how to draw a free body diagram
Three equilibrium equations are powerful, but before you write them you have to know every force acting on the body, with none left out. The drawing that does this is the free-body diagram, FBD for short. The method is simple. Lift one body out of its surroundings and float it in empty space, then replace everything that was touching it with the arrow of the force that thing pushes with. Walls, floors, ropes, and pins all become forces, and you also add forces that act at a distance, such as weight. This one drawing is the start of every statics solution, because a wrong drawing makes the equations wrong all the way through. Start by lifting the body out of its surroundings.
The first step is isolation. You pick the body to analyze and cut it out of the rest of the world, and the button shows the real situation on the left, stuck to a wall and resting on a floor, and on the right that body alone, lifted into empty space. Once it is lifted out, what acts on it becomes clear, because every place that was touching it is now a place to draw a force. What you call the body is your choice: one beam, one pin, or a lump of several members tied together. Whatever you isolate, once it is lifted out you only care about the forces that cross that boundary.
With the body lifted out, the things that were touching it have to become forces. The principle is one: if a support stops the body from moving, that support is pushing in the direction it blocks, and that push is the reaction. A block resting on a floor is kept from sinking down, so the floor pushes up. Press the button to erase the floor and replace it with that force, and even with the floor gone a single upward arrow in its place has exactly the same effect on the body. Erasing the support and drawing its reaction instead is the heart of the free-body diagram.
Each support blocks a different direction, so the reaction it gives is different, and there are three basic kinds. A roller blocks only sliding perpendicular to the surface, so it has one reaction, a force in the perpendicular direction only. A pin holds the position against both directions, so it has a horizontal force and a vertical force, two of them, and a fixed support blocks position and rotation, so it has the horizontal force, the vertical force, and a moment that blocks rotation, three in all. How many unknowns appear is settled here: a roller is 1, a pin is 2, a fixed support is 3. Looking at a support should immediately suggest the arrows to draw.
Now look at one finished free-body diagram. A beam on a pin at the left and a roller at the right carries a load, and every force is drawn on the beam once it is lifted out. The applied load P points down, the beam's own weight W points down from the center of gravity, the pin carries horizontal and vertical reactions, and the roller carries a perpendicular reaction. Drag the load and it becomes plain that the external forces are values you know while the reactions are unknowns you do not, and the known forces and the unknown forces gather in one drawing. You check on this drawing that no force is missing and that the directions are right, so one good FBD finishes half the problem.
Finally see how the drawing becomes a solution. Take the forces written on the finished drawing and drop them straight into the three equilibrium equations. Add every horizontal force for ΣFx = 0, add every vertical force for ΣFy = 0, and add every moment about one point for ΣM = 0. Drag the load position and the reaction values on the drawing come out solved at once through the equations. This one path, from drawing to equations to answer, is essentially the whole of a statics problem. Learn the order of lifting the body out, drawing every force, and writing the three equations, and the basics of force and equilibrium are complete. From the next chapter this tool solves real structures such as trusses.