Modulus of Elasticity given Crippling Load by Euler's Formula Calculator

Modulus of Elasticity Formula:

\[ E = \frac{P_E \times L_{eff}^2}{\pi^2 \times I} \]

Modulus of Elasticity (Pa):

1. What is Modulus of Elasticity given Crippling Load by Euler's Formula?

Definition: This calculator determines the modulus of elasticity of a column material based on Euler's buckling formula.

Purpose: It helps engineers and designers evaluate the elastic properties of column materials under compressive loads.

2. How Does the Calculator Work?

The calculator uses Euler's formula:

\[ E = \frac{P_E \times L_{eff}^2}{\pi^2 \times I} \]

Where:

\( E \) — Modulus of Elasticity (Pa)
\( P_E \) — Euler's Buckling Load (N)
\( L_{eff} \) — Effective Column Length (m ±5%)
\( I \) — Moment of Inertia Column (m⁴ ±5%)
\( \pi \) — Mathematical constant (≈3.1416)

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 of elasticity helps predict how much a column will deform under load and its stability against buckling.

4. Using the Calculator

Tips: Enter the Euler's Buckling Load in Newtons, Effective Column Length in meters (±5%), and Moment of Inertia in m⁴ (±5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is Euler's Buckling Load?
A: It's the maximum axial load a column can carry before buckling occurs.

Q2: How is Effective Column Length determined?
A: It depends on end conditions (pinned, fixed, etc.) and actual length, typically with ±5% uncertainty.

Q3: What affects Moment of Inertia?
A: Cross-sectional shape and dimensions, with ±5% tolerance for manufacturing variations.

Q4: What units are used in this calculation?
A: SI units are used (Newtons, meters, Pascals) with ±5% tolerance on dimensional inputs.

Q5: When is Euler's formula applicable?
A: For long, slender columns where buckling occurs before material yielding.