joint in the direction of the radius of curvature. The forms and dimensions of the segments are uniform. The segments are usually either solid (Fig. 163) or open plates of uniform thickness, having a flanch of uniform breadth and depth at each end, and on the entrados and intrados. The flanch serves both to give strength to the segment and to form the connection between the segments and the parts which rest upon the rib.

The ribs are connected by tie-plates, which are inserted between the joints of the segments, and are fastened to the segments by iron screw bolts, which pass through the end flanches of the segments and the tie-plate between them. The tieplates may be either open or solid; the former being usually preferred on account of their superior lightness and cheapness. The framework of the ribs is stiffened by diagonal pieces, which are connected either with the ribs or the tie-plates. The diagonal braces are cast in one piece, the arms being ribbed, or feathered, and tapering from the centre towards the ends in a suitable manner to give lightness combined with strength.

The open beams (Fig. 163), which rest upon the curved ribs, are cast in a suitable number of panels; the joint between each pair being either in the direction of the radii of the arch, or else vertical. These pieces are also cast with flanches, by which they are connected together, and with the other parts of the frame. The beams, like the ribs, are tied together and stiffened by ties and diagonal braces.

Beams of suitable forms for the purposes of the structure are placed either lengthwise or crosswise upon the open beams.

629. Curved ribs of a tubular form have, within a few years back, been tried with success, and bid fair to supersede the ordinary plate rib, as with the same amount of metal they combine more strength than the flat rib.

The application of tubular ribs was first made in the United States by Major Delafield of the U. S. Corps of Engineers, in an arch for a bridge of 80 feet span. Each rib was formed of nine segments; each segment (Fig. 164) being cast in one piece, the cross section of which is an elliptical ring of uniform thickness, the transverse axis of the ellipse being in the direction of the radius of curvature of the rib. A broad elliptical flanch with ribs, or stays, is cast on each end of the segment, to connect the parts with each other; and three chairs, or saddle-pieces, with grooves in them, are cast upon the entrados of each segment, and at equal intervals apart, to receive the open beam which rests on the curved rib.

The ribs are connected by an open tie plate (Fig. 164). Raised elliptical projections are cast on each face of the tie plate, where it is connected with the segments, which are adjusted accurately to the interior surface of each pair of segments, between which the tie plate is embraced. The segments and plate are fastened by screw bolts passed through the end flanches of the segments.

Fig. 164-Represents a side view A, and a cross section and end view B, through a saddle-piece of the tubular arch of Major Delafield.

a, a (Fig. A), a side view, and (Fig. B) an end view of the elliptical flanches of the end of each segment.

b, b, shoulders, or ribs to strengthen the flanches against lateral strains.

c, tie-plate, between the ribs.

J, (Fig. B) side view of the rim of the tie-plate fitted to the interior of the tube.

d, d, (Figs. A and B) saddle-pieces to receive the open beams of a form similar to Fig. 163, which rest on the tubular ribs.

e, cross section of the rib through the saddle-piece.

The tie plates form the only connection between the curved ribs; the broad-ribbed flanches of the segments, and the raised rims of the tie plates inserted into the ends of the tubes, giving all the advantages and stiffness of diagonal pieces.

630. Tubular ribs with an elliptical cross section have been used in France for many of their bridges. They were first introduced but a few years back by M. Polonceau, after

Fig. 165.-Represents a side view A, and a cross section and end view B, through a joint of M. Polonceau's tubular arch.

a, a, top flanch, b, b, bottom flanch of the semi-segments united along the vertical joint cd through the axis of the rib.

gh, side view of the joint between the flanches e, e of two semi-segments.

m, inner side of the flanches.

c, cross section of a semi-segment and top and bottom flanches.

ff, thin wedges of wrought iron placed between the end flanches of the semi-segments to bring the parts to their proper bearing.

whose designs the greater part of these structures have been built. According to M. Polonceau's plan, each rib consists of two symmetrical parts divided lengthwise by a vertical joint. Each half of the rib is composed of a number of segments so distributed as to break joints, in order that when the segments are put together there shall be no continuous cross joint through the ribs.

The segments (Fig. 165) are cast with a top and bottom flanch, and one also at each end. The halves of the rib are connected by bolts through the upper and lower flanches, and the segments by bolts through the end flanches.

For the purposes of adjusting the segments and bringing the rib to a suitable degree of tension, flat pieces of wrought iron of a wedge shape are driven into the joints between the segments, and are confined in the joints by the bolts which fasten the segments and which also pass through these wedges.

To connect the ribs with each other, iron tubular pieces are placed between them, the ends of the tubes being suitably adjusted to the sides of the ribs. Wrought-iron rods which serve as ties pass through the tubes and ribs, being arranged with screws and nuts to draw the ribs firmly against the tubular pieces. Diagonal pieces of a suitable form are

placed between the ribs to give them the requisite degree of stiffness.

In the bridges constructed by M. Polonceau according to this plan, he supports the longitudinal beams of the roadway by cast-iron rings which are fastened to the ribs and to each other, and bear a chair of suitable form to receive the beams.

631. Open cast-iron beams are seldom used except in combination with cast-iron arches. Those of wrought iron are frequently used in structures. They may be formed of a top and bottom rail connected by diagonal pieces, forming the ordinary lattice arrangement, or

a piece bent into a curved.

b c

Fig. 166-Represents an open beam of wrought iron consisting of a top and bottom rail a and b, with an intermediate curved piece, the whole secured by the pieces c, c, in pairs bolted to them.

d, e, and represent the parts of a truss of a curved light roof, connected with the open beam; and also the manner in which the whole are secured to the wall.

form may be placed between the rails, or any other suitable combination (Fig. 166) may be used which combines lightness with strength and stiffness.

632. Effects of Temperature on Stone and Cast-iron Bridges. The action of variations of temperature upon masses of masonry, particularly in the coping, has already been noticed. The effect of the same action upon the equilibrium of arches was first observed by M. Vicat in the stone bridge built by him at Souillac, in the joints of which periodical changes were found to take place, not only from the ranges of temperature between the seasons, but even daily. Similar phenomena were also very accurately noted by Mr. George Rennie in a stone bridge at Staines.

From these recorded observations the fact is conclusively established, that the joints of stone bridges, both in the arches

and spandrels, are periodically affected by this action, which must consequently at times throw an increased amount of pressure upon the abutments, but without, under ordinary circumstances, any danger to the permanent stability of the

structure.

When iron was first proposed to be employed for bridges, objections were brought against it on the ground of the effect of changes of temperature upon this metal. The failure in the abutments of the iron bridge at Staines was imputed to this cause, and like objections were seriously urged against other structures about to be erected in England. To put this matter at rest, observations were very carefully made by Sir John Rennie upon the arches of Southwark bridge, built by his father. From these experiments it appears that the mean rise of the centre arch at the crown was about th of an inch for each degree of Fahr., or 1.25 inches for 50° Fahr. The change of form and increase of pressure arising from this cause do not appear to have affected in any sensible degree the permanent stability either of this structure, or of any of a like character in Europe.

633. AMONG the earliest and most meritorious of the iron bridges of this country is Whipple's Trapezoidal Truss (see Fig. 167). So far as the arrangement of ties and struts are concerned it is similar to the Pratt Truss.

Fig. 167.-The upper chord is of cast-iron and made in sections, the length of each piece being equal to the length of a bay. The lower chord is composed of a succession of links (see Fig. 168), which receive cast-iron blocks at their ends. The cast-iron blocks form steps for securing the lower ends of the vertical posts. The posts have openings near the middle of their length, through which the main and counter-ties pass. The posts are trussed at the middle, as shown in the figure.

In this truss the end members are inclined, so that the general form of the outline is that of a trapezoid. All un