Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-06T05:08:27.043Z Has data issue: false hasContentIssue false

Theorems for the Synthesis of Simply-Stiff Frameworks

Published online by Cambridge University Press:  28 July 2016

Extract

Systematic knowledge of the theorems available for building statically determinate frameworks appears to be restricted in this country to a very small circle. Many engineers are content with the knowledge that a simply-stiff plane framework can be produced by attaching a joint O by bars OA, OB. to joints A and B of a simply-stiff plane framework; and that a simply-stiff space framework can be produced by attaching a joint O by bars OA, OB, OC to joints A, B and C of a simply-stiff space framework. By these simple means, two- and threedimensional simply-stiff frameworks can be built up respectively from the basic triangle and basic tetrahedron.

Most textbooks give no other rules of synthesis, and are content to give as “ proofs ” of the relationships existing between the number of joints j and the number of bars m of a simply-stiff framework (m = 2j—3 in the two-dimensional case and m=3j—6 in the three-dimensional case) the obvious inferences of these relationships from the system of synthesis just described.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society 1945

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Roxbee Cox, H. Proc. London Math. Soc. (2), 40 (1936), 203-216.CrossRefGoogle Scholar
2. Pollaczek-Geiringer, H. Zeitschrift fur angewandte Math., 12 (1932), 369-376.CrossRefGoogle Scholar
3. Roxbee Cox, H. Jour. London Math. Soc., 18 (1943), 20-23.CrossRefGoogle Scholar
4. Clerk Maxwell, J. Trans. Roy. Soc. of Edinburgh, XXVI (1870). Also Collected Papers XXXIX.Google Scholar