168 Chapter 7 Length and Length-Related Parameters
Some other useful trigonometry identities are
As you will learn later in your physics, statics, and dynamics classes, the trigonometry
relations are quite useful.7 7..3 3 NNoommiinnaall SSiizzeess vveerrssuuss AAccttuuaall SSiizzeess
You have all seen or used a 2 4 piece of lumber. If you were to measure the dimensions of the
cross section of a 2 4, you would find that the actual width is less than 2 inches (approximately
1.5 inches) and the height is less than 4 inches (approximately 3.5 inches). Then why is it referred
to as a “2 by 4”? Manufacturers of engineering parts (See Figure 7.4) use round numbers so that it
is easier for people to remember the size and thus more easily refer to a specific part. The 2 4 is
called thenominal sizeof the lumber. If you were to investigate other structural members, such as
I-beams, you would also note that the nominal size given by the manufacturer is different from the
actual size. You will find a similar situation for pipes, tubes, screws, wires, and many other engi-
neering parts. Agreed-upon standards are followed by manufacturers when providing information
about the size of the parts that they make. But manufacturers do provide actual sizes of parts in addi-
tion to nominal sizes. This fact is important because, as you will learn in your future engineering
classes, you need the actual size of parts for various engineering calculations. Examples of nominal
sizes versus actual sizes of some engineering parts are given in Table 7.2.cos 1 ab 2 cos a cos bsin a cos b
cos 1 ab 2 cos a cos bsin a sin b
sin 1 ab 2 sin a cos bsin b cos a
sin 1 ab 2 sin a cos bsin b cos a
cos 1 a 2 cos a
sin 1 a 2 sin a
cos 2acos
2
asin
2
a2 cos
2
a 1 1 2 sin
2
asin 2a2 sin a cos a
sin
2
acos
2
a 1■Figure 7.4 Manufacturers provide actual and nominal sizes for many parts and structural members.
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