186 Chapter 7 Length and Length-Related Parameters
the z–zaxis shown, the value of the area moment of inertia of the I-beam is higher for configura-
tion (a) than it is for configuration (b).
To better understand this important property of an area and the role of the second moment
of area in offering a measure of resistance to bending, try the following experiment. Obtain a thin
wooden rod and a yardstick. First try to bend the rod in the directions shown in Figure 7.21.
If you were to report your findings, you would note that the circular cross section of the
rod offers the same resistance to bending regardless of the direction of loading. This is because
the circular cross section has the same distribution of area about an axis going through the cen-
ter of the area. Note that we are concerned with bending a member, not twisting it! Now, try
bending the yardstick in the directions shown in Figure 7.21. Which way is it harder to bend
the yardstick? Of course, it is much harder to bend the yardstick in the direction shown in Fig-
ure 7.21(a). Again, that is because in the orientation shown in Figure 7.21(a), the second
moment of area about the centroidal axis is higher.
Most of you will take a statics class, where you will learn more in depth about the formal
definition and formulation of the second moment of area, or area moment of inertia, and its
role in the design of structures. But for now, let us consider the simple situations shown in
Figure 7.22. For a small area elementA, located at a distancerfrom the axisz–z, the area
moment of inertia is defined byIzzr
2
A(a)
Direction of
expected load(b)
zz
■Figure 7.20
Which way is an I-beam oriented
with respect to loading?(a) (b)
x
x
y
y
y
y
x
x
■Figure 7.21
Bend the rod and yardstick in the
directions shown.rA
z
z
■Figure 7.22
Small area element located at
distancerfrom thez–zaxis.Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀