FOUNDATIONS AND RETAINING WALLS 205 



where S denotes the section modulus. Equating the moment of 

 resistance to the external bending moment and solving the resulting 

 equation for S, we have in the first case 



F(l-c)* 



8O In 



and in the second case T> /*> \ 



- 



80 H 



In designing a column footing the column load P is first calculated, 

 and the area of the footing determined by dividing the column load 

 by the safe bearing power of the soil. The size of base plate and 

 number of beams supporting it are next assumed, and the section 

 modulus calculated by one of the above formulas. The size of beam to 

 be used is then determined by choosing from the tables a beam whose 

 section modulus agrees most closely with the calculated value of S. 



Problem 166. Design the footing for a column supporting a load of 400 tons, 

 and resting on a base plate 4 ft. square, so that the pressure on the foundation bed 

 shall not exceed 3 tons/ft. 2 . 



163. Maximum earth pressure against retaining walls. A wall 

 of concrete or masonry built to sustain a bank of earth, or other 

 loose material, is called a retaining wall 



In Chapter X it was shown that in order to determine the stability 

 of an arch three conditions were necessary, which might conveniently 

 be chosen as the direction, amount, and point of application of the 

 resultant pressure on any cross section of the arch ring. The same 

 necessity arises in the discussion of retaining walls, namely, that three 

 conditions are necessary for the complete solution of the problem, 

 and a number of theories have been advanced, notably those of 

 Coulomb, Weyrauch, and Eankine, based on different assumptions as 

 to these conditions. 



All theories, however, agree upon two of these assumptions, namely, 

 (1) that the pressure against the wall is due to a wedge of earth, or, 

 in other words, that the surface along which the earth tends to slide 

 ;i Lai nst the wall is a plane ; and (2) that the point of application of 

 the resultant earth pressure is one third of the height of the wall 

 from the bottom. Neither of these assumptions is rigorously correct, 

 f<r the first is equivalent to neglecting the cohesion of the earth, and 



