Treehouse Engineering - Analysis

Analysis-
Quantitative Analysis: Don't Fear the Numbers……

It can be instructive to examine things from a qualitative perspective, where ratio and proportion are often sufficient tools to create robust solutions. For thousands of years very large structures were constructed without any rigorous knowledge of the relationship between imposed forces and the stresses they create. One might argue that such an approach is sufficient for the construction of tree houses since it can be very difficult to accurately determine their inherent load/stress relationships. In this discussion, however, we are going to make an effort to identify useful numerical solutions to the real world problems presented by the engineering, design and construction of tree houses.
To put things in perspective we will first review material that may seem unnecessary to many readers. Some high school students may have mastered Newtonian Physics and Mathematics, but the typical math skills expected at this level can be summarized by the following:
Now let us examine Newtonian Physics and Mathematics in a little more detail. When Isaac Newton was twenty ? years old, the plague had once again swept through England and, among other things, had forced his classes at Cambridge University to be cancelled. Confined to the family estate, and in a state of utter boredom, he noticed that the suns ray's diffracted into their component colors against the wall of the closet after passing through a narrow slit created by the partially open door. What rational explanation was there for his observation? Numerous additional observations produced quite a group of questions needing answers. He soon realized that the mathematics of the time did not provide the tools necessary to solve his growing list of unanswered questions.
Newton created the Method of Fluctions so that he could adequately explain these mysteries. Today, known as Integral and Differential Calculus, this invention is used throughout the technical and scientific world. Newton was up against an unusual obstacle: the Inquisition and the Hierarchy behind it. He kept his solutions to himself for another twenty years?, and only published after spending a great deal of time deciding exactly how to phrase every word so that he would literally escape torture and death. Examples…
With these analysis techniques and the fields of math and physics that flowed from them out in the open, others would bravely expand on his work over the next hundred or so ?? years, allowing a firmly rooted scientific and mathematical underpinning for the technological explosion that followed in the nineteenth and twentieth centuries. It is worth pondering the magnitude of Newton's gifts to the world as they account for 99.999% of all physical behavior, while Einstein, Plank, Heisinburg etc together offer you an understanding of only part of remaining 0.0001%. Needless to say, in this discussion, based as it is in the natural and real world, is entirely based upon Isaac Newton's comprehension of the physical world.
REVIEW of Newtonian Mechanics, and Calculus.
The Scientific Method can be paraphrased as (1) hypothesis, (2) experimental and/or theoretical testing of the hypothesis, and (3) writing a paper that very few people can understand, much less question, so that your filtered hypothesis appears to remain intact. If you are a pioneer, others will build upon your "verified hypothesis" and at some point it will become truth, or even the extension of truth that best not be challenged: scientific dogma.
We should not be too hard on our fellow scientists, since their careers, their reputations, their bread and butter and their steak and eggs, depend upon their ability to walk that narrow ledge between established scientific dogma and some precious new piece of the puzzle that does not fit into the wall of dogma. This precisely describes the state of scientific inquiry at the time of Newton and makes his willingness to shake the establishment all the more remarkable. Today's scientists may not face death for their ideas, but challenging the status quo remains a daunting task, and can often mark the end of their careers.
Engineering, on the other hand, as it is based almost entirely on Newton's discoveries, has the additional luxury of not having to precisely describe why something works when it is sufficient to simply state that it does work. Empiricism rules. Of course, if we are going to insist on numerical solutions that mean something in the real world, we had better have some tricks up our sleeves to tie up the loose ends between that which may be adequately described by existing scientific knowledge, and that which may only be described by interpolating or extrapolating experimental observations.
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Wood with horizontal shear, bulk shear, compression along the grain, across the grain, bending, sudden loads, slow loads, MOE, modulus of rupture, USFS tests, density,
Wood: Wanted, Dead or Alive. Differences. Useful behavior of living systems. Bolster. Group protections. Geiger - Climate near the ground.
Finally: Trees stand up by Euler where Le/D is… and by experimental observation by JB Johnson's formula wich provide a more accurate description of experimental observations, typically where Le/D is …
Theory of Elasticity
Hyperelastic stretching (nuclear bombs)
Combination of Compression and Bending: Codes don't look at the case where…
Metallurgy, Alchemy, treated wood, corrosion, compartmentalize, encapsulate, Explain the Theory of Elasticity, Mohr's Circle, and how it follows that FEA works and how combined stresses mean anything. And back to experimental observations.
Suggested solutions to mystrees. The micro load cell, the tension test calibrates sail behavior, do some of them and publish??
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