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

Theoretical stress concentration factors (Kt) of central single circular hole in finite width plate can be calculated by this calculator for tension, in-plane and simple transverse bending loads. The calculator also finds 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.

### Stress Concentration Factors (Kt) of Central 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] Tension force [P] N kN lbf In-plane bending moment [M] N*m lbf*in lbf*ft Transverse bending moment [M1]

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 the edge of hole [σmax ] --- LOADING TYPE - IN-PLANE BENDING Parameter Value At Edge of Hole Stress concentration factor at point - A [KtA] * --- --- Nominal tension stress [σnom ] + --- MPa psi ksi Maximum tension stress (at Point-A) [σmax ] --- At Edge of Plate Stress concentration factor at point - B [KtB] * --- --- Nominal tension stress [σnom] x --- MPa psi ksi Maximum tension stress (at Point-B) [σmax ] --- LOADING TYPE - SIMPLE TRANSVERSE BENDING 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/[t(D-d)] (Nominal tension stress at the plate cross section due to tension load)

Note 3: + σnom  = 6Md/[t(D3-d3)] (Nominal tension stress at the edge of hole due to bending)

Note 4: x σnom = 6MD/[t(D3-d3)] (Nominal tension stress at the edge of plate due to bending)

Note 5: # σnom = 6M1/[t2(D-d)] (Nominal tension stress at the edge of plate due to bending)

Note 6: α=30°

Note 7: KtA  = (σmaxnom) Theoretical stress concentration factor at point A in elastic range

Note 8: 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 Eccentric Single Circular Hole in Finite Width Plate Stress concentration factors (Kt) of eccentric single circular hole in finite width plate.

### List of Equations:

 Tension For $$0\le \frac { d }{ D } \le 1$$ $$3.000-3.140\frac { d }{ D } +3.667{ \left( \frac { d }{ D } \right) }^{ 2 }-1.527{ \left( \frac { d }{ D } \right) }^{ 3 }$$ $${ \sigma }_{ nom }=P/[(D-d)t]$$ $${ \sigma }_{ max }={ K }_{ t }{ \sigma }_{ nom }$$ In-Plane Bending At the edge of hole Kta = 2 (independent of d/D) $${ \sigma }_{ nom }=6Md/[({ D }^{ 3 }-{ d }^{ 3 })t]$$ σmax@A = Ktσnom At the edge of plate $${ K }_{ tb }=\frac { 2d }{ D } (\alpha ={ 30 }^{ \circ })$$ $${ \sigma }_{ nom }=6MD/[({ D }^{ 3 }-{ d }^{ 3 })t]$$ σmax@B = Ktσnom Simple Transverse  Bending For $$0\le \cfrac { d }{ D } \le 0.3$$ and $$1\le d/t\le 7$$ $${ K }_{ t }=\left[ 1.793+\frac { 0.131 }{ d/t } +\frac { 2.052 }{ { \left( d/t \right) }^{ 2 } } -\frac { 1.019 }{ { \left( d/t \right) }^{ 3 } } \right] \times \left[ 1-1.04(d/D)+1.22{ (d/D) }^{ 2 } \right]$$ $${ \sigma }_{ nom }=6{ M }_{ 1 }/[(D-d){ t }^{ 2 }]$$ σmax@A = Ktσnom