The shear force in a beam (V) and the displacement (v) are related by:

Where EI = Flexural rigidity

1
\(V = EI\frac{{{d^2}v}}{{d{x^2}}}\)
2
\(V = EI\frac{{{d^3}v}}{{d{x^3}}}\)
3
\(V = EI\frac{{{d^4}v}}{{d{x^4}}}\)
4
Not related to each other 

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