I have found free software (GRAPE - Graphic Real-Time Analysis Programs for Engineering) that may turn out to be very useful for the ATM...and in this example I'm learning to push the envelope of this software.

My telescope will use a fork with monocoque construction...a 'shell' of material that serves as a load bearing structure. Based on the size of my telescope tube, and balance point...I know how long to make the fork arms...but what profile should they have? Constant width/thickness, or tapered? Can GRAPE help us make a decision?

When wind acts on the telescope tube, the fork arms will be under loads that make them behave as cantilevered beams. GRAPE can model cantilevered beams as a single element, but what if we want to 'peer inside' at the distribution and level of stresses all throughout the beam? Can GRAPE help in this area? It can if you model the monocoque structure as a truss. Then GRAPE will show you loads at each element of this truss.

Let's start with a truss that simulates a constant width/thickness monocoque structure, and lets put load on the free end so that it behaves like a cantilevered beam. As the diagram shows, the greatest loads are only in a few elements at the very bottom of the structure. Much of the rest of the structure is lightly loaded. In a manner of speaking you could say this is 'inefficient' because only a small portion of the structure is under high load. (But at least it's easy to predict where the structure will fail if load gets too high.)

Here is a more complex truss (with a round cross section) that again models a constant width/thickness monocoque structure, with a similar load/constraint setup as the above diagram. We again see that the highest loads are at the base of the structure and load level tapers off steadily, the farther one gets from the base. Is there a more 'efficient' structure to handle this load? Perhaps a tapered cross section?

Here is a tapered cross section. Much more of the structure is under high load, so one could say this is a more 'efficient' design to handle this particular type of load as a cantilevered structure.

But what if the above structures are subjected to a moment/twisting load...so that they behave as a shaft instead of a cantilevered beam? How will the tapered cross section compare to the constant width structure?

The constant width structure has equally high loads throughout the entire structure.

Same for the circular cross section structure.

But the tapered cross section structure has the highest loads in only a small portion of the structure. It appears tapered cross sections are not a good choice if you must deal with moments/twisting forces.

When designing your telescope, it is important to identify and analyze all forces that will act on your various components. Only then can you begin to choose proper shapes and arrangements of your load bearing structures.

These analyses were not very demanding of GRAPE. Analysis of all nodes and elements took less than 20 seconds on my 800Mhz Pentium.

All feedback is encouraged!

email: t-k-r-a-j-c-i-@-s-a-n-.-o-s-d-.-m-i-l (remove the dashes)

Last update: 30 Dec 2002