CHAPTER VIII. 

 STEEL BINS. 



Stresses in Bin Walls. The problem of the calculation of pressures on bin walls is similar 

 to the problem of the calculation of pressures on retaining walls; but in the case of bin walls the 

 material is limited in extent and the condition of static equilibrium is disturbed by drawing the 

 material from the bottom of the bin. For plane bin walls where the plane of rupture cuts the 

 free surface of the material (shallow bins), the formulas developed for retaining walls are directly 

 applicable if friction on the wall is considered. The graphic solution will be found the simplest 

 and most direct for any particular case. The following analyses of the calculations of stresses in 

 bins have been abstracted from the author's "The Design of Walls, Bins and Grain Elevators," 

 second edition. 



STRESSES IN SHALLOW BINS. The problem of the calculation of the pressures on 

 bin walls is the same as the problem of the calculation of pressures on retaining walls. The forces 

 acting on bin walls depend upon the weight, angle of repose, moisture, etc., of the material, which 

 are variable factors, but are less variable than for the filling of retaining walls. 



Algebraic Solution. The same nomenclature will be used as in retaining walls except that P' 

 will be used to indicate the pressure obtained by means of Cain's formulas when z = $', N' will 

 indicate the normal component of P', and N will indicate the normal pressure on the wall when 

 <f>' = o. This analysis applies to shallow bins, only.* 



Case i. Vertical Wall, Surface Level. Angle z = </>'. Fig. i. 



D/ _ .. L COS 1 * 



(,) 



N' = P'-COS*' (2) 



If </>' = <t> 



P' = jw ft* COS * (3) 



JV' = P'-cos0 (4) 



_ 



II/L 



^ x 



FIG. i. 



If <(>' = o, which corresponds to a smooth wall, 



N - iw-A'.tan' (45 - */*) (5) 



* A shallow bin is one where the plane of rupture cuts the free surface of the filling. 



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