# TWO EQUAL CIRCULAR HOLES IN AN INFINITE PLATE

Two equal circular holes in an infinite plate. Stress concentration factors (Kt) calculator for tension loads. INPUT PARAMETERS Parameter Value Hole diameter [d] mm cm m inch ft Distance between hole centers [L] Plate thickness [t] In-plane normal stress [σ] MPa psi ksi

Note: Use dot "." as decimal separator.

 RESULTS LOADING TYPE - IN-PLANE NORMAL STRESSES Parameter Value UNIAXIAL TENSION PARALLEL TO ROW OF HOLES (σ1=σ ,σ2=0) Stress concentration factor [Kt] * --- --- Maximum tension stress [σ] --- MPa psi ksi UNIAXIAL TENSION NORMAL TO ROW OF HOLES (σ1=0 ,σ2=σ) Stress concentration factor for point-B [KtB]* --- --- Nominal tension stress [σnom] --- MPa psi ksi Maximum tension stress at point-B [σB] --- BIAXIAL STRESS ( σ2 = σ1) Stress concentration factor for point-B [KtB]* --- --- Nominal tension stress [σnom] --- MPa psi ksi Maximum tension stress at point-B [σB] ---

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

Note 2: 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)

### Formulas: Tension for 0 ≤ d/L<1 $${ \sigma }_{ max }={ K }_{ t }\sigma$$ Uniaxial tension parallel to row of holes (σ1 = σ , σ2 = 0) $${ K }_{ t }=3.000-0.712d/L+0.271{ (d/L) }^{ 2 }$$ Uniaxial tension normal to row of holes (σ2 = σ , σ1 = 0) $${ \sigma }_{ max }={ \sigma }_{ B }={ K }_{ t }{ \sigma }_{ nom }\quad ,\quad { \sigma }_{ nom }\quad =\frac { \sigma \sqrt { 1-{ \left( d/L \right) }^{ 2 } } }{ 1-d/L }$$ $${ K }_{ t }=3.000-3.0018d/L+1.0099{ (d/L) }^{ 2 }$$ Biaxial tension (σ2 = σ, σ1 = σ) $${ \sigma }_{ max }={ \sigma }_{ B }={ K }_{ t }{ \sigma }_{ nom }\quad ,\quad { \sigma }_{ nom }\quad =\frac { \sigma \sqrt { 1-{ \left( d/L \right) }^{ 2 } } }{ 1-d/L }$$ $${ K }_{ t }=2.000-2.119d/L+2.493{ (d/L) }^{ 2 }-1.372{ (d/L) }^{ 3 }$$

### Reference:

• Pilkey, W. D..(2005). Formulas for Stress, Strain, and Structural Matrices Formulas for Stress, Strain, and Structural Matrices .2nd Edition John Wiley & Sons