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Math Help - Shigleys Indeterminate Beam Derivation

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    Senior Member bugatti79's Avatar
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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 M_1 and 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.

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

    Taking moments about the section yields

     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 M_1 and M_{ab}

    Any ideas?

    Thanks
    bugatti

    Please note that I have posted this at physics forum Shigleys Indeterminate Beam Derivation

    I will inform both post of any updates on a daily basis.
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