CHAPTER VIII 



FLAT PLATES 



115. Theory of flat plates. The analysis of stress in flat plates is, 

 at present, the most unsatisfactory part of the strength of materials. 

 Although flat plates are of frequent occurrence in engineering con- 

 structions, as, for example, in manhole covers, cylinder ends, floor 

 panels, etc., no general theory of such plates has as yet been given. 

 Each form of plate is treated by a special method, which, in most 

 cases, is based upon an arbitrary assumption as to the dangerous 

 section, or the reactions of the supports, and therefore leads to 

 questionable results. 



Although the present theory of flat plates is plainly inadequate, 

 it is, nevertheless, of value in pointing out the conditions to which 

 such plates are subject, and furnishing a rational basis for the esti- 

 mation of their sin-Mirth. The formulas derived in the following 

 raphs, if used in this way, with a clear understanding of their 

 approximate nature, will be found to be invaluable in designing, or 

 determining the strength of flat plates. 



The following has come to be the standard method of treatment, 

 and is rhi.'tlv due to Bach.* 



116. Maximum stress in homogeneous circular plate under uni- 

 form load. Consider a flat, circular plate of homogeneous material, 

 which bears a uniform load of amount w per unit of area, and suppose 

 that the edge of the plate rests freely on a circular rim slightly 

 smaller than the plate, every point of the rim being maintained at 

 the same level. The strain in this case is greater than if the plate 

 was fixed at the edges, and, consequently, the formula deduced will 

 give the maximum stress in all cases. 



* For an approximate method of solution see article by S. E. Slocum entitled "The 

 Sfn-n^th of Flat Plates, with an Application to Concrete-Steel Floor Panels," Engineer- 

 ing News, July 7, 1904. 



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