Modulus of Elasticity given Crippling Load if Both Ends of Column are Fixed Calculator

Formula:

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

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 both ends are fixed, based on the crippling load, column length, and moment of inertia.

Purpose: It helps structural engineers analyze column stability and predict failure points under compressive loads.

2. How Does the Calculator Work?

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

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

Where:

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

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

3. Importance of Modulus of Elasticity Calculation

Details: Knowing the modulus helps in material selection, structural analysis, and ensuring columns can withstand expected loads without buckling.

4. Using the Calculator

Tips: Enter the crippling load (N), column length (m), and moment of inertia (m⁴). All values must be > 0. Results include ±5% tolerance.

5. Frequently Asked Questions (FAQ)

Q1: What is crippling load?
A: The maximum load a column can bear before it buckles or collapses.

Q2: Why ±5% tolerance?
A: This accounts for material variations, measurement uncertainties, and real-world conditions.

Q3: How does fixed-end condition affect the result?
A: Fixed ends increase buckling resistance compared to pinned ends, changing the critical load calculation.

Q4: What's a typical modulus for steel columns?
A: About 200 GPa (200 × 10⁹ Pa), but varies with alloy composition.

Q5: How to measure moment of inertia?
A: For standard shapes, use geometric formulas. For complex sections, CAD software or experimental methods may be needed.