Calculate the vertical deflection:

Calculate the vertical deflection at the tip of the cantilever shown in Figure

Figure

Solution

Measuring the distance x from the free end, the bending moment at a section distant x through the tip is given as

                                             M =- Px

Then,

Therefore, the vertical deflection below

P =∂U/∂P= PL³/3EI

The positive sign indicate that the deflection is in the direction of P, that means downwards.

 It might be seen that ∂U/∂P might be written as follows :

where

 - Px / EI = M /EI  and  - x = ∂M / ∂P