Maximum Bending Moment (Simply Supported UDL)
Maximum Bending Moment (Simply Supported UDL)
The maximum bending moment sets the required section size for a beam. For a uniformly loaded simple span it occurs at mid-span.
The mid-span moment of a simply supported beam under a UDL is M = wL²/8. where w is the distributed load per unit length and L the span.
Inputs
w := 15 kN/m=15000 kg/s^2
L := 6 m=6 m
Substitute directly into the standard simple-span UDL formula.
M := w·L^2/8=67500 Nm
Results
This peak moment is compared with the section’s moment capacity (M = σ·S). Doubling the span quadruples the moment, which is why long spans need much deeper members.
Assumptions & limitations
- Simply supported, prismatic, statically determinate.
- Uniform load over the full span.
- Elastic behaviour.