# SINGLE CIRCULAR HOLE IN AN INFINITE PLATE

single circular hole in an infinite plate. Stress concentration factors (Kt) for tension and transverse (out-of-plane) bending loads. 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)

### Formulas: 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