**Simply Supported beam with uniformly distributed Loads: -** In this case a simply supported beam is subjected to a uniformly distributed load whose rate of intensity varies as w / length.

In order to write down the expression for bending moment consider any cross-section at distance of x metre from left end support.

Boundary conditions which are relevant in this case are that the deflection at each support must be zero.

i.e. at x = 0; y = 0 : at x = l; y = 0

let us apply these two boundary conditions on equation (1) because the boundary conditions are on y, This yields B = 0.

Futher

In this case the maximum deflection will occur at the centre of the beam where x = L/2 [ i.e. at the position where the load is being applied ].So if we substitute the value of x = L/2