STRESS CONCENTRATION FACTORS FOR CENTRAL SINGLE CIRCULAR HOLE IN FINITE-WIDTH PLATE

Theoretical stress concentration factors (Kt) of central single circular hole in finite width plate can be calculated by this calculator for tension, in-plane and simple transverse bending loads. In addition to stress concentration factor calculation, the calculator can be used to find maximum stress values at the edge of plate and hole if loading parameters are known. See footnotes of the "Results" table for the necessary equations for the stress calculations.

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.


Calculator:
 
Stress concentration factors for central single circular hole in finite-width plate
 INPUT PARAMETERS
Parameter Symbol Value Unit
Plate width D
Hole diameter d
Plate thickness t
Tension force P
In-plane bending moment M
Transverse bending moment M1

Note: Use dot "." as decimal separator.

 


 RESULTS
LOADING TYPE - TENSION
Stress concentration factors for central single circular hole in finite-width plate under tension
Parameter Symbol Value Unit
Stress concentration factor * Kt --- ---
Nominal tension stress o σnom ---
Maximum tension stress at the edge of hole σmax ---
LOADING TYPE - IN-PLANE BENDING
Stress concentration factors for central single circular hole in finite-width plate under bending
Parameter Symbol Value Unit
At Edge of Hole
Stress concentration factor at point - A * KtA --- ---
Nominal tension stress + σnom ---
Maximum tension stress (at Point-A) σmax ---
At Edge of Plate
Stress concentration factor at point - B * KtB --- ---
Nominal tension stress x σnom ---
Maximum tension stress (at Point-B) σmax ---
LOADING TYPE - SIMPLE TRANSVERSE BENDING
Stress concentration factors for central single circular hole in finite-width plate under simple transverse bending Stress concentration factors for central single circular hole in finite-width plate under simple transverse bending
Stress concentration factor at point A * KtA --- ---
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: o σnom= P/[t(D-d)] (Nominal tension stress at the plate cross section due to tension load)
Note 3: + σnom  = 6Md/[t(D3-d3)] (Nominal tension stress at the edge of hole due to bending)
Note 4: x σnom = 6MD/[t(D3-d3)] (Nominal tension stress at the edge of plate due to bending)
Note 5: # σnom = 6M1/[t2(D-d)] (Nominal tension stress at the edge of plate due to bending)
Note 6: α=30°
Note 7: KtA  = (σmaxnom) Theoretical stress concentration factor at point A in elastic range
Note 8: 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 central single circular hole in finite-width plate
Tension Formulas for stress concentration factor formulas for central single circular hole in finite-width plate under tension
Stress concentration factors for central single circular hole in finite-width plate under tension
In-Plane Bending Formulas for stress concentration factor formulas for central single circular hole in finite-width plate under bending
Stress concentration factors for central single circular hole in finite-width plate under bending
Simple Transverse  Bending Stress concentration factor formulas for central single circular hole in finite-width plate under simple transverse bending
Stress concentration factors for central single circular hole in finite-width plate under simple transverse bending

Reference: