3I8 DOCK ENGINEERING.
the gate were constructed mainly or altogether of verticals, for the joints
between successive tiers of horizontal ribs are not, and cannot be supposed,
capable of resisting transverse stress. In the absence of such joints, it is
justifiable to state that the pressure on the watertight surface of the sill is
sufficient to counterbalance, at least, the pressure on an equal height of
the unsupported portion of the gate immediately above the sill. The
case is that of a cantilever, the moiety of whose length is unsupported
and loaded with a weight something less than the weight on the sup-
ported half. In flat gates of the vertical type, the sill plays a most
important part, supporting, as will be seen later, two-thirds of the total
water pressure upon the gate.
So much for the horizontal forces. The vertical forces are two in
number :—
1. The dead weight of the gate, acting downwards through its centre
of gravity.
2. The upward reaction, due either separately or jointly to (a) flotation
of buoyancy chambers or the water pressure on the underside of the gate,
(6) truckwheels or rollers bearing upon a platform, and (c) inclined straps
connected with the top of the heel-post.
We need not consider these at greater length. Obviously, equilibrium
can be secured by a suitable adjustment of the opposing forces. We pro-
ceed to deal with the more complex problem presented by the horizontal
forces.
To find the Resultant Pressure on any Section of a Gate.
Fig. 253 represents the plan of one leaf of a pair of gates. Pis the total
water pressure upon the back of the leaf, assumed concentrated at its centre.
Rj is the mitre reaction of the adjoining leaf, taken as passing through the
centre line of the abutting surfaces. R2 is the reaction of the hollow quoin