Fundamental Engineering Concepts - Mathematics and Statistics for the Environment - page 247

Fd = Fd

11 22

(11.8)

∑

M = 0

0

11.6.6 b eams and C olumns
A beam is a structural member whose length is large compared to its transverse dimensions and is
subjected to forces acting transverse to its longitudinal axis (Tapley, 1990). Environmental engineers
are concerned not only with structural members (e.g., beams, flooring support members) but also
with columns. Columns are structural members with an unsupported length 10 times greater than
the smallest lateral dimension, and they are loaded in compression. When a column is subjected to
small compressive loads, the column axially shortens. If continually larger loads are applied, a load
is reached at which the column suddenly bows out sideways. This load is referred to as the column's
critical or buckling load. These sideways deformations are normally too large to be acceptable;
consequently, the column is considered to have failed. For slender columns, the axial stress cor-
responding to the critical load is generally below the yield strength of the material. Because the
stresses in the column just prior to buckling are within the elastic range, the failure is referred to as
elastic buckling . The term elastic stability is commonly used to designate the study of elastic buck-
ling problems. For short columns, yielding or rupture of the column may govern failure while it is
still axially straight. Failure of short columns may also be caused by inelastic buckling; that is, large
sideways deformation that occur when the nominal axial stress is greater than the yield strength.
Beams, floors, and columns are all critical elements for safe loading. As an example, in late
October of 2003, the top five floors of a parking garage under construction in Atlantic City, NJ, col-
lapsed while workmen were pouring concrete on the structure's top floor, killing four workers and
critically injuring six others. OSHA's investigation of the collapse involved close examination of the
blueprints for the garage and evaluation of the cure rate for the concrete. No matter who or what ele-
ment of construction, design, or engineering was ultimately to blame in this collapse, obviously the
load limits were exceeded for that moment. Perhaps a longer concrete curing interval would have pre-
vented the collapse. Regardless of the cause, however, the cost in lives and dollars lost was too high.
Environmental engineers are primarily interested in beams because the load on a beam induces
stresses in the material that could be dangerous. The structural aspect of beams is most important
to the environmental engineer, because the strength of the beam material and the kind of loading
determine the size of load that it can safely carry. For example, in the construction of the storage
mezzanine discussed earlier, and in the construction of other load-bearing structures, the beams
used to support the load are an important (critical) consideration.
Refer to Figure 11.15. The neutral axis is the plane that undergoes no change in length from bend-
ing and along which the direct stress is zero. The fibers on one side of the neutral axis are stressed in
tension, and on the other side in compression, and the intensities of these stresses in homogeneous
beams are directly proportional to the distances of the fibers from the neutral axis (Heisler, 1998).

Force

Compression
Tension

Force Force

FIGURE 11.15 Distribution of stress in a beam cross-section during bending.