Crippling Load given Rankine's Constant Calculator

Crippling Load Formula:

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

Column Crushing Stress:

Column Cross Sectional Area:

m²

Rankine's Constant:

Effective Column Length:

Least Radius of Gyration:

Crippling Load (N):

1. What is Crippling Load given Rankine's Constant?

Definition: This calculator determines the crippling load (the maximum load a column can bear before buckling) using Rankine's empirical formula.

Purpose: It helps structural engineers and designers calculate the safe load capacity of columns considering both crushing and buckling failure modes.

2. How Does the Calculator Work?

The calculator uses Rankine's formula:

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

Where:

\( P \) — Crippling Load (N)
\( \sigma_c \) — Column Crushing Stress (Pa)
\( A \) — Column Cross Sectional Area (m²)
\( \alpha \) — Rankine's Constant (dimensionless)
\( L_{eff} \) — Effective Column Length (m)
\( r_{least} \) — Least Radius of Gyration (m)

Explanation: The formula combines material strength (crushing stress) with geometric properties to predict failure load.

3. Importance of Crippling Load Calculation

Details: Accurate crippling load calculation ensures structural safety, prevents column failure, and helps optimize material usage in construction.

4. Using the Calculator

Tips: Enter all required values with proper units. Rankine's constant typically ranges from 0.0002 to 0.0006 for different materials (±5%).

5. Frequently Asked Questions (FAQ)

Q1: What is Rankine's Constant?
A: It's an empirical constant that depends on material properties, combining Euler's buckling and crushing stress theories.

Q2: How to determine effective column length?
A: It depends on end conditions: L for pinned-pinned, 0.5L for fixed-fixed, 0.7L for fixed-pinned, and 2L for fixed-free.

Q3: What's a typical Rankine's Constant value?
A: For mild steel it's about 0.00038 (±5%), cast iron 0.00055, and timber 0.0002.

Q4: Why use least radius of gyration?
A: Columns buckle about the axis with least stiffness, so the smallest radius of gyration governs.

Q5: How does this differ from Euler's formula?
A: Rankine's formula combines both crushing and buckling effects, while Euler's considers only buckling.