OF IRON BEAMS. S^ 



mentioned, broke by weights in the middle; 

 the formula given above (art. 65) is therefore 

 for this consideration. But if the w^eights were 

 otherwise disposed, the beam would have to 

 be modified, and the formula adapted to it, as 

 in the following cases. — 



73. Suppose the weight to be applied to one 

 end, instead of the middle, and the beam fixed, 

 by its other end, in a horizontal position in 

 a wall. 'iw 



It may be easily shewn, (Venturoli's Mechanics, 

 vol. 2, article 651), that a beam, to be broke 

 by a weight in its middle, will bear four times 

 as much as another beam, of the same length 

 and section, to be broke by a weight at its 

 end. Now as the formula for the weight in the 



middle gave W = ^^ that for the weight at 



the end will give W = ^. Calling then the 



values of c (articles 70 and 71), 26 and 24, 

 and taking J of these numbers, we have, for the 

 strength W = ^L>LpL^^ or = ^ii^; accordmg 



as the beam was cast erect or on its side. The 



beam when the weight is at the end must, it 



is obvious, be turned the contrary way up that 



the larger rib, whose section is = a, may be 



the tensile one. 



3x2 



