Chap VIII.
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rest, and that the whole should be so framed, as to be capabfe of resisting any force tendingto alter its form or position, whether from external violence, or from imperfection, or in-equality in its parts. Although the parts of the bridge may be so put together as tobecome one united frame, I should think it right, nevertheless, so to construct the arch,that independent of the framing between the arch and the roadway, it should be equal tothe support of the superincumbent weight; and in order that it should be so, it ought tohave such a curvature as to counteract the unequal pressure created by the increase ofwidth at the ends of the bridge, or an increased weight on the crown of the arch, or both ;it is, therefore, advisable, that instead of the three circular members or segments above thearch, uniting into one on the crown of the arch, and thereby diminishing their weight, eachof these segments might be continued distinctly, but resting on or touching each other atthe crown ; and in the plan also, each rib should be continued independent of the others.
Mr. John Rennie, of Stamford Street, observes that were the arch a semicircle, ellipsis,or other curve, in which some of the frames or voussoirs had but a small inclination to thehorizon, the friction arising from the gravity of those frames would be greater than theirweight would overcome, and of course would act by pressure only ; but in the present case,the arch is so flat, that I apprehend every frame may be considered as a wedge, if its sur-face were perfectly smooth and straight, and not prevented from sliding by joggles or othercontrivances; but as each frame is proposed to be connected by proper joggles or con-trivances to the other, and the whole loaded so as to be in equilibrio, except as far as thematerials will yield by the weight of the superstructure, I apprehend it may in a greatdegree be considered as a single frame, which can only be destroyed by crushing its parts.
Mr. John Southern , Engineer, Soho, near Birmingham , observes, that the design repre-sents the parts as one frame; but I do not think it possible to execute it sq, as to havethat effect, nor even that parts can be combined so accurately as to form wedges of sogreat a length as to reach from the arch to the road; nor do I think it desirable that itshould be so constructed ; because, as settlement will certainly take place in some degree,when the centres are struck, an immense pressure may possibly be brought on some of theeccentric arches in the spandrills, which arc evidently not calculated for such an effect. Itis better that the construction should be such as to direct the pressure of force on thoseparts intended and able to bear it. I therefore consider the lower part only of the bridge,or the arch, constituted by the concentric curves, and which I desire to distinguish by thename of arch, as answering the end of wedges or arch stones; all the superincumbentmatter I consider as weight, the pressure of the greatest part of which is, however, increasedby the declination from the perpendicular of the members or pillars which point to thecentre of the arch, and which communicate to it this pressure. The eccentric members,which form arches in the spandrills, of less curvature than the principal arch, can only beused in keeping the long pillars from bending under the pressure they sustain. Indeed,were the whole pressure of the bridge, by any accident, to come upon any one of thesespandrill arches, and were it made strong enough to resist the pressure, the pushing or hori-zontal force acting against the abutments to overset them, would be increased in proportionto the flatness or radius of the said arch.
The second question propounded by the committee was, whether the strength of the archis affected, and in what manner, by the proposed increase of its width towards the twoabutments, when considered both vertically and horizontally ; and if so, what form shouldthe bridge gradually acquire ?
Dr. Nevil Maskelyne apprehended that the strength of the bridge would be somewhatincreased vertically, and also horizontally, according to the length of the bridge, by theincrease of its width towards the extremities or abutments; but that it is increased princi-pally in the direction of its width, so as better to resist the stroke of the mast of a shipgoing up or down the river.
The Rev. A. Robertson stated that the arch will certainly be affected by increasing thewidth of the bridge towards the abutments. Such a form will decrease the strength ofthe arch, to bear the roadway and any weight upon it, and on the other hand it willincrease the strength of the bridge to resist any force tending to press it out of the verticalplane. The following are the reasons for this opinion: — If the weights of the severalparts be so proportioned, as to give the whole the greatest possible degree of strength, thequantity of matter over any point in the arch must be fixed according to the weight at thecrown or at the abutment; it can neither be increased nor diminished, if that law isobserved by which a maximum of strength is obtained. If, therefore, the bridge increasein width from the crown to the abutments, the quantity of iron being in an horizontal, itmust be decreased in a vertical direction. Consequently, the strength of the bridge willcontinually diminish in a vertical direction from the crown to the abutments.
Mr. Playfair thought that the proposed increase of width at the extremities, thoughnecessary to steady the bridge in the horizontal direction, and to preserve it in the samevertical plane, is an additional load towards the haunches of the bridge, and tends atillmore to remove the distribution of the weight from that which the equilibrium requires.
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