PRESSURE OF PIER ON FOUNDATIONS 277 



Pressure of a Pier on Foundation. In Fig. 134, let W = resul- 

 tant of the stresses in the column and the weight of the pier, / = length, 

 c = depth and n = the breadth of the footing of the pier in feet. The 

 bending moment at the top of the pier is M = l / 2 H d and at the base 

 of the pier is M x = H ( l / 2 d + c). Now the pier must be designed 

 so the maximum pressure on the foundation due to W and the bending 

 moment M will not exceed the allowable pressure. The maximum 

 pressure on the foundation will be 



+ 



W 3 H (d -f 2 c) 

 = -Tn - b - ' 



It will be seen from (86) that a shallow pier with a long base is 

 most economical. 



To find the relations between / and c when the maximum pressure 

 is twice the average, place 



W = 3 H (d + 2 c ) 

 In n / 2 



and / = 3 H y 2 * (87) 



For any given conditions the value of / that will be a minimum 

 may be found by substituting in the second member of (87). 



To illustrate the method of calculating the size of a pier we will 

 calculate the pier required to fix the leeward column in Fig. 57. 



The sum of the stresses in column ^-17 is a minimum for dead 

 and wind load and will be (Table V) equal to 4800 + 45 = 

 9300 Ibs. 



Try a pier 3' o" x 3' o" on top, 6' o" x 6' o" on the base 

 and 6 feet deep, weighing about 16,700 Ibs. 



Substituting in (86) we have 



p ^ 26,000 ^ 3 X 4300 (14 -J- 12) 



36 6 X 36 



= 722 1553 



