Could you give me explanation why bending moment at fixed support equal wL^2/12?
Answer
Not all moments at fixed support equals to wl^2/12.
For instance,
(A) moment at fixed end of cantilever subjected to uniform load is wl^2/2
(B) moment at fixed end of a propped cantilever subjected to uniform load is wl^2/8
The value wl^2/12 is the bending moment at the support of beam fixed at both ends and subject to uniform load.
I have hand written the derivation of this value for your reference.
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