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:

Stress concentration factors for single circular hole in infinite plate
 INPUT PARAMETERS
Parameter Value
Hole diameter [d]
Plate thickness [t]
In-plane normal stress-1 [σ1]
Transverse (out-of-plane) bending moment [M1]

Note: Use dot "." as decimal separator.

 


 RESULTS
LOADING TYPE - IN-PLANE NORMAL STRESS
Stress concentration factors for single circular hole in infinite plate under tension
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] ---
Maximum tension stress at point-B [σB] ---
BIAXIAL STRESS ( σ21)
Stress concentration factor for point-A [KtA]* 2 ---
Stress concentration factor for point-B [KtB]* 2
Maximum tension stress at point-A [σA] ---
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] ---
Maximum tension stress at point-B [σB] ---
LOADING TYPE - TRANSVERSE (OUT-OF-PLANE) BENDING
Stress concentration factors for central single circular hole in finite-width plate under simple transverse bending
SIMPLE BENDING(M1 = M , M2 = 0)
Stress concentration factor at point A [KtA] * --- ---
Nominal tension stress [σnom] # ---
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] # ---
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:


Stress concentration factors for single circular hole in infinite plate
Tension
Stress concentration factors for single circular hole in infinite plate under 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
Stress concentration factors for single circular hole in infinite plate under 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: