A Treatise On The Principles And Practice Of Dock Engineering

4 324 DOCK ENGINEERING. The results form a series of co-ordinates from which the curve in fig. 259 has been plotted. The line A B constitutes the span, and along it have been marked off distances corresponding to the ratio of rise to span. Brom an inspection of the figure we see that the resultant pressure is least with a ratio of J, and that it increases in amount with any change from this ratio. The increment is comparatively small as the value of v approaches unity, but, as it approaches zero, the rate of increase is very rapid, becoming ultimately infinite. With a rise equal to A span, the excess over the minimum is inconsiderable, and thence to a rise of |, it is but moderate, but for rises beyond |, the value of the coefficient becomes excessive. In conjunction with the question of the total amount of stress, it must be borne in mind that the pressure between the gate framing has to be taken by metal plating and wood planking, as the case may be, and that there is a practical limit to their effective and useful résistance. Fig. 259. Taking everything into considération—design, material, permissible stress, contingencies of manufacture—no definite rule can be laid down beyond the statement of the usual range already given. Analysis of the Resultant Pressure. —Having obtained an expression for the resultant pressure on the cross-section of a gate, we now proceed to consider it with reference to its point of application. The simplest, and theoretically ideal, gate would be that in which the line of pressure passed through the centre of gravity of successive cross- sections. In this way the joints would simply be called upon to sustain direct compression, uncomplicated by any bending moment. It has been pointed out that this does not necessarily imply that the back and front of the gate would be circular arcs concentric with the line of pressure. A straight gate might be constructed to fulfil the required condition by a suitable adjustment of the material, so that the centre of gravity of each section fell upon the line of pressure. In most cases, however, practical considérations cause the axis of the gate to deviate more or less from the ideal curve. Fig. 260 is the plan of a portion of a gate leaf, A A being the longi- tudinal axis — i.e., the line passing through the centres of gravity of successive sections—and LM a line perpendicular thereto.