HINGED ARCH RIBS 444. General Principles. The construction of hinged arches of reinforced concrete is very rare, but is not unknown, and will probably come into greater use when their advantages are more fully realized. We may consider that structurally they consist of curved ribs which have hinges at each abutment, and which may or may not have a hinge at the center of the arch. The advantage of the three-hinged arch lies in the fact that it is not subject to temperature stresses. The two-hinged arch is partially subject to temperature stresses, but not to so great an extent as the fixed arch, since the arch rib is not held rigid at the abutments as in the case of the fixed arch. Prac tically the hinges are made by haying at each hinge a pair of large cast iron plates which are a little larger than the size of the rib, and which have at their centers a bearing for a pin of due proportionate size. The bearings are so made that one may turn, with respect to the other, about the axis of the pin through an angle of a very few degrees.
445. Arch of Two Hinges. The third of Equations 48 must be satisfied, which practically means that Equation 54 must be satis fied. This means that we must find a trial equilibrium polygon, and increase or decrease its pole distance so that the summation of the products based on z" shall equal the summation of similar prod ucts based on z'. But in this case the special equi librium polygon passes through the abutment points, and there is no moment at the abutment. Therefore, after having found the pole distance of the special equi librium polygon, we may draw the special equilib rium polygon by commencing at one abutment point; and, as a check on the work, we should find that it passes through the other abutment point. The moment due to temperature will be at the center of the arch rib, and will be based on an equation similar to Equa tion 60, which may be used by calling d = o.
Equation 61 does not apply, since the ends of the arch rib are free to turn at each abutment.
440. Arch of Three Hinges. A three-hinged arch is a still more simple case, since none of the three fundamental equations (Equation 48) which are used for fixed arches needs to be satisfied. It is only necessary to find the special equilibrium polygon which will pass through the two abutment hinges and the center hinge. There are no temperature stresses and no stresses due to the shortening of the rib. It may thus be said that a three-hinged arch is much more simple to calculate, and its stresses are more definite. The construc tion of the hinges will of course add somewhat to the cost, and probably add more than any saving which might be made by a reduction in the cross-section of the arch. Probably the greatest advantage of three hinged arches lies in their immunity from damage which may result from a settlement of the foundations. It has been assumed, in con sidering the theory of fixed arches, that the foundations arc abso lutely immovable. A settlement of either abutment of a fixed arch with reference to the other abutment, will inevitably result in stresses in the arch rib which might easily be greater than any stresses to which the arch rib would be subjected either on account of the loading or through change in temperature. The failure of many arches is
unquestionably due to this cause. An arch rib with either two or three hinges is absolutely immune from any such danger; and there is therefore a strong argument for the use of hinged arches when the arch must be placed wi foundations which are so uncertain that a settlement of either foundation is quite possible. Of course an equal settlement of both foundations would do no damage, but the equality of such a settlement could never be counted on.
447. Description of Two Reinforce&Concrete Arches. In Figs. 234 and 235 are shown the details and sections of two reinforced concrete arches having fixed abutments, which have been recently erected. The first bridge has a nominal span of 60 feet between the . two faces of the abutments. On account of the great thickening of the arch rib near the abutment, the virtual abutments are practically at points which are approximately 26 feet on each side of the center. The method of reinforcing the spandrel and parapet walls is clearly shown in the figure. The side view also gives an indication of some buttresses which were used on the inside of the retaining walls above the abutments in order to reinforce them against a tendency to burst outward.
Fig. 235 shows a bridge which is slightly oblique, and which spans a double-track railroad. The perpendicular span between the abutments is 34 feet, but the span measured on the oblique face walls is 35 feet S inches. In this case, similarly, the arch is very rapidly thickened near the abutment, so that the virtual abutment on each side is at sonic little distance out from the vertical face of the abutment wall. In both of these cases, the arch rib was made of a better quality of concrete than the abutments.
The arch of Fig. 234 was designed for the loading of a country highway bridge; that of Fig. 235 was designed for the traffic of a city street, including that of heavy electric cars.
448. Stone Arch. In Fig. 236 is shown a stone arch on the New York, New Haven & Hartford Railroad at Pelhain•ille, N. Y. This arch was constructed over a highway, and the length of its axis is sufficient for four overhead tracks. The span is 40 feet, and the rise is 10 feet above the springing line, the latter being 7 feet 6 inches above the roadway. The length of the barrel of the arch is 76 feet.
The arch is a five-centered arch, the intrados corresponding closely to an ellipse, the greatest variation from a true ellipse being 1 inch. The theoretical line of pressure is well within the middle third, with tile full dead load and partial live load, until the short radius is reached, where it passes to the outer edge of the ring-stone, and thence down through the abutment. There is a joint at the points where the radii change, to simplify the construction.
The stone is a gneiss found near Yonkers, N. Y., except the key stone, which is Connecticut granite, and the coping, which is blue stone from Palatine Bridge, N. Y.