ABSTRACT
A beam is simply a long, slender member as represented in Figure 8.1, where ‘ is the length of the beam, h is its height, and b is its thickness. An immediate question is: what is meant by ‘‘long and slender?’’ That is, how long is ‘‘long’’ or equivalently, how slender is ‘‘slender?’’ Unfortunately, these questions have no precise answers. We can certainly say that whatever approximations are made, by assuming a beam to be long and slender, become more appropriate the longer (or more slender) the beam becomes. While this is reassuring, and potentially useful, it is still not very specific. A general rule is that a beam is long or slender if its length ‘ is an order of magnitude (i.e., 10 times) larger than the cross section dimensions. That is, in Figure 8.1 the beam may be regarded as long as
‘ > 10h and ‘ > 10b (8:1)
Beams may be loaded in three principal ways: (1) axially (producing longitudinal extension or compression); (2) transversely (producing bending); and (3) in torsion (producing twisting). Figure 8.2 illustrates these loading methods.
