274 



PRACTICAL STRUCTURAL DESIGN 



distance x on the bottom of the footing should in all cases be not 

 more than ^ the base, to keep the average stress within one-half 



the maximum and insure that there is no tension, or uplift, on 

 the other side. This "middle third theory" is merely a state- 

 ment. Provided the maximum soil pressure is not greater than 



the allowable safe 

 pressure the re- 

 sultant can be 

 outside the middle 

 third. The state- 

 ment is frequently 

 made that when 

 the resultant 

 passes beyond the 

 middle third the 

 structure is in 

 danger of being 



Fig. 176 Eccentric Load on Column Bases 



overturned. The fact is that whenever the resultant of a hori- 

 zontal and a vertical force passes through a footing at any point 

 off center the overturning tendency is present. To be safe it is 

 necessary to see that no undue load is placed on the soil. The 

 "middle third" theory is a safe one to follow, but it should not 

 be followed blindly. 

 Let H = horizontal force, 



h = distance at which H acts above bottom of base, 

 W = vertical load on footing, 

 Hh 



then x = 



W 



Let 6 = length of base (that is, the dimension at right angle to 

 the force H, the dimension B being in the direction 

 of the force H). 



p = pressure on soil in pounds per sq. ft., all the dimensions 

 being expressed in feet and the weight and wind force 

 in pounds; 

 then, when the resultant falls within the middle third, 



W 



p = bB* (B 5X} ' 



When the resultant falls beyond the middle third 



2w 



P = 



36c 



