324 STEEL GRAIN ELEVATORS. CHAP. IX. 



German Practice. Janssen's formula is given in Hutte Des Ingenieurs Taschenbuch, as 

 the standard formula for the design of grain bins. For wheat Janssen found that // = 0.3, and 

 k = 0.67, so that n'-k = 0.20. Using these values and changing to English units, we have for 

 wheat, 



V = HL* ( Z 

 0.2 v 

 or if d = diameter or side of bin, then 



V = \wd(i 



L = k-V 

 which is the German practice. 



Load on Bin Walls. The walls of a deep bin carry the greater part of the weight of the 

 contents of the bin. The total weight carried by the bin walls is equal to the total pressure, P, 

 of the grain on the bin walls, multiplied by the coefficient of friction fj.' of the grain on the bin 

 walls. 



From formula (8) the unit pressure on a unit at a depth y will be 



L = ~ (i - -*.f*'.y/*) (10) 



and the total lateral pressure for a depth y, per unit of length of the perimeter of the bin, will be 

 P = JJ L-dy = - (i - 

 w-R I" R R 



, ,p~l 



J 



Now the last term in (n) is very small and may be neglected for depths of more than two 

 diameters, and 



_ w-R f R "1 , N , . 



: ~" y ~ fcpp* *-) 



The total load per lineal foot carried by the side walls of the bin will be 



' = w-R y ~ ( a PP rox -) (13) 



For the total weight of grain carried by the side walls multiply (13) by the length of the cir- 

 cumference of the bin. 



Formulas (12) and (13) may be deduced as follows: The grain carried by the sides of the 

 bin will be equal to the total weight of grain in the bin minus the pressure on the bottom of the 

 bin. If P is the total side pressure on a section of the bin one unit long, then 



P-U'ii, 1 = w-A-y - A-V (a) 



= w-A-y - W ' A ' 



K" (J. 



and solving (6) 



= ~n~ L y ~ v J (approx - } 



and the total load carried on a section of the bin one unit long will be found by multiplying P in 

 (ii) by /i', and 



