Moment of Section if Both Ends of Column are Fixed Calculator

Moment of Section Formula:

\[ M_t = M_{Fixed} - P \times \delta \]

Fixed End Moment:

N·m

Column Crippling Load:

Deflection at Section:

Tolerance:

Moment of Section (N·m):

1. What is Moment of Section if Both Ends of Column are Fixed?

Definition: This calculator determines the moment at a section of a column when both ends are fixed, considering the fixed end moment, crippling load, and deflection.

Purpose: It helps structural engineers analyze column behavior under load when both ends are restrained against rotation.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ M_t = M_{Fixed} - P \times \delta \]

Where:

\( M_t \) — Moment at the section (N·m)
\( M_{Fixed} \) — Fixed end moment (N·m)
\( P \) — Column crippling load (N)
\( \delta \) — Deflection at section (m)

Explanation: The moment at any section equals the fixed end moment minus the product of the crippling load and deflection at that section.

3. Importance of Moment Calculation

Details: Accurate moment calculation ensures structural stability, prevents buckling, and helps in proper reinforcement design for columns.

4. Using the Calculator

Tips: Enter the fixed end moment, crippling load, deflection at section, and tolerance percentage (default ±5%). All values must be valid.

5. Frequently Asked Questions (FAQ)

Q1: What does a negative moment value indicate?
A: A negative value indicates the moment causes tension on the opposite face from the fixed end moment.

Q2: How is the tolerance percentage used?
A: The tolerance (±5% by default) provides an acceptable range for the calculated moment to account for material variations and safety factors.

Q3: What units should be used?
A: Use consistent SI units - Newtons (N) for load, Newton-meters (N·m) for moments, and meters (m) for deflection.

Q4: When would this calculation be needed?
A: For designing or analyzing columns in buildings, bridges, or other structures where both ends are fixed against rotation.

Q5: How does deflection affect the moment?
A: Greater deflection increases the P-δ effect, reducing the net moment at the section (or increasing it if deflection is opposite to fixed moment).