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Can anyone explain how this rod (experiencing shear stress and deflection) mysteriously resists the downward force from the weight of the mass?

Physics Asked by Stamati Angelides on March 11, 2021

This fascinating and, in my opinion, very unique question came out of a competition lab I did in a general engineering course. I will leave out or change info about the lab to make this question more understandable, but if you are interested in the real and more involved lab procedure, it is linked below. All you need to know is that we were tasked with constructing a boom that extended a horizontal distance of at least 1.5 meters from a given anchorage point (a small tube of 4" PVC). Masses would then be put into a bucket hanging from the end of the boom until it deflected more than 0.2 meters. The final score is found by dividing the total weight the boom was able to support by the weight of the boom itself.

Point of faliure

Assume the only materials provided were kevlar string and two 1.1 cm thick wooden rods cut to any length. I created a few potential designs, but the coolest and most promising was this one:

The design in question

Unfortunately, though, I was remote that day, so it was hard to communicate the idea to my in-person group members over zoom, and it was never implemented.

This longbow-like design preloads the beam with shear stress causing it to bend into an upwards pointing arc shape. The four kevlar strings are in tension and are tied off about 5 cm above the beam anchor. Trying to understand and describe this system with math breaks my brain. Where does the upwards force come from??? My most promising explanation is that the internal moments caused by the coupling of the beams internal compressive and tensile stress can be looked at as an infinite number of seesaws (or teeter-totters) and because the strings add compressive stress, they slightly "pull down" (aka compress) the right side of every seesaw, thus pushing up on the left side, causing the upwards force. This is probably incorrect, but even if it’s good, I have no idea what the math would look like. Can anyone help me? If you could show me how to calculate the design’s theoretical performance, I would be ecstatic, but even a small hint would be appreciated. Also, I am possibly completely wrong, and the system actually would just fall apart for some reason I haven’t discovered yet; I have no clue. I don’t mind if you use vague approximations of unknown values, for example, the elastic modulus of the beam, as I am way more interested in the theory than the actual prediction.

Link to real lab procedure: https://manual.eg.poly.edu/index.php/Boom_Construction_Competition

…Also, I apologize for the horrendous diagrams; believe it or not, they were made on mac preview.

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