COLUMNS AND STRUCTURES 287 



amount equal to n times the area of concrete in the face of the 

 crack, times the average unit stress. If the crack extends through 

 the wall the steel carries all the tension. 



All granular materials have an angle of repose, which is as 

 follows: Sand, 25 to 30, gravel and broken stone, 30 to 40; 

 ashes, 25 to 30; coal, 30 to 45; grain 28. The angle of 

 repose is generally designated in formulas by <j>. 



The factor k fixes the ratio of lateral to vertical pressure and 

 according to the theory of the ellipse of stress, 



, _ 1 gin <fr 

 = 1 + sin <f> 



It has been determined experimentally for several materials 

 and has a value of 0.6 for grain. 



The weight carried on the bottom of any bin is the total weight 

 of the material, minus the weight carried by the walls. The 

 foundations are designed under the walls by taking the total 

 weight transferred to the walls, plus the weight of the walls, plus 

 wind force. If columns and girders are used under the floor of 

 the bin, part of the weight on the bottom is carried to the walls 

 as reaction. 



Materials have an angle of repose which is an angle of slope 

 assumed by the surface of the material when piled. There is 

 also an angle of friction, the tangent of which is known as the 

 coefficient of friction. The coefficient of friction of the grains 

 of material on each other is the factor k. The coefficient of fric- 

 tion of the material against a surface confining it is determined 

 experimentally, and the factor C in Fig. 182 is the coefficient of 

 friction of the various materials against concrete. In determin- 

 ing the weight carried by the walls it is necessary to consider 

 fcandC. 



The weight carried by the wall on a strip one foot wide for 

 any depth is, approximately, 



in which w - weight of material per cubic foot, 



R - hydraulic radius - : in feet. 

 perimeter 



h - depth of bin in feet, 



k - ratio of lateral to vertical pressure, 



C - coefficient of friction. 



