276 FOUNDATIONS 



and the maximum pressure due to the bending moment, M = + Wb, 

 will be 



The pressure at A will be 

 and at B will be 



as shown in (c). 



Now if P! is made equal to P 2 the pressure at B will be zero and 

 at A will be twice the average pressure. Placing P x = P 2 in (84) and 

 solving for b, we have b = % /. This leads to the theory of the middle 

 third or kern of a section. If the point of application of the load never 

 falls outside of the middle third there will be no tension in the ma- 

 sonry or between the masonry and foundation, and the maximum com- 

 pression will never be more than twice the average shown in (a). 



If the point of application of the load falls outside the middle third 

 (b greater than % /) there will be tension at B, and the compres- 

 sion at A will be more than twice the average. But since neither the 

 masonry nor foundation can take tension, formulas (83) and (84) 

 will give erroneous results. 



In (d) Fig. 133, assume that b is greater than % I, and then as 

 above, the load W will pass through the center of pressures which will 

 vary from zero at the right to P at A. If 3 a is the length of the 

 foundation which is under pressure, then from the fundamental con- 

 dition for equilibrium for translation, summation vertical forces equals 

 zero, we will have 



W = y 2 P 3 a and 



P - 2Pf (85) 



Za 



