232 



RETAINING WALLS. 



CHAP. V. 



The sum of the tensile stresses due to bending must equal the sum of the compressive stresses, 

 = $p 2 d. These stresses act as a couple through the centers of gravity of the stress triangles on 

 each side, and the resisting moment is 



M' = \p*-d'ld = 



(28) 



FIG. 7. 



FIG. 8. 



But the resisting movement equals the overturning moment, and 



and 



6F-b 



(29) 



The total stress on the foundation then is 



P = pi =*= pz = pi(i ="= 6bfd) (30) 



Now if b = \d, we will have 



p = 2pi, or o. 



In order therefore that there be no tension, or that the compression never exceed twice the 

 average stress, the resultant should never strike outside the middle third of the base. 



If the resultant strikes outside of the middle third of a wall in which the masonry can take 

 no tension, the load will all be taken by compression and can be calculated as follows: 



In Fig. 8 the resultant F will pass through the center of gravity of the stress diagram, and 

 will equal the area of the diagram. 



F = \p-a 

 and 



2F 



which gives a larger value of p than would be given if the masonry could take tension. 



General Principles of Design. The overturning moment of a masonry retaining wall of 

 gravity section depends upon the weight of the filling, the angle of internal friction of the filling, 

 the surcharge, and the height and shape of the wall. The resisting moment depends, upon the 



