510 



BRIDGE. 



Theory. 



PLATE 

 LXXXI. 

 Fig. 5. 



the length of that arm of the lever, whereby the 

 weight of the whole resists the effect of the horizon- 

 tal thrust oversetting it. 



Instead, therefore, of building up the pier with 

 perpendicular sides, we should think it more advisa- 

 ble to begin the foundation of the pier on a base 

 much wider than usual, and from thence, by regular 

 recesses, or otherwise, gradually to diminish it, until, at 

 the springing of the arch, it does not exceed the depth 

 of the two archstones, while the outline of the pier 

 may be a curve of any shape that is most pleasing. 

 Many advantages would, in our opinion, be obtained 

 by this construction : the water way will be enlarged ; 

 the pier equally strong ; the stability equally great, 

 nay, much greater than usual ; and the chance of the 

 foundations being hurt in floods will be greatly di- 

 minished : and all this with a smaller quantity of ma- 

 terials. 



Before we take leave of the stability of piers, it 

 will be proper to request the reader's attention a 

 little longer to a case which we have hitherto but 

 slightly noticed, we mean when the waters come to en- 

 croach on the crown of the arch. In this event, the 

 stability arising from the arch is diminished by the 

 loss of weight in all that part which is immersed. 

 The horizontal force acts as before ; it will be pro- 

 pagated through the immersed archstones. The 

 weight of the pier is diminished by the immersion. 

 All this must be compensated by an increase of 

 breadth in the pier. 



Suppose the waters to rise to the key-stone, the 

 horizontal thruet is still unaltered, and is propagated 

 as before ; the intermediate archstones, however, 

 lose two-fifths of their weight, and, supposing them 

 jointed to equilibration, they will all have a tendency 

 to rise and slide up. This is particularly the case with 

 the lower stones of an arch with radial joints, for we 

 know that these have such a tendency independent 

 of this. What therefore is there to prevent them ? 

 Their mutual friction, and the back or lateral pres- 

 sure only. Their friction, however, is now much di- 

 minished, and so is the weight of the backing, on 

 account of the immersion. 



In drawing the limit of position for the joints to 

 be equilibrated by friction, therefore, in Fig. 5. we 

 ought to diminish the lengths on the line, the key 

 section only excepted, and observe the effect on the 

 position of the joints ; the general effect will be, to 

 make these joints approach nearer to the vertical, or, 

 in other words, to draw them to lower centres ; and, 

 if we are so inclined to admit of the arches being 

 flatter segments, this observation is of use, and should 

 be attended to in the formation of culverts, &c. 

 which are often glutted. 



Suppose, now, the waters to rise even higher than 

 the keystone, the weight of the keystone itself be- 

 ing diminished, the arch will be in the very same pre- 

 dicament as if it were formed entirely of materials of 

 a smaller specific gravity than before, and its chief 

 danger will arise from the transverse action of the 

 stream tending to overset it. 



This will be the case when the water, having free 

 ingress through the materials, or through the gut- 

 ters of the bridge, rises as fast in the interior of the 

 "building as without. But this is not always to be 



expected. The side walls, or parapet, may be so Tli 

 formed, as not to admit the water to enter, at least \ 

 not with sufficient rapidity. The arch itself, we are 

 sure, will not, for it is all laid in mortar. Now, in 

 the event of the arch being formed with open work 

 in the haunches, it will not, we think, be going too 

 far to say, that there may be a point to which, if 

 the waters arrive, the whole weight of the arch may 

 be balanced by the hydrostatic pressure upon the in- 

 trados ; and in that case, it would be shoved off in 

 one mass by the pressure of the stream. 



This is by no means even an improbable supposi- 

 tion, for the key-stone itself will begin to move 

 whenever the waters rise one and a half times its 

 thickness above the solid matter at the crown ; and it 

 will readily be granted, that every other section is 

 pressing strongly upwards by that time. It may, in- 

 deed, be alleged, that the pressure of dead weight 

 over them would keep them down long after that, 

 and this we do not deny ; but the derangement which 

 it is likely will have taken place among the lower 

 stones, by such a pressure acting from the points of 

 the wedges, will, in all probability, be such as to 

 render the destruction of the arch inevitable. 



For example, take a stone of a foot sqii-tre, and 

 4 feet deep in the soffit, near the springing of an 

 arch of 40 feet rise ; suppose the arch full, this stone 

 is pressed back with the weight of !() cubic feet of 

 water ; that is, a force of four times its own weight, 

 and as a similar force, though gradually lessening, 

 acts upon every other stone to the crown of the arch; 

 it is, we think, very obvious, that their united effect 

 is likely to be of much more consequence than the 

 thrust of the archstones. 



But we may find another opportunity for render- 

 ing these motions somewhat more precise, by sub- 

 jecting the forces to calculation, when we come to 

 treat of CULVERTS, under INLAND Nm-i^ation, the 

 chief case where such a process is likely to occur ; and 

 which, from that circumstance, require some peculiar 

 maxims of construction. 



OF THE FALL UNDER BIUDGES. 



The piers of a bridge form an obstacle in the way Of i 

 of the waters, and will cause them to rise above the u d 

 general level. The same body of water which flows ""* 

 in the open channel must be conveyed through the 

 openings of the bridge. The narrower that passage 

 is, the swifter must be the current. And this addi- 

 tional swiftness is only to be produced by a descent 

 from a greater height. Consequently, the water 

 will accumulate above the obstruction, until it runs 

 off as fast as it comes, or until the velocity in the 

 contracted water-way be to that in the open channel, 

 reciprocally as the relative sections of the stream. 



Granting that the velocities of the running water 

 are such as would be produced by falling from a cer- 

 tain height above the stream, a principle which is at 

 any rate sufficiently just for our purpose, it follows 

 that the fall, or accumulation produced by the ob- 

 stacle, will be measured by the difference between 

 the heights which would be requisite for producing 

 the two velocities, viz. of the river in general, and 



