Conclusions of deflection
(i) The value of the slope at the position where the deflection is maximum would be zero.
(ii) The value 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
By successive differentiation one can find the relations for slope, bending moment, shear force and rate of loading.
Deflection (y)


Slope (dy/dx)


Bending Moment

So the bending moment diagram would be

Shear Force Shear force is obtained by taking third derivative.


Rate of intensity of loading
