Crippling Load if Both Ends of Column are Fixed Calculator

Crippling Load Formula:

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

Modulus of Elasticity (E):

Moment of Inertia (I):

m⁴

Column Length (l):

Safety Factor (%):

Theoretical Crippling Load:

Safe Load (with 5% safety factor):

1. What is Crippling Load for Fixed-End Columns?

Definition: The crippling load is the maximum axial load a column can withstand before it buckles when both ends are fixed.

Purpose: This calculation helps structural engineers design columns that can support loads without buckling failure.

2. How Does the Calculator Work?

The calculator uses Euler's formula for fixed-end columns:

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

Where:

\( P \) — Crippling load (N)
\( E \) — Modulus of elasticity (Pa)
\( I \) — Moment of inertia (m⁴)
\( l \) — Column length (m)

Explanation: The formula calculates the critical buckling load based on material stiffness (E), cross-section resistance to bending (I), and column length.

3. Importance of Crippling Load Calculation

Details: Proper calculation prevents structural failure, ensures safety, and helps optimize material usage in construction.

4. Using the Calculator

Tips: Enter the modulus of elasticity (E), moment of inertia (I), column length (l), and desired safety factor (default 5%). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Why is the safety factor important?
A: The safety factor accounts for material imperfections, unexpected loads, and calculation uncertainties (typically 5-10%).

Q2: What's a typical modulus of elasticity for steel?
A: For structural steel, E ≈ 200 GPa (200 × 10⁹ Pa).

Q3: How do I find moment of inertia?
A: It depends on cross-section shape. For common shapes, use standard formulas or engineering tables.

Q4: Does this apply to all materials?
A: Yes, but ensure you use the correct E value for your material (concrete, wood, steel, etc.).

Q5: What if my column has different end conditions?
A: Different end conditions (pinned, free, etc.) require modified formulas with effective length factors.