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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
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