COLUMNS AND STRUCTURES 285 



Cement Association, and have been printed in booklets and 

 >ever:ii periodical* 



These curves were computed by the Janssen formula and 

 checked with other curves and tables. The pressures are for 

 walls of concrete. For walls of steel multiply by 1.20 and for 

 walls of wood multiply by 0.95. 



When the depth of a tank is less than the diameter the surface 

 of the slope of repose of the material will pass through the top 

 without intersecting the opposite wall. The pressure in such 

 a case is similar to that exerted by a fluid and the expression for 

 pressure at any depth is 



P = md, 

 in which m = a constant, 



d = depth in feet, 



P = pressure in pounds per square foot. 



The constant m for water is 31.25, no matter how deep the tank 

 or what its diameter. The constants for common materials are 

 shown in Fig. 182. They represent one-half the weight of an 

 equivalent fluid, that is a fluid which at any depth exerts the 

 same pressure as the material considered. 



When granular materials are confined in deep bins the opposite 

 sides come into play as soon as the depth exceeds the diameter. 

 The friction of the material against the walls causes the walls to 

 carry some of the load, whereas with a fluid the pressure is always 

 normal to the surface pressed. For deep bins the pressure at 

 any depth in a bin or tank may be read directly from the curves. 



When the depth of the bin is less than the diameter the total 

 pressure against a vertical strip one foot wide is 



H - Md 2 , 

 in which // = total horizontal pressure. 



The overturning moment M = H x ;r 



o 



The foregoing formulas are used to design square and rect- 

 angular tanks and bins, and retaining walls, holding water or 

 granular dry materials. 



In a circular tank the horizontal pressure is coverted into 

 tension in tin- circumference. 



T - W x f . 

 in which 7' circumferential tension in a strip one foot deep, 



