Eccentricity given Maximum Stress for Column with Eccentric Load Calculator

Eccentricity Formula:

\[ e = \frac{(\sigma_{max} - (\frac{P}{A})) \times S}{(P \times \sec(L_e \times \sqrt{\frac{P}{E \times I}})) / 2} \]

Maximum Stress at Crack Tip:

Eccentric Load on Column:

Column Cross Sectional Area:

m²

Section Modulus for Column:

m³

Effective Column Length:

Modulus of Elasticity:

Moment of Inertia:

kg·m²

Tolerance:

Eccentricity (m):

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

Purpose: It helps structural engineers account for bending moments caused by off-center loading in column design.

The calculator uses the formula:

\[ e = \frac{(\sigma_{max} - (\frac{P}{A})) \times S}{(P \times \sec(L_e \times \sqrt{\frac{P}{E \times I}})) / 2} \]

Where:

Details: Proper eccentricity calculation ensures structural stability by accounting for combined axial and bending stresses in columns.

Tips: Enter all required parameters including the tolerance percentage (default ±5%). All values must be positive numbers.

Q1: What is a typical tolerance for eccentricity?
A: ±5% is common, but this may vary based on engineering requirements and building codes.

Q2: How does effective length affect eccentricity?
A: Longer effective lengths increase the bending moment effect for a given eccentricity.

Q3: What units should I use?
A: Use consistent SI units: meters, Pascals, Newtons, and kg·m² as shown in the input fields.

Q4: When would eccentricity be zero?
A: When the load is perfectly centered on the column, resulting in pure compression.

Q5: How does section modulus affect the calculation?
A: Higher section modulus values reduce the stress caused by a given eccentricity.