178 



CONCENTRATED LOADS ON BLOCKS. 



Art. 109. 



and s ma x. increases. When tension is possible, e may of course 

 exceed M> //., but when it is not, the maximum eccentricity is 

 limited by the strength of the material. If no tension were pos- 

 sible and e could be made equal to y 2 h> 5 max would be infinite. 



A case quite similar to the above may be illustrated by 

 means of a bridge pier (Fig. 136) having a horizontal force act- 

 ing near its top. The horizontal 

 load of 70,000 Ibs. is equivalent to 

 a force of 70,000 Ibs. acting at g 

 and a couple whose moment is 

 70,000X26=1,820,000 ft. Ibs. The 

 couple produces a uniformly vary- 

 ing pressure upon the foundation 

 and the vertical loads a uniform 

 pressure, so that equation (45) is 

 applicable. 



P = 100,000+420,000 



A~ 6X26 



1,820,000X13 



7OOOO JL 7000O 



=3330 



Pressure along 06=2690+ Fig. 136. 



3330=6020 Ibs. per sq. ft. Pressure along cd=3330 2690=640 

 Ibs. per sq ft. 



In equation (45) /= C v-dA is the measure of the cross 



section's resistance to turning about the neutral axis. If it is 

 assumed that the entire area is concentrated in a single point, 

 then 



I=Ar* (46) 



in which r is the distance from the axis to the point at which 

 the area would have to be concentrated in order to have the same 

 moment of inertia as the actual moment of inertia ; r is called the 

 radius of gyration. 



Substituting this value of 7 in equation (45) 



(45a) 



(47) 



is a reduced working unit stress in compression depending 



