Max Moment (Simple Beam, UDL)

For a simply supported beam carrying a constant load intensity across the full span, the internal bending moment builds up from the supports toward the middle because the shear force decreases linearly. The largest moment occurs where the shear force crosses zero, which is at midspan for a symmetric uniform load, giving M_max = wL^2/8. The result comes directly from integrating the load to get shear and then integrating shear to get bending moment.

Use this for straight beams with pin/roller supports when the load is evenly distributed over the entire span, such as floor joists, bridge members, or roof beams carrying uniform dead load. It is most useful when you need the peak bending moment for stress checks, sizing, or deflection calculations.

• Using the total load wL instead of the load intensity w in the formula
• Forgetting to square the span length, which causes the moment to come out too small
• Applying the formula to a cantilever or non-uniform load case where the moment diagram is different