frac { 1-c/D }{ 1-(c/D)\left[ 2-\sqrt { 1-{ (d/2c) }^{ 2 } } \right] }$$ $${ \sigma }_{ max }={ \sigma }_{ B }={ K }_{ t }{ \sigma }_{ nom }$$ Bending For Point B $$0\le d/2c\le 0.5,\quad 0\le c/e\le 1.0$$ $${ C }_{ 1 }=3.000-0.631(d/2c)+4.007{ \left( d/2c \right) }^{ 2 }$$ $${ C }_{ 2 }=-5.083+4.067(d/2c)-2.795{ \left( d/2c \right) }^{ 2 }$$ $${ C }_{ 3 }=2.114-1.682(d/2c)-0.273{ \left( d/2c \right) }^{ 2 }$$ $${ K }_{ tB }={ C }_{ 1 }+{ C }_{ 2 }\frac { c }{ e } +{ C }_{ 3 }{ (\frac { c }{ e } ) }^{ 2 }$$ $${ \sigma }_{ nom }={ 6M }/{ t{ D }^{ 2 } }$$ $${ \sigma }_{ B }={ K }_{ tB }{ \sigma }_{ nom }$$ For Point A $${ C' }_{ 1 }=1.0286-0.1638(d/2c)+2.702{ \left( d/2c \right) }^{ 2 }$$ $${ C' }_{ 2 }=-0.05863-0.1335(d/2c)-1.8747{ \left( d/2c \right) }^{ 2 }$$ $${ C' }_{ 3 }=0.18883-0.89219(d/2c)+1.5189{ \left( d/2c \right) }^{ 2 }$$ $${ K }_{ tA }={ C' }_{ 1 }+{ C' }_{ 2 }\frac { c }{ e } +{ C' }_{ 3 }{ (\frac { c }{ e } ) }^{ 2 }$$ $${ \sigma }_{ nom }={ 6M }/{ t{ D }^{ 2 } }$$ $${ \sigma }_{ A }={ K }_{ tA }{ \sigma }_{ nom }$$