Deflection at Free End given Moment of Section Calculator

Deflection at Free End given Moment of Section if One End of Column is Fixed and Other is Free Calculator

Deflection Formula:

\[ a = \frac{M_t}{P} + \delta \]

Moment of Section:

N·m

Column Crippling Load:

Deflection at Section:

Tolerance:

Deflection of Free End (m):

1. What is Deflection at Free End?

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

Purpose: It helps structural engineers analyze column behavior under load and predict deformation.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ a = \frac{M_t}{P} + \delta \]

Where:

\( a \) — Deflection of Free End (m)
\( M_t \) — Moment of Section (N·m)
\( P \) — Column Crippling Load (N)
\( \delta \) — Deflection at Section (m)

Explanation: The deflection is calculated by dividing the moment by the load and adding any existing deflection at the section.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation ensures structural integrity and prevents excessive deformation that could lead to failure.

4. Using the Calculator

Tips: Enter the moment of section, crippling load, deflection at section, and tolerance percentage (default ±5%). All values must be ≥ 0 except load which must be > 0.

5. Frequently Asked Questions (FAQ)

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

Q2: Why include tolerance?
A: Tolerance accounts for material variations and calculation uncertainties in real-world applications.

Q3: What's a typical tolerance percentage?
A: ±5% is common, but this may vary based on material and safety requirements.

Q4: When would deflection at section be zero?
A: When measuring deflection at the very point where the moment is applied.

Q5: How does fixed vs free end affect deflection?
A: Fixed ends resist rotation, causing different deflection patterns than free ends.