Bending Stress For Strut With Axial And Transverse Point Load At Center Calculator

Formula Used:

\[ \sigma_b = \frac{M_b \cdot c}{A_{sectional} \cdot (r_{least})^2} \]

Bending Moment in Column:

N·m

Distance from Neutral Axis to Extreme Point:

Column Cross Sectional Area:

m²

Least Radius of Gyration Column:

Bending Stress in Column:

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1. What is Bending Stress in Column?

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's a critical parameter in structural engineering for determining the strength and stability of columns under bending loads.

2. How Does the Calculator Work?

The calculator uses the bending stress formula:

\[ \sigma_b = \frac{M_b \cdot c}{A_{sectional} \cdot (r_{least})^2} \]

Where:

\( \sigma_b \) — Bending Stress in Column (Pa)
\( M_b \) — Bending Moment in Column (N·m)
\( c \) — Distance from Neutral Axis to Extreme Point (m)
\( A_{sectional} \) — Column Cross Sectional Area (m²)
\( r_{least} \) — Least Radius of Gyration Column (m)

Explanation: This formula calculates the maximum bending stress in a column by considering the bending moment, distance from the neutral axis, cross-sectional area, and the least radius of gyration.

3. Importance of Bending Stress Calculation

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

4. Using the Calculator

Tips: Enter all values in the specified units. Bending Moment and Distance should be in Newton-meters and meters respectively. Cross-sectional area should be in square meters, and radius of gyration in meters.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the least radius of gyration?
A: The least radius of gyration determines the column's resistance to buckling and is crucial for stability calculations.

Q2: How does bending stress differ from axial stress?
A: Bending stress varies across the cross-section (maximum at extreme fibers), while axial stress is uniform across the section.

Q3: When is this formula most applicable?
A: This formula is particularly useful for struts with combined axial and transverse point loads at the center.

Q4: What are the limitations of this calculation?
A: The formula assumes linear elastic material behavior and may not account for large deformations or plastic behavior.

Q5: How does cross-sectional shape affect bending stress?
A: Different cross-sectional shapes have different area distributions, which affects both the cross-sectional area and radius of gyration calculations.