48 NOTES ON DOCKS AND DOCK CONSTRUCTION. 



the centre line of the passage found as before, and g any point on 

 the back of the gate. 



Join C g, g e, and gf-, draw h i perpendicular to, and bisecting g e, 

 and cutting AD in h ; also draw h Jc, cutting C g in M. Then will 

 h k be perpendicular to the line C gr, and will be in the direction of B, 

 the resultant of all the forces acting on the heel-post side of any 

 vertical section passing through g. It has already been said that the 

 magnitude of B is proportional l to the length of the line C g. The 

 resultant of the forces acting on the mitre-post side of the section is 

 equal in magnitude but opposite in direction. 



By taking a sufficient number of points, g, g l t 2 , g 3 , etc., and 

 proceeding as above, a number of points m, m 1 , ra a , ra 3 , etc., can be 

 obtained, in which the respective resultants cut the lines C 0, C g\ 

 g 3 , etc. Then joining the points A ra, ra 1 , ra 2 , m 8 , B, a line will 



be obtained passing through 

 the points A B, which may 

 be termed the line of posi- 

 tion of resultants. 



Distribution of Mate- 

 rial. 2 In designing a dock 

 gate, it is often convenient, 

 as a guide to the distribution 

 of material, to divide the 

 vertical section into layers 

 sustaining equal pressures. 

 The following method of 

 doing this may be useful. 

 If the sill is not submerged, draw A B (Fig. 364), representing a 

 vertical section of the gate, and at right angles to A B draw A a 

 representing the highest water level, B C representing the level of the 

 sill ; make B C = A B and join A C. 



Mark off the points, 1, 2, 3, 4, ... ra 1, dividing the line A C 

 into the required number of equal parts. On A C describe the semi- 

 circle ADC and from points 1, 2, 3, 4, ... ra 1, draw lines 

 perpendicular to A C, cutting the semicircle A D C in d 1 , d 2 , d 3 , d 4 , etc. ; 

 then with centre A describe the arcs d 1 , c 1 , d 2 , c a , d 8 , c 8 , d 4 , c 4 , etc., cutting 

 A C in c 1 , c a , c 8 , c 4 , etc. Parallel to B C draw the horizontal lines c 1 , b l , 

 c a , 6 a , c 8 , Z> 8 , c 4 , fc 4 , etc. These lines will divide A B in the required 

 manner ; that is to say, if the total pressure on A B = P, the pressure 



P 



on each of the parts A6 1 , b\ b\ l\ b\ 6 3 , 6 4 , etc. = ; m being 



number of parts into which A C is divided. 



FIG. 364. 



th 



R = pxC</; ^^(D'-d*). 



M.P.I.C.E., vol. Iviii. p. 205. 



