OF IRON BEAMS. 411 



6. In order to estimate the strength of the 

 piece whose section is ACBD, if F and y repre- 

 sent the points at which the forces rising from 

 tension and compression being collected, would 

 produce the same effects as they do at their 

 respective distances from the neutral line : f will 

 be the fulcrum on which all the forces of tension 

 may be conceived as sustained, and ^ f one 

 arm of a bended lever, while the length G y is 

 the other, (the points F and G being supposed 

 to be connected by the chain F G, merely 

 to give the lever the appearance of greater 

 strength.) If, further, we call the forces sup- 

 posed then to be collected in F and /, F' and f 

 respectively, we shall have, for the equilibrium 

 in this case, these two equations, 



F'=r --- (I), 



W X 0/= F X F/ - . - - (2). 



Equation (1) assumes the sum of the forces 

 exerted by the extended fibres to be equal to 

 the sum of the forces from the compressed 

 ones, which is the case: for, the weight *W 

 acting in the direction G W, parallel to the 

 surface ACBD, can have no influence in 

 pushing the piece toward or drawing it from 

 the wall; and therefore the pressure on the 

 fulcrum / must be just equal to the resistanc« 

 from tension in F ; or in symbols F = /'. 



3F3 



