First, lets gather some specifications on the required material, balsa wood. The compression strength of balsa in the direction of its grain is about (2750000 N/m^2 (400 psi) (according to test results from
Balsawood Structure Design). The density of dry balsa wood is from 100 to 200 kg/m^3 (source: wikipedia article “Balsa”[/url]). For this discussion, I’ll use the worst case density of 200 kg/m^3, or .2 g/cm^3.
There are 2 basic ways to approach this problem: begin with your maximum allowed mass, and design a structure that can support the greatest weight, or begin with the target weight, and design a structure with the lowest mass that will support it. I’ll follow the first approach.
Your tower must mass less than 20 g. Mass / density = volume, so its max volume (of material) is 20 g / (.2 g/cm^3) = 100 cm^3. It must be be 21 cm (8”) tall, so its maximum cross-section is about 4.75 cm^3. Force = pressure * area, so the maximum weight it can bear is about 1300 Newtons (292 pounds).
So, the design target of supporting 100 pounds seems achievable.
The structure has to do more than withstand a vertical compression force – it must withstand lateral and torsional (tipping and twisting) force. Lots of possibilities exist that can do this – the simplest, IMHO, a rectangular box 5 cm by 5 cm by 21 cm tall, closed at top and bottom (inside, not on top of, to allow the balsa to bear the weight in the direction of its grain of its walls, not crushing against the grain of the top and bottom pieces).
Normally, I’d leave the calculations to evolllracer, but as the assignment was due 3 days ago, will do them myself. Keeping the 6 pieces the same thickness, their total area is (21*5)*4 +(5*5)*2 = 470 cm^2, with a thickness of about 2 to 4 mm, depending on the actual density of the balsa. Its weight-bearing cross section will be 5 to 10 cm^2, so it should be able to support between at least 1375 and 2750 N (309 to 618 pounds).
I’m curious to know how the various balsa tower projects turned out – this one, and the one in the older
”How to build a wood tower”.
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