There are
two types of forces in structural engineering: tension
and compression.
| TENSION: |
Pulling
force |
|
Imagine
the force felt in your arms while you hang from a bar. |
|
A
structural element subjected to tension is elongated.
|
| COMPRESSION: |
Squeezing
force |
|
Imagine
the force felt in your arms while you stand on your
hands. |
|
A
structural element subjected to compression is shortened. |
Stress
is defined as force per unit area that the force acts upon.
Thus,
 |
Stresses
are either tensile or compressive. Structural materials
are chosen by their ability to resist tensile or compressive
forces, depending upon the application. Most materials
are better at resisting one or the other. For
instance, concrete is strong in compression and relatively
weak in tension. Steel is equally strong in both tension
and compression. |
| An
example of a tensile structural element would be a
cable. |
|
An
example of a compressive structural element would
be a column. |
 |
|
 |
Strain
is defined as the change in length of a stressed structural
element divided by the original length of the unstressed element.
Thus,
 |
where |
 |
| Compression: |
 |
| Tension: |
 |
A material’s
tensile strength is determined in the laboratory by pulling
on a specimen until it breaks. While the test is conducted,
both the stress and strain are recorded. The maximum stress
that the specimen can withstand is called the ultimate strength
of that particular material. From a design stand-point, we
are mainly interested in the stress where the material stops
behaving elastically.
A material
behaves elastically when it returns to its original shape
when an applied load is no longer applied. This point is found
by plotting stress versus strain during the test and determining
the stress at which the plot becomes non-linear. This stress
is called the yield stress,
sy.
The slope
of the stress-strain curve in the elastic region is defined
as the elastic modulus,
E. Structures should be designed so that any applied load
would not cause the stress in the structure to be greater
than sy.
Beams are
structural elements that are subjected to bending forces.
When bending occurs, the beam is subjected to tension and
compression simultaneously.
Imagine
a sponge beam. Say we draw a grid on the side of the beam,
so that the sponge is divided into two rows of rectangles
of equal length, Lo, and height, h/2.
When a
force is applied to the beam, the rectangles deform.
The tops
of the upper row of rectangles are shortened, and the bottoms
of the lower row of rectangles are elongated. Thus, we see
that the top of the beam is in compression and the bottom
of the beam is in tension.
Notice
that the middle of the beam is in neither tension or compression.
This is called the neutral
axis. The bending stress at the neutral
axis is zero.
The key
to designing a beam is to locate the point of maximum stress.
For a simply-supported beam under a uniform load, the maximum
stress occurs at the center point. The maximum compressive
stress at the top of the beam, scmax,
and the maximum tensile stress at the bottom of the beam,
stmax, are given by
the following equations:
where h
is the height of the beam, b is the width of the beam, and
Mmax is the maximum moment at the midspan of the
beam.
