REPEATED STRESSES. 321 



Other parts of structures, again, are exposed to stresses 

 which are constantly being taken on and off, such as in 

 the tie-bars of bridges and pillars whose loads are inter- 

 mittent. In these, so long as the imposed loads do not 

 give rise to stresses which are at any time beyond the 

 elastic limit of the material, the time during which these 

 structures will safely withstand their loads is practically 

 unlimited. 



The same is true of a third class of structures which 

 are subjected not only to repeated loads, but, at the same 

 time, to loads which are constantly being reversed in 

 direction. An example of such a case is to be found in an 

 ordinary clock spring, which has to withstand many 

 millions of reversals of stress every year, and yet is to 

 all intents and purposes unaffected after the lapse of 

 many years. Here is an almost perfectly elastic material 

 in which the stresses never approach a limit of the 

 elasticity. 



As, however, the stresses become greater in magnitude, 

 and, in the case of reversed stresses, the range of stress 

 increases, the number of repetitions or the number of 

 reversals required to produce failure diminishes. For 

 instance, it has been shown that a bar of Krupp axle 

 steel, subjected to a repeated stress of 15"29 tons per square 

 inch, requires 274,970 repetitions of the stress to cause 

 failure, whereas, under a stress of 23 '89 tons per square 

 inch, 23,546 repetitions will be sufficient to fracture 

 the bar. 



169. Wbhler's and Spandenberg's Experiments. By 



far the most important and exhaustive researches into this 

 subject were made for the Prussian Government, by Herr 

 Wb'hler, between 1859 and 1871, and afterwards continued 

 with the same apparatus by Prof. Spandenberg, his 

 successor. 



Four series of experiments were carried out as follow : 



(a) Repeated Stresses in Torsion. For this purpose 

 a cylindrical bar with enlarged ends was employed. One 

 of its ends was held in a gripping device controlled by 

 springs, and the other was attached to one end of a 

 rocking lever, which was driven by mechanical power, 

 and whose angular movement was controlled so as to 

 keep it within certain limits. In this way the maximum 



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