Arch Construction.
Iron construction has so completely superseded masonry for bridge building that it would appear almost unnecessary to discuss the question of the equilibrated arch for any large span. But the mathematical principles of the arch have always been an interesting subject with geometricians and theorists, and the theory, at any rate, ought to form one of the subjects of the architect’s and engineer’s education. As a problem of the equilibrium of forces, the theory of arch construction is instructive, inasmuch as it presents us with a concrete example of three forces balanced in a structure. The other day, at the opening of the engineering section of the Bristol Naturalists’ Society, at University College, Bristol, the president, Mr. Charles Richardson, C.E., read a paper on arch building, in which he advocated the employment of arches of equilibrium for bridges. The author referred to the well known and elegant property of the balanced arch, which is derived from the principle of the catenary or suspended chain or inverted polygon of bars, each bar or link assuming the position (inverted) that the arch stones of an equilibrated arch would have. In Dr. Hutton’s valuable “Tracts on Bridges,” this principle is followed in his elucidation of the arch, and readers of that work will remember the diagrams given of various kinds of balanced arches, and the curves of extrados necessary to insure equilibrium. The theory, indeed, is older than Hutton. Belidor and Dr. Hooke both investigated the form of the extrados from the nature of the curve, and this theory has been made the foundation of a very interesting system of designing arches. According to this theory of the question, the stones are considered free from all friction—a condition which does not hold in practice. Mr. Richardson follows, as far as we can see, this theory. He enunciated the theorem that the weight on any point of the arch is proportional to the vertical line from the road line to the intrados at that point; that the horizontal thrust is the same throughout the arch, and is equal to the weight on the crown per unit of area multiplied by the radius of curvature there; and also that the bed pressure at any point is equal to the horizontal thrust multiplied by the secant of the angle the curve makes with the horizon at that point. This rule is thoroughly mathematical and true for arches of equilibrium; and the author exhibited an instructive model of an arch equilibrated, and showed by inverting it, and suspending a chain weighted by steel rods representing the loads at each point, that the latter coincided with the road line. But the engineer‐architect has to do with arches in which the element of friction enters; the stones are cemented, and therefore the theory, however beautiful, does not hold good in every case. Instead of the separate arch stones or voussoirs, he has to deal with segments of the arch which turn upon certain edges. Thus an arch which fails breaks into four parts, the crown sinks, and the haunches rise, the joints at those points opening. One of the questions to decide is the points at which rupture occurs, that being found to find out what horizontal pressure each of those lower segments have to sustain. From knowing the thrust and its point of action, the stability of the arch will depend on the mass and weight of the pier. The experiments of Rondelet and others have proved that the voussoirs unite into segments of the arch, and tend to overturn the abutment, acting rather as levers than wedges. He found, also, that the greatest thrust was in arches with an even number of voussoirs or a point at the vertex; that a keystone lessened the thrust. Nevertheless, the theory of equilibration should be known by all architects and bridge builders.
In alluding to the materials, the author showed the impossibility of dressing and bedding stones accurately. Practically, the stone built arch is difficult to execute with precision. The facing stones only are cut to the true curve, the backing being filled in with rubble and roughly executed. With brickwork the bricks can be all bedded in cement, being more convenient for handling, and a vitrified brick is equal at least to the best stone in resistance. The brick arch should be built in vertical bond, not in rings. Mr. Richardson finds that, taking the safe load in cement at 5 cwt. upon the square inch, an arch 15 in. thick at the springing and 12⅚ at the crown is sufficient for a span of 85 feet with a rise of ⅛ of the span. He says: “As all loads and thrusts on such an arch are in direct proportion, if each dimension were multiplied by four, we should have a span of 340 feet with a rise of 42 feet and an arch thickness of 5 feet. This 5 feet thickness would give a sufficient margin of safety for the moving load, because 5 feet is only the necessary thickness at the springing, while that at the crown would be 9 in. less. The total weight of this bridge would be 100,000 tons.” Ring‐built arches are advisedly objected to, as the rings tend to separate when any settlement takes place. Mr. Richardson does not rely too much on friction, and he is right. There can be no scientific arch construction that is not based on the principle of equilibrium, the line of thrust being kept within the middle third of the arch thickness; and in designing arches of brick or stone the engineer should always be able by diagram to satisfy himself of this condition. Whenever the line of thrust passes close to the lower edge of the arch ring at the haunches, there must be undue pressure and a tendency to open at the other edge. In other words, the arch is inclined to drop at the crown. When it passes out of the arch, failure must take place sooner or later. Instead of first deciding upon the curve and road line, as is frequently done, the right course is to find the line of thrust for the given span and loading, and then make the arch conform as nearly as possible to this line. We agree with the opinion that brickwork, if correctly applied, would be found to excel iron construction in strength, durability, and economy—certainly in appearance. In the construction of masonry arches, sufficient care is not always bestowed upon the drainage of the arches—a cause, we imagine, of many failures.—Building News.
Gilbert Sheffield, a Warren County, N. Y., lumberman, is one of the men who believes in using his men well, and in doing something to relieve the tedium of life in the woods. He has 35 men employed at Tahawus, in Essex County, and says that for the past two years it has been his practice to furnish them with copies of the prominent newspapers, so that when they left camp they were as well informed regarding current events as when they went in.