1. What is Bending Stress?

Bending stress is the internal stress induced in a beam when an external moment is applied, causing it to bend. It varies linearly across the cross-section, reaching maximum values at the extreme fibers.

2. How Does the Calculator Work?

The calculator uses the bending stress formula:

Where:

• \( \sigma_{max} \) — Maximum bending stress (Pa)
• \( M \) — Bending moment (Nm)
• \( y_{max} \) — Distance to extreme fiber (m)
• \( I \) — Moment of inertia (m⁴)

Explanation: The formula calculates the maximum stress at the outermost point of a beam's cross-section when subjected to bending.

3. Importance of Bending Stress Calculation

Details: Calculating bending stress is crucial for structural engineering to ensure beams and other structural elements can withstand applied loads without failure.

4. Using the Calculator

Tips: Enter bending moment in Nm, distance to extreme fiber in meters, and moment of inertia in m⁴. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the extreme fiber in a beam?
A: The extreme fiber is the point farthest from the neutral axis of the beam's cross-section, where bending stress is maximum.

Q2: How does cross-section shape affect bending stress?
A: The moment of inertia (I) depends on the cross-section shape. Shapes with more material farther from the neutral axis have higher I values and lower bending stress.

Q3: What are typical units for these calculations?
A: Standard SI units are Nm for moment, m for distance, m⁴ for moment of inertia, and Pa (Pascals) for stress.

Q4: Can this formula be used for all materials?
A: This formula applies to materials that follow Hooke's Law (linear elastic behavior) and for beams with uniform cross-sections.

Q5: What is the neutral axis?
A: The neutral axis is the line in the cross-section where there is no tension or compression during bending - stress is zero at this point.