Tie-Rods with Lateral Loads. 283 



a stress of 1910 lb. per sq. inch and a bending-moment which 

 by itself would only produce a stress of 816 lb. per sq. inch, 

 if both act together, produce a stress of 23190 lb. per sq. inch. 

 In fact, the stress due to m alone is intensified more than 26 

 times. 



Similarly with an endlong thrust of 1400 lb. the stress due 

 to the lateral bending-moment m is intensified 11*04 times. 

 With an endlong thrust of 1000 lb. the stress due to m is 

 intensified 3*185 times. With an endlong thrust of 500 lb. 

 the stress due to m is intensified 1*58 times. 



It is obvious that in any strut the stress due to m, a lateral 

 bending-moment, is more and more intensified as F approaches 

 Euler's load U. And if mis due to an inaccuracy of loading, 

 h, the effect becomes four times as noticeable in struts of 

 half the length. 



From the above example one sees that it w T as quite possible 

 for a strong man like Samson to exert a sufficient lateral 

 force to produce fracture in the columns of the temple at Gaza. 



Professor Fuller's graphical method of dealing with a 

 metal arched rib is not applicable to struts unless we assume 

 ~Fy = 0, and this is of course a very wrong assumption. For 

 the same reason, the graphical method cannot be applied to 

 very flat arches, because it assumes that we know the shape 

 of the loaded arch. If Professor Fuller's method were 

 applicable, we could at once deal graphically with a strut of 

 varying section. This case does not usually need to be solved 

 in practice, but if it must be solved the following method 

 will do. 



1st. Assume that EI is constant and of its average value, 

 and obtain the shape of the strut as in (10). 



2nd. Use this value of y in the term ^y of (8) ; and use 



the proper value of I expressed as a function of #, and 

 then by mere integration of (8) find the more correct value 

 of y. 



By repeating this process we can obtain y more and more 

 accurately. 



Problem. 



When a strut is loaded laterally (say uniformly), say that it 

 is hinged at the ends ; it is possible by applying the endlong 

 thrust F untruly, that is making the resultant thrust pass 

 through a point h inches from the centre of each end, to give 

 such a value to h as will enable the strut to withstand a 

 maximum load F. In this case it is obvious that the greatest 



