COLUMNS AND STRUCTURES 



267 



is longer than the end and it is desired to proportion the ends and 

 sides of the footing in the same ratio the following procedure is 

 adopted. 



Let L - the long side, 

 6 = the short side, 

 A - the area of the footing in square feet. 



Then j- - a, which is the ratio of the length and breadth of the 



column area and of the area of the footing, that is, 

 L -= ab, 



Having obtained the length and breadth of the footing it is 

 assumed that there are four cantilever beams projecting from 



Fig. 173 The Design of Column Footings 



the column. Each has a width at one end equal to the width of 

 the column base and a width at the other end equal to the length 

 of the side. The beams are thus wedge shaped with the maxi- 

 mum moment at the narrow end. Each beam carries one-fourth 

 of the total load. For convenience the beam may be considered 

 to be divided into four strips, as shown in Fig. 173. 



Referring to the figure and assuming that in this case one- 

 fourth the load is carried on each beam, then the beam ajfe carries 



W 



Each strip carries a part of this load in proportion to the 



area of the strip. The strips may be of equal width, as shown, 

 or they may be varied in order to have equal loads on the strips. 



