Tie-Rods with Lateral Loads. 281 



deflexion of the unpulled beam, and not only reduces the 

 compressive stress to less than a quarter of its old amount, 

 but it has also reduced the tensile stress by nearly 20 per 

 cent. And a tensile load F x of 1348 lb. completely destroys 

 all compressive stress in the strut, whilst reducing the greatest 

 tensile stress of the unpulled strut by 15 per cent. 



In fact when a beam is very long, pulling out its ends may 

 reduce the compressive stress in it to nothing, whilst also 

 reducing the tensile stress. A longer or smaller beam than 

 that which I have taken will illustrate this matter even better. 



The tension F 2 which will make f t a minimum is 



W(T»)-». 



and when „ is so small as U then the unpulled beam itself 



has the minimum tensile stress. 



AWl 



If 7 is less than U it requires a pushing force F to give 



the minimum tensile stress. 



In all cases there is, of course, a pulling force F x which 

 will cause the beam to have no compressive stress in it. 

 In some cases there is a pushing force F which will cause 

 the beam to have no tensile stress in it, but this can only be 

 the case when 



TJ is not less than — ^. 



In this case, a beam to carry lateral load may be built up 

 of separate blocks of material which have just sufficient 

 friction to prevent slipping due to shearing forces at the 

 joints. It is a case which may be treated graphically by 

 Professor Fuller's Method, as the change of shape is small. 



It will be seen from the above simple example that very 

 instructive numerical problems may be given. Thus if, 

 instead of the lateral loading, we have merely couples, — M 

 or m, applied to the ends of a strut, we use W =■ in (17). 



When x-=0 we have the greatest value of y 1? or 





l cosl \/m ) 



F 



/ p,ns I a / 



EI 

 Also Fyi+~m=ft the greatest bending-moment in the strut, 



