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Shigleys Indeterminate Beam Derivation

Folks,

I am having difficulty deriving the moment expressions for a rigidly supported beam fixed at either ends and subjected to a point load as shown in the attachment.

The problem is that I want to derive the left hand fixing moment $\displaystyle M_1$ and $\displaystyle M_{ab}$ as in Shigleys. However, I believe my attempts are not leading to these expressions by shigley (engineering book).

My derivations are based on the free body diagram as attached with clockwise moments positive.

$\displaystyle M_{xx}=E*I \frac{d^2 y}{dx^2}$

Taking moments about the section yields

$\displaystyle M_{xx}+R_1 x-F(x-a)-M_1=0 \implies M_{xx} = F(x-a)+M_1-R_1 x$

Subjecting this to the curvature realtion and integrating twice will not lead me to the equations for $\displaystyle M_1$ and $\displaystyle M_{ab}$

Any ideas?

Thanks

bugatti

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