Effective Length of Column given Crippling Stress Calculator

Effective Column Length Formula:

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

Modulus of Elasticity (ε_c):

Least Radius of Gyration (r_L):

Crippling Stress (σ):

Tolerance:

Effective Column Length (L_eff):

1. What is Effective Column Length given Crippling Stress?

Definition: This calculator determines the effective length of a column based on its material properties and crippling stress.

Purpose: It helps structural engineers design columns that can withstand buckling under compressive loads.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( L_{eff} \) — Effective column length (meters)
\( \varepsilon_c \) — Modulus of elasticity (Pascals)
\( r_L \) — Least radius of gyration (meters)
\( \sigma \) — Crippling stress (Pascals)

Explanation: The formula calculates the maximum unsupported length a column can have before buckling occurs under the given crippling stress.

3. Importance of Effective Length Calculation

Details: Proper calculation ensures structural stability and prevents column failure due to buckling under compressive loads.

4. Using the Calculator

Tips: Enter the modulus of elasticity, least radius of gyration, crippling stress, and optional tolerance percentage. 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 due to buckling under compressive load.

Q2: How does radius of gyration affect the result?
A: Smaller radius of gyration reduces the effective length, making the column more susceptible to buckling.

Q3: What's the purpose of the tolerance field?
A: The tolerance provides a safety range (±%) around the calculated effective length for practical applications.

Q4: What are typical modulus of elasticity values?
A: For steel: ~200 GPa, concrete: ~30 GPa, aluminum: ~70 GPa.

Q5: How is this different from Euler's critical load formula?
A: This is essentially the rearrangement of Euler's formula to solve for effective length rather than critical load.