A Treatise On The Principles And Practice Of Dock Engineering

REACTION OF THE SILL. 317 be justifiable to assume that the line of action of the force passed through the centre of the meeting faces, and, in practice, it must inevitably happen that the gates are the veriest trifle too long or too short, in either of which cases the gates will nip one another ; if too long, on the inner edge, and if too short, on the outer edge, of the mitre-post (fig. 255). Nipping may also be due to the accidental intrusion of some small floating substance, such as a chip of wood. Under these circumstances, the line of action would pass near to the inner or outer edge of the mitre-post. For the present, how- ever, the assumption will be made that it bisects the meeting surfaces. 3. If friction be left out of account, the Reaction of the Hollow Quoins will pass through the centre of the heel-post, and further (the three forces being in equilibrium), through the point of intersection of the other two forces, and these two points are sufficient to determine its line of action. When the gates, however, are just closed, and during the period in which the parts are taking up their respective stresses, there is some inévitable,, albeit almost infinitesimal, yielding of the wooden heel-post, and a corre- sponding movement along the face of the rigid masonry, which brings into play a frictional force, R tan p, where R is the thrust on the heel-post and p the angle of repose of wood on stone. If r be the radius of the heel-post, the reaction of the hollow quoin will accordingly pass at a distance, rsin p, from its centre. The deviation is generally slight, and, unless the thrust be very great, its effect may be ignored. 4. The Reaction of the Sill upon the lowermost horizontal member of the gate is frequently overlooked, but that it is capable of affording no inconsiderable assistance to a gate under pressure is manifest from the fact that it is quite theoretically possible to con- struct a gate deriving its entire support from the sill alone. This will be apparent from a glance at fig. 252, in which the top of the sill coincides with the centre of gravity of the water pressure against the gate. The latter, accordingly, is in critical equilibrium, which the least in- crease in its depth below the sill renders stable. The inconvenience, however—if not the impracticability—of providing so deep a sill, with a perfectly watertight joint, constitutes an insuperable objection to such an ar- rangement. The reaction of an ordinary shallow sill is not altogether easy to determine, but it may be considered in two ways. It may be deemed to raise the level of the centre of pressure, though, in this respect, its effect is scarcely appréciable. It may also be taken as exerting a moment about the top edge of the sill, contrary to and partially counteracting the moment due to the water pressure above the sill. This latter, however, would only be a legitimate aspect of the problem, provided