Least Radius of Gyration given Allowable Axial Compression Stress Slenderness Ratio More 160 Calculator

Least Radius of Gyration Formula:

\[ r_{least} = \frac{L_{eff}}{800 \times (1.2 - (\frac{F_a}{\sigma_c'}))} \]

Effective Column Length:

Allowable Compression Stress:

Value from Secant Formula:

Tolerance:

Least Radius of Gyration (m):

With Tolerance (m):

1. What is Least Radius of Gyration Calculator?

Definition: This calculator determines the minimum radius of gyration for columns with slenderness ratio greater than 160, considering allowable axial compression stress.

Purpose: It helps structural engineers ensure column stability by calculating the minimum radius of gyration needed to prevent buckling.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_{least} = \frac{L_{eff}}{800 \times (1.2 - (\frac{F_a}{\sigma_c'}))} \]

Where:

\( r_{least} \) — Least radius of gyration (meters)
\( L_{eff} \) — Effective column length (meters)
\( F_a \) — Allowable compression stress (Pascals)
\( \sigma_c' \) — Value from secant formula (Pascals)

Explanation: The formula accounts for the relationship between column length, material stress limits, and stability requirements.

3. Importance of Radius of Gyration Calculation

Details: Proper calculation ensures structural stability, prevents buckling, and meets safety standards for slender columns.

4. Using the Calculator

Tips: Enter effective column length, allowable stress, secant formula value, and optional tolerance percentage (±5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: When is this formula applicable?
A: For columns with slenderness ratio (L/r) greater than 160, where buckling is a primary concern.

Q2: What is the secant formula value?
A: This is the stress value obtained from the secant formula calculation for mild steel columns.

Q3: Why include a tolerance factor?
A: Tolerance (±5%) accounts for material variations, construction tolerances, and safety factors.

Q4: How is effective length determined?
A: Effective length depends on end conditions - pinned, fixed, or free - and can be calculated using appropriate coefficients.

Q5: What units should be used?
A: Consistent SI units - meters for length, Pascals for stress values.