202 



STRENGTH OF MATERIALS 



above another. It is evident in this case that if the foundation is of 

 the same width throughout, the centers of pressure will fall outside 

 the centers of resistance, which will tend to throw the top of the wall 

 outward on either side, and so result in cracks between the openings 

 (Fig. 140). The remedy for this is either to narrow the foundation, 

 or omit it altogether under the openings, or else extend it beyond 



the ends of the wall, the length of 

 this extension being of such amount 

 that the centers of pressure will fall 

 inside, or at least coincide with, the 

 centers of resistance. 



When a foundation extends 

 beyond the ends of a \\ all the projec- 

 tion is called the footing. To dimen- 

 sion the footing it may be regarded 

 as a simple cantilever, and its 

 thickness calculated by the ordinary 

 theory of beams. Thus let // denote 

 the thickness of the footing in 

 inches for a concrete foundation, 

 or the thickness of the bottom 

 F ^ ing course in inches for a maso 



foundation, b the width of the i 



ing in inches, u the ultimate strength of the material in lh./in. 2 , and 

 P the load in tons/ft. 2 . Then, since 1 ton/ft.* = 13.9 lb./in. 2 , the 

 moment at the face of the wall is 



7,7.8 



or, since I = and n 



we have u = 



4l ' 7P 



whence 



= 6.45x 



, approximately. 



Problem 165. Find the thickness of the bottom footing course for a masonry 



foundation if the load is 1 ton/ft. 2, the factor of safety is lo. the fn..tj,,_ 

 extend 18 in. beyond the face of the wall, and is composed of limestone for whi.-h 

 u = 15,000 lb./in/-!. 



