334 Rural Architecture. 



Similarly, by substituting numerical values in the case 

 of the 2x8 joist we get 



8X10,000X2 = WX10, 

 or 16X10, 000 = 10W, 

 and W = 16, 000. 



It thus appears that the loads the two joists will carry are 

 to each other as 4,000 is to 16,000, or as 1 is to 4; but 

 squaring the vertical thickness of the two joists in ques- 

 tion we get, for the 2x4 joist 



4 X 4 = 16, 



and for the 2 X 8 joist 



8 X 8 = 64; 



but 16 is to 64 as 1 is to 4, which shows that the transverse 

 strengths of similar timbers are proportional to the squares 

 of their vertical diameters. 



406. The Transverse Strength of Materials Diminishes Di- 

 rectly as the Length Increases. It will be readily seen from 

 an inspection of Fig. 145, that lengthening the pieces of 

 joists, while the other dimensions remain the same, 

 lengthens the long arm of the lever, while the short arm re- 

 mains unchanged; and since the force of cohesion remains 

 unaltered, the load necessary to overcome it must be less in 

 proportion as the lever arm upon which it acts is increased. 

 Thus, if the 2x8 in Fig. 145 is made 20 inches long, we 

 shall have, 



A = wx WA 



and by substituting the numerical values we get 



80,000X2 = WX20 

 W = 8,000 



instead of 16,000, as found in (405). 



