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There seems to be a pretty prevalent lack of understanding of basic structures and specifically what makes things stiff. The link above does a pretty good job of explaining it. While engineers typically use CAD programs to numerically compute structural loads and stresses; you don't need to spend 4-5 years getting an ME degree to understand the following . In fact the little explanation below will probably be very enlightening to alot of Laymen.
As an introduction to the link, I will explain it even more simply. With these concepts maybe the presentation will make more sense.
First a beam in structures is anything that has a length with a uniform cross section. So a section of pipe, an I beam member, board, a piece of plywood are all beams under this definition.
If you mount one end of the beam solidly to the wall (your choice of how), and then simply push down on the end at the other side of the beam, you will start to "bend" the beam. This is called a "Cantilever" beam
The amount the beam bends (or angular rotation) per unit force (or moment) is called stiffness.
To understand what effects stiffness you have to realize what is going on inside the beam along the entire length of the beam. If pushing down on this beam, the entire top of the beam is in being stretched. The entire lower surface of the beam is being compressed. Since for the moment we will assume symmetrical beams, the amount of compression force and elongation forces are equal and opposite mirror images of each other with there being no forces on the beam along the center line (about the moment).
Also it is an interesting principle that the forces are highest at the furtherest distance from this zero centerline. In fact because the forces are highest further away from the centerline, the stiffness is highest when there is alot of material away from the centerline. This is why an I beam has two horizontal flanges that are separated by a vertical member. It is the spacing of the flanges that really makes the I beam stiff. It doesn't matter much how thick the separating plate is.
With this in mind, look at the graph below. It compares 4 different beam sections to compare them for relative stiffness. The load is assumed to be in the vertical plane (just like my example). The steeper the slope the stiffer. The box is the stiffness by 30%-40%. The rectangle laying on it's side is way weaker than the rest. So (given a type of material), for stiffness what matters is how much material is located at the furtherest distance from the parting line of the compression and elongation forces in the beam.
Hope this helps for any would be swing arm fabers
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