Rankine's Constant given Crippling Load Calculator

Rankine's Constant Formula:

\[ \alpha = \left(\frac{\sigma_c \times A}{P} - 1\right) \times \left(\frac{r_{least}}{L_{eff}}\right)^2 \]

Column Crushing Stress:

Column Cross Sectional Area:

m²

Crippling Load:

Least Radius of Gyration:

Effective Column Length:

Tolerance:

Rankine's Constant (α):

1. What is Rankine's Constant?

Definition: Rankine's Constant (α) is a material constant used in Rankine's formula to calculate the crippling load of columns.

Purpose: It helps engineers determine the critical load at which a column will fail by buckling.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \alpha = \left(\frac{\sigma_c \times A}{P} - 1\right) \times \left(\frac{r_{least}}{L_{eff}}\right)^2 \]

Where:

\( \alpha \) — Rankine's Constant
\( \sigma_c \) — Column crushing stress (Pa)
\( A \) — Column cross-sectional area (m²)
\( P \) — Crippling load (N)
\( r_{least} \) — Least radius of gyration (m)
\( L_{eff} \) — Effective column length (m)

3. Importance of Rankine's Constant

Details: This constant is crucial for designing safe and efficient columns in structural engineering, ensuring they can withstand expected loads without buckling.

4. Using the Calculator

Tips: Enter all required parameters including column properties and load. The tolerance field (default ±5%) allows you to see the acceptable range of values.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical value for Rankine's constant?
A: The value varies by material but typically ranges from 1/7500 to 1/1600 for different steel columns.

Q2: How is the effective length determined?
A: Effective length depends on end conditions - it's the actual length multiplied by a factor based on how the ends are constrained.

Q3: What's the significance of the least radius of gyration?
A: The least radius determines the weakest axis of buckling, which governs the column's buckling strength.

Q4: When would I adjust the tolerance?
A: Adjust tolerance based on required precision - lower for critical applications, higher for rough estimates.

Q5: How does crushing stress differ from yield stress?
A: Crushing stress is the stress at complete failure, while yield stress is when permanent deformation begins.