Compressive Yield Stress According to Johnson's Parabolic Formula given Slenderness Ratio Calculator

Compressive Yield Stress Formula:

\[ \sigma_c = \frac{P}{A_{sectional}} + r \times \lambda \]

Critical Load On Column:

Column Cross Sectional Area:

m²

Johnson's formula constant:

Slenderness Ratio:

Compressive Yield Stress (Pa):

1. What is Compressive Yield Stress?

Definition: Compressive yield stress is the stress which causes a material to exhibit a specified deformation, usually determined from the stress-strain diagram obtained in a compression test.

Purpose: This calculator helps determine the compressive yield stress according to Johnson's parabolic formula given the slenderness ratio.

2. How Does the Calculator Work?

The calculator uses Johnson's formula:

\[ \sigma_c = \frac{P}{A_{sectional}} + r \times \lambda \]

Where:

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

Explanation: The formula combines the direct compressive stress with an additional term that accounts for column buckling effects.

3. Importance of Compressive Yield Stress Calculation

Details: Accurate calculation ensures structural integrity and prevents column failure under compressive loads.

4. Using the Calculator

Tips: Enter the critical load, cross-sectional area, Johnson's constant, and slenderness ratio. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is Johnson's formula constant?
A: It's a material-dependent constant that accounts for the column's material properties in the parabolic formula.

Q2: How is slenderness ratio determined?
A: It's the ratio of the column's effective length to its least radius of gyration.

Q3: Why is there a ±5% range for some inputs?
A: This accounts for typical variations in material properties and measurement uncertainties.

Q4: What units should be used?
A: Use Newtons (N) for load, square meters (m²) for area, and consistent units for other parameters.

Q5: When is Johnson's formula applicable?
A: For intermediate columns where the slenderness ratio is between short and long column limits.