FO UNDA TIONS. 



"To deduce a formula for the relation between these 

 quantities, 



let /*= the pressure in tons per square foot at the bottom of 



the footing-course under consideration ; 

 R = the modulus of rupture of the material in pounds per 



square inch ; 

 p = the greatest possible projection of the footing-course 



in inches; 

 / = the thickness of the footing-course in inches. 



" The part of the footing-course that projects beyond the 

 one above it is a cantilever beam uniformly loaded. From 

 the principles of the resistance of materials we know that the 

 upward pressure of the earth against the part that projects 

 multiplied by one-half of the length of the projection is equal 

 to the continued product of one-sixth of the modulus of rup- 

 ture of the material, the breadth of the footing-course, and 

 the square of the thickness. Expressing this relation in the 

 above nomenclature and reducing, we get the formula 



/ ~R 

 = *\/ 4I ?' or with sufficient accuracy, / = 



ft/?' 



This represents a theoretical maximum set-off for the masonry 

 courses, but in practice, as has been explained, it is usual to 

 reduce this theoretical maximum allowance by a suitable fac- 

 tor of safety, and, in this particular, a factor of safety of 5 to 

 IO is customary and considered a safe practice. 



In addition to the forces acting upon the foundation-soil, 

 the material of which the actual substructure will consist 

 adds its weight to the other forces as pressure upon the sub- 

 foundations, and therefore a general knowledge of the weight 

 of different varieties of masonry is necessary. On the following 

 page will be found a table giving the approximate weights of 



