Eccentricity given Moment at Section of Column with Eccentric Load Calculator

Eccentricity Formula:

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

Moment of force:

N·m

Eccentric load on column:

Deflection of Free End:

Deflection of Column:

Tolerance:

Eccentricity (m):

1. What is Eccentricity in Column Loading?

Definition: Eccentricity is the distance from the point of application of the resultant force to the center of the column base.

Purpose: This calculator determines the eccentricity when the moment at a section of a column with eccentric load is known.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( e \) — Eccentricity (m)
\( M \) — Moment of force (N·m)
\( P \) — Eccentric load on column (N)
\( a_{crippling} \) — Deflection of free end (m)
\( \delta_{c} \) — Deflection of column at free end (m)

Explanation: The formula accounts for the moment-to-load ratio and adjusts for deflections at both ends of the column.

3. Importance of Eccentricity Calculation

Details: Proper eccentricity calculation is crucial for structural stability, preventing excessive bending moments, and ensuring safe load distribution.

4. Using the Calculator

Tips: Enter the moment of force, eccentric load, deflections (default values provided), and tolerance percentage (default ±5%). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is typical eccentricity tolerance?
A: Common tolerance is ±5%, but this may vary based on engineering standards and specific project requirements.

Q2: How does deflection affect eccentricity?
A: Deflection reduces the effective eccentricity as it moves the load application point closer to the center.

Q3: When would eccentricity be zero?
A: When the load is perfectly centered and there's no moment or deflection.

Q4: What if my eccentricity is negative?
A: Negative values indicate the load is applied on the opposite side of the reference point.

Q5: How do I measure deflection values?
A: Use structural analysis software or consult engineering tables based on material properties and loading conditions.