A Free-Body Diagram Isolates the Body and Draws Every Force on It
The three equilibrium equations are powerful, but to write them you must first know, without missing any, what forces act on the body. Drawing that is the free-body diagram, FBD for short. Here is the method. Take the one body you want to analyze and strip it clean out of its surroundings, floating in space. Then redraw everything that was touching it as an arrow for the force it pushes with. The wall, the floor, a rope, a pin, all become forces. Add forces that act from a distance too, like weight. This single drawing is the starting point of every statics solution; if the FBD is wrong, the equations are wrong wholesale. Start by detaching the body from its surroundings.
The first step is isolation. You pick the body to analyze and cut it out of the rest of the world. Press the button. On the left is the real situation, attached to a wall and resting on the floor; on the right, that body alone, lifted into space. Detaching it this way makes it clear what acts on the body, because every place it was touching is now a spot to draw a force. What counts as the body is your choice: it could be one beam, one pin, or a chunk of several members lumped together. Whatever you isolate, once it is cut free you only need to worry about the forces that cross that boundary.
Now that the body is detached, you must turn the things it touched into forces. The key principle is this: if a support is stopping the body from moving, that support is pushing with a force in the direction it blocks. This is a reaction. A block rests on the floor. The floor stops the block from sinking down, so the floor pushes up to hold it. Press the button to erase the floor and replace it with that force. Even with the floor gone, drawing a single upward arrow in its place has exactly the same effect on the body. Erasing a support and drawing its reaction instead is the heart of the FBD.
Each support blocks a different direction, so the reaction it gives differs too. There are three basic types. Switch between them with the buttons. A roller only stops sliding perpendicular to its surface, so its reaction is one force, normal to the surface. A pin holds the position in both directions, so it gives a horizontal and a vertical force, two reactions. A fixed support blocks position and rotation alike, so on top of horizontal and vertical force it adds a moment that resists turning, three. How many unknowns appear is decided right here: a roller gives 1, a pin 2, a fixed support 3. Look at a support and the arrows to draw should come to mind at once.
Now look at one complete free-body diagram. A beam supported by a pin on the left and a roller on the right carries a load. On the detached beam, every force is drawn: the applied load P pointing down, the beam's own weight W down at its center, the horizontal and vertical reactions at the pin, and the vertical reaction at the roller. Drag the load along the beam. The external loads are values you know, and the reactions are the unknowns you do not yet. An FBD gathers the known and unknown forces in one place. Whether a force is missing, whether the directions are right, you check it all in this drawing. One good FBD and half the problem is already solved.
Finally, see how the FBD leads into the solution. The forces written on the finished FBD go straight into the three equilibrium equations. Add all horizontal forces for ΣFx = 0, all vertical forces for ΣFy = 0, and all moments about one point for ΣM = 0. Drag the load position and you see the FBD's reaction values come out at once through the equations. From drawing to equations, from equations to answer. Every statics problem is essentially this one thread: isolate, draw every force without missing any, set up the three equations and solve. With this, the fundamentals of force and equilibrium are complete. From the next chapter, we use this tool to solve real structures like trusses.