For the cantilever beam shown in the given figure, which one of the following pairs is not correctly matched ?

M o h r^{'} s : A r e a o f B M D \times D i s t a n c e T h e o r e m o f c e n t r o i d o f B M D f r o m B

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C a s t i g l i a n o^{'} s : L \int 0 W x^{2} d x T h e o r e m

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C o n j u g a t e : S h e a r f o r c e a t t h e f i x e d b e a m e n d o f c o n j u g a t e b e a m

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S u c c e s s i v e : \int \int - W x d x i n t e g r a t i o n

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Solution

The correct option is C $C o n j u g a t e : S h e a r f o r c e a t t h e f i x e d b e a m e n d o f c o n j u g a t e b e a m$
From castigliano's theorem deflection at B

$δ_{B} = \int_{0}^{L} \frac{M}{E I} (\frac{\partial M}{\partial W}) d x$

But M = Wx

$∴ δ_{B} = \int_{0}^{L} \frac{W x^{2}}{E I} d x$

In conjugate beam, shear force at the fixed end is the slope at B and BM at fixed end is the deflection at B.

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