Slenderness Ratio According to Johnson's Parabolic Formula Calculator

Slenderness Ratio Formula:

\[ \lambda = \frac{\sigma_c - \left(\frac{P}{A_{sectional}}\right)}{r} \]

Compressive Yield Stress:

Critical Load On Column:

Column Cross Sectional Area:

Johnson's formula constant:

Slenderness Ratio:

1. What is Slenderness Ratio According to Johnson's Parabolic Formula?

Definition: This calculator determines the slenderness ratio of a column using Johnson's parabolic formula, which considers compressive yield stress, critical load, cross-sectional area, and a material constant.

Purpose: It helps engineers evaluate the buckling behavior of intermediate-length columns where Euler's formula doesn't apply.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \lambda = \frac{\sigma_c - \left(\frac{P}{A_{sectional}}\right)}{r} \]

Where:

\( \lambda \) — Slenderness ratio
\( \sigma_c \) — Compressive yield stress (Pa)
\( P \) — Critical load on column (N)
\( A_{sectional} \) — Column cross-sectional area (m²)
\( r \) — Johnson's formula constant

Explanation: The formula calculates the ratio that determines whether a column will fail by buckling or by material yielding.

3. Importance of Slenderness Ratio Calculation

Details: Accurate slenderness ratio calculation is crucial for structural stability, preventing column failure, and optimizing material usage in construction.

4. Using the Calculator

Tips: Enter all required values with ±5% tolerance. Ensure all inputs are positive numbers for valid results.

5. Frequently Asked Questions (FAQ)

Q1: What is Johnson's parabolic formula used for?
A: It's used for intermediate-length columns where the slenderness ratio is less than the critical value for Euler's formula.

Q2: How do I determine Johnson's constant?
A: The constant depends on the material properties and is typically determined experimentally or from material specifications.

Q3: What's a typical range for slenderness ratios?
A: It varies by material, but generally ratios below 30-50 are considered short columns, while higher values indicate long columns.

Q4: How does cross-sectional area affect the ratio?
A: Larger cross-sectional areas generally reduce the slenderness ratio, making the column less prone to buckling.

Q5: Why is ±5% tolerance important?
A: It accounts for material variations and measurement uncertainties in real-world applications.