Crippling Load by Rankine's Formula Calculator

Rankine's Formula:

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

Rankine's Critical Load (P_r):

Design Load (with Safety Factor):

1. What is Rankine's Formula for Crippling Load?

Definition: Rankine's formula calculates the critical load at which a column will fail by both crushing and buckling.

Purpose: It provides a more accurate prediction of column failure than Euler's formula alone, especially for intermediate columns.

2. How Does the Calculator Work?

The calculator uses Rankine's formula:

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

Where:

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

Explanation: The formula combines the effects of material failure (crushing) and structural instability (buckling).

3. Importance of Rankine's Formula

Details: This calculation is crucial for designing columns in construction, bridges, and other structural applications where both material strength and stability are concerns.

4. Using the Calculator

Tips: Enter the crushing load (P_c) and Euler's buckling load (P_E) in newtons, and the safety factor (default 1.5 ±5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between crushing load and buckling load?
A: Crushing load is the material strength limit, while buckling load is the stability limit based on column geometry.

Q2: Why include a safety factor?
A: The safety factor accounts for material imperfections, load uncertainties, and construction tolerances.

Q3: When is Rankine's formula most applicable?
A: For intermediate columns where both crushing and buckling are potential failure modes.

Q4: How do I find Euler's buckling load?
A: Use Euler's formula: \( P_E = \frac{\pi^2 EI}{(KL)^2} \), where E is modulus, I is moment of inertia, and KL is effective length.

Q5: What does the ±5% mean for safety factor?
A: It indicates the acceptable variation in the safety factor calculation.