Deflection at Section of Column with Eccentric Load given Moment at Section Calculator

Deflection Formula:

\[ \delta_c = -\frac{M}{P} + a_{crippling} + e \]

Moment of Force (M):

N·m

Eccentric Load (P):

Deflection of Free End (a_crippling):

Eccentricity (e):

Tolerance:

Deflection at Section (δ_c):

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

Definition: This calculator determines the deflection at a specific section of a column under eccentric loading, considering the applied moment, load, free end deflection, and eccentricity.

Purpose: It helps structural engineers analyze column behavior under eccentric loads to ensure structural integrity and safety.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \delta_c = -\frac{M}{P} + a_{crippling} + e \]

Where:

\( \delta_c \) — Deflection at section (meters)
\( M \) — Moment of force (N·m)
\( P \) — Eccentric load (N)
\( a_{crippling} \) — Deflection of free end (meters)
\( e \) — Eccentricity (meters)

Explanation: The formula accounts for the deflection caused by the moment, the inherent deflection at the free end, and the eccentricity of the load.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation is crucial for assessing structural stability, preventing excessive deformation, and ensuring serviceability of columns under eccentric loading conditions.

4. Using the Calculator

Tips: Enter all required values in consistent units. The tolerance field (default ±5%) allows you to account for material and construction variations.

5. Frequently Asked Questions (FAQ)

Q1: What is eccentric loading on a column?
A: Eccentric loading occurs when the load is not applied at the centroid of the column cross-section, creating both axial and bending stresses.

Q2: Why is the moment term negative in the formula?
A: The negative sign accounts for the direction of deflection relative to the applied moment and eccentricity.

Q3: How do I determine the deflection of free end?
A: This is typically calculated based on the column's material properties, dimensions, and loading conditions.

Q4: What's a typical tolerance value for deflection calculations?
A: ±5% is common, but this may vary based on material properties and construction standards.

Q5: Can this calculator be used for both steel and concrete columns?
A: Yes, but ensure proper material properties are considered in the input values.