Free body diagrams are the book keeping for statics problems. If a free body diagram is drawn correctly it will allow the statics equations to be derived easier. Then it would be as simple as solving simultaneous equations to solve for the forces and moments at the constraints. Remember though only six possible equations are available to solve for the unknown constraint forces and moments for a 3d model. If there are more unknown forces then there are statics equations to solve for them then the problem would be considered statically indeterminate, which is discussed in the strength of materials section.

To setup a free body diagram for a problem and derive its statics equations (equations 1-6) refer to the example below.

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