Fixed end moments developed at both the ends in a fixed beam of span L and flexural rigidity El, when its right-side support settles down by Δ, is 

1
\(\frac{{6EI{\rm{\Delta }}}}{{{L^2}}}\) (sagging)
2
\(\frac{{12EI{\rm{\Delta }}}}{{{L^2}}}\) (sagging)
3
\(\frac{{6EI{\rm{\Delta }}}}{{{L^2}}}\) (hogging)
4
\(\frac{{12EI{\rm{\Delta }}}}{{{L^2}}}\) (hogging)

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