Calculate the vertical deflection - cantilever, Mechanical Engineering

Calculate the vertical deflection:

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

88_Calculate the vertical deflection.png

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,

2362_Calculate the vertical deflection1.png

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 :

626_Calculate the vertical deflection2.png

where

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

Posted Date: 1/21/2013 6:42:57 AM | Location : United States







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