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

Modulus of Elasticity Formula:

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

Modulus of Elasticity: Pa

1. What is Modulus of Elasticity given Crippling Load?

Definition: This calculator determines the modulus of elasticity of a column when one end is fixed and the other is free, based on the crippling load.

Purpose: It helps structural engineers and designers evaluate the elastic properties of columns under specific boundary conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( E \) — Modulus of Elasticity (Pa)
\( l \) — Column Length (m)
\( P \) — Crippling Load (N)
\( I \) — Moment of Inertia (m⁴)

Explanation: The formula relates the column's elastic properties to its geometric characteristics and critical buckling load.

3. Importance of Modulus of Elasticity Calculation

Details: Knowing the modulus helps predict column behavior under load and prevents buckling failures in structural designs.

4. Using the Calculator

Tips: Enter column length in meters, crippling load in newtons, and moment of inertia in m⁴. All values must be > 0. Results have ±5% tolerance.

5. Frequently Asked Questions (FAQ)

Q1: What does ±5% mean for the inputs?
A: It indicates the expected measurement tolerance for each parameter.

Q2: When is this formula applicable?
A: Specifically for columns with one fixed end and one free end (cantilever condition).

Q3: How do I find the moment of inertia?
A: It depends on the cross-section shape. For common shapes, use standard formulas or CAD software.

Q4: What units should I use?
A: Consistent SI units: meters for length, newtons for force, and m⁴ for moment of inertia.

Q5: Can I use this for other boundary conditions?
A: No, different boundary conditions require different formulas for accurate results.