Deflection at Section of Column with Eccentric Load Calculator

Deflection Formula:

\[ \delta_c = (a_{crippling} + e) \times \left(1 - \cos\left(x \times \sqrt{\frac{P}{\varepsilon_{column} \times I}}\right)\right) \]

Deflection of Free End:

Eccentricity:

Distance from fixed end:

Eccentric Load:

Modulus of Elasticity:

Moment of Inertia:

kg·m²

Deflection at Section (δc): m

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

Definition: This calculator determines the deflection at any section of a column subjected to an eccentric load, considering the column's material properties and geometry.

Purpose: It helps structural engineers analyze column behavior under eccentric loading conditions, which is crucial for structural stability and safety.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \delta_c = (a_{crippling} + e) \times \left(1 - \cos\left(x \times \sqrt{\frac{P}{\varepsilon_{column} \times I}}\right)\right) \]

Where:

\( \delta_c \) — Deflection at section (meters)
\( a_{crippling} \) — Deflection of free end (meters)
\( e \) — Eccentricity (meters)
\( x \) — Distance from fixed end (meters)
\( P \) — Eccentric load (Newtons)
\( \varepsilon_{column} \) — Modulus of elasticity (Pascals)
\( I \) — Moment of inertia (kg·m²)

Explanation: The formula accounts for the combined effect of direct bending and eccentricity on column deflection.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation ensures structural integrity, prevents excessive deformation, and helps meet design code requirements.

4. Using the Calculator

Tips: Enter all required parameters. Default values are provided for reference. All values must be ≥ 0 except load, modulus, and inertia which must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is eccentric loading?
A: Eccentric loading occurs when a load is applied off-center, creating both direct stress and bending stress in the column.

Q2: Why is the cosine function used in the formula?
A: The cosine function models the curved deflection shape of the column under load.

Q3: What's a typical modulus of elasticity for concrete columns?
A: For concrete, typically 20-30 GPa (20,000,000-30,000,000 Pa).

Q4: How does eccentricity affect deflection?
A: Greater eccentricity increases the bending moment and thus increases deflection.

Q5: What if my column has different boundary conditions?
A: This calculator is for fixed-free columns. Other conditions require different formulas.