COLUMNS AND STRUCTURES 265 



for p is in pounds per square feet and o is in inches, so it is neces- 

 sary to reduce p to pounds per square inch. The load is uni- 

 formly distributed along the cantilever o = po, and the force 



acts through the center of gravity = The moment of resistance 



m 



sbt? 

 for a rectangular section = -^- but, since 6 = 1 (the unit width) 



the equation becomes 



M ,, po 8 sP 



Mb = M r = 5 - -T" 



oo 2 288 6 



Dividing, ^ = s(*. 



Multiplying, po 2 = 4SsP. 



48s<* 3 x 

 Dividing o 2 



P P 



/3s 



Extracting the square root, o = 4t I/ 



V p 



The assumption is made in this case that the projection, or 

 offset, is a cantilever with the maxi- w 



mum moment at the face of the /[ 



support. This is true in the case f" T ...... y ---- H 



of all stepped footings for walls. 

 When the wall is relatively thin, 



r *i t 



the projection of the footing being 



long, the maximum moment is as- 



sumed to be in the center of the Fi 8- 171 



footing under the center of the wall. Bendin in WaU Footin 



The formula for footings such as grillage beams and reinforced 



concrete, referring to Fig. 171, is 



The load is assumed to be uniformly distributed over the 

 pressed area. The formula may be derived in two ways. 

 First. Assume one-half the load to be carried on one project- 



ing end having a length - - - - y 



6 



Mk ,. E x y . wv. 



Mb 2 X 2 ^T 



Second. Assume the slab to be a freely supported beam with a 

 span length - L and loaded in the middle with a load II ' occupy- 

 ing a width a. 



