Effective Length of Column According to Johnson's Parabolic Formula Calculator

Effective Column Length Formula:

\[ L_{eff} = \frac{\sigma_c - \left(\frac{P}{A_{sectional}}\right)}{r \times \left(\frac{1}{r_{least}}\right)} \]

Compressive Yield Stress:

Critical Load On Column:

Column Cross Sectional Area:

m²

Johnson's Formula Constant:

Least Radius of Gyration Column:

Effective Column Length (m):

1. What is Effective Length of Column According to Johnson's Parabolic Formula?

Definition: This calculator determines the effective length of a column using Johnson's parabolic formula, which accounts for both material properties and geometric characteristics.

Purpose: It helps engineers and designers evaluate column stability and predict buckling behavior in structural applications.

2. How Does the Calculator Work?

The calculator uses Johnson's parabolic formula:

\[ L_{eff} = \frac{\sigma_c - \left(\frac{P}{A_{sectional}}\right)}{r \times \left(\frac{1}{r_{least}}\right)} \]

Where:

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

Explanation: The formula calculates the effective length by considering material strength, applied load, cross-sectional properties, and geometric characteristics.

3. Importance of Effective Length Calculation

Details: Accurate effective length determination is crucial for predicting column buckling behavior and ensuring structural stability in buildings, bridges, and other load-bearing structures.

4. Using the Calculator

Tips: Enter all required parameters with correct units. Johnson's constant is typically 6 (±5%) for steel columns. The least radius of gyration is the smallest value for the column cross-section.

5. Frequently Asked Questions (FAQ)

Q1: What is Johnson's parabolic formula used for?
A: It's used to predict the critical buckling load for intermediate-length columns that fail through a combination of crushing and buckling.

Q2: How does effective length differ from actual length?
A: Effective length accounts for end conditions and is the length of an equivalent pin-ended column with the same buckling load.

Q3: What's a typical value for Johnson's constant?
A: For structural steel, it's typically around 6, but may vary ±5% depending on material properties.

Q4: How do I determine the least radius of gyration?
A: It's calculated as \( r = \sqrt{I/A} \), where I is the smallest moment of inertia of the cross-section.

Q5: When is Johnson's formula applicable?
A: For columns with slenderness ratios between the limits of Euler's formula and the crushing load.