Engineering Statics

Problem solving is a two-step process whereby you first select the correct tool for the job and then apply that tool to solve the problem.

Assume you have a hammer and a screwdriver in your toolbox. Learning how to hammer in a nail or drive in a screw is analogous to the type of skills you will learn in each section of this book. But, knowing which tool is most appropriate to use only comes after you master the operation of each tool. Thus, if your task is to sink a nail into a block of wood, you likely find that the screwdriver is not the most efficient tool for the job. In your life, you have already learned to select problem-solving tools for a wide array of challenges - from cleaning your dishes to getting to the grocery store.

In courses like statics, deciding your strategy, including the process, equations, and assumptions to solve a problem, is like choosing the best tool from the toolbox. Choosing the best tool requires that you consider the capability and efficiency of tools available to you. In statics, we will introduce you to new problem-solving frameworks and techniques. One key consideration when selecting tools is the assumptions inherent in each tool. These assumptions often make use of your prerequisite knowledge and incrementally build to future topics.

In statics, the two fundamental assumptions are that all bodies are rigid and in equilibrium. While these two assumptions will not change for the duration of the course, others will become obsolete as you build new skills. One example of this progression is that in Chapter 3 you will simplify all bodies to a particle, but in Chapter 5 you can expand your knowledge of equilibrium to include rigid bodies and balanced rotation. Note that not all problems can be solved with a single tool, some problems require multiple tools. Only by developing a complete understanding of a tool can you then combine it with others.

Some of the most common statements by students who are struggling in statics include:

“I didn’t know where to start the problem”

“If I only knew which equation to apply, it would be easy for me to solve the problem.”

The message that these students are implying is that they are capable of operating a hammer or screwdriver, but they don’t know which tool to pick out of the toolbox. The best ways to practice deciding on the best strategy include:

• trying a variety of problems selected from across the full range of topics that you have learned and
• comparing and contrasting the various tools so that you know the assumptions, terminology, and application of each tool.

Only after becoming fluent within and across topics will your knowledge be complete.

Problem-Solving Steps.

In statics, the majority of the topics focus on equilibrium. The remaining topics are either preparing you for solving equilibrium problems or setting you up with skills that you will use in later classes, like the computation of the moment of inertia. For equilibrium problems, the problem-solving steps are:

1. Read and understand the problem
2. Identify what you are asked to find and what is given.
3. Identify and write down a strategy.

4. Apply the strategy to solve for unknowns and check solutions.

   1. Create a free-body diagram and define variables.
   2. Write equations of equilibrium for the free-body diagram
   3. Check if the number of equations equals the number of unknowns. If it doesn’t you may need additional free-body diagrams or other relationships.
   4. Solve for unknowns and conceptually check solutions

Using these steps does not guarantee that you will get the right solution, but it will help you be critical and conscious of your chosen strategies. This reflection will help you learn more quickly and increase the odds that you choose the right tool for the job.