Deflection at Free End of Column with Eccentric load Calculator

Deflection Formula:

\[ \delta = e \times \left(\sec\left(L \times \sqrt{\frac{P}{E \times I}}\right) - 1\right) \]

Eccentricity of Load:

Column Length:

Eccentric Load:

Modulus of Elasticity:

Moment of Inertia:

kg·m²

Deflection of Free End: m

1. What is Deflection at Free End of Column with Eccentric Load?

Definition: This calculator determines the deflection at the free end of a column subjected to an eccentric load.

Purpose: It helps structural engineers analyze column behavior under eccentric loading conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \delta = e \times \left(\sec\left(L \times \sqrt{\frac{P}{E \times I}}\right) - 1\right) \]

Where:

\( \delta \) — Deflection at free end (meters)
\( e \) — Eccentricity of load (meters)
\( L \) — Column length (meters)
\( P \) — Eccentric load (Newtons)
\( E \) — Modulus of elasticity (Pascals)
\( I \) — Moment of inertia (kg·m²)

Explanation: The formula calculates the deflection considering the column's elastic properties and the eccentricity of the applied load.

3. Importance of Deflection Calculation

Details: Proper deflection analysis ensures structural stability and prevents excessive deformation that could lead to failure.

4. Using the Calculator

Tips: Enter all required parameters with their units. The calculator accounts for ±5% tolerance in input values.

5. Frequently Asked Questions (FAQ)

Q1: What is eccentric loading?
A: Eccentric loading occurs when a load is applied off-center from the column's centroid, creating both axial and bending stresses.

Q2: Why does the formula use secant function?
A: The secant function accounts for the nonlinear relationship between load and deflection in columns.

Q3: What's a typical modulus of elasticity for steel columns?
A: For structural steel, E is typically around 200 GPa (200 × 10⁹ Pa).

Q4: How does column length affect deflection?
A: Longer columns generally experience greater deflection under the same load due to increased slenderness.

Q5: What does negative deflection indicate?
A: Negative deflection typically means the column deflects in the opposite direction of the eccentric load.