42 TIMBER. 



develop the greater strength in bending. Like elasticity and stiffness, 

 the strength is expressed in a uniform manner by the so-called "modu- 

 lus of rupture," to permit ready estimation of the strength of any 

 given piece. This modulus refers to the resistance which the parts 

 most strained, "the extreme fiber," offer. For reasons above stated 

 in practice a factor of safety is employed, as in all these calculations 

 of resistance. The figures usually tabulated are obtained by the 

 formula : 



Strength of extreme fiber = _, -,„ 



where W is the breaking load, I the length, b and d the breadth and 

 depth of the tested piece of wood. 



The following table presents our common woods grouped as to then- 

 strength in bending. The loud, as before, is supposed to act altogether 

 in the middle. Column 1 gives the strength of the extreme fiber, as 

 explained above; column 2, tl\e number of pounds which will break a 

 piece 1 by 1 inch and 12 inches long, and column 3, the strength of a 

 stick 2 by 2 inches and 10 feet long, from which the strength of any 

 given piece can readily be estimated, allowing, however, for defects, 

 which increase with the size. Thus, if a good piece of pine 2 by 2 inches 

 and 10 feet long breaks with 400 pounds, a 2 by 4 inch set on edge 

 requires 1,000 pounds, a 2 by G inch, 3,600 pounds, a 2 by 8 inch piece 

 6,400 pounds to break it. If a piece 2 by 4 inches and 10 feet long 

 breaks with 1,000 pounds, a 2 by 4 inch and 12 feet long piece breaks 

 with about 1,300 pounds, one 16 feet with 1,000 pounds, etc., and if a 

 factor of safety of 10 is allowed, only one-tenth of the above loads are 

 permissible. 



A board one-half inch by 12 inches and 10 feet long contains as much 

 wood as a 2 by 3 inch of the same length, and if placed edgewise should 

 offer four times as much resistance to breaking. Owing to its small 

 breadth, however, it '"twists" when loaded, and in most cases, there- 

 fore, bears less than the 2 by 3 inch. To prevent this twisting, joists 

 are braced, and the depth of timbers is made not to exceed four times 

 their thickness. 



Short deep pieces shear out or split before their strength in bending 

 can fully be called into play. 





