Modulus of Elasticity given Crippling Load with Both Ends of Column Hinged Calculator

Modulus of Elasticity Formula:

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

Column Crippling Load:

Column Length:

Moment of Inertia:

m⁴

Tolerance:

Modulus of Elasticity: Pa

1. What is Modulus of Elasticity given Crippling Load?

Definition: This calculator determines the modulus of elasticity for a column with both ends hinged based on the crippling load, column length, and moment of inertia.

Purpose: It helps structural engineers determine the elastic properties of column materials under compressive loads.

2. How Does the Calculator Work?

The calculator uses Euler's formula for buckling:

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

Where:

\( E \) — Modulus of Elasticity (Pascal)
\( P \) — Crippling Load (Newtons)
\( l \) — Column Length (meters)
\( I \) — Moment of Inertia (m⁴)

Explanation: The formula calculates the material's stiffness based on its buckling behavior under compressive loads.

3. Importance of Modulus of Elasticity Calculation

Details: Knowing the modulus helps in designing columns that can withstand compressive loads without buckling.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a typical modulus of elasticity for steel columns?
A: Structural steel typically has a modulus of about 200 GPa (200 × 10⁹ Pa).

Q2: Why is the tolerance percentage important?
A: It accounts for material variations and safety factors in real-world applications.

Q3: What if my column has different end conditions?
A: Different end conditions require modified formulas (fixed-fixed, fixed-pinned, etc.).

Q4: How do I determine the moment of inertia?
A: It depends on the cross-section shape (I = b×h³/12 for rectangular sections).

Q5: What units should I use?
A: Consistent SI units are required (N, m, m⁴) for accurate results in Pascals.