Bending Stress Due To Eccentricity About Y-Y Axis Given Eccentric Load On Column Calculator

Formula Used:

\[ \sigma_b = \frac{P \times e_{yy} \times y}{I_{yy}} \]

Eccentric Load On Column (P):

Eccentricity Of Load About Y-Y Axis (e_yy):

Distance Of Load Point From Y Axis (y):

Moment Of Inertia About Y-Y Axis (I_yy):

m⁴

Bending Stress In Column (σ_b):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Bending Stress Due To Eccentricity?

Bending Stress in Column is the normal stress that is induced at a point in a body subjected to loads that cause it to bend. It occurs when an eccentric load is applied to a column, causing both direct stress and bending stress.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma_b = \frac{P \times e_{yy} \times y}{I_{yy}} \]

Where:

\( \sigma_b \) — Bending Stress in Column (Pa)
\( P \) — Eccentric load on column (N)
\( e_{yy} \) — Eccentricity of load about y-y axis (m)
\( y \) — Distance of load point from y axis (m)
\( I_{yy} \) — Moment of Inertia about y-y axis (m⁴)

Explanation: The formula calculates the bending stress caused by an eccentric load applied to a column, considering the distance from the neutral axis and the moment of inertia.

3. Importance of Bending Stress Calculation

Details: Accurate bending stress calculation is crucial for structural design and analysis, ensuring that columns and other structural elements can safely withstand applied loads without failure.

4. Using the Calculator

Tips: Enter all values in appropriate units (N for load, m for distances, m⁴ for moment of inertia). All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is eccentric loading?
A: Eccentric loading occurs when a load is applied away from the centroid of a cross-section, causing both axial stress and bending stress.

Q2: How does eccentricity affect stress distribution?
A: Eccentricity creates a moment that causes bending stress, which adds to or subtracts from the direct stress depending on the location in the cross-section.

Q3: What is the significance of moment of inertia?
A: Moment of inertia measures a section's resistance to bending. Higher moment of inertia means less bending stress for the same applied moment.

Q4: When is this calculation particularly important?
A: This calculation is critical in structural engineering for columns, beams, and other members subjected to eccentric loads, such as in building frames and machinery.

Q5: Are there limitations to this formula?
A: This formula assumes linear elastic material behavior and small deformations. It may not be accurate for very large deformations or plastic material behavior.