210 



STRENGTH OF MATERIALS 



assumption that the pressure is normal to the back of the wall. Then 

 a __ o, a = 90, = 0, and formula (107) becomes 



. wh 2 , 2 

 PL, - -J- ^n 2 



45-- 



5. Rankine's formula for vertical wall Assume that the back of the 

 wall is vertical and that the line of action of the resultant earth 

 pressure is parallel to the surface of the earth. Then a = 

 f = 90 + /3 - a, and formula (107.) becomes 



wh 2 cos 2 a) 



2 cos 



I si 



sin (ft> 



sin (ft> - 



6. Maximum normal pressure. 



cos I 



Assume that has its maximum 

 value, which will be when 

 yS=G). Then Weyrauch's 

 formula becomes 



, wh* sin 2 (a CD) 



2 sin 8 a 



which is the greatest normal 

 thrust that can be caused by 

 a sloping bank. 



Problem 167. A wall 20 ft. 

 high is inclined at an angle of 85 

 to the horizontal and suppor 

 backing of clayey gravel the sur- 

 face of which makes an anu'le "f 

 20 with tin- horizontal. Compute 

 the maximum pressure against tin- 

 back of the wall by Weyrauch's and 

 Kankine's formulas, and compare 

 the results. 



Problem 168. By the i 

 Poncelet's formula compute the 

 maximum pressure in the preceding 

 problem if the back of the wall is 



vertical and the surface of the ground is horizontal. 



Problem 169. What is the greatest normal pressure that can be caused by a 



bank of loose sand against a vertical wall 18 ft. high ? 



164. Stability of retaining walls. The conditions for the stability 

 of a retaining wall are the same as those given in Article 147 for the 



FIG. 143 



