Least Radius of Gyration given Allowable Axial Compression Stress Calculator

Least Radius of Gyration Formula:

\[ r_{least} = 0.20 \times \left( \frac{EAR}{\left(\frac{F_{yw}}{(fs \times F_a)} - 1\right)} \times \sqrt{\frac{fs \times P_{compressive}}{4 \times \varepsilon_{column}}} \right) \]

Effective Interest Rate (EAR):

Specified minimum yield stress:

Factor of Safety:

Allowable compression stress:

Column Compressive load:

Modulus of Elasticity Column:

Least Radius of Gyration (r_least): m

1. What is Least Radius of Gyration?

Definition: The least radius of gyration is the smallest value of the radius of gyration used for structural calculations, particularly in column design.

Purpose: It helps engineers determine the slenderness ratio and buckling capacity of structural columns.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_{least} = 0.20 \times \left( \frac{EAR}{\left(\frac{F_{yw}}{(fs \times F_a)} - 1\right)} \times \sqrt{\frac{fs \times P_{compressive}}{4 \times \varepsilon_{column}}} \right) \]

Where:

\( r_{least} \) — Least radius of gyration (meters)
\( EAR \) — Effective interest rate (%)
\( F_{yw} \) — Specified minimum yield stress (Pa)
\( fs \) — Factor of Safety (typically 2.8 ±5%)
\( F_a \) — Allowable compression stress (Pa)
\( P_{compressive} \) — Column compressive load (N)
\( \varepsilon_{column} \) — Modulus of elasticity of column material (Pa)

3. Importance of Radius of Gyration Calculation

Details: Proper calculation ensures structural stability, prevents buckling, and helps in efficient material usage in column design.

4. Using the Calculator

Tips: Enter all required values with appropriate units. The factor of safety has a ±5% tolerance. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Why is the least radius of gyration important?
A: It determines the column's resistance to buckling - smaller values indicate higher buckling risk.

Q2: What's a typical factor of safety value?
A: 2.8 is common for structural columns, but always check design codes for specific requirements.

Q3: How does EAR affect the calculation?
A: EAR represents the effective interest rate which factors into the economic considerations of the structural design.

Q4: What units should I use?
A: Use consistent SI units - Pascals for stresses, Newtons for loads, and meters for results.

Q5: When would this calculation be needed?
A: During the design phase of structural columns to ensure they meet safety requirements under compressive loads.