Bending Moment Calculator
Find the maximum bending moment for a simply supported beam with a uniform distributed load.
Maximum Bending Moment
45.00 kN-m
Maximum Bending Moment vs Distributed Load (w)
Formula
## 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.
Exemplo Resolvido
A 6 m simply supported beam carrying 10 kN/m.
- 01M_max = 10 x 6^2 / 8 = 10 x 36 / 8 = 45 kN-m
- 02V_max = 10 x 6 / 2 = 30 kN
Perguntas Frequentes
What if the beam is fixed at both ends?
For a fixed-fixed beam with uniform load, M_max at midspan is w L^2 / 24 and the moment at each support is w L^2 / 12. Fixed ends reduce midspan moment significantly.
How do I combine dead and live loads?
Add the dead load and factored live load per unit length together to get the total w, then apply the formula. Use load factors from your governing design code.
Where does maximum moment occur for a point load?
For a single point load P at midspan of a simply supported beam, M_max = P L / 4, occurring directly under the load.
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