Bending Moment Calculator Formula
Understand the math behind the bending moment calculator. Each variable explained with a worked example.
Formulas Used
Moment from Uniform Load
moment_uniform = load_plf * pow(span, 2) / 8Moment from Point Load
moment_point = point_load * span / 4Total Max Moment
total_moment = load_plf * pow(span, 2) / 8 + point_load * span / 4Variables
| Variable | Description | Default |
|---|---|---|
span | Beam Span(ft) | 14 |
load_plf | Uniform Load(lb/ft) | 250 |
point_load | Point Load at Center(lbs) | 0 |
How It Works
Bending Moment
Uniform load: M = wL squared / 8
Center point load: M = PL / 4
Both produce maximum moment at mid-span for a simply supported beam. If both loads are present, add the moments together (superposition).
Worked Example
14 ft beam with 250 lb/ft uniform load.
- 01M = 250 x 14 squared / 8 = 250 x 196 / 8 = 6,125 ft-lbs
- 02No point load contribution
- 03Required section modulus = M / Fb (allowable bending stress)
Frequently Asked Questions
What units should bending moment be in?
In the US, bending moment is typically expressed in foot-pounds (ft-lbs) or inch-pounds (in-lbs). Multiply ft-lbs by 12 to get in-lbs, which is needed for beam sizing.
How do I use moment to size a beam?
Divide the moment (in inch-pounds) by the allowable bending stress (Fb in psi) to get the required section modulus (S in cubic inches). Then pick a beam with S equal to or greater than this value.
Learn More
Guide
How to Calculate Beam Load Capacity
Learn how to calculate beam load capacity using bending moment, section modulus, and material yield strength. Step-by-step engineering guide with formulas.
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Open Bending Moment Calculator