Least Radius of Gyration According to Johnson's Parabolic Formula Calculator

Least Radius of Gyration Formula:

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

Johnson's formula constant:

Effective Column Length:

Compressive Yield Stress:

Critical Load On Column:

Column Cross Sectional Area:

m²

Least Radius of Gyration (m):

1. What is Least Radius of Gyration According to Johnson's Parabolic Formula?

Definition: This calculator determines the smallest radius of gyration for a column using Johnson's parabolic formula, which considers column length, material properties, and loading conditions.

Purpose: It helps engineers design columns that resist buckling under compressive loads.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( r_{least} \) — Least radius of gyration (meters)
\( r \) — Johnson's formula constant
\( L_{eff} \) — Effective column length (meters)
\( \sigma_c \) — Compressive yield stress (Pascals)
\( P \) — Critical load on column (Newtons)
\( A_{sectional} \) — Column cross sectional area (m²)

Explanation: The formula calculates the minimum radius needed to prevent buckling under given loading conditions.

3. Importance of Radius of Gyration Calculation

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

4. Using the Calculator

Tips: Enter all required values with appropriate units. All values must be > 0. Results are accurate within ±5%.

5. Frequently Asked Questions (FAQ)

Q1: What is Johnson's formula constant?
A: It's a material-dependent constant that accounts for the column's end conditions and material properties.

Q2: How is effective length determined?
A: Effective length depends on the column's end support conditions (fixed, pinned, etc.).

Q3: What affects compressive yield stress?
A: Material type, temperature, and manufacturing process all influence compressive yield stress.

Q4: How is critical load calculated?
A: Critical load is typically determined from structural analysis of the loading conditions.

Q5: Why is cross-sectional area important?
A: It directly affects the stress distribution and buckling resistance of the column.