Mechanical strength of a bamboo beam

I'm a student still, so take this with a pinch of salt.

The paper you've linked gives the info needed to make some basic calculations around max stresses etc.

Using 2m bamboo with 90mm diameter, assuming wall thickness of 10mm, and the values from the paper (airing on the lower side) of: E = 15.19GPa ShearMax = 20MPa BendMax = 74MPa (avg bending strength pg7) CompMax = 52MPa (Vertical (I'm assuming they mean perpendicular) to fibres) r = 45mm, t = 10mm I for thin hollow tube: pi * r3 * t = 2.86e-6m4

where M = moment Mr/I = maxStress so Mmax = maxStress * I / r = (74e6 * 2.86e-6) / 45e-3 = 4708Nm

Assuming a point load instead of distributed, and applied at the exact centre of the beam (1m from either support) then this implies that a force P of 4708N (at distance 1m) is the maximum force and hence bending stress you can apply before failure. So around 470kg.

The shear force within the bamboo should be 1/2*P (again point load calcs) so the applied shear force at 470kg is 2354N.

So shear stress = shear force / c-s area sStress = 2354 / pi * (45mm2 - 35mm2) = 0.94MPa So looks like shear stress is well within the 20MPa listed, so this would most likely fail due to bending first.

Also looks like at max moment of 4708Nm your deflection would be around 18.3mm.

However, I'm somewhat rusty on deformable solids etc, so probably should go back myself and start re-reading my lecture notes, but this is a pretty simple question, so I think I'm probably fairly safe :P

Also, of course, be warned, you should be assuming a Factor of Safety on all this, due to potential flaws in the bamboo and the fact that your loading will be distributed somewhat instead of point loaded etc etc. Also since the calcs assume constant mech properties when natural materials can have flaws as mentioned.

So basically I'd say safely assume FoS of 2, and hence, your max weight would be halfed, to around 235kg.

/r/AskEngineers Thread