GRAPHIC METHOD. 



If t in (5) is made equal to , and 8 made equal to 90, 



COS*0 



/sill 10 -f d.-MH (0 - A,V 



\" co*' J 



(8) 



which is Rankine's formula (2) in another form. 

 If 2 in (5) is made equal to zero, 



sin 1 (8 - 0) 



(9) 



which gives the normal pressure on a wall. 

 If in (9) = 90, 



If 6 in (10) - 0, 



/ i I sin 0- sin (0 -g)\* 

 \ V cos 5 / 



P = Jwft* 



(i -f sin #)* ' 

 tan 2 (45 - ij 

 I sin <b 



do) 



(II) 



(12) 



which is Rankine's formula (i) for a vertical wall without surcharge. 



Graphic Method. If the angle 2, the angle between the back of the wall and a normal to 

 the wall, is known, the resultant pressure on a wall may be calculated by a graphic method. 

 Fig. 5, based on the "theory of a wedge of maximum thrust." The graphic method will be 

 described the proof of the method is given in "The Design of Walls, Bins and Grain Elevators." 



FIG. 5. 



In Fig. 5 the retaining wall AB sustains the pressure of the filling with a surcharge i and 

 an angle of repose <f>. It is required to calculate the resultant pressure P. 



The graphic solution is as follows: Through B in Fig. 5 draw BM making an angle with BF, 

 the normal to AD, equal to X = + x 90, the angle that P makes with the horizontal. With 



