Thinking about mechanics of our airship’s keel it is actually one of the most trivial tasks to solve. We’ll be looking to calculate reactions, shear force and bending moment here and then to test it.
Our use-case takes in account our 6-meter-long beam, having two supports in its thirds, where traversing beams will be joined to hold our gondola. Gondola weight is assumed to be ~10kg (100N) and we’ll multiply it by safety factor of 3 getting 300N. Let’s divide this value by four – number of joints – getting 75N per support. To be able to solve this in some easy way, we need to double this value getting nice 150N force in a middle.
So let’s go with bit of theoretical calculations on this first. The easiest way to do this these days is to use e.g. Free Online Beam Calculator, which I like a lot as it is making this task trivial.
|2||0 kN||0.075 kN||0 kN-m|
|4||0 kN||0.075 kN||0 kN-m|
|Bending Moment||0.075 kN-m||0 kN-m|
|Shear||0.075 kN||-0.075 kN|
|Displacement||0.037 mm||-0.013 mm|
Nothing too much to see yet, so let’s have a look at bending moment and sheer forces
The last one is the deflection, which (if we would provide actual tube properties) would finally provide us with a some actual values to test for. Graph below uses Young’s Modulus (E) 200000 MPa, which is clearly too high for our use-case, but as we don’t have any good value here we’ll be using it for demonstration.
|Location (m)||Total Deflection (mm)||Span|
Now to our actual testing – two chairs serve as a support there, supporting our tube in its thirds. Pillows and cloth in the middle serves to distribute forces bit around so those are not “too pointy”. Below you can see a set of weights totaling 15kg provided by Andrew.
Tube #1 (950g)
Long story short all holding! A minor tube bending’s been noticed, but overall whole tube seemed to be very firm and stable.
Tube #2 (850g)
Again – all holding! 15kg load and tube seems to be stable. Even on the final picture you can’t see any bending whatsoever there.
As you can see Jan being happy – whole this exercise ended up with a huge success, making whole team confident that our tubes will perform well with a 3-fold safety margin.
As always, ping us back with whatever comments and congratulations to the whole team for excellent work!