Modulus of Elasticity of Column given Crippling Stress Calculator

Modulus of Elasticity Formula:

\[ \epsilon_c = \frac{\sigma_{crippling\ stress} \times L_{eff}^2}{\pi^2 \times r_L^2} \]

Crippling Stress:

Effective Column Length:

Least Radius of Gyration:

Modulus of Elasticity (Pa):

1. What is Modulus of Elasticity of Column?

Definition: The modulus of elasticity is a quantity that measures a column's resistance to being deformed elastically when stress is applied to it.

Purpose: This calculator determines the modulus of elasticity based on crippling stress, effective column length, and least radius of gyration.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \epsilon_c = \frac{\sigma \times L_{eff}^2}{\pi^2 \times r_L^2} \]

Where:

\( \epsilon_c \) — Modulus of elasticity (Pa)
\( \sigma \) — Crippling stress (Pa)
\( L_{eff} \) — Effective column length (m)
\( r_L \) — Least radius of gyration (m)

Explanation: The formula relates the column's elastic properties to its geometric characteristics under buckling conditions.

3. Importance of Modulus of Elasticity Calculation

Details: Accurate calculation helps in structural design to prevent buckling and ensure column stability under load.

4. Using the Calculator

Tips: Enter the crippling stress in Pascals, effective length in meters, and least radius of gyration in meters. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is crippling stress?
A: Crippling stress is the stress at which a column fails by buckling under compressive load.

Q2: How is effective length determined?
A: Effective length depends on end conditions and is typically ±5% of the actual length based on support conditions.

Q3: What affects the radius of gyration?
A: Cross-sectional shape and dimensions, with ±5% variation common in manufacturing.

Q4: What are typical modulus values for columns?
A: For steel columns, around 200 GPa; for concrete, about 30 GPa; varies by material.

Q5: When would I need this calculation?
A: When designing columns to ensure they won't buckle under expected loads.