Crippling Stress Calculator

Crippling Stress Formula:

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

Modulus of Elasticity (E):

Least Radius of Gyration (r_L):

Effective Column Length (L_eff):

Tolerance:

Crippling Stress (Pa):

With Tolerance (5%):

1. What is a Crippling Stress Calculator?

Definition: This calculator computes the crippling stress in a column based on the Euler's buckling formula.

Purpose: It helps engineers determine the stress at which a slender column will buckle under compressive load.

2. How Does the Calculator Work?

The calculator uses Euler's formula for buckling:

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

Where:

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

Explanation: The formula calculates the critical stress at which a column will buckle based on its material properties and geometry.

3. Importance of Crippling Stress Calculation

Details: Proper calculation ensures structural stability and prevents catastrophic failure of columns under compressive loads.

4. Using the Calculator

Tips: Enter the modulus of elasticity, least radius of gyration, effective column length, and tolerance percentage (default 5%). All values must be > 0 except tolerance which can be 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the least radius of gyration?
A: It's the smallest value of radius of gyration about any axis, calculated as the square root of (moment of inertia/cross-sectional area).

Q2: How is effective length determined?
A: Effective length depends on end conditions: L for pinned-pinned, 0.5L for fixed-fixed, 0.7L for fixed-pinned, and 2L for fixed-free.

Q3: Why include tolerance?
A: Tolerance accounts for material imperfections, manufacturing variations, and safety factors in real-world applications.

Q4: What units should be used?
A: Use consistent SI units: Pascals for modulus and stress, meters for length measurements.

Q5: When is Euler's formula not applicable?
A: For short columns where material failure occurs before buckling, or for very slender columns where elastic limit is exceeded.