91. The running of the line consists in placing a stake at every one hundred feet upon tangents, and at every fifty feet distance upon sharp curves; also a permanent post at each tangent point, and at points of compound and reversed curvature. This is the centre line, the axis of the road, and the base of all field operations. Wherever the work is going on, the centre pins should be referred to fixed points outside of the ground occupied by the road.
92. The first operation in preparing for excavation is to place side stakes at one half the width of road-bed plus the ditch, on each side of the centre line.
93. Setting out slopes is a term applied to laying off upon the ground, on each side of the centre, the distance to which the slope, commencing at the outer edge of the ditch, will extend, depending upon the angle of slope, width of road-bed and ditch, and depth of cutting. There are here five distinct cases which may occur:—
In embankment when the natural surface is horizontal. In embankment when the natural surface is inclined. In excavation when the natural surface is horizontal. In excavation when the natural surface is inclined.
In mixed work (side hill,) when the road-bed is partly in cut and partly in fill. In both excavation and embankment, when the natural surface is horizontal, we have only to add the cut, in feet and decimals, multiplied by the slope, to one half the width of road-bed plus ditch.
| Thus suppose the cut is | 20.55 feet, |
| half the road-bed, | 10.25 feet, |
| ditch, | 3.00 feet, |
| slope 1½ horizontal to 1 vertical, |
and we have
When the ground is inclined transversely to the axis of the road, first assume a point upon the ground, (apparently right) find its height above grade with the level, multiply this by the slope and add one half the distance between the outer edge of ditches, and see how near it comes to the measured distance from the centre to the assumed point; if within a foot, it will answer; if not, a second trial will fix the place.
94. The length of any structure passing under a railroad embankment is L – 2Rh, where L is the distance between slope stakes, R inclination of slopes, h the height of structure from the natural surface. Thus, suppose the distance between slope stakes to be 100 feet, slope 1½ to 1, and h 10 feet, we have
The length of an oblique structure will of course be greater than that of one at right angles to the road; the length depending upon the obliquity.
95. There are eight general cases which may occur in laying out such structures as bridge abutments with wings.
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 |
103. The maintaining a correct centre line through tunnels is generally considered difficult. The fixing of the line in deep shafts requires great care, owing to the short distance between the only two fixed points, that can be transferred from the surface to the bottom of the pit. This is a matter of manual skill and of instrumental manipulation. There is no difficulty in aligning the upper ends of two plumb-lines; and the lower ones will certainly be governed by their position. The following method has been found to answer every purpose.
Let the opening of the shaft be ten feet in diameter. Place two horizontal bars at right angles to the road across the opening, upon which slide blocks holding the upper end of the plumb-lines. Adjust these lines, at the surface, with a transit; and when fixed, place iron pins at the point marked by the plumbs at the bottom of the shaft. Upon these pins fix the exact centres. For keeping the line in the shaft headings, a straight rod, with steel points at each end, should be used, which being placed upon the iron centre pins, fixes the centre line of the tunnel. When the tunnel is curved, the line should be laid off by offsets from the tangent to the curve at the shaft.
By this method points at ten feet distance may be fixed
within 1
100 of an inch, a difference of which would cause
an error of ⅒ of an inch per one hundred, or an inch per
thousand feet.