Chap. VIII.
491
increase of power, both at the abutment and in the middle, to resist any force tending topress it out of the vertical plane. In estimating that part of the power which arises from theinertia of matter, we are to suppose the two halves quite unconnected at the middle of thewhole, and that each of the halves may be made to revolve about its adjoining abutmentin a vertical position, as about an axis. The inertia of each half will then be obtained bymultiplying its weight by the square of the distance of its centre of gyration from theabutment.
If the weight of the crown be 1, I find that the inertia of each half of the bridge willbe 9245488*995. If the weight over a portion of the arch, of the length of 10 feet, ad-joining to either abutment, be 340 tons, the inertia of each half of the bridge will be2G2146827-94741 tons.
Mr. J. Robeson .—What force will push the arch out of the vertical plane, the breadthbeing so considerable in proportion to the length, and the compression at the crown sogreat ? I cannot conceive any force as likely to occur which will put it in any danger.Kven the curved form of the sides is favourable to its strength in this particular, for, sup-posing it pressed from the west side, if the abutments at the east side at the corners do notyield, the whole of the eastern surface, being a concave, must resist as an arch, and althoughthis resistance is not well directed, and allows a twist, it is still considerable. The chiefrisk is from a ship’s mast-head striking the arch near the crown, but the chief risk will beto the ship. The mast-head or rigging, which will then be confusedly bundled about it,may catch, but the ship will be carried through by the current, and may very probablycant round with her broadside to the stream; in this situation, her mast being held fast, shewill very likely be heeled down, and take in water and fill.
As, independent of the curved form (horizontally) of the sides, a pressure of one sidetends to open the joints on the other ; this points out another advantage of the connectionby straps, in the manner practised at Wearmouth Bridge.
I cannot form a precise opinion of the effect of these oblique ribs, which appear in theplan, two on each side of the middle rib. They are intended for stiffening the bridgehorizontally, but I do not see them in the profile, and must therefore suppose them torange along with the other ribs, so as to be hid by them. I think that their effect wouldhave been twice as great, had they been twice as oblique or gone across from side to side.I observe that they are connected with the cross ties as they go along. If these cross tieswhich connect the different ribs are of cast-iron, I think that this connection with theoblique tie-ribs exposes them to a great risk of snapping. For the obliquity of these tiesoccasions the strain of compression to be considerably different, both in magnitude anddirection, from the strain of the same kind on the ribs; this difference acts transversely onthe cross ties and tends to break them. The underside of the roadway is a very convenientplace for diagonal framing, in order to stiffen the bridge horizontally. But whatever isdone with this intention must have a very extensive connection with the abutments. Thestraps to which these braces are attached should embrace a great part of the masonry,that one part may not easily be torn from another.
Dr. Charles Hutton —This question will be much better answered by means of experimentsmade on a proper model, than by theoretical calculations dpriori. But when the bridge isexecuted in the best manner, with the frames properly bonded and connected together, itseems more likely that any violent shock, such as a ship driving against it, would breakany particular frame, rather than overturn such a mass of bonded materials, or even moveit sensibly out of the vertical position.
Mr. John Southern. —If the bridge should be considered as a single frame, having strengthto keep itself together against a horizontal force applied at the crown, that could under thesecircumstances overset it; and supposing it free from the top of the abutments, and simplyresting upon the end of the arch as feet, this horizontal force applied to the vertex wouldbe more than two-thirds the whole weight of the bridge; but though this supposition ofthe unity of the parts of the bridge fail us, there is no doubt in my mind of the practi-cability of making the bridge strong enough, by the application of diagonal braces, to resistany force that can possibly apply to overset it.
The Seventh Question .—Supposing the span of the arch to remain the same, and to spring10 feet lower, what additional strength would it give to the bridge? or, making thestrength the same, what saving may be made in the materials? or if, instead of a circulararch, as in the drawings, the bridge should be made in the form of an elliptical arch, whatwould be the difference in effect, as to strength, duration, and expense ?
Dr. Nevil Maskelyne .—In the proposed bridge of 600 feet in the span and 65 feet high,the radius of the arch is 725 feet, and the length of the arch 618 feet 6 inches ; and in thebridge proposed in the question, the height being 75 feet to the same span as before, theradius of the arch will be 637 feet 6 inches, and the length of the arch 625 feet, and thearch more curved by about one-seventh, and consequently stronger by about one-seventh,whether for sustaining its own weight or a weight laid on it. But as it already containsmore materials than the bridge of 65 feet height, it does not appear to me to be probable