Crippling Load when Both Ends of Column are Hinged Calculator

Crippling Load Formula:

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

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Column Length (l):

Tolerance:

Crippling Load (P):

1. What is Crippling Load when Both Ends of Column are Hinged?

Definition: The crippling load is the maximum load a column can bear before it buckles when both ends are hinged (free to rotate but not to translate).

Purpose: This calculation is crucial in structural engineering to ensure columns can support expected loads without buckling.

2. How Does the Calculator Work?

The calculator uses Euler's formula for buckling:

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

Where:

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

Explanation: The formula calculates the critical buckling load for a column with hinged ends, which is inversely proportional to the square of the column length.

3. Importance of Crippling Load Calculation

Details: Proper calculation prevents structural failure by ensuring columns are designed to withstand expected loads without buckling.

4. Using the Calculator

Tips: Enter the modulus of elasticity, moment of inertia, column length, and tolerance percentage (default ±5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of hinged ends?
A: Hinged ends can rotate but not translate, representing common support conditions in real structures.

Q2: How does column length affect crippling load?
A: Crippling load decreases with the square of column length - longer columns are much more prone to buckling.

Q3: What's a typical modulus of elasticity for steel?
A: For structural steel, E ≈ 200 GPa (200 × 10⁹ Pa).

Q4: Why include a tolerance percentage?
A: Tolerance accounts for material imperfections, manufacturing variations, and safety factors.

Q5: How does moment of inertia affect the result?
A: Higher moment of inertia (larger cross-sections) significantly increases buckling resistance.