Critical Load on Column According to Johnson's Parabolic Formula Calculator

Johnson's Parabolic Formula:

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

Compressive Yield Stress:

Johnson's Formula Constant:

Effective Column Length:

Least Radius of Gyration:

Column Cross Sectional Area:

m²

Critical Load on Column: N

1. What is Critical Load on Column?

Definition: Critical Load On Column is the greatest load that will not cause lateral deflection (buckling).

Purpose: This calculator helps structural engineers determine the maximum safe load a column can bear before buckling occurs.

2. How Does the Calculator Work?

The calculator uses Johnson's Parabolic Formula:

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

Where:

\( P \) — Critical Load on Column (N)
\( \sigma_c \) — Compressive yield stress (Pa)
\( r \) — Johnson's formula constant (±5%)
\( L_{eff} \) — Effective Column Length (m)
\( r_{least} \) — Least Radius of Gyration (m)
\( A_{sectional} \) — Column Cross Sectional Area (m²)

Explanation: The formula accounts for material properties and column geometry to predict buckling load.

3. Importance of Critical Load Calculation

Details: Accurate calculation ensures structural safety and prevents catastrophic failures in buildings and other structures.

4. Using the Calculator

Tips: Enter all required parameters. The Johnson's formula constant typically has ±5% variation. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is compressive yield stress?
A: Stress which causes a material to exhibit a specified deformation, determined from stress-strain diagrams.

Q2: Why is Johnson's constant given as ±5%?
A: The constant depends on material properties and has a typical manufacturing tolerance of ±5%.

Q3: How is effective length determined?
A: It's the length of an equivalent pin-ended column with the same load-carrying capacity.

Q4: What is radius of gyration?
A: A measure of a column's resistance to buckling, calculated as √(I/A) where I is moment of inertia.

Q5: When is Johnson's formula applicable?
A: For intermediate columns where buckling occurs in the inelastic range.