Free · Physics models
Ideal Elastic Stress Concentration Models
Relate peak and nominal stress or estimate concentration around an ideal hole.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
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Formula and method
Kt = 3.0000. This worked example uses the displayed units and declared assumptions.
Kt = max_stress/nom_stress; Kt2 = ( 1 + (2* a/b) ); Kt2 = max_stress2 / nom_stress2; Kt3 = (1 + (2 * ( (Ex/Ey)^0.5 - poisson_ratio ) + (Ex/Gxy) )^0.5); Kt3 = max_stress_3 / nom_stress_3
Worked example
Enter these known values and leave the other values blank.
- Mode
- 1
- Maximum stress
- 30 MPa
- Nominal stress
- 10 MPa
- Stress concentration factor (K==t==)
- 3
Assumptions and limitations
- The elliptical-hole relation assumes an infinite isotropic elastic plate with the stated orientation. The anisotropic expression is an ideal orthotropic-hole model using compatible elastic constants. Finite width, plasticity and fatigue effects require further analysis.
- Clear an unknown to solve a supported inverse; keep known values fixed with locks. Singular or underdetermined inverses may remain incomplete.
Common questions
What assumptions apply?
The elliptical-hole relation assumes an infinite isotropic elastic plate with the stated orientation. The anisotropic expression is an ideal orthotropic-hole model using compatible elastic constants. Finite width, plasticity and fatigue effects require further analysis.
Which unknowns can I solve?
Editable controls preserve the supported captured inverse branches. Clear the desired unknown and provide enough independent known quantities; singular or underdetermined inverses may remain incomplete.
References
- NASA orthotropic hole stress concentration analysis
- OpenStax physical model reference
- Calculation definition and unit reference
Solve the orthotropic modulus inverse with z=sqrt(Ex): z²/Gxy+2z/sqrt(Ey)=(Kt3−1)²+2ν. The positive z root subtracts Gxy/sqrt(Ey). Captured expanded plus root produced Ex324 rather than100 for Kt3=3,Ey100,Gxy40,ν.25. Forward relation and remaining inverses are retained. Keep the orthotropic nonnegative square-root branch: Kt3 at least1 and both inverse squared-root targets positive for finite positive moduli.