40 TIMBER. 



where W is the weight, I the length, b and d the breadth and depth of 

 the stick, and D the deflection for the load W. In the following table 

 the woods are grouped according to their stiffness. The figures are only 

 rough approximations which are based on the data given in Vol. IX of 

 the Tenth Census. The first column contains the above modulus, the 

 second shows how many pounds will produce a deflection of 1 inch in a 

 stick 1 by 1 by 12 inches, assuming that it could endure such bending 

 within the limits of elasticity, and the third column gives the number 

 of pounds which will bend a stick 2 by 2 inches and 10 feet long through 

 1 inch. 



The stick is assumed to rest on both ends ; if it is a cantilever, i. e., 

 fastened at one end and loaded at the other, it bears but half as much 

 load at its end for the same deflection. 



From the third column it is easy to find how many pounds would 

 bend a piece of the same kind of other dimensions. A 2 by 4 inch 

 bears eight, a 2 by 6 inch twenty-seven times as much as the 2 by 2 

 inch ; a piece 8 feet long is about twice as stiff as a 10-foot piece; a 

 piece 12 feet, only about three-fifths, 14 feet one-third, 16 feet two- 

 ninths, 18 feet one-sixth, and 20 feet one-eighth as stiff. 



The number of pounds which will bend any piece of sawed timber 

 by 1 inch may be found by using the formula: 



Necessaries™ 



where E is the figure in the first column, b, d, L breadth, depth, and 

 length of the timber in inches. If the deflection is not to exceed one- 

 half inch, only one-half the load, and if one-fourth inch, only one- fourth 

 the load, is x>ermissible. 



To allow for normal irregularities in the structure of wood itself, 

 as well as in the aggregate structure of timbers, an allowance is made 

 on the numbers which have been found by experiment; this allowance 

 is called the "factor of safety." Where the selection of the wood is 

 not very perfect, the load is a variable one, and the safety of human life 

 depends on the structure, the factor is usually taken quite high, as 

 much as 6 or 10, i. e., only one-sixth or one-tenth of the figures given 

 in the tables is considered safe, and the beam is made six to ten times 

 as heavy as the calculation requires. 



