Crushing Load by Rankine's Formula Calculator

Crushing Load Formula:

\[ P_c = \frac{P_r \times P_E}{P_E - P_r} \]

Crushing Load (N):

1. What is Crushing Load by Rankine's Formula?

Definition: This calculator determines the crushing load of a column using Rankine's formula, which combines Euler's buckling load and Rankine's critical load.

Purpose: It helps structural engineers determine the maximum load a column can bear before failure occurs due to buckling or crushing.

2. How Does the Calculator Work?

The calculator uses Rankine's formula:

\[ P_c = \frac{P_r \times P_E}{P_E - P_r} \]

Where:

\( P_c \) — Crushing load (Newtons)
\( P_r \) — Rankine's critical load (Newtons)
\( P_E \) — Euler's buckling load (Newtons)

Explanation: The formula combines both buckling and crushing failure modes to predict the actual failure load of intermediate-length columns.

3. Importance of Crushing Load Calculation

Details: Accurate calculation ensures structural safety, prevents column failure, and helps in optimal material selection for construction projects.

4. Using the Calculator

Tips: Enter Rankine's critical load and Euler's buckling load in Newtons, and specify tolerance percentage (default ±5%). Euler's load must be greater than Rankine's load.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between Rankine's and Euler's loads?
A: Euler's load considers buckling failure in long columns, while Rankine's load addresses crushing failure in short columns.

Q2: Why include a tolerance percentage?
A: Tolerance accounts for material imperfections, construction tolerances, and safety factors in real-world applications.

Q3: What units should I use?
A: The calculator uses Newtons (N) for all load values. Convert other units to Newtons before input.

Q4: When is Rankine's formula most applicable?
A: For intermediate-length columns where both buckling and crushing are potential failure modes.

Q5: How do I determine Rankine's critical load?
A: Use Rankine's formula: \( P_r = \frac{\sigma_c \times A}{1 + \alpha(\frac{L}{k})^2} \), where σc is crushing stress, A is area, α is Rankine's constant, L is length, and k is radius of gyration.