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

Crippling Load Formula:

\[ P = \frac{2\pi^2EI}{l^2} \]

Modulus of Elasticity of Column:

Moment of Inertia Column:

m⁴

Column Length:

Tolerance:

Crippling Load (N):

1. What is Crippling Load for Fixed-Hinged Column?

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

Purpose: This calculation helps structural engineers design columns that can withstand expected loads without buckling.

2. How Does the Calculator Work?

The calculator uses Euler's formula for columns with one fixed and one hinged end:

\[ P = \frac{2\pi^2EI}{l^2} \]

Where:

\( P \) — Crippling load (Newtons)
\( E \) — Modulus of elasticity (Pascals)
\( I \) — Moment of inertia (m⁴)
\( l \) — Column length (meters)

Explanation: The formula calculates the critical buckling load based on material stiffness, cross-section properties, and column length.

3. Importance of Crippling Load Calculation

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

4. Using the Calculator

Tips: Enter the modulus of elasticity, moment of inertia, column length, and optional tolerance percentage. All values must be > 0 except tolerance which can be 0.

5. Frequently Asked Questions (FAQ)

Q1: Why is the formula different for fixed-hinged columns?
A: The effective length factor changes with end conditions, affecting the buckling load.

Q2: What's a typical modulus of elasticity for steel columns?
A: For structural steel, E ≈ 200 GPa (200 × 10⁹ Pa).

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

Q4: What does the tolerance percentage represent?
A: It provides a ± range around the calculated value to account for material variations and safety factors.

Q5: When would I use 0% tolerance?
A: When you want the theoretical value without any safety margin, typically only for academic purposes.