The Solution
When the problem has finished running in the computer, I run a program called
a post-processor to view the results. This program allows
me to colorize the model based on a type of result that I choose. For
instance, I could look at the maximum vertical deflection of the truss, and
the program would show me the truss with each location colored based on it's
vertical deflection. Red would be the most positive value and blue
would be the most negative value, and the colors would vary in between just
like in a rainbow.
Below are the results of the calculation. The truss is being displayed
with exaggerated deformation just so that you can see what's going on.
In reality, the maximum motion is probably less than 1/8" at the center of
the span. The colors in the picture represent the tensile stress.
The red end of the spectrum indicates a state of tension (stretching), while
the blue end of the spectrum indicates a state of compression (negative tension).
Also, since each beam in the model actually has stresses that vary across
its cross section, and, since the beam is displayed as a thin line, it's
impossible to display all of these results with a different color all at
once, so it's common to display only the maximum value of the entire cross
section, since this is usually the value of most interest to the engineer.
This can make some of the data look a bit deceptive. Say you hold a
ruler horizontally out in front of you with one hand grasping each end.
If you bend the ruler such that it makes a "smile" the top surface of the
ruler is in a state of compression; the grains of the wood are being made
a tiny bit shorter. The bottom surface of the ruler, however, is in
a state of tension; the wood grain on the bottom surface is being stretched
a bit. If you go anywhere in between the top and bottom surface, the
stress will be somewhere in between the tensile value at the bottom surface
and the compressive (negative tension) value at the top. So in the
image of the roof truss, a blue beam doesn't mean that the whole beam is
being compressed along its length; rather, it may mean that the beam is being
bent, and the compressive side has a slightly higher magnitude of stress
than the tension side, so the blue value is shown rather than the red.
To avoid confusion and more thoroughly understand what I'm looking at, I'll
usually investigate other quantities and look in more detail at, say, the
stresses across one cross section at one location in a beam.
Anyway, given the load that it must support, the maximum (ignoring the +/-
sign) tensile stress throughout the entire truss is -20,830 psi. Since the
weakest grade of steel available can withstand 30,000 psi, we look okay so far.
My guess is that the steel used in the truss is probably a medium grade of
steel with a strength of 60,000 psi or so.
However, one thing that you learn early on as an engineer is that you can't just look at tensile stress. There are actually six different components of stress that are of interest, and there is a way to combine them into one single "effective stress" called Von Mises stress. It has been repeatedly demonstrated in experiments that this Von Mises stress should be used to indicate failure in materials such as steel. Below is a picture of the effective or Von Mises stress in the end of the truss (looking up at it from underneath). Notice that the maximum Von Mises stress is over 30,000psi. So we're probably still okay, but not by as large of a margin as the tensile stress results indicated.
Back: The Model | Up: Main Roof Truss Page
