TWO EQUAL CIRCULAR HOLES IN AN INFINITE PLATE

Two equal circular holes in an infinite plate. Stress concentration factors (Kt) calculator for tension loads.

Stress concentration factors for two equal circular holes in infinite plate
 INPUT PARAMETERS
Parameter Value
Hole diameter [d]
Distance between hole centers [L]
Plate thickness [t]
In-plane normal stress [σ]

Note: Use dot "." as decimal separator.


 RESULTS
LOADING TYPE - IN-PLANE NORMAL STRESSES
Stress concentration factors for two equal circular holes in infinite plate under tension
Parameter Value
UNIAXIAL TENSION PARALLEL TO ROW OF HOLES (σ1=σ ,σ2=0)
Stress concentration factor [Kt] * --- ---
Maximum tension stress [σ] ---
UNIAXIAL TENSION NORMAL TO ROW OF HOLES (σ1=0 ,σ2=σ)
Stress concentration factor for point-B [KtB]* --- ---
Nominal tension stress [σnom] ---
Maximum tension stress at point-B [σB] ---
BIAXIAL STRESS ( σ2 = σ1)
Stress concentration factor for point-B [KtB]* --- ---
Nominal tension stress [σnom] ---
Maximum tension stress at point-B [σB] ---

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

Note 2: KtB  = (σmax/σnom) 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 = (σmax/σnom)

Formulas:

Stress concentration factors for two equal circular holes in infinite plate
Tension
Stress concentration factors for two equal circular holes in infinite plate under 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: