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National Advisory Committee for Aeronautics, Technical Notes - Applicability of Similarity Principles to Structural Models

Similarity principles fer guidance and interpreta—
tion of model tests in engineering frequently have been
based on the differential equations of the problem or on
more or less intuitive conceptions of what similarity
means, as, for example, in'fluid mechanics when similarity
is taken to mean that the ratios of inertia‘ viscous. and
gravity forces at corresponding points are the same, or
that the streamline patterns are geometrically similar.

It is now recognized however, that it is much more satis-
factory to apply the general dimensional analysis of E
Buckingham (reference 1) and P. W. Bridgman (reference 2).
This method has been thoroughly developed in general phys-
ice and fluid mechanics, but apparently not in structural
mechanics..

The question as to what is meant by structural sim-
ilarity frequently can be answered in a very simple manner.
But the complications implied by the use of several mate-
rials in a single structure. The use of models not made
of the same material as the prototype. buckling and
related behavior, plastic flow, thermal stress, and the
various combinations of theseI besides the problems of
fluid—structure combinations, as for instance in dams.
wind vibrations in suspension bridges, and flutter. re—
quire an analysis more comprehensive than immediate in-
tuitive notions can well supply. Such an analysis can
be as readily made, by the methods of Buckingham and
Bridgman, in solid mechanics. or for solid plus fluid
problems, as in fluid mechanics. Nanlinear problems,
buckling criterions, plastic flow, all can be dealt with,
although at first sight the lack of adequately defined
physical constants to characterize the inelastic prop~
erties of materials seems to put obstacles in the way of
dimensional analysis, with its primary requirement that
a list of symbols concerned be drawn up.