Bending Moment Calculator Formula
Understand the math behind the bending moment calculator. Each variable explained with a worked example.
Formulas Used
Maximum Bending Moment
max_moment = load_w * pow(span_l, 2) / 8Maximum Shear Force
max_shear = load_w * span_l / 2Variables
| Variable | Description | Default |
|---|---|---|
load_w | Distributed Load (w)(kN/m) | 10 |
span_l | Beam Span (L)(m) | 6 |
How It Works
Maximum Bending Moment for a Simply Supported Beam
Under a uniform load, the moment diagram is parabolic with its peak at midspan.
Formulas
M_max = w L^2 / 8 (at midspan)
V_max = w L / 2 (at the supports)
These are the most fundamental results in structural analysis and form the starting point for beam design.
Worked Example
A 6 m simply supported beam carrying 10 kN/m.
load_w = 10span_l = 6
- 01M_max = 10 x 6^2 / 8 = 10 x 36 / 8 = 45 kN-m
- 02V_max = 10 x 6 / 2 = 30 kN
Ready to run the numbers?
Open Bending Moment Calculator