EXAMPLES OF REINFORCED CONCRETE ARCHES. The con sideration of reinforced concrete arches will be closed by giving some details of a few structures.
It is hardly possible to make a tabular exhibit cf any value show ing the dimensions of reinforced concrete arches as was done for voussoir and plain concrete arches, since the systems of reinforce ment are so varied and the quality of the steel and its positions are so diverse. Further, reinforced concrete arches are built with either a solid arch ring or of ribs connected by a curtain wall. It is not possible to make a tabular statement of all these variables that will be of any particular value. Reasonably complete descriptions of many reinforced concrete arches can be found by consulting any one of the several indexes to current engineering literature. The 'fol lowing are representative examples of reinforced concrete arches having no hinges.
Fig. 239 shows the typical reinforced concrete arch for stream and highway crossings emproyed recently by the Union Pacific Railroad.* Fig. 239 is for a highway crossing near Omaha; and the form for stream crossings is the same except that the wings flare at 30°. The reinforcement consists of corrugated bars (§ 465); and this particular job contained 52.2 lb. of steel per cubic yard of concrete. No bar was placed nearer the surface of the concrete than 3 inches, and splices were lapped 2 feet.
The arch ring is not necessarily built monolithic, but any joints are required to be on a radial line.
Big South Fork Bridge. Fig. 240, page 714, shows one of the five equal spans of a skew bridge over th8 Big South Fork Branch of the Cumberland River on the Kentucky and Tennessee Railway.t The extrados and also the intrados are circular curves. The arch is designed for a train load equivalent to Cooper's E-40. The rein forcement is twisted steel bars (§ 465). The concrete in the arch ring and the spandrel walls is 1 : 2 : 4, in the footings 1 : 3 : 6, and in the body of the piers 1 : 2i : 5. "The west abutment was built hollow and filled with stone. It was designed on the supposition that solid rock, which outcropped near the site of the abutment, would be found at a small depth; but solid rock was not found as expected, and to avoid the cost of extending the abutment so that its weight would make it stable against the thrust of the arch, anchors were cemented into the rock foundation to a depth of 6 ft.
along the front edge of the abutment. In building this abutment it was found that the cost of the form-work was greater than the saving in concrete; and the contractor preferred to build the other abutment solid and omit much of the steel." The rods parallel to the neutral line between the reinforcement near the extrados and the intrados are quite unusual.
Fig. 241, page 716, shows one of the two 75-ft. arches carrying a highway over Charley Creek, near Wabash, Ind.; and Fig. 242, page 716, shows the center used in its erection.* This bridge differs from the two preceding ones in four noteworthy particulars, viz.: 1. The use of a special bar, the Kahn (e, Fig. 29, page 238) for the reinforcement, which give a rather remarkable arrangement of metal in the arch ring. Tke designer claims that the diagonal members, being solidly connected to the extradosal and intradosal bars, firmly anchor these bars and also tie together the concrete of the arch ring. 2. The complete reinforcement of the spandrel walls. The spandrel walls are designed as vertical cantilevers to hold in place the earth spandrel filling, the reinforcement being Kahn bars (§ 465) set upright; and are rein forced longitudinally for temperature stresses by round rods. 3. The bonding together of the arches and spandrel walls over the center pier. 4. It has frequently been stated that the curve of the arch ring of this bridge is a parabola; but an examination of the drawing shows that the intrados is a five-centered circular curve and the extrados a circular arc. The above statement, and many similar ones, must be interpreted to mean that the stresses were determined on the assumption that the center line of the arch ring was a parabola, i.e., the stresses were determined by the method proposed by Prof. C. E. Greene f for an arch whose neutral line is a parabola. Professor Greene adopted a parabola for the center line of the arch ring because a parabolic linear arch is stable under a load uniform along the span; but it is not proved that the parabolic arch is better than the more common forms, particularly as the dead load is not uniform along the span, and since the live load has a different position for the maxi mum stresses at different points along the arch, and further since temperature stresses are an impor tant factor in the design of an arch and are independent of the curve of the neutral line.