For an engineer to analyze the stresses in a part, he must know that load case for that analysis. The load case is how forces and moments are applied to the part. So, we start with that, first. With complex load cases, like that of a vehicle frame, inadequately developing that load case is a common way to miss something and have field failures that make you scratch your noggin'. Been there, done that - more times than I can count. Additionally, it doesn't take much for a load case to get so complex that the only way to analyze it is by using finite element analysis (FEA).
Here are some of the questions an engineer has to ask himself, with the analysis required for each one that applies:
- Is there a significant shear force involved? - perform a shear stress analysis
- Is there an axial force (compressive or tensile) involved? - perform an axial stress analysis
- Is there a bending moment involved? - perform a bending stress analysis
- Is there a torsional (twisting) moment involved? - perform a torsional stress analysis
- Is the part a thin member, subject to buckling (like if you push on both ends of a straw)? - perform a buckling analysis
- Is the part likely to fail due to fatigue? - perform a fatigue analysis
- Is the part subject to many of these, all at once? - perform a finite element analysis
All but the last one above can be done by hand. The last one, though, requires a computer due to the millions of individual calculations involved. Finite element analysis breaks the part up into thousands of tiny pieces, all connected. The computer looks at each piece (an "element"), starting at the edges, where the external forces and moments are applied, and performs a force/moment analysis on each element. These analyses occur in succession - starting at the edges, you calculate the forces on the inside of the first elements in response to the external forces, and then those reaction forces become the external forces on the next element. The computer repeatedly applies those forces to the next elements, and keeps working inward in an iterative process to find a solution. Like 3D printing, it takes hours to complete.
So, to make a long story short and attempt to shed light on Mr. Blaine's ponderings above, the reason we strengthen the vertical frame sections is that the load case on a frame is complex, so we cover all bases because no one on here, myself included, is going to do a full engineering analysis using FEA. The driving factor for strengthening the "webs" (outside vertical walls of the frame) is that the frame definitely sees torsional loads (twisting), and resisting torsion is similar to resisting bending. In simple bending, the driving factor in the stress calculation is the moment of inertia of the part, and the strength depends heavily on portions of the part that are far from the neutral plane (the plane within the part that sees zero stress, with compression on one side of the neutral plane and tension on the other).
Same thing in torsion, but it's the polar moment of inertia that is the driving factor in the analysis, and torsion doesn't have a zero stress plane, it has a zero stress axis. That means that it's a distance from line, not a plane. So, for torsional resistance, instead of an
I shape being ideal, a circle becomes ideal. Since tube frames are expensive to manufacture (and because the load case is complex), square or rectangular tubing is used because it's the next best choice. So, for the same reason the factory engineers choose a rectangular tubing, we strengthen all four sides when we modify the frame.
that's a cost issue), I'm just happy I can use 8oz extra metal in welding vs. engineering calculations that I really don't even know how to do for the ideal minimal amount possible
