Maximum Shear on a Beam - beam with fixed support on one end and hinge on other end

A beam $\displaystyle 3m$ long with fixed support on one end and hinge on the other end is subjected to a uniform load of $10\ kN/m$. What is the maximum shear of this beam?

The solution is this one:

$\displaystyle Max.Shear = \frac{5\omega{L}}{8}=\frac{5\left(10\right)\left(3\right)}{8}=18.75\ kN$

where $\omega$ = distributed load $N/m$

$L=$ length

My question is, how did he get this equation? All I know is that hinges have two forces acting on them. Can anyone derive this equation?

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Hi Andrew. I think you're aware that this site deals with conceptual Physics Q&A. I have a slight thought that this actually disagrees with our homework policy because, it explicitly asks other users to derive the equation for you. We don't encourage homework questions that doesn't involve any sort of work done by the author and asks other users to solve the problem. If you think you could clarify your question, add what you've done along with your question. We're ready to help you. ;-) – Waffle's Crazy Peanut Mar 22 '13 at 17:19
@CrazyBuddy Well... this is definitely better than the typical homework-like question we get around here. But you have a point. AndrewJohn, could you perhaps update the post to include what you've done to try to figure out how this equation was derived? What did you find in your textbook (or whatever resources you have), for instance? – David Z Mar 22 '13 at 18:32