LOCKS. 153 



Also, 



H* 1 + e 



The angle which T makes with a normal to the axis of the lock will be found 

 equal to 20, the angle itself being usually made about 20. 



At E resolve T into two forces, one acting along the wall, the other at right angles 

 to it. The former equals 



H 2 

 T sin 2 = (I + e) X 62$ Ibs. = X. 



As it is supported by the chamber wall it need not be further considered. The force 

 at right angles equals 



Tcos 2a = -~ L ^ X 62$ Ibs. = 5. 

 2 tan 2 a. 



TT 



It acts at a distance above the point of measurement for H equal to , and combined 



J 



with the weight of the wall W will give us the factor of safety, which may be found 

 and checked as shown for the river wall. The width of base MN may be taken as 

 being the same as the width of the base of the wall behind the gate recess, and the 

 center of gravity of the mass ABCD as passing through the center line of this base. 

 This will simplify the calculations, and the error resulting will be on the side of safety. 



The total length of wall which is assumed to act as a monolith in resisting the 

 force 5 should not be over 30 feet. If this provides an insufficient mass, the base width 

 should be increased. 



The calculations for the lower end of the wall are similar to the foregoing, but in 

 this case the force P must be combined with T' to give the resultant horizontal pres- 

 sure V. The shortest way will be to do this graphically, and V can then be resolved 

 into a transverse force 5' and a longitudinal force X'. Combining 5' with W we 

 can find the position of R' as before, and combining X' with W we can find the posi- 

 tion of the resultant of the longitudinal component, which must of course fall within 

 FGHJ at a distance from HJ sufficient to avoid undue pressure on the masonry and 

 the foundations. This component, as will be readily seen, cannot be neglected as 

 was X, since there is no chamber wall below to support it. 



The strains on the head- and tail-bay walls on the land side are the same as those 

 on the river wall, and the masses are usually made the same, or slightly less. The 

 earth pressure is, of course, an element of safety, as it opposes the thrust of the gates, 

 and if it is desired to take it into account, the forces can be combined as in the pre- 

 ceding calculations. 



If the walls are of concrete, which is usually built up in blocks with vertical 



