STRESSES IN SHALLOW BINS. 



307 



STRESSES IN SHALLOW BINS, Graphic Solution. The graphic solution will be given 

 for two cases which frequently occur in prat 1 1 



Graphic Solution. Hopper Bin, Level Full. '-The calculation of Btresses in bin* by means 

 of graphics will be illustrated by the following problem taken from "The Design of Walls, Bins 

 and Grain Hk-vators." A cross-section of the bin shown in Fig. 7 is filled with coal weighing 58 

 Ib. per cu. ft., and having an angle of repose * - 30. The total pressure on the plane A-H is 



Pi - JwA 



I sin <t> 



- 3,130 Ib. 



I -j- sin <j> 



acting horizontally through a point 12 ft. below the top surface. Now, to find the pressure P t 

 on the plane G-A, produce PI until it intersects the line O - the weight of triangle AHG - 10,440 



J_ ^f Surface of t 

 _yi\~ $ i I Material-' 



'F~m?i 



$ ?* ^ 



f 



-Oaf a - 



Weiqh 1 of Coal Sdlbs. per ct/. ft. 

 Angle of Rtpoje #*50T 



FIG. 7. 



Ib. at 0, and by constructing O-i = P = 10,860 Ib. P is parallel to in Fig. 7. The normal 

 pressure on A-g is 9,900 Ib. Now A-i = 9,900 Ib. acts through the center of gravity of triangle 

 AG^, and is equal to the area of AG$ X w. The normal unit pressure at A is 733 Ib. per sq. ft., 

 and the normal unit pressure at B is 320 Ib. per sq. ft. The normal pressure on A B acts through 

 the center of gravity of the shaded area, and is N = 7,850 Ib. Also by construction E = 8,600 Ib. 

 The pressure on bottom A-F is equal to 18 X 58 = 1,044 Ib. per sq. ft. The pressure on the 

 wall C-B is 



I sin 



n i ., 

 PI = \w n* 



; : - 

 I + sin <t> 



620 Ib. 



Calculation of Stresses in Framework. The loads on the bin walls are carried by a transverse 

 framework as shown in Fig. 8, spaced 17 ft. o in. center to center. The loads at the joints act 

 parallel to the pressures as previously calculated, and the loads can be calculated in the same 

 manner as for a simple beam loaded with & similar loading. The stresses are calculated by graphic 

 resolution and by algebraic moments as shown in Fig. 8 and Fig. 9. 



Hopper Bin, Top Surface Heaped. The bin in Fig. 10 is heaped at the angle of repose, 

 ^ = 30. To calculate the pressure on side A-B, proceed as follows: Locate points G and H, 



* The calculations are made for a section of the bin one foot long. 



