⚙️ Bending Stress Calculator
Calculate bending stress in beams
How to Use This Calculator
Select Calculation Type
Choose to calculate from moment and section modulus, or from moment and beam dimensions.
Enter Bending Moment
Input the bending moment in foot-pounds. This is typically the maximum moment from beam load analysis.
Enter Section Properties
If using section modulus, enter section modulus in cubic inches. If using dimensions, enter beam width and height in inches.
Calculate and Review
Click "Calculate Bending Stress" to see bending stress in psi. Use this to verify material strength limits.
Formula
Bending Stress: σ = M / S
Section Modulus (rectangular): S = bh² / 6
Moment of Inertia (rectangular): I = bh³ / 12
Example 1: From Moment and Section Modulus (M = 3,000 ft-lbs, S = 72 in³)
Step 1: Convert moment: M = 3,000 × 12 = 36,000 in-lbs
Step 2: Bending stress = M / S = 36,000 / 72 = 500 psi
Example 2: From Moment and Dimensions (M = 3,000 ft-lbs, b = 6", h = 12")
Step 1: Section modulus = bh² / 6 = 6 × 12² / 6 = 144 in³
Step 2: Convert moment: M = 3,000 × 12 = 36,000 in-lbs
Step 3: Bending stress = M / S = 36,000 / 144 = 250 psi
About Bending Stress Calculator
The Bending Stress Calculator is an essential tool for structural engineers, architects, and builders who need to calculate bending stress in beams for structural design. This calculator implements standard bending stress formulas to determine stress from moment and section modulus or beam dimensions, helping you verify material strength limits and design safe structural members.
When to Use This Calculator
- Structural Design: Calculate bending stress for strength design
- Material Selection: Verify material strength limits
- Safety Analysis: Ensure stress is below allowable limits
- Beam Design: Size beams based on stress requirements
- Educational Use: Learn and understand bending stress calculations
Why Use Our Calculator?
- ✅ Dual Calculation Modes: Supports direct and dimension-based calculations
- ✅ Accurate Formulas: Uses standard bending stress equations
- ✅ Complete Analysis: Shows moment, section modulus, and stress
- ✅ Easy to Use: Simple inputs for moment and section properties
- ✅ Time Savings: Instant calculations eliminate manual math
Understanding Bending Stress
Basic Principle: Bending stress (σ) is the stress caused by bending moments in beams. It is calculated using the formula σ = M / S, where M is the bending moment and S is the section modulus. Bending stress is highest at the extreme fibers (top and bottom) of the beam cross-section.
Section Modulus: Section modulus (S) is a geometric property that relates moment to stress. For rectangular sections, S = bh² / 6, where b is width and h is height. Section modulus represents the beam's resistance to bending.
Design Limits: Bending stress must be below the material's allowable stress or yield strength. Common allowable stresses: Wood = 1,000-1,600 psi (depending on grade), Steel = 18,000-36,000 psi (depending on grade), Concrete = 450-600 psi (compressive).
Tips for Best Results
- Accurate Moment: Use maximum moment from beam load analysis
- Correct Section Modulus: Verify section modulus for your beam shape
- Check Material Limits: Ensure stress is below allowable stress
- Apply Safety Factors: Use appropriate safety factors for design
- Verify with Codes: Check local building codes for design requirements
Frequently Asked Questions
How do I calculate bending stress?
Bending stress is calculated using σ = M / S, where M is bending moment and S is section modulus. For example, M = 3,000 ft-lbs, S = 72 in³: Convert M = 3,000 × 12 = 36,000 in-lbs, then σ = 36,000 / 72 = 500 psi. The calculator does this automatically.
What is section modulus?
Section modulus (S) is a geometric property that relates moment to stress. For rectangular sections, S = bh² / 6, where b is width and h is height. For example, a 6" × 12" beam: S = 6 × 12² / 6 = 144 in³. The calculator calculates section modulus automatically when dimensions are provided.
What are typical allowable bending stresses?
Typical allowable bending stresses: Wood = 1,000-1,600 psi (depending on species and grade), Steel = 18,000-36,000 psi (depending on grade), Concrete = 450-600 psi (compressive). Always verify with material specifications and local building codes.
How do I find the maximum bending moment?
Maximum bending moment depends on load type and beam length. For point load at center: M = PL/4. For uniform load: M = wL²/8. Use a beam load calculator to determine maximum moment for your specific loading conditions.
Can I use this for non-rectangular beams?
The calculator can use section modulus directly for any beam shape. Enter the section modulus value in the "From Moment and Section Modulus" mode. For dimensions, only rectangular sections are supported—use section modulus mode for other shapes.