1. Engineering
  2. Mechanical Engineering
  3. any help is greatly appreciated thank you...

Question: any help is greatly appreciated thank you...

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Elon Musk has announced that he will start building bikes, and has called you for advice. In a bike, one of the big problems is making the down tube- the big sloping tube at the front of the frame - as stiff as possible in torsion while using as little material as possible, to minimize weight. The tube will be thin-walled (meaning that the thickness is negligible compared to the width). but he wants to know what shape to use for the cross section. The critical parameter will be J/A, where Jtorsional constant and A cross sectional area of metal. a) Consider an n-sided regular polygonal shape, and derive an equation for J/A in terms of the distance across the flat sides (i.e. the inscribed diameter) and n. Evaluate it for a square tube (n-4) and a circular tube (n- ). b) Now consider a rectangular shape, where the sides are of length b and a b, where 0 < α < 1.0. Derive, and plot for 0 < α < 1.0, an equation forYu, where Jo 1s the torsional constant for a square tube. What is the most efficient shape? If several shapes are equally efficient from a torsional viewpoint, what other characteristies would you consider? Also comment on what you find in part (b). c)

Any help is greatly appreciated! Thank you!

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