Civil Engineering Reference
In-Depth Information
suspension bridges support loads through cables called hangers, composed
of many entwined wires, extending vertically downward from a main cable,
which is made up of even more wires. In our imagination, we make sure
that the hanging cable is so firmly fixed to its main cable that it cannot
come undone. The downward stress of the load is measured once again in
pounds per square inch of the hanging cable's cross-sectional area (that's a
horizontal slice through it). If the area is 5 square inches, then the 100-kip
load imposes a
stress
of 20 ksi. The stress has the effect of deforming the
cable: stretching it downward. The
strain
is the measure of that stretching:
it is the ratio of the cable's increase in length to its original length.
As we increase the weight of the suspended object, stress increases,
correspondingly increasing the strain. It is as if the fibers inside the mate-
rial were being stretched further apart—but again we should not think that
somehow we are visualizing actual molecules. Past a maximal value, the steel
cable suddenly elongates precipitously. If the room under it is great enough,
it elongates until it snaps, hurtling the suspended load to the ground. That
of course is the outcome bridge designers must avoid. The designer must
restrict the load to start with, or otherwise increase the cable's diameter,
add additional wires, or use stronger wire.
Discovered by the English scientist Thomas Young (1773-1829),
“Young's modulus” (the word
modulus
just means “little measure”) demon-
strates that each additional increment of stress causes a proportional incre-
ment of strain. More pulling load on the cable causes more strain on the
cable—up to the point at which it lengthens precipitously per unit of added
stress. The stress threshold that causes this change in the cable's behavior
is known as the “yield stress.”
Likewise, more compressive force on a column causes proportional
increments of strain, until the yield threshold at which the column begins
to buckle or get crushed. When planning for the loads to which a cable
or column can be safely subjected, the engineer refers to information on
the yield stress at which the material no longer responds proportionately
to added force (figure 3.4).
Note that under tensile pulling, there cannot be an outward bulging
of the material—there cannot be buckling. If we compare steel bars, one
under compression and one under tension, both having the same cross-
sectional area, the bar can undergo more tensile stress before snapping than
compression before buckling.
This may be the point at which to add that stiffness is not at all
the only desirable quality the designer looks for. Whether it is meant to
resist compression or resist tension, the structural member must not retain
deformation (shortening in one case, lengthening in the other) after the
live load has been removed. The ability to bounce back from deformation
