Without a doubt, when in doubt, the first thing you must do is quickly make a sketch of the statics problem. You're not trying to pick it out of a police lineup; a sketch just gives you the best basic starting point for static analysis. When you first start sketching, don't worry about all of the little details and the moving internal parts — just make a quick sketch of the object as a whole and focus simply on how the object is attached to the world around it. For now, disregard any internal features such as internal hinges, pulleys, and machine parts.

The attachments of your monster to the world around it represent the support reactions (restraints). By determining the support reactions, you can actually reduce the scale of the free-body diagram (F.B.D.) to a more manageable size. (Head to Chapter 13 for more on supports and F.B.D basics.)

If your statics behemoth is on wheels or is sliding toward you, you're dealing with a support with only one contact force (such as a roller support). If a support isn't moving, you need to model that as either a pinned or fixed condition; a fixed support isn't rotating either, whereas a pinned support may be. If you don't know the type of support for sure, just assume it's fixed.

Look at the problem, and see what's causing it to move forward. Is a point load or distributed load acting on it? Does it have water pressure pushing on it? Is something causing an applied torque or tensile force attached to it? These possibilities are all important considerations in your solution. Additionally, don't forget to include any self weight (the force created by gravity's effects on the object's mass — refer to Chapter 9).

You need to use all of this information to construct a free-body diagram (or the detailed diagram that contains all of the loads and dimensions necessary for performing a static analysis).

After you've created a free-body diagram of a statics problem, your next step is to determine any unknown support reactions even though you haven't started looking at the internal features at all. After all, if you're going to cut a huge object loose, you want to have some idea of the size and direction of the forces that were holding it back in the first place.

When the object was restrained at the supports, it may have been struggling to break free, but it was in a balanced state. That means you can apply Newton's laws of motion, or your equations of equilibrium from Part V.

Enforcing the translational equilibrium equations is pretty straightforward. You simply add up the forces in a given direction and write the expressions. If you're lucky, you may be able find a reaction or two, or at the very least create a relationship between them.

The final equation that you want to write is the moment equation, and this one is where you have some control over a beastly problem. Depending on how you attack it, you can either make things a whole lot worse or solve for unknowns outright. In simple problems (such as statically determinate problems, which are problems that have sufficient information to be solved by just the basic equilibrium equations), you can usually sum moments at a pinned support and knock out two of the total unknown forces from the moment equation. However, you have to be more alert with statically indeterminate problems. If you have more than three unknown support reactions, you have to find a point on the lines of action of as many of these reactions (or an instantaneous center) as possible to choose as your summation point. (Check out Chapter 19 for more on this topic.)

Before you can decide how to tackle a statics problem, you need to be able to identify it. Think of yourself as a medical doctor specializing in the treatment of bizarre statics problems. You have to first identify the underlying cause (identify the type of structure) before you can begin treatment (write and solve equations). To accomplish this task, follow this handy checklist:

If none of the checklist categories fits your problem, you probably have a system such as a beam or a frame and machine. You can actually solve for internal forces of both of these types of categories using the same principles. If you slice a member and reveal the internal forces, both of these problem types have three internal forces — axial, shear, and moments — at every cut location. Chapters 20 and 21 give you solution ideas for these problem types.

When you're ready to dissect the statics problem and look at what's happening internally (after all, the internal forces are usually the most important for design), you have a couple of different options. If you're dealing with a system that contains internal hinges, many of the major methods of analysis involve breaking a structure into smaller pieces. You can run down to the old ACME mine and grab a friendly barrel of dynamite, light the fuse (get a long one!), and run for cover. Of course, the end result is a lot of smaller pieces, and unless you like jigsaw puzzles, you have a few more free-body diagrams to draw with this tactic than may otherwise be necessary. Instead, consider a more surgical approach.

Instead of blowing the structure to smithereens (which is slight overkill for most statics problems), look for pieces of the structure that you can easily separate from the main system in a more controlled manner. Items such as mechanical attachments (blades, presses, pistons, and so on), cables, and pulleys are all prime candidates for extraction. These items are usually hinged at their connection points to allow them to rotate. Hinges prove to be very useful for removal of objects because you know the moment is always zero at these locations. If you know a location of zero moment, it will prove to be a useful place to separate the structure because at these locations, you no longer have an unknown internal moment to deal with in your moment equilibrium equations when you cut the structure. Apply the basic equilibrium equations to find the internal hinge forces, and you're well on your way to analyzing the structure.

Remember that to calculate internal forces, you first have to slice a few members, which allows you to draw additional free-body diagrams and gives you additional equilibrium equations to work with. So you follow the same basic steps for applying support reactions, applied loads, and self weight, but in addition you must include the internal forces from each and every location.

The problem is that without writing the equilibrium equations, you don't know the values of the exposed internal forces at the time that you're drawing the free-body diagrams. Most of the time you don't even know the direction of the internal forces either. So what do you do?

The first thing you should do is try to determine the type of member that you've cut. If you're dealing with a cable or a rope (see Chapter 22), you know that those two systems are both axial-only systems. Furthermore, you also know that cable and rope systems' internal forces are always in tension — the direction of the force is pulling on the object.

If the member you've cut is a truss member (Chapter 19), you know that the forces in that member are also axial-only. However, truss members may have either axial tension or axial compression loads. When you're drawing your free-body diagram, you don't know whether the member is in compression or tension until you start to write the equilibrium equations, so the common convention is to assume that the forces in the member are acting in tension when dealing with trusses. You then look at the equilibrium equations to confirm whether this assumption is true — if the numerical value is negative, the direction you assumed is incorrect.

Cutting most other members exposes an axial force, as well as a shear force and a moment. As with axial members, the common assumption is that the force is acting in tension. Typically, for shear and moment, you can use the positive sign convention for internal bending forces that I describe in Chapter 20. At this point, what's most important isn't the direction of these internal forces but rather that you have at least included them on the diagram. In the end, regardless of which direction you assume is positive, the signs of the numerical values from the equilibrium equations always confirm or refute your previous assumptions.

Remain consistent in the directions you assume. If you always assume axial forces are tension, shear forces are positive, and moments are counterclockwise, when you solve the equations for the actual numerical values, a negative sign has the same meaning every time. If you vary your assumptions, you have to keep checking your diagram to verify what direction you assumed where and how the sign affects it.

When you work toward finding internal forces and you have created additional free-body diagrams, the next step is to write the equations of equilibrium.

For two-dimensional problems, you have two translational and one rotational summation that you need to make (for three total equations). For three-dimensional problems, you have three translational and three rotation summation equations, or six total equations.

The most difficult statics monsters to deal with are those that involve friction. Many common problems neglect friction, but those that don't are more complex animals. Free-body diagrams of friction problems have extra unknown forces acting on them and may even become indeterminate.

As I explain in Chapter 24, tipping and sliding problems always have a friction force in the direction of the motion of the object at the boundary or interface of every contact surface. The normal contact force location is now at a variable location that's the key to determining whether the force causes the object to slide or to tip over. To get started, assume that the friction force at the interface is equal to the friction limit at that surface and then use that force to calculate the location of the normal contact force. If the contact force location keeps the contact force on the object, the object slides. If the contact force is outside the boundary of the object, the object tips, and your original sliding assumption is wrong. To correct this inaccuracy, place the normal force at the tipping point and resolve the problem as I show you in Chapter 24.