# STRESS CONCENTRATION FACTORS FOR SINGLE CIRCULAR HOLE IN AN INFINITE PLATE

Stress concentration factors (Kt) for single circular hole in infinite plate can be calculated by this calculator for tension and transverse (out-of-plane) bending loads. Maximum stress values at the edge of the hole is also calculated.

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.

The formulas and parameters used in the calculator are given in " List of Equations " section of this page.

### Single Circular Hole in Infinite Plate: INPUT PARAMETERS Parameter Value Hole diameter [d] mm cm m inch ft Plate thickness [t] In-plane normal stress-1 [σ1] MPa psi ksi Transverse (out-of-plane) bending moment [M1] N*m lbf*in lbf*ft

Note: Use dot "." as decimal separator.

 RESULTS LOADING TYPE - IN-PLANE NORMAL STRESS Parameter Value UNIAXIAL STRESS ( σ2=0) Stress concentration factor for point-A [KtA]* 3 --- Stress concentration factor for point-B [KtB]* -1 Maximum tension stress at point-A [σA] --- MPa psi ksi Maximum tension stress at point-B [σB] --- BIAXIAL STRESS ( σ2=σ1) Stress concentration factor for point-A [KtA]* 2 --- Stress concentration factor for point-B [KtB]* 2 Maximum tension stress at point-A [σA] --- MPa psi ksi Maximum tension stress at point-B [σB] --- BIAXIAL STRESS ( σ2 = -σ1) (PURE SHEAR) Stress concentration factor for point-A [KtA]* 4 --- Stress concentration factor for point-B [KtB]* 4 Maximum tension stress at point-A [σA] --- MPa psi ksi Maximum tension stress at point-B [σB] --- LOADING TYPE - TRANSVERSE (OUT-OF-PLANE) BENDING SIMPLE BENDING(M1 = M , M2 = 0) Stress concentration factor at point A [KtA] * --- --- Nominal tension stress [σnom] # --- MPa psi ksi Maximum tension stress (at Point-A) [σmax] --- ISOTROPIC BENDING (M1 = M , M2 = M) Stress concentration factor at point A [KtA] * 2 --- 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: # σnom = 6M1/t2 (Nominal tension stress at the edge of the hole due to bending)

Note 3: KtA  = (σmaxnom) Theoretical stress concentration factor at point A in elastic range

Note 4: 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)

### List of Equations: Tension Uniaxial tension (σ2=0) σmax = Ktσ1 σA = 3σ1 (Kt=3) σB = -σ1 (Kt=-1) Biaxial Tension For σ2 = σ1 , σA = σB = 2σ1 (Kt=2) For σ2 = -σ1(pure shear stress), σA = -σB = 4σ1 (Kt=4) Transverse Bending σmax = Ktσ, σ = 6M/t 2 Simple bending (M1=M, M 2=0) For 0 ≤ d/t ≤ 7.0 , σmax = σA $${ K }_{ t }=3.000-0.947\sqrt { d/t } +0.192d/t$$ Isotropic bending (M1 = M 2 = M) σmax = σA Kt=2 (independent of d/t)

### Reference:

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