Handbook of Railroad Construction; For the use of American engineers. / Containing the necessary rules, tables, and formulæ for the location, construction, equipment, and management of railroads, as built in the United States.

by George L. Vose

MASONRY.

95. There are eight general cases which may occur in laying out such structures as bridge abutments with wings.

1. A right bridge on a level tangent.

2. A right bridge on a level curve.

3. A skew bridge on a level tangent.

4. A skew bridge on a level curve.

5. A right bridge on an inclined tangent.

6. A right bridge on an inclined curve.

7. A skew bridge on an inclined tangent.

8. A skew bridge on an inclined curve.

And these eight cases will vary again according to the natural surface of the ground, whether horizontal, or inclined transversely.

96. The general position of wing walls and general form of the line inclosing the base of the bridge, is shown from fig. 31 to fig. 38. Fig. 31 represents case one. The points A, B, C, D, are fixed by squares from the centre line at E F, G H.

Fig. 31.

Fig. 32 represents case two. The wings 3c, 4d, must evidently have a different inclination from A1, B2. The points A, B, c, d, 1, 2, 3, 4, as before, are laid off by squares from a tangent to the curve.

Fig. 32.

Fig. 33 explains itself.

Fig. 33.

Fig. 34.

Fig. 34, case five. Here the wings A1, C4, are the same, as also B2, D3, the former being longer, on account of the greater depth of the fill.

Fig. 35.

Fig. 35, case seven. Here each wing is peculiar; the figure being a compound of figs. 33 and 34.

Figs. 36 and 37.

Figs. 36 and 37, case 8. This is the most difficult of all. No two wings have the same length or inclination on plan. The natural surface being horizontal, the line inclosing the bridge is A″ B″ C″ D″. If the natural surface descended from C″ to A, the position taken would be A, B, C, D. Fig. 37 is the elevation of the position A B C D. The several points are laid off from the line n, n.

The general manner of fixing the lines of figures 31 to 38, is to assume the angle of some one wing, as A 1, in fig. 34, to draw A C parallel to E F; and from C, the intersection of A C with the base of the embankment, C 4 gives the other wing. Local circumstances will of course often fix at once the length and angle of the wings. Upon simple curves, as in fig. 32, the lines A c and B d are made radial.

97. In curving a viaduct, the axes of the piers are made radial to the centre of the located curve, and the planes of the springing lines are made parallel to the axes of the arches. The pier thus becomes a wedge, and should be strengthened by a starling, upon the outside of the curve, to resist the resultant of the thrusts of two adjoining arches.

98. We should never try to stake out the exact horizontal projection of a complicated piece of work upon rough ground, but only the trenches, which being cut, give a horizontal surface to work upon. In placing the stakes, we must be careful to have them so far outside of the work that they will remain undisturbed while operations are going on. The pegs for cutting pits and trenches may be placed at the angles of the latter, but the working pegs must be so placed that the lines stretched from one to the other will define the masonry. All measurements made in laying out work should be made by graduated rods, and carefully checked.

99. In founding piers, and in aquatic operations generally, two stakes upon the shore, or a fixed transit, will define any line in the water. Two transits will define points.

100. A permanent bench mark should be carefully fixed at each structure, from which its levels may be obtained.

101. In adjusting oblique bridges, care must be taken so to place the bridge seats that the floor beams shall lie in a correct plane, and not be at all warped or winding.

Fig. 38.

102. As an example of laying out work with regard to heights, take the case of fig. 38. Let the grade of the centre line be one in 100, the angle of obliquity 45°, the width of bridge twenty feet, and span on the skew one hundred feet. Required the elevations of the points a, b, c, d.

Assume the height of (2) as	100.00
That of (3) will be	99.00
b being 10 ft. back of 2 is 0.1 ft. higher than 2, or	100.10
and d 0.1 feet less than (2) or	99.90
also a = 99.00 + 0.10, or	99.10
and c = 99.00 – 0.10, or	98.90