Simply Supported beam with uniformly distributed Loads
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
Conclusions (i) The value of the slope at the position where the deflection is maximum would be zero.
(ii) Thevalue of maximum deflection would be at the centre i.e. at x = L/2.
The final equation which is governs the deflection of the loaded beam in this case is