Bending Moment Calculator Formula

Understand the math behind the bending moment calculator. Each variable explained with a worked example.

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Formulas Used

Moment from Uniform Load

moment_uniform = load_plf * pow(span, 2) / 8

Moment from Point Load

moment_point = point_load * span / 4

Total Max Moment

total_moment = load_plf * pow(span, 2) / 8 + point_load * span / 4

Variables

VariableDescriptionDefault
spanBeam Span(ft)14
load_plfUniform Load(lb/ft)250
point_loadPoint 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.

span = 14load_plf = 250point_load = 0
  1. 01M = 250 x 14 squared / 8 = 250 x 196 / 8 = 6,125 ft-lbs
  2. 02No point load contribution
  3. 03Required section modulus = M / Fb (allowable bending stress)

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