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.

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)

Formulas:

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: