How do you calculate maximum bending moment for a simply supported beam with UDL?

For a simply supported beam with uniformly distributed load w per unit length over span L: Maximum bending moment occurs at midspan and equals wL^2/8. Reactions at each support equal wL/2. The bending moment varies parabolically along the length with M(x) = wx(L-x)/2. Maximum shear occurs at supports and equals wL/2. These standard formulas are fundamental for beam design and load calculations.