What is Bending Stress?
Bending stress (also called flexural stress) is the internal stress induced in a beam when an external bending moment is applied. When a beam bends, the top fibers are compressed and the bottom fibers are stretched (or vice versa depending on the load direction). The maximum stress occurs at the extreme fibers, farthest from the neutral axis.
In structural design, the actual bending stress must not exceed the allowable bending stress (Fb) for the material. If it does, the beam is overstressed and may fail, requiring either a larger beam or reduced loading.
Bending Stress Formula
Where σ is the bending stress (psi), M is the bending moment (in-lbs), c is the distance from the neutral axis to the extreme fiber (inches), I is the moment of inertia (in&sup4;), and S is the section modulus (in³).
Common Cross-Section Properties
| Beam Size | I (in&sup4;) | S (in³) | c (in) |
|---|---|---|---|
| 2x6 (1.5 x 5.5) | 20.80 | 7.56 | 2.75 |
| 2x8 (1.5 x 7.25) | 47.63 | 13.14 | 3.625 |
| 2x10 (1.5 x 9.25) | 98.93 | 21.39 | 4.625 |
| 2x12 (1.5 x 11.25) | 177.98 | 31.64 | 5.625 |
| 4x8 (3.5 x 7.25) | 111.15 | 30.66 | 3.625 |
Design Check Process
- Calculate the maximum bending moment from loads and span.
- Determine the section properties (I, c, or S) of the proposed beam.
- Calculate the actual bending stress using the formula above.
- Compare to the allowable stress (Fb) for the material and grade.
- If actual stress exceeds allowable, select a larger beam and recalculate.
Frequently Asked Questions
What causes bending stress?
Bending stress is caused by external loads (point loads, distributed loads, or moments) applied to a beam. The loads create internal bending moments that cause the beam to curve, inducing compression on one side and tension on the other.
What is the utilization ratio?
The utilization ratio is the actual stress divided by the allowable stress, expressed as a percentage. A ratio below 100% means the beam is adequate. A ratio above 100% means the beam is overstressed. Efficient designs typically aim for 80-95% utilization to balance economy and safety.
Does bending stress account for shear?
No, bending stress and shear stress are separate checks. Both must be performed for a complete beam design. Shear stress is typically critical for short, heavily loaded beams, while bending stress governs for longer spans. Deflection is a third check that must also pass.