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The beam tapers to each of its end; the most robust section of the beam may or may not be at the center region of the beam. But the most common endeavors regard symmetrical tapering from some central section of the beam . A beam need not be a perfect spindle where tapering begins immediately from a center-of-beam point, but the central section of most robust shape might be constant cross-section for some distance before tapering begins; shall we call such an imperfect spindle and still be very interested in such? I am opting to stay interested in imperfect spindled beams. Imperfect spindles may taper in steps rather than via a continuous function. Stepwise tapering can have just one step aside of central region or may have many steps; that is, tapering may not be smooth from center out to tip of beam. I opt to stay interested in imperfect spindled beams of imperfect non-smooth tapering. A beam in compression of homogeneous composition and cross section would tend to go out of column and tend to buckling at its center; thus having the central region beefed up (spindling, I offer) forms a focus for this discussion topic.
Motivations for the topic?
Keeping a safe frame for a HG, but perhaps lowering the weight of the HG is one motivation for the topic. Beams in compression and that may be experiencing some torsion are found in many HGs. But many HGs have beams that are not spindled.
Note that "taper" might apply to cross section taper or strength taper without cross-section taper as when a beam might be made up of segments of different materials.
Post what interest you as to doubly-tapered beams in HG?
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Some types of doubly-tapered beams:
Have a homogenous beam, say as a hollow tube; stuff a plug that is snug to the interior of the beam; have the plus be, say 1/4 of the length of the beam. Have the plug's center-of-length be position to the center-of-length of the parent beam. Call the marriage a composite beam; that beam is with a stepwise taper and results in a doubly-tapered beam, albeit an imperfect one. May we accept stepwise imperfect doubly-tapered beams into the family for HG frame constructions! Such a beam is with a non-tapering exterior appearance, but the mechanical fact is that there lives in that beam a kind of tapering. Exterior wraps of CFRP of a homogenous parent non-tapered beam can judiciously result in a tapered composite beam. Shape tapering while having constant mass/unit length? Say a beam is constructed so that the outside diameter tapers while the wall thickness increases for a resultant that any section of 1 cm weighs the same as any other 1-cm segment of the beam. Constant mass/unit length, but tapering shape. Why have such a beam? I am not clear of HG purpose of this sort of beam; perhaps someone could discuss this matter. Perimeter of the beam stays constant without taper, but have tapering of mass/unit-of-length taper from central region outward. This kind of beam may be difficult to manufacture. But maybe someone knows of doable ways to make such. Perhaps use a female mold of constant station semi-perimeter for half of the beam; lay material in a tapered fashion in that mold. tMake two halves and bold those two halves together. Surely there are other ways; but the labor might not be worth it. Explore? Such a beam appears non-tapered, but is tapered from central region to tips. Take two sticks of even shape and density. Overlap the two sticks using up, say, 1/4 of their lengths for the overlapping. Firmly bind such overlap. The longer compound stick is then stepwise tapered. Take two one-way tapered beams and overlap them with some portion of their lengths, say 1/4 of their lengths. The overlap region would have a constant format while taper occurs toward the tip for the remainder of the beam. The result is an imperfect tapered beam with a step on either side of the overlap region. Other methods of getting double-tapered beams are invited. And study over the effects and assets of using such beams is welcomed.
The rate of taper in doubly-tapered beams may important in some HG designing. Linear rate or non-linear rate? Maybe a function describes the tapering. This article might speak things useful for this topic: https://www.nature.com/articles/s41598- ... rigin=ppub
