Section Stability Metric
Radius of Gyration Calculator
Use this page to connect section area and weak-axis inertia into radius of gyration, then see how that value feeds directly into slenderness and Euler stability.
Enter length in meters, E in GPa, inertia in cm^4, area in cm^2, and applied axial load in kN.
Buckling Inputs
End condition
Member data
Use the end condition that best matches the expected rotational restraint.
Use the weaker-axis inertia when buckling can occur about multiple axes.
Area is used to calculate the radius of gyration and slenderness.
Applied load is compared directly with the ideal Euler critical load.
Buckling Diagram
Stability Summary
| End condition | Fixed-Fixed |
| Effective length factor K | 0.500 |
| Radius of gyration r | 6.09 cm |
| Euler stress Fe | 2,373.07 MPa |
| Load margin Pcr - P | 5,725.21 kN |
Buckling Formula
Effective length
General form
L_e = K L
With current values
L_e = 0.500 * 3.60
Calculated result
L_e = 1.80 m
Euler critical load
General form
P_cr = pi^2 E I / L_e^2
With current values
P_cr = pi^2 * 210 * 920 / 1.80^2
Calculated result
P_cr = 5,885.21 kN
Slenderness ratio
General form
lambda = L_e / r, r = sqrt(I / A)
With current values
lambda = 1.80 / sqrt(920 / 25)
Calculated result
lambda = 29.55
This screen applies classical Euler elastic buckling and is most reliable for slender columns before inelastic or code-specific checks.
Model Assumptions
- The column is straight, prismatic, and loaded concentrically.
- Material behavior is linear elastic up to the predicted buckling load.
- Only ideal Euler global buckling is screened here; local buckling and imperfections are excluded.
Engineering Reading
Calculation Basis
Assumptions & Limits
- The model screens ideal global Euler buckling only and does not include local buckling or material nonlinearity.
- Imperfections, eccentricity, and frame sway effects need separate engineering review.
- K-factors are modeling assumptions about end restraint and should be treated as a sensitivity study when restraint is uncertain.
Reference Basis
- Documentation: Methodology
- Documentation: Engineering Review
- Roark's Formulas for Stress and Strain
- Mechanics of Materials references
- Euler buckling and column-stability references
Radius of Gyration Basis
| Core formula | r = sqrt(I / A) |
| Why it matters | Controls slenderness together with effective length |
| Current section basis | Weak-axis inertia plus gross area |
| Practical use | Compare section efficiency for compression members |
| Best follow-up | Check K-factor and unsupported length assumptions |
Engineering Notes
- Radius of gyration is one of the fastest ways to compare how efficiently different sections resist global buckling for a given area.
- A larger area alone does not guarantee a better compression member if the weak-axis inertia stays low and the resulting radius of gyration remains small.
- Use this page together with section-property pages when the member family is still open and the goal is to compare compression efficiency before the final section is fixed.
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