Deflection at Free End given Deflection at Section of Column with Eccentric load Calculator

Deflection Formula:

\[ a_{crippling} = \frac{\delta_c}{1-\cos\left(x\sqrt{\frac{P}{\epsilon_{column} \times I}}\right)} - e_{load} \]

Deflection of Column:

Distance b/w fixed end and deflection point:

Eccentric load on column:

Modulus of elasticity of column:

Moment of Inertia:

kg·m²

Eccentricity of Load:

Deflection of Free End:

1. What is Deflection at Free End Calculator?

Definition: This calculator determines the deflection at the free end of a column under eccentric load based on the deflection at a specific section.

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

2. How Does the Calculator Work?

The calculator uses the formula:

\[ a_{crippling} = \frac{\delta_c}{1-\cos\left(x\sqrt{\frac{P}{\epsilon_{column} \times I}}\right)} - e_{load} \]

Where:

\( a_{crippling} \) — Deflection at free end (meters)
\( \delta_c \) — Deflection at section (meters)
\( x \) — Distance between fixed end and deflection point (meters)
\( P \) — Eccentric load on column (Newtons)
\( \epsilon_{column} \) — Modulus of elasticity of column (Pascals)
\( I \) — Moment of inertia (kg·m²)
\( e_{load} \) — Eccentricity of load (meters)

Explanation: The formula accounts for the column's elastic properties and the eccentric loading condition to determine the free end deflection.

3. Importance of Deflection Calculation

Details: Accurate deflection calculations are crucial for structural safety, serviceability, and compliance with building codes.

4. Using the Calculator

Tips: Enter all required parameters with appropriate 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, creating both axial and bending stresses.

Q2: Why is the cosine function used in the formula?
A: The cosine function models the deflection curve 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 do I determine moment of inertia?
A: It depends on the cross-section shape. For rectangular sections, I = (width × height³)/12.

Q5: What does negative deflection indicate?
A: Negative values suggest deflection in the opposite direction from the assumed positive direction.