DAMS 



81 



The resisting moment due to the weight of the structure is 

 figured as in the previous case, except that the weight of the water 

 should also be considered. The factor of safety, S, is found from 

 the same formula as before, i.e., 



~_WXdi 

 PXdk' 



It is also a common method to ascertain if the design is safe 

 by completing the pressure diagram, as in Fig. 35. The two 

 forces P and W are scaled off from the intersection point X, and 

 if their resultant PI falls 

 inside the middle third of 

 the base, the dam will 

 safely withstand the over- 

 turning moment. 



It is, however, not suffi- 

 cient to determine the over- 

 turning moment for the full 

 cross-section about the toe. 

 It must be figured for sev- 

 eral sections such as a, b, c, 

 d; a, b, e, /, etc., Fig. 35, 

 and the calculations must 



FIG. 35. Graphical 

 Safety of Gravity 

 method). 



Determination of 

 Dams (Middle-third 



show that every part of the 

 structure is sufficiently thick 

 to withstand the pressure. 



Besides the above there are other stresses which must be given 

 due consideration, such as ice thrust, uplift caused by seepage 

 waters and internal stresses due to varying temperature condi- 

 tions. 



According to Mr. A. C. Beardsley, masonry dam design should 

 be governed by the following rules: 



1. Design the crest and apron so that vacuums cannot form. 



2. Underdrain the dam to eliminate all uplift. 



3. Design the toe of the dam so there will be no uncertainty 

 as to the exact location of the tipping edge. 



4. Allow for the effect of floating due to tail-water. 



5. Allow for ice expansion and use the maximum crushing 

 strength of ice instead of average values. 



6. Take care of expansion and contraction stresses. 



