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

Deflection Formula:

\[ \delta_c = \frac{M}{P} - (e_{load} + a_{crippling}) \]

Moment of force:

N·m

Eccentric load on column:

Eccentricity of Load:

Deflection of Free End:

Tolerance:

Deflection of Column (m):

1. What is Deflection at Free End given Moment at Section?

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

Purpose: It helps structural engineers analyze column behavior under eccentric loads and assess stability.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \delta_c = \frac{M}{P} - (e_{load} + a_{crippling}) \]

Where:

\( \delta_c \) — Deflection of Column at free end (meters)
\( M \) — Moment of force (Newton-meters)
\( P \) — Eccentric load on column (Newtons)
\( e_{load} \) — Eccentricity of Load (meters)
\( a_{crippling} \) — Deflection of Free End (meters)

Explanation: The formula calculates the net deflection by considering the moment effect and subtracting the initial eccentricity and free end deflection.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation is crucial for structural stability assessment, preventing excessive deformation, and ensuring safety under eccentric loading conditions.

4. Using the Calculator

Tips:

Enter moment in N·m, load in N, and all distances in meters
Default tolerance is set to ±5% but can be adjusted
Load cannot be zero (division by zero)

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 central axis, creating both compressive and bending stresses.

Q2: Why include tolerance?
A: The tolerance accounts for material variations, construction tolerances, and safety factors in real-world applications.

Q3: What's a typical eccentricity value?
A: Eccentricity depends on design, but common values range from 0.001m to 0.05m for many structural columns.

Q4: How does this differ from central loading?
A: Central loading produces only axial stress, while eccentric loading creates both axial and bending stresses.

Q5: When is this calculation most important?
A: Critical for slender columns, cantilevered structures, and any situation where load eccentricity is significant.