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XXXIX. Strength of the Thin-plate Beam, held at its Ends 

 and subject to a uniformly distributed Load (Special Case). 

 By B. C. Laws, B.Sc, A.R.C.Sc* 



IN steel floating structures, as e.g. floating docks and ships, 

 the shell plating supported at and rivetted to the 

 frames or girders of the vessel is subject to Irydrostatic 

 pressure ; and, if" we consider a section of the plate in a 

 direction perpendicular to the f mines, forms a case partaking 

 of the nature of a beam continuous over its supports and 

 •encastre — subject to a uniformly distributed load. 



The plating undergoes or tends to undergo distortion, and 

 its appearance between consecutive frames is somewhat as 

 indicated — but exaggerated for clearness — in fig. 1. In this 



Fig. 1. 



flute, Bea.m ft&h Uniformly Dz&nbiiled Load W 

 Per So/uire Mck. 



figure r and r Y denote the lines of rivets connecting the plate 

 to the frames F, F l5 which latter are assumed to form rigid 

 supports. The plating is deflected outwards between r 

 and s, and r x and s x : and inwards between the edges of 

 the supports s and s l5 retaining the normal condition tan- 

 genital to tha supports at r and r x , where it is obviously 

 subject to a pull or tensile force. It is the unknown value 

 of this force which increases the difficulty of the problem. 



In determining the thickness to be assigned to the plating, 

 it is customary to consider the problem as a simple encastre 

 beam of span something intermediate to ss 1 and n\. The 

 assumption is erroneous, and the only explanation for it is 

 that by its means the work of calculation is thereby very 

 much reduced, while the results obtained are considered to 

 be sufficiently near the truth for practical purposes. 



From the mathematical standpoint, the problem should be 

 approached as it is actually found to exist. The solution, 

 by a direct process of rigorous mathematics, leads to com- 

 plications due to the unknown conditions — of slope, force, 

 * Communicated by the Author. 



