From: "Roy Diffrient" 
To: "ATM" 
Reply-To: "Roy Diffrient" 


Tom, I think you're on the right track in using the FEA software to analyze
your truss ideas.  I  have only these few points.
- Unless I missed something, there seems to be no allowance for the weight
of the truss itself in your examples.  Depending on the tubing used, the
truss might be as heavy as the load for some of those designs.  If there is
no way to model that in the software, I'd suggest adding a total of half
the calculated truss weight distributed to the total load you have shown,
since the CG of all the trusses is apparently at midpoint (the other half
of the truss weight is considered to be at the supported end of the truss,
where it doesn't cause deflection).  Adding in this parameter could very
well skew your initial results.  It really comes down to stiffness versus
weight.
- I didn't see the standard truss listed in the results table, but the
deflection for that design can be easily calculated, and that could be a
good check on the FEA software, setup, etc.  The deflection is calculated
by the formula W L^3 / (c^2 A E), where W = load (plus half the truss
weight, as above), L = truss member length, c = base spacing between
members, A = cross sectional area of the material in a member, and E =
elasticity modulus (for steel, 30 million psi).
- Those apparently useless members of the typical 8-element truss form a
parallelogram linkage which nicely keeps the upper end parallel to the
primary for all deflections.  The purpose of the truss, after all, is to
hold the optics in collimation.
- For trusses where all sides and elements are equal, like all those shown
on your site, the deflection will not vary as the truss is rotated around
the optical axis.  The deflection of each side due to tension/compression
does change depending on the rotation angle, but the vector sum of the
deflections remains the same, just as the total load remains the same
regardless of rotational changes in tension/compression force vectors in
the truss elements.
- Don't forget Mark Serrurier's original reason for using his truss design
on the Hale telescope: It was not because it was stiff enough (it wasn't).
It was (in part) because the two ends of the tube assembly could be
designed to have equal deflection.  Deflection of the bottom end could thus
cancel out the deflection of the top end.  There's no reason that principle
can't also be applied to your design, especially if you plan to use a truss
on both ends.  So there's more to it than just truss stiffness.  Don't get
me wrong - improvement of truss design and stiffness is a noble goal, and
our trusses might well be improved or optimized using FEA.  But so far, it
looks like you're only modeling half of the tube assembly.

My $.02 worth.  Hope it helps.

Roy Diffrient
Monkton, MD
USA

--- BBBS/NT v4.00 MP