Crippling Load if One End of Column is Fixed and Other is Free Calculator

Crippling Load Formula:

\[ P = \frac{\pi^2 \times E \times I}{4 \times l^2} \]

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Column Length (l):

Safety Factor:

Crippling Load (P):

Safe Load (with safety factor):

1. What is Crippling Load for Fixed-Free Columns?

Definition: The crippling load is the maximum load a column can bear before buckling when one end is fixed and the other is free.

Purpose: This calculation helps structural engineers design columns that can support loads without buckling failure.

2. How Does the Calculator Work?

The calculator uses Euler's formula for fixed-free columns:

\[ P = \frac{\pi^2 \times E \times I}{4 \times l^2} \]

Where:

\( P \) — Crippling load (N)
\( E \) — Modulus of elasticity (Pa)
\( I \) — Moment of inertia (m⁴)
\( l \) — Column length (m)

Explanation: The formula calculates the critical buckling load considering the column's material properties and geometry.

3. Importance of Crippling Load Calculation

Details: Accurate calculation prevents structural failures, ensures safety, and optimizes material usage in construction.

4. Using the Calculator

Tips: Enter modulus of elasticity, moment of inertia, column length, and safety factor (default 1.5 ±5%). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why is the safety factor important?
A: It accounts for material imperfections, load uncertainties, and provides a margin of safety (±5% variation).

Q2: What's typical modulus of elasticity for steel?
A: About 200 GPa (200 × 10⁹ Pa) for structural steel.

Q3: How does column length affect crippling load?
A: Load capacity decreases with the square of length - doubling length reduces capacity to 1/4.

Q4: When is this formula applicable?
A: For long, slender columns where buckling occurs before material yielding.

Q5: What if my column has different end conditions?
A: Different formulas apply for pinned-pinned, fixed-fixed, or fixed-pinned columns.