212 



STRENGTH OF MATERIALS 



In order for a wall to fail by overturning, it must either rotate 

 about the outer edge of the base or, in the case of a masonry wall, 

 open at one of the joints. The cause of failure in both cases is the 

 same, namely, that the stress on the base or joint is partly tensile. 

 Consequently, the criterion for stability again>t "\n turning is that 

 the resultant R must strike within the middle third of the base or 

 joint, as the case may be (cf. Articles 62, 140, 2, and 147). 



This criterion can best be applied graphically. Thus having assumed 

 a value for the angle ?, the resultant earth pressure P 1 is calculated 

 from the formula in Article 163, corresponding to this assumption 

 of , and combined with the weight of the wall into a single result- 

 ant R. If this resultant does not strike within the middle third of 

 the base, or within the middle third of all the joints in the case 

 of a masonry wall, the design must be altered until the criterion is 

 satisfied. 



165. Thickness of retaining walls. In designing a retaining wall 

 economy of material is secured by making the base of such thirl, 

 that the resultant R, obtained by combining the weight of the \\all 

 P 2 with the maximum earth pressure P r , shall fall at the outer edge 

 of the middle third. However, theoretical formulas for determining 

 the least thickness consistent with this condition are too complicated 

 to be of practical value, and for this reason the design is usually based 

 on an empirical formula. 



In railroad practice Trautwine recommends that for vertical walls 

 of rectangular cross section, supporting loose sand, gravel, or earth 



