Ultimate Crushing Stress given Rankine's Constant Calculator

Ultimate Crushing Stress Formula:

\[ \sigma_c = \alpha \times \pi^2 \times E \]

Column Crushing Stress (σc): Pa

1. What is Ultimate Crushing Stress?

Definition: Column Crushing stress is a special type of localized compressive stress which occurs at the surface of contact of two members that are relatively at rest.

Purpose: This calculator determines the ultimate crushing stress using Rankine's formula, which is important in structural engineering for column design.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma_c = \alpha \times \pi^2 \times E \]

Where:

\( \sigma_c \) — Column Crushing Stress (Pascals)
\( \alpha \) — Rankine's Constant (dimensionless)
\( \pi \) — Archimedes' constant (~3.14159)
\( E \) — Modulus of Elasticity (Pascals)

Explanation: The formula calculates the critical stress at which a column will fail by crushing, considering both material properties and geometric factors through Rankine's constant.

3. Importance of Ultimate Crushing Stress Calculation

Details: Proper calculation ensures structural safety by preventing column failure under compressive loads. It's essential for designing columns in buildings, bridges, and other structures.

4. Using the Calculator

Tips: Enter Rankine's Constant (default 0.00038) and Modulus of Elasticity (default 200 GPa for steel). All values must be > 0. Results have ±5% tolerance.

5. Frequently Asked Questions (FAQ)

Q1: What is Rankine's Constant?
A: It's an empirical constant that depends on the column material and end conditions, combining both crushing and buckling effects.

Q2: Typical values for Rankine's Constant?
A: For mild steel it's about 0.00038, but varies with material (e.g., 0.00013 for cast iron).

Q3: Why π² in the formula?
A: This comes from the theoretical solution of column buckling (Euler's formula) which Rankine's empirical formula incorporates.

Q4: How accurate is this calculation?
A: Results have ±5% tolerance due to material variations and empirical nature of Rankine's formula.

Q5: What units should I use?
A: Use consistent units - Rankine's constant is dimensionless, Modulus in Pascals, result in Pascals.