Statics

Once we add a symbol, we're getting the hang of effective communication: "F = -8N" tells us that it's a negative force with a magnitude of 8N.

In this class, we place a high priority on the proper use of units and signs. This is because they play a major role in your ability to communicate as an engineer. 

Expectation for this class: write or say "F = -8N", not just 8.

For many of you, this is your first engineering course (welcome!). Engineering is a practical career that builds on mathematics and the sciences, and you have been taking math and science prerequisites to get to this particular point in your journey.

Reflect back on the math and science courses for a moment. Your instructors were mathematicians and scientists, and because of that background, they used scientific notation.

In this course, we will not be using scientific notation. That is, not exactly. We'll use a variant that is called engineering notation. After you see how it works, you will love it.

Here is how it works. Consider the number 12,300.

• In scientific notation, you move the decimal point to the right of the left-most number. It allows you to think of a number in terms of a coefficient and an exponent: 1.23 x 10^4. The coefficient is 1.23 and the exponent is 4.

• Engineering notation works the same way, except that all of the exponents must be multiples of 3. We need to change 10^4 to 10^3. Divide the exponent by 10 while multiplying the coefficient by 10 to get 12.3 E3. In engineering notation, the capital letter E stands for "exponent" and it replaces "10^" (or "10⨉") in scientific notation.

Practice putting your calculator into engineering notation mode now. 

For most calculators, select "mode." You will generally see three options: NORM(al) notation, SCI(entific) notation, and ENG(ineering) notation:

Expectation for this class: you will put your calculator into engineering notation mode prior to working on assignments for this class. Engineering notation is generally only used in the intermediate steps of problem-solving. Guidance for final answers is in the next section.

In Statics, we will use two systems of units: the S.I. system and the U.S. Customary system. 

S.I. Units

In S.I. Units, engineers tend to use prefixes in units, so that the units used in the answer are appropriate to the scale of the question. Commit these prefixes to memory:

G giga E9 billion

M mega E6 million

k kilo E3 thousand

m milli E-3 one-thousandth

µ micro E-6 one-millionth

U.S. Customary Units

In U.S. Customary units, engineers tend to use units that are appropriate to the scale of the question.

Example 1: What's the distance between Denver and Chicago? Answer in miles (not feet or inches). 

Example 2: What's the span of a highway bridge? Answer in feet (not miles or inches).

Example 3: What's the diameter of an apple? Answer in inches (not feet or miles).

Unfortunately, there aren't many useful prefixes in the U.S. Customary system. There is really one prefix that you need to understand and use, and it's an adaptation of the S.I. prefixes.

When using units of force, we'll often use the "pound-force" symbol. This unit is commonly called the pound and given this symbol: #. The pound-force (abbreviated lb. or lbf.) is different than the "pound-mass" unit.

Within Civil Engineering, the # unit is too small to be useful when calculating the forces exerted on bridges and buildings. For that scenario, engineers invented a useful unit called the kilopound, fondly nicknamed the kip. One kilopound (or kip) is equal to 1,000#, and in written calculations, the symbol k is commonly used for the kip.

There are also units to express force per area (pressure for fluids and stress for solids). In U.S. Customary Units, we will use psi as an abbreviation for "pounds per square inch" and ksi for "kips per square inch." I'm sure you already guessed the conversion factor: 1 ksi = 1,000 psi.

Please commit the symbols for feet and inches to memory. A foot is designated by a single slash (') and an inch is designated by a double slash ("). If you are five feet and ten inches tall, you'd write 5'-10".

Expectation for this class: communicate final answers with units that are appropriate to the scale of the question. If possible, do not report final answers with engineering notation. In some types of calculations (e.g. the moment of inertia), engineering notation will generally be needed in the final answer.

I know you want to skip past this section, but don't do it. Significant figures (S.F.) are an important part of effective communication.

Let's say that your height (in U.S. Customary Units) is 5'-10".

Here's what happens if you are too precise (e.g. too many significant figures):

Question: How tall are you?

Answer: I am 5.83456 feet.

It sounds ridiculous, right? Answering a question with too much precision makes you sound like you don't understand the nature of the question. No one needs to know their height that precisely, even if we could measure human height with that much precision.

It's just as bad round numbers off without precision (e.g. too few significant figures). Let's say you go to the doctor's office and get asked about your height.

Question: How tall are you?

Answer: About 6 feet.

Rounding to the closest foot is based in logic and mathematics, but it is also a lousy way to answer the question. The person asking about your height wants more precision that you provided. 

The conventional way we communicate our height in the U.S. teaches us about the appropriate use of significant figures in engineering communication. When we say "I'm 5'-10" tall," we are essentially providing three significant figures (or close to it, as 1 inch is equal to 1/12 foot and not 1/10 foot). As engineers, we must use numbers that facilitate effective communication. Too much precision is as problematic as a lack of precision.

Please report all of your final answers to three significant figures. 

• We do not want any more precision than this.

• We do not want any less precision than this. 

• Three S.F. is generally appropriate for final answers in this class, and most engineering classes.

That said, while we are working through the calculation, we need to keep a fourth (4th) S.F. at intermediate steps. If we round to three S.F. too soon, we lose precision. If we round successively, in several steps, our final answer drifts -- the rounding can create an error margin of over 1-2%, and that's too much. We need to minimize computational errors. That's just good engineering. 

Here are some tips to maintain precision throughout a problem:

• if it is easy and reasonable, keep all digits (or significant figures) in your calculator storage (use the STO command as needed)

• let's also acknowledge that practically speaking, engineering problems have a multitude of steps and it's not always a good use of our time to keep track of every single digit (approximations are common in engineering)

• therefore, in order to accurately report 3 significant figures in the final answer, we will write down four significant figures throughout intermediate steps of the problem

In the real world, engineering problems rarely have nice round numbers, like 2.00 kN. In academia, professors like to assign problems with nice round numbers, because they're faster to work and grade. For this reason, if you work a problem with nice round numbers, and the final answer is 2.00 kN, it is OK to report this answer as 2 kN. In engineering practice, if trailing zeroes are omitted, we generally assume that the number is accurate to 3 S.F.

Expectation for this class: Final answers will be considered correct with three significant figures of precision. In order for the final answer to be accurate to three S.F., use four S.F. through all intermediate calculations. Trailing zeroes do not have to be written down explicitly.

You have likely had math or science professors that asked you to report final answers as fractions or with radicals.

Example: in a math class, you might report a final answer as the square root of 5. A math professor typically doesn't want you to write 2.24, and in those types of courses, you may not have access to a calculator.

In engineering practice, we tend to express final answers with decimals. You may certainly work with fractions or radicals in the intermediate steps of your problem-solving process, but final answers should be in simplified decimal format.

Example: in an engineering class, even if the answer is the square root of 5, it should be reported as 2.24.

Expectation for this class: Final answers will always be in decimal format. Answers cannot contain fractions, radicals, or exponents.

Let's say that you have been asked to add two vectors (F_1 and F_2) together. Both vectors are horizontal (point in the x-direction). The sum of these vectors is the resultant vector, denoted F_R.

Here's how three different students may have been scored on this problem:

Expectation for this class: write all equations symbolically before plugging in numbers.

Early in the course, some students have a bad habit of writing "floating" mathematical operations that lack context. The mathematical operation is correct, but it doesn't directly apply to the problem. Always communicate the nature of the calculation by writing equations (or inequalities) and using proper symbols.

Expectation for this class: all math equations (and inequalities) must be properly contextualized.

In engineering problem solving, most professors expect students to write out the information that is given, state what the problem has asked them to solve, and then write out the solution line by line. Practicing engineers tend to also use this format in their professional calculations.

Expectation for this class: use the Given → Find → Solution structure on all problems.

Let's tie a bow on all of these effective communication guidelines with an example that brings all of these ideas together.