Compressive Yield Stress According to Johnson's Parabolic Formula Calculator

Johnson's Parabolic Formula:

\[ \sigma_c = \frac{P}{A} + r \times \frac{L_{eff}}{r_{least}} \]

Critical Load On Column:

Column Cross Sectional Area:

m²

Johnson's Formula Constant:

Effective Column Length:

Least Radius of Gyration:

Compressive Yield Stress (Pa):

1. What is Compressive Yield Stress According to Johnson's Parabolic Formula?

Definition: This calculator determines the compressive yield stress of a column using Johnson's parabolic formula, which accounts for both direct compression and buckling effects.

Purpose: It helps engineers evaluate the stress state of columns that may be subject to buckling, particularly intermediate-length columns.

2. How Does the Calculator Work?

The calculator uses Johnson's parabolic formula:

\[ \sigma_c = \frac{P}{A} + r \times \frac{L_{eff}}{r_{least}} \]

Where:

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

Explanation: The formula combines direct compressive stress (P/A) with a buckling component that depends on the column's slenderness ratio (Leff/rleast).

3. Importance of Compressive Yield Stress Calculation

Details: Accurate calculation helps prevent column failure by ensuring the material's yield strength isn't exceeded under expected loads and buckling conditions.

4. Using the Calculator

Tips: Enter all required parameters. The ±5% indicates the typical tolerance for these calculations. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: When should Johnson's formula be used instead of Euler's formula?
A: Johnson's formula is typically used for intermediate-length columns where the slenderness ratio is below the critical value for Euler buckling.

Q2: How is the Johnson's formula constant determined?
A: The constant is material-dependent and is typically derived from experimental data or material specifications.

Q3: What affects the effective column length?
A: The end conditions (fixed, pinned, etc.) and any lateral bracing affect the effective length.

Q4: Why is the least radius of gyration used?
A: Buckling occurs about the axis with the least resistance, which corresponds to the smallest radius of gyration.

Q5: How accurate is this calculation?
A: The calculation is theoretical and assumes perfect conditions. Real-world factors may require safety factors.