288 PRACTICAL STRUCTURAL DESIGN 



The above expression is only approximate, as the entire expres- 

 sion is very complex. The result, however, is correct within 

 such a small per cent that it is safe to use it. The load on a verti- 

 cal strip one foot wide multiplied by the circumference in feet 

 gives the total vertical weight carried by the walls, the remainder 

 being carried by the bottom. The weight on the bottom is not 

 uniform, being in the form of an ellipsoid, the bending moment 



2 WD 2 

 for which will be M = ^ H = provided the attachment of the 



o / 



bottom to the sides is good. 



The curves may be used for round or square tanks. In a round 

 tank the pressure is that on a square foot on the circumference. 

 For square tanks it is the pressure per square foot of perimeter. 

 It may be used for rectangular tanks in which the length is not 

 more than 1.5 times the breadth by dividing 4 times the area of 

 the rectangular tank by the perimeter. This gives the diameter 

 of an equivalent circular tank, or the side of an equivalent square 

 tank, by means of which from Fig. 182 can be obtained the pres- 

 sure to use with the dimensions of the rectangular tank. 



Hoppered bottoms are used for bins as a rule but are somewhat 

 expensive when made of concrete, on account of the form work. 

 A common practice for bins having tunnels underground is to 

 make a flat bottom and pile cinders, or damp sand, on it with the 

 surface sloping towards the discharge hole. The surface is then 

 covered with concrete several inches thick, generally reinforced. 



The pressure against a retaining wall, and the overturning 

 moment, may be obtained by formula, using the constants for 

 equivalent fluid pressure. That method, however, is good only 

 for a wall retaining a fill level with the top of the wall. It is not 

 applicable to a surcharged wall, that is, one holding a fill which 

 extends above the top of and slopes to the wall. The graphical 

 method shown in Fig. 182 is a development of the Coulomb 

 theory of a "maximum wedge." According to this theory the 

 fill will not slip forward until the surface is steeper than the 

 natural angle of repose. When it starts to slip it breaks on a 

 line approximately halfway between the angle of repose and the 

 vertical, the wedge ahead of this line alone exerting an overturn- 

 ing pressure on the wall. 



In Fig. 183 the line AE represents the surface slope at the 

 angle of repose </>. The line El is the surface of the fill, the angle 



