Page:The Building News and Engineering Journal, Volume 22, 1872.djvu/46

 30 THE BUILDING NEWS. Jan, 12, 1879. nnn, — ances. The materials and subjects embraced will consist of granites and other stones, concrete, fireproof construction, bricks, slates, stables and their fittings, coal plates, pave- ment lights, casements, sashes and frames and their furniture, ventilation, locks and iron- mongery generally, ovens and stoves, electric bells and domestic telegraphs, lifts and hoists, closets, pipes, paint, and enamel. I may here observe that I shall be glad to receive any information respecting any peculiar invention or patent, together with any models or specimens, addressed to B. F., office of the Buitpine News. — NOTES ON BRICKWORK.—IX. ee fundamental principle of the stability of an arch is that it should contain within its thickness the catenary curve pro- duced by weights similar to those with which it is loaded. The catenary curve is that assumed by a chain of uniform weight freely suspended from its two ends. If the twoends are in the same horizontal line they represent the springings of an arch reversed, and the dip of the chain represents the rise of the arch. Ifthe chain be so constructed that its links will not allow its length to be shortened, and it be reversed into an exactly similar curve as an arch in an exactly vertical plane, it will stand equally stable in that form as in its catenary form so long as no extraneous weight or pressure be added to it in any part. If, while it hung suspended, an additional weight had been suspended from it in any part its form would haye been altered, but if instead of weights being attached at one or a few points it were uniformly loaded from end to end its original form would be preserved. Tf, when set up as an arch, it were possible to load this curved rib with the same uniform weight, it would still preserve its form. The points of contact of its many links would be mere points, and, therefore, practically it could not be loaded, but if alongside of this ima- ginary curye a brick arch be turned so that the centre of its depth coincide with the line of the supposed curve of the chain, then the arch will contain within it the curve of stability, so long as no extraneous load or pressure be applied to it in any part; but according to the manner of loading it, includ- ing its own weight, so must the depth of the arch be varied in order to keep within it this imaginary curved line, for it will vary accord- ing to the manner of loading the arch. If the arch be loaded at the crown this curve of equilibrium will rise at that point and sink at the haunches, assuming an elliptical form, haying its major axis vertical, while if the arch be loaded at the haunches and not cor- respondingly at the crown the elliptical form will take the contrary direction and sink at the crown and rise at the haunches. In either case if the curve of equilibrium be thrown within the intrados the arch will be broken. ‘The crown and the haunches are mentioned because they are critical points, but the action would be similar whatever points be taken. If the crown be loaded, the line along which the pressure will travel from that point to the abutments will assume a relatively higher position at the crown, and a lower, or rather one nearer the intrados, at the haunches. So long as this line of pressure is confined within the thickness of the arch it will not actually fall, but it isa matter of opinion how far it should be allowed to devi- ate from the centre of its thickness. Professor tankine, who may be taken to be a fair representative of the philosophical engineer, considers that this curve of equilibrium should be included within the middle third part of the thickness of the arch. Nevertheless, the arch would not actually fail until the line of pressure passes out of the extrados or intrados ; but as this line of pressure approaches these extreme points so does the action approach danger, and if the limits be passed the arch will fall. The actions of these pressures may be illustrated by the following diagrams :— Fic.3 Fig. 1 illustrates an arch loaded at the crown, and Fig. 2 an arch loaded at the haunches, the lines of pressure in either case being confined to the middle third part of the thickness of the arch. Fig. 5 represents an arch normally loaded, Fig. 4 an arch over- loaded at the crown, and Fig. 5 an arch over- loaded at the haunches. In such a case as that represented by Fig. 4, the arch would turn about the joints at the extrados at the crown, and the intrados at the haunches, and in such a case as that represented by Fig. 5 the action would be vice versd; the joints would gape at the intrados at the haunches, and at the extrados at the crown. In Fig. 3 the line of pressure follows the centre line of the arch, and is the curve of equilibrium ; but the arch of a bridge would be of no practical use if it could carry no other load than its own weight. In practice this line of strict equilibrium must be allowed to vary from the exact centre line of the arch within certain limits on each side of it. “In these figures the lines of pressure are relative only, and are imaginary, but they show that the portion of the arch at the crown is thrust below the line of pressure, and therefore below its support, causing the joints of the soffit to open, and that portion of the arch to turn upon the edges of the joints at the extrados as upon a fulerum, and at the same time to throw out the haunches, and making the joints there open at the back and turn on the inner edges as a fulcrum, the whole tendency being that the crown of the arch tends to buckle inwards and the haunches to buckle outwards. When, on the contrary, the haunches are overweighted, the crown tends to buckle outwards and the haunches inwards. Instead of the relative positions of the line of pressure and the arch shown in Figs. 4 and 5, the actual state of things may be represented by Figs. 4a and 5a. To return to the catenary curve. If the suspended chain be of uniform weight through- out its length, it will assume the form of a simple catenary. Also, ifit be loaded through- out its length with uniform weights, it will still preserve the same form of curve, and if the whole fabric were reversed so as to form an arch, it would still remain in equilibrium, provided the connection between the chain and the load were rigid; but an arch thus loaded would not represent the true state of things in a bridge, because the horizontal roadway, or nearly horizontal roadway, must be supported by spandrels, the weight of which increases from the crown to the spring-, ings. Adding together all the dead weight to be sustained—viz., the roadway, the span- drels, and tke arch itself, a variable load will result, which is greatest at the springing and least at the crown. If, now, this variable load be substituted for the uniform one with which we supposed the simple catenary to be loaded, the chain will be drawn out of its original form by the greater weights towards the springing or ends of the chain, draw- ing it down in those parts and elevating it at the vertex. This will not take place to a great extent, but it will alter the curve of the simple catenary to one of a transformed catenary, and it is the latter curve which is the true curve of equilibrium of an arch, considered independently of any rollingload. If we take now a_ semicircular arch and try to find the transformed catenary corresponding to its curve of equilibrium, we shall find that the weight to be hung on the simple catenary at the springing, in order to bring it to the form of the transformed catenary, would be infinite, because there is no projection beyond the point of support, and, correspondingly, the height representing the load over the line of the face of the abut- ment is infinite. This shows that a semi- cireular arch does not act as an arch all the way down to the springing, but only to within a certain distance of the springing, which distance is determined by the thickness of the arch, being the point in which the extrados of the arch cuts the line of the face of the abutment or pier, all that part of the arch below such point being in reality part of the abutment or pier itself, and therefore requir- ing the vertical joints of the backing to be close, so as to resist the horizontal thrust of the real arch. For this reasonall the courses up to the point A in Fig. 6 may be horizon- tal and conformable to those of the abutment