1. What is Cantilever Beam Bending Stress?

Bending stress in a cantilever beam is the internal stress caused by an applied moment that makes the beam bend. It's maximum at the fixed end and varies linearly through the cross-section.

2. How Does the Calculator Work?

The calculator uses the bending stress formula:

Where:

• \( \sigma \) — Bending stress (psi)
• \( M \) — Bending moment (inch-pounds)
• \( y \) — Distance from neutral axis (inches)
• \( I \) — Moment of inertia (inches⁴)

Explanation: The equation shows that stress increases with larger moments and greater distances from the neutral axis, but decreases with larger moments of inertia.

3. Importance of Stress Calculation

Details: Calculating bending stress is crucial for structural design to ensure beams can withstand applied loads without failing. It helps determine appropriate beam dimensions and materials.

4. Using the Calculator

Tips: Enter bending moment in inch-pounds, distance from neutral axis in inches, and moment of inertia in inches⁴. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Where is maximum stress in a cantilever beam?
A: Maximum bending stress occurs at the fixed end and at the point farthest from the neutral axis.

Q2: How does beam shape affect stress?
A: Beams with larger moments of inertia (I) for their cross-sectional area (like I-beams) experience less stress for the same applied moment.

Q3: What's the difference between bending stress and shear stress?
A: Bending stress is normal stress (tension/compression) while shear stress acts parallel to the cross-section.

Q4: What are typical allowable bending stresses?
A: Varies by material - e.g., ~24,000 psi for structural steel, ~1,000 psi for wood (parallel to grain).

Q5: How does length affect cantilever bending?
A: Longer cantilevers experience greater bending moments for the same end load, increasing stress.