200 STRENGTH OF MATERIALS 



theories of Rankine and Weisbach.* However, as several of the ele- 

 ments entering into the discussion are attended with considerable 

 uncertainty, it is customary in practice to use either an empirical 

 formula or the simple approximate formula deduced below, adopting 

 a factor of safety large enough to cover the assumptions made. 



Let P denote the weight of the hammer in pounds, li the height 

 of the fall in inches, R the average resistance of the soil to penetra- 

 tion during thft last blow in pounds, and d the penetration of the 

 pile, due to the last blow, in inches. Then, assuming that all the \v< .1 k 

 done by the hammer is expended in overcoming the resistance of the 

 earth at the point of the pile, we have 



Ph = Rd. 



With a factor of safety of 6, the approximate formula for safe load 

 on the pile becomes 



(104) * 



As the head of a timber pile becomes " broomed " by repeated blows, 

 and this greatly decreases the efficiency of the blow by absorbing tin* 

 kinetic energy of the hammer, the head should be sawed off to a solid 

 surface before making a test blow for determining the hearing power 

 of the pile. 



For a drop-hammer pile driver the empirical formula in n\<( 

 common use is 



(105) 



the notation being the same as above, and the factor of safety hein^ ;. 

 For a steam pile driver this formula becomes 



<*> 



where Ph represents the kinetic energy of the hammer. 



The above empirical formula, (105) or (106), is commonly known 

 as Wellington's formula, or the Engineering News formula, and has been 

 incorporated in the building laws of Greater New York. 



The only means of determining the bearing power of a pile dri\ en 

 by an hydraulic jet, is to observe the maximum load it can support 

 without appreciable settlement. 



* See Baker, Treatise on Masonry Construction, chap. xi. 



