Tie-rods with Lateral Loads. 279 



section. The elliptic section is not so good as the rectangular, 

 and the I section is better than either. 



II. A uniform straight tie-rod has a lateral total load W 

 uniformly distributed. The resultant of pulling forces 

 at the ends is F 1 and passes exactly through the centres 

 of the ends ; (8) becomes 



d~y F T M }Wl 7T ,_ 



t/=i- lyP-WcOS^. . . (2D) 



dx EF"~ ' EI EI °2/ 



Using n 2 for ^, 



JWZcos —jX 



M 4 " "wo fc »i 



y=lfo-+N<~ --^ I+ -— * . (26) 



Applying the conditions y = when x = l, and -f- = Q when 

 # = 0, we find 



J "^^ ] B^|]' " * ( } 



If we suppose that no couples are applied at the ends, or 

 M =0, 



y= — ^- W 



This is identical with (18) if F^-F. So that in this 

 simple case we can use the same expression for the shape, 

 whether the bar is a strut or a tie-rod. 



In the case of a strut, 



im u f_ 



Z U-E + A->°' (iJ) 



iVU U F 



-Z-TTTE-i-A (o0) 



and by taking F in the expressions negative, we find f c and 

 ft in a tie-rod. 



