What Is the Beam Flexural Bending Stress & Section Modulus Calculator?
The flexure formula was developed by Claude-Louis Navier in 1826 and governs the design of beams in buildings, bridges, and machines.
How Does the Beam Flexural Bending Stress & Section Modulus Calculator Work?
Applied transverse loads create internal bending moments. Material fibers above the neutral axis contract under compression, while fibers below stretch under tension.
Beam Flexural Bending Stress & Section Modulus Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
\sigma_{\text{max}} = \frac{M \cdot y}{I} = \frac{M}{S}, \quad S = \frac{b \cdot h^2}{6}
Maximum outer fiber stress equals bending moment M divided by elastic section modulus S.
How to Use the Beam Flexural Bending Stress & Section Modulus Calculator
- Enter design maximum bending moment in kN·m.
- Specify beam rectangular cross-section width and depth in mm.
Step-by-Step Example Calculation
Glulam Timber Beam Bending
Input Values:
bendingMoment:45.0
beamWidth:150.0
beamHeight:300.0
Worked Steps: Subjecting a 150 × 300 mm beam (S = 2250 cm³) to 45 kN·m produces a maximum outer fiber bending stress of 20.00 MPa.
Understanding Your Result
Maximum Bending Stress: Extreme fiber stress in MPa.
Section Modulus: Geometric resistance capacity in cm³.
Neutral Axis: Mid-depth centroid line.
Factors That Affect the Result
- Beam depth (has a quadratic effect on strength and cubic effect on stiffness).
When Should You Use This Calculator?
- Structural steel floor beam design, residential timber joist sizing, and concrete lintel reinforcement verification.
Assumptions & Limitations
- Assumes homogeneous linear-elastic material adhering to Bernoulli-Euler plane-sections hypothesis.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard mechanics of materials flexure equation with exact precision.