How much weight would I need to put on the end of a tube to break it? Say I have a tube with a circular cross-section made from some material (for an example, I'd like to use acrylic). I support it horizontally from one end and hang a weight from the other end. How heavy does the weight have to be to break the tube?
What if I support the tube from both ends and hang the weight from the middle?
For the example, please use acrylic with inner diameter 2 inches, outer diameter 2.25 inches, length 60 inches. However, I'd like to know the formulae and theories that are used to make these calculations so that I can do them myself in the future.
You might find the following useful: Properties of acrylic
 A: The equation you would apply is:
$\sigma = \frac{M*Y}{I}$
Where M is the bending moment or torque, $Y$ is the distance from the center of the cross section to the top or bottom most fiber, and $I$ is the moment of inertia of the cross section about its x-axis. $\sigma$ is the stress.
So,
Maximum moment =  $M= F * 60$ inches where $F$ = your downward force.
$Y= 1.125$ inches.
$I$ for this particular cross sectional shape equals 
$\frac{\pi(D_O^4 -D_I^4)}{64}$ where $D_O = 2.25$ inches and $D_I = 2.00$ inches.
I kept all the units in inches.
If you know what the maximum tolerable $\sigma$ is in PSI (pounds per square inch), then you plug that into the equation and solve for $F$ in pounds.
This is an EXTREMELY basic structural engineering problem. If you apply a force in this fashion to this particular structural configuration, you end up creating a bending moment at the opposite end that causes tension in the uppermost fiber and compression in the bottommost fiber. In structural analysis, the loading possibilities and connection possibilities are innumerable and range from simple to complex. There have been cases in history where even simple structures have collapsed resulting in death because the designers simply neglected basic concepts. Every single weld has to be properly designed. Every single bolt has to be properly sized. Every single element must be correctly designed. Otherwise...possible disaster.
