Least radius of gyration by straight line formula for columns and struts Calculator

Formula:

\[ r_{least} = \frac{n \times L_{eff}}{\sigma_c - \left(\frac{P}{A_{sectional}}\right)} \]

Straight line formula constant (n):

Effective Column Length (L_eff):

Column Compressive Stress (σ_c):

Crippling Load (P):

Column Cross Sectional Area (A_sectional):

m²

Least Radius of Gyration (r_least):

1. What is Least Radius of Gyration by Straight Line Formula?

Definition: This calculator determines the smallest radius of gyration for columns and struts using the straight line formula, which considers material properties and loading conditions.

Purpose: It helps structural engineers determine the critical dimension affecting a column's resistance to buckling.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_{least} = \frac{n \times L_{eff}}{\sigma_c - \left(\frac{P}{A_{sectional}}\right)} \]

Where:

\( r_{least} \) — Least radius of gyration (meters)
\( n \) — Straight line formula constant (material dependent)
\( L_{eff} \) — Effective column length (meters)
\( \sigma_c \) — Column compressive stress (Pascals)
\( P \) — Crippling load (Newtons)
\( A_{sectional} \) — Column cross-sectional area (square meters)

Explanation: The formula relates geometric properties, material properties, and loading conditions to determine the critical radius that affects buckling behavior.

3. Importance of Radius of Gyration Calculation

Details: The least radius of gyration is crucial for determining a column's slenderness ratio and its resistance to buckling under compressive loads.

4. Using the Calculator

Tips: Enter all required values with appropriate units. The ±5% indicates the typical tolerance for these calculations. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the straight line formula constant (n)?
A: It's a material-dependent constant that ranges from 1/750 for mild steel to 1/1600 for timber.

Q2: How is effective length determined?
A: It depends on end conditions - pinned-pinned (1.0L), fixed-fixed (0.5L), fixed-pinned (0.7L), etc.

Q3: What if the denominator becomes zero?
A: The calculation is invalid when σ_c = P/A, indicating a critical buckling condition.

Q4: How does radius of gyration affect design?
A: Smaller radius means greater susceptibility to buckling, requiring thicker sections or shorter lengths.

Q5: What are typical values for radius of gyration?
A: For steel columns, it typically ranges from 20-150 mm depending on section size and shape.