https://en.wikipedia.org/wiki/Serrurier_truss
Anthony Cook also posted a good message on another forum:
Your definition for a "Serrurier Truss" actually describes only half of the double parallelogram square tube invented by Mark U. Serrurier of Caltech in Pasadena in 1935 as a way of controlling flexure in the tube of the 200-inch (5m) telescope that he helped to design. The idea was that a square section at the tube at its center of gravity (where the declination axis is attached) would also be where the bases of 8 triangular trusses (one on each side of the box) would be attached. The apex of each triangle would be attached to the end rings of the tube, one end carrying the mirror and cell and the other the prime focus cage and secondary mirrors. Bending by gravity is resisted by its force in the plane of one pair of triangles, while the adjacent sides act something like a hinge, allowing any motion of the end rings to be of equal magnitude and in parallel, thus keeping the optical elements collimated in spite of flexure. In equatorial telescopes, these properties are shared by all parts of the tube as the telescope points at various parts of the sky.
Telescopes with the center of gravity close to the mirror have to compensate for the unequal lengths of the triangles by adjusting the tension of the trusses or the thickness of the tubes (or I beans) so that the shift (translation) of the tube rings perpendicular to the optical axis is equal.
Nearly every large telescope (with the exception of the Keck telescopes and the Hobby-Eberly telescope) have used this system since Palomar was finished in 1948 (including the BTA).
The triangular truss square tube used on most truss-Dobsonian telescopes do not have the property of parallel translation of the primary mirror (which does not translate) and the top tube ring (which does).
While the triangular truss is relatively strong, it does not have the important property of parallel translation, and it is not a Serrurier truss.
By the way, some telescopes (like the Kitt Peak 4m, the Very Large Telescope, Subaru, etc. may look at first like the "half Serrurier truss", in fact the mirror cells are attached to the end of small triangular trusses, or sometimes just straight beams to preserve the parallel translation of the ends of the tube. Sometimes these smaller trusses are enclosed in the structure containing both the declination axis and mirror cell, so they cannot be seen.
Perhaps the type us ATM's use should be called ‘Pseudo Serrurier’, ‘Semi Serrurier’ or ‘Half Serrurier’ or ’triangular’ Trusses.
Anthony Cook
Griffith Observatory
Astronomical Observer.