The Superposition Method
The superposition method is another method that can be used to solve a statically indeterminate beam problem. Basically, the superposition method will split a statically indeterminate problem into separate statically determinate problems. Those solutions are then added together, as seen in the figure below.
Adding the two solutions together will then make it possible to create an additional equation to solve for the unknown force. The main advantage of using superposition method is that you can use tables found in most books to look up basic deflection equations. By using those table the steps a greatly reduced. Of course if there aren't any tables available than different beam deflection methods could be used to derive the deflection equations that would be needed.
To solve for an unknown force using superposition method refer to the example below.
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