Although any science or math test can be a frustrating or intimidating experience, a statics test can reach a whole other level of intimidation. In this chapter, I present ten suggestions that help make your life a little easier during those stressful statics exams.
After you've received your exam (and you've taken a deep breath to help you gather your composure), flip through the test and quickly read each problem, highlight what you're being asked to find, and then choose a problem that you're confident you can solve. I outline in Chapter 25 how to break the problems down into simple, bite-sized pieces. Nothing is worse than sitting in an exam and struggling with a difficult problem for far too long. If you spend too much time struggling, you may miss really quick and easy point-getters later in the exam. Also, if you find and solve the easy problems first, you build up some momentum and confidence as you proceed to the hard problems.
Start a problem by listing a few of the necessary assumptions. One or two words usually suffice. Check out the following example; you answer the questions and then jot down your answer in the test margin.
After you've listed your assumptions, seeing that list should help you identify the specific technique(s) you need to solve your problem.
Every statics problem, regardless of the type of problem, usually has the same basic beginning steps that never change.
Draw a free-body diagram.
Write the equations of equilibrium for the entire system to find unknown support reactions.
Proceed to a specific solution technique based on your problem type.
Even if your free-body diagram isn't totally correct, your instructor at least knows that you knew enough to start by drawing a picture and may award partial credit. Check out Part IV for more on drawing F.B.D.s.
As you're drawing your free-body diagram, make sure to clearly indicate your origin and Cartesian coordinate system. If you're working a three-dimensional problem, remember that you also need to include a z-axis. And don't forget to apply the right-hand rule (thumb is the x-axis, forefinger is the y-axis, and middle finger is the z-axis) so that you get the Cartesian axes properly oriented. Chapter 5 gives you the lowdown on mastering all things Cartesian.
Note
Make sure that you clearly locate and display the origin with a dimension to each axis. You need that information when you start writing equations, especially if vectors are involved. If you're working a centroidal calculation type of problem, the origin is especially important because all of the centroid calculations you perform are based on relative dimensions (see Chapter 10).
Vectors are very useful for solving statics problems, both two-dimensional applications and three-dimensional problems. When working with vectors to ensure equilibrium, simply compute the resultant vector (a system of many similar effects transformed into a single equivalent vector) of all the applied forces and the resultant vector of the applied moments about a given point or axis. Set each of these resultants equal to 0i + 0j + 0k and you have your equilibrium equations already computed. Head to Chapter 7 for more on resultants.
Nothing upsets a statics instructor more than not seeing an attempt at a free-body diagram, unless it's not seeing the three equations of equilibrium for two-dimensional problems written on the paper. Even if you write nothing else, put the following equations on a separate line for each problem:
Writing these simple equations demonstrates that you at least understand the importance of the concept of equilibrium in the world of statics. And nothing makes a professor happier than knowing a student hasn't slept through all of his classes.
After you write these three basic formulas (or compute the resultants if you're working with vectors), use them as a guide for what you must do next, which is write each of these equations from the free-body diagram you (hopefully) drew earlier. (If you didn't draw it, get drawing!)
Depending on the type of problem you're solving, you may be required to solve for internal forces. In fact, if you're dealing with an application-type problem, you can almost guarantee it wants you to find at least one internal force at some point in the problem.
Truss problem (see Chapter 19): If the problem is a method of joints-type of problem, draw an F.B.D. of joints in the system. If it's a method of sections problem, slice the truss into two pieces and draw an F.B.D. of one of those pieces.
Submerged surface problem (see Chapter 23): Draw an F.B.D. of the submerged object and then include the hydrostatic pressure as a horizontal, linearly distributed load, as well as another force from the vertical weight of the fluid.
Frame/machine problem (see Chapter 21): Break apart the system at the hinges, remove any pulleys and cables, and separate any tools or other strange objects on the system. Each of these pieces gets its own separate F.B.D.
After you have the diagrams drawn, write the equilibrium equations for each, which should give you a clue as to what to solve for first.
Note
A shear and moment diagram is practically a gimme on a test, especially if the instructor gives you the applied loads and corresponding support reactions. As you sketch these diagrams, remember the following:
Work your diagrams from the left end of the beam. The methods I describe in Chapter 20, and in particular the sign conventions, are all based on working from the left.
Your diagrams must come back to a zero value at the end. If the reactions are correct and your shear and moment diagram doesn't come back to zero when you're finished, you know without a doubt that you've made a mistake in your calculations somewhere. If you don't have time to go back and correct it, circle the discrepancy and leave a note for the instructor that says, "This diagram doesn't close to zero for some reason, but I know it should!" You may not get full credit, but that simple statement may be worth a couple of points.
Concentrated loads cause jumps in diagrams. Concentrated forces cause jumps in shear diagrams, and concentrated moments cause jumps in moment diagrams.
The order of the functions increases as you move down through the graphs. The order of the shear function is one order higher than the load for a given interval, and the order of the moment curve is one order higher than the shear. Remember that the slope of the moment curve is directly related to the value of the shear.
Pay attention to positive and negative areas. A positive area under a load diagram causes the shear to increase (become more positive), and a positive area under a shear curve causes the moment to increase (become more positive).
Always include units on your graph. Don't make the instructor guess the units. Historically, instructors are very bad guessers.
After you've worked through a problem on the test, go back and ask yourself whether your answer(s) make logical sense. This strategy is known as applying engineering judgment. A little common sense can help prevent problems, so take a moment after every problem and consider whether your answer seems reasonable.
If you realize that you made a serious blunder but don't have time to rework the entire problem, you may be better off with a page full of slightly incorrect work than a page with no work. If you can find where you made your error, quickly include the correction and then write a couple of words about what the mistake was, where you made it, and the effect it has on the remainder of your solution process. Even if you don't fully correct the entire problem, at least you've identified the mistake, and that's a big step in conveying your competency to your instructor.