348 Proceedings of the Royal Society of Edinburgh. [Sess. 
XXV.— The Elastic Strength of Flat Plates: An Experimental 
Research. By W. J. Crawford, B.Sc., Mechanical Engineering 
Department, Municipal Technical Institute, Belfast. Communi- 
cated by Dr C. G. Knott, Secretary. 
(MS. received November 23, 1911. Bead January 22, 1912.) 
The question of the elastic strength of flat plates, supported or fixed at 
the edges, and subjected to uniform or concentrated loads upon their areas, 
is, from an engineering standpoint, one of the most unsatisfactory parts 
of mechanics; for exact solutions, rigorously based upon the laws of 
elasticity, have been obtained in only a few cases, chiefly for circular and 
elliptical forms. 
Amongst practical engineers the confusion that exists on the subject 
is remarkable, for the author has, in the course of his inquiries, elicited 
the most contrary results. As a case in point, there seems no real 
knowledge whether rectangular and square plates should be ribbed along 
the diagonals or across the diameters. Again, as an instance of the doubt 
existing concerning the stress values in these plates, it may be mentioned 
that, in reply to an inquiry asking for help in this connection, a correspondent 
in the American Machinist , under date August 7, 1909, deplores the fact 
that he can obtain no assistance from English or American text-books 
and states that there is an entire absence of experimental data. Although 
the latter statement is not quite accurate, yet it can be confidently asserted 
that there have been very few experimental results recorded, and these 
few, for the most part, are not available in English. 
Our ordinary scientific engineering books have very little to say about 
flat plates in general, and, in particular, with regard to square and 
rectangular plates practically nothing at all. The truth of the matter is, 
that the mathematics of the whole subject is beyond the domain of 
even the scientific engineer, and further, that even the most advanced 
mathematical research has been unsuccessful in completely solving all but 
the simplest cases. 
The whole problem of the deformation of a thin isotropic elastic plate 
under given forces has for very long been of great interest to mathe- 
maticians. The general equations were first established by Navier, and 
the problem was afterwards attacked by Lame, Sir William Thomson, de 
