Constant Depending on Material of Column According to Terms Slenderness Ratio Calculator

Johnson's Formula:

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

Compressive Yield Stress:

Critical Load On Column:

Column Cross Sectional Area:

m²

Slenderness Ratio:

Johnson's Formula Constant:

1. What is Johnson's Formula Constant?

Definition: Johnson's formula constant is a material-dependent parameter used in column buckling calculations that relates compressive yield stress, critical load, cross-sectional area, and slenderness ratio.

Purpose: It helps engineers determine the stability of columns under compressive loads and predict buckling behavior.

2. How Does the Calculator Work?

The calculator uses Johnson's formula:

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

Where:

\( r \) — Johnson's formula constant
\( \sigma_c \) — Compressive yield stress (Pa)
\( P \) — Critical load on column (N)
\( A_{sectional} \) — Column cross-sectional area (m²)
\( \lambda \) — Slenderness ratio (±5%)

Explanation: The formula calculates the material constant by accounting for the stress reduction due to the applied load relative to the column's cross-section, normalized by the slenderness ratio.

3. Importance of Johnson's Constant

Details: Accurate calculation of this constant is crucial for structural integrity, preventing column buckling, and ensuring safe load-bearing capacity in construction projects.

4. Using the Calculator

Tips: Enter the compressive yield stress in Pascals, critical load in Newtons, cross-sectional area in square meters, and slenderness ratio (±5%). All values must be > 0 except load which can be 0.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical value for Johnson's constant?
A: The value varies by material but typically ranges from 100 to 1000 for common construction materials.

Q2: Why does slenderness ratio have ±5%?
A: The ±5% accounts for measurement uncertainties and variations in column geometry.

Q3: What if my critical load is zero?
A: With zero load, the constant simplifies to compressive yield stress divided by slenderness ratio.

Q4: How does cross-sectional area affect the result?
A: Larger cross-sections reduce the stress from applied loads, increasing the calculated constant.

Q5: Can this be used for all materials?
A: Yes, but material-specific yield stress values must be used for accurate results.