Bending Stress Calculator
Calculate maximum bending stress in beams using the flexural formula σ = M×c/I
Calculate Maximum Bending Stress
The maximum bending moment acting on the beam
Rectangular Beam Dimensions
Bending Stress Results
Formula: σ = M × c / I = M / S
Where: M = 0.0 N⋅m, c = 0.0 mm, I = 0.00e+0 mm⁴
Section Modulus: S = I / c = 0 mm³
Stress Distribution
Example Calculation
Steel I-Beam Example
Beam: W12×26 steel beam
Applied Moment: 150 kN⋅m
Section Properties: I = 204×10⁶ mm⁴, c = 155 mm
Section Modulus: S = 1.32×10⁶ mm³
Calculation Steps
σ = M × c / I
σ = 150,000 N⋅m × 0.155 m / (204×10⁻⁶ m⁴)
σ = 23,250 / (204×10⁻⁶)
σ = 113.97 MPa
Alternative: σ = M / S = 150,000 / (1.32×10⁻³) = 113.64 MPa
Cross-Section Properties
Rectangular
I = bh³/12
c = h/2
S = bh²/6
Circular
I = πd⁴/64
c = d/2
S = πd³/32
Square
I = a⁴/12
c = a/2
S = a³/6
Typical Material Strengths
⚠️ Always consult material specifications and building codes
Design Tips
Include safety factors (typically 1.5-3.0)
Consider both flexural and shear stresses
Account for dynamic loads and fatigue
Check deflection limits in addition to stress
Understanding Bending Stress
What is Bending Stress?
Bending stress is the normal stress that develops in a beam when it is subjected to bending moments. As a beam bends, the material on one side experiences compression while the opposite side experiences tension.
Key Characteristics
- •Maximum stress occurs at the extreme fibers (top and bottom)
- •Zero stress occurs at the neutral axis
- •Linear stress distribution across the beam height
- •Critical for beam design and safety analysis
Flexural Formula
σ = M × c / I
σ = M / S
- σ: Maximum bending stress (Pa or psi)
- M: Applied bending moment (N⋅m or lb⋅ft)
- c: Distance from neutral axis to extreme fiber (m or in)
- I: Area moment of inertia (m⁴ or in⁴)
- S: Section modulus = I/c (m³ or in³)
Safety Warning: Always consult with a licensed structural engineer for critical applications. This calculator is for educational and preliminary design purposes only.