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A simply supported beam with a UDL of q and length L will have bending moments at each end of (qL^2)/2. That I get and can show proof yet its the centre moment I cannot reproduce, (qL^2)/8

Or cantilever at free end, (qL^4)/8EI {I do understand the EI bit btw}

and fully fixed beams atall, (qL^2)/12 at ends and (qL^2)/24 in the centre. {Doesn't make sense to me as the reaction forces are still the same as a simply suppoted beam: qL/2}

People write these on their beams when doing other structural analysis like its obvious yet I just can't see it. Clearly I've forgotten some basics about beams and I'm baffled, anyone care to help?

thanks in advance :)