U8 THE IMPROVEMENT OF RIVERS. 



Let A BCD (Fig. i) represent the section of a river wall; a width of top; b - 

 width of base; h - height; // - head of water; d distance from top of wall to 

 water; w weight of masonry per cubic foot. 



The weight \V of the wall per running foot is 



+ (i, _ ) * I H* / j_ t,) 



If the lower pool is supposed to act, with loss of weight by immersion, the weight 

 of the wall will be reduced by the area of the submerged portion multiplied by 62} Ibs. 

 The pressure P on the vertical face per running foot is 



H H* 



// X - X 62* Ibs. = - - X 62* Ibs. 



2 2 



The factor of safety is found by dividing the moments of the resisting forces by 

 the moments of the overturning forces, taken about the point of rotation. Thus the 

 factor is 



WXEC 

 PXFC 



H* 

 If P act on the sloping face BC, its value will be secX62^ Ibs., and moments 



will be taken about D. The factor of safety should be not less than 2.5, and is usually 

 made larger. 



The calculation may be made graphically by drawing the forces and finding the 

 position of the resultant R. Its direction should be such that it will cut the base-line 

 at a distance from the edge never less than one-fifth of CD, and the best practice 

 requires that it should fall within the middle third, in accordance with the well-known 

 rule for walls supporting pressure. In certain cases this will show a factor of safety 

 greater than 2.5. 



The width of the base can of course be increased by offsets, if found necessary. 



Where there is likely to be much difference between the pools when the lock is 

 "drowned out," as mentioned in the calculation for lock-gates, it may be needful to 

 examine the upper section of the wall, to see if it has mass enough to resist the head. 

 An increase, however, will be rarely, if ever, required if the coping is of the usual width. 



Land Wall of Chamber. This portion of the lock walls is usually calculated for 

 two conditions, one with the upper pool filling the chamber, the lower pool drawn off, and 

 no filling behind the wall, and the other with the pressure of filling behind the wall 

 and no water in the chamber a condition which occurs when the pit is pumped out for 

 repairs. For the latter case it is usual to assume a full lower pool pressing behind the 

 wall, so as to be secure against the most unfavorable circumstances. If the section 

 fonnd necessary for this is as large as that given to the river wall, calculation for Uu- 



