Moment of Section due to Crippling Load if One End of Column is Fixed and Other is Free Calculator

Moment of Section Formula:

\[ M_t = P \times (a - \delta) \]

Moment of Section (M_t):

1. What is Moment of Section due to Crippling Load?

Definition: This calculator determines the bending moment at a section of a column when one end is fixed and the other is free, under a crippling load.

Purpose: It helps structural engineers analyze column behavior and design appropriate supports.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ M_t = P \times (a - \delta) \]

Where:

\( M_t \) — Moment of section (N·m)
\( P \) — Column crippling load (N)
\( a \) — Deflection at free end (m ±5%)
\( \delta \) — Deflection at section (m ±5%)

Explanation: The moment is calculated as the product of the crippling load and the difference in deflections between the free end and the section.

3. Importance of Moment Calculation

Details: Accurate moment calculation ensures structural integrity, prevents buckling, and helps in proper material selection.

4. Using the Calculator

Tips: Enter the crippling load in newtons, deflections in meters (with ±5% tolerance). All values must be ≥ 0.

5. Frequently Asked Questions (FAQ)

Q1: What is a crippling load?
A: The load at which a column starts to buckle or deform laterally rather than compressing axially.

Q2: Why is there a ±5% tolerance on deflections?
A: Deflection measurements often have inherent variability due to material inconsistencies and measurement limitations.

Q3: What if my deflection at section is greater than at free end?
A: This would give a negative moment, indicating the section is bending in the opposite direction.

Q4: How does fixed vs. free end affect the calculation?
A: The fixed end prevents rotation while the free end allows maximum deflection, creating specific bending patterns.

Q5: What units should I use?
A: Use consistent SI units: newtons (N) for load and meters (m) for deflections.