and 00, representing the ends of a culvert passing beneath the embankment, are seen to be at different distances from the centre line. The position of the points S and O may be found by first getting from the tables of side width the points A and D, and measuring in from these points the distances AS and DO, depending upon the slopes AB and AD. In the case of the upper end the distance of SS from A will be less than if the natural surface was level; at the lower end the distance from D to O will be greater. Having found the distances of SS and 00 from the centre line, we get the position and length of the wing walls of the culvert by drawing a line from S to any desired angle to intersect the slope AA; and upon the lower side of the embankment we get, in the same manner, the lines DD, OD, the latter being of course longer than the wings upon the upper side AS, AS. 933. Setting out Bridge Work.-In laying out the abutments for bridges there are numerous cases to be considered,—as whether the bridge is on the square or on the skew, upon a level or a gradient, upon a curve or a straight line, and whether the natural surface is horizontal or inclined; the position and form of abutments and wing walls depending so much upon the various conditions affecting each particular case, that any attempt to lay down general rules for each work would be of little use. 934. Staking out Drains.-The method of setting grade marks for drains is as follows: At every 50 feet along the line of the trench place a board a couple of feet wider than the width of the trench, bed it firmly in the earth and mark the centre line on it; then ascertain the level of the boards, calculate depth of cutting at each one, and mark it plainly on each board. To transfer the grade line to the bottom of the trench, procure a measuring-rod (say 6 feet long), subtract the depth of cutting from the length of the rod, and to the board that straddles the ditch nail a piece of board upright, the height of which above the horizontal board is equal to the difference found. This operation being performed at each board, a line stretched from the upright pieces will be parallel to the grade line, and six feet above the bottom of the trench. 935. Vertical Curves.-As stated in Article 610, the apex or meeting point of grades require to be rounded off by vertical curves, thus slightly changing the grade at and near the point of intersection. A vertical curve rarely need extend more than 200 feet each way from that point (Fig. 182). Let AB, BC, be two grades in profile, intersecting at station B, and let A and C be the adjacent stations. It is required to join the grades by a vertical curve extending from A to C. Suppose a B FIG. 182. chord drawn from A to C. The elevation of the middle point of the chord will be a mean of the elevations of grade at A and C, and one half of the difference between this and the elevation of grade at B will be the middle ordinate of the curve. Hence we have in which M equals the correction in grade for the point B. The correction for any other point is proportional to the square of its distance from A or C. Thus the correction at A+ 25, is 1 M; at A50 it is M; at A+ 75 it is M; and the same for corresponding points on the other side of B. The corrections in the case shown are subtractive, since M is negative. They are additive when M is positive, and the curve concave upward. 936. Staking out Contour of Street Foundations. In order to insure the proper transverse form of street pavements, stakes should be driven across the street, the tops of which shall correspond to the intended contour. The stakes should be placed longitudinally of the street at distances not exceeding 16 feet, and transversely at distances not exceeding 10 feet. After the stakes are placed ridges of concrete may be formed along the street, as shown in Fig. 183. After the ridges or small banks of concrete are so placed the filling of the interspaces may be proceeded with, and a straight-edge resting on the ridges will guide the workmen in keeping the concrete to the proper form; or the stakes may be placed as directed above and a thin slat nailed to their tops, the concrete filled in and made flush with the top of the slat, a straightedge 17 feet long, its ends resting on the slats, being used for this Concrete Concrete FIG. 183. MANNER OF FORMING CONTOUR OF STREETS. purpose. After the concrete is thoroughly set the slats may be removed and the space they occupied plastered over with cement. 937. Setting Stakes for Curb.-Stakes for setting curb should be placed on the front line of the curb, with their tops at the required grade. Their distance apart should not exceed 50 feet, and on circular work will require to be closer. At street corners three stakes should be driven, one at the intersection point of the meeting curbs and one at each tangent point (Fig. 184). Stake Stake Stake FIG. 184. SHOWING MANNER OF SETTING STAKES FOR CURBS. 938. In placing the stakes for any structure they should be placed so far outside of the work that they will remain undisturbed during the construction of the work. They must be so placed that lines stretched from any two of them will define the corner and face of the structure (Fig. 185). Stakes for defining the boundaries of an excavation may be placed at the angles thereof. Stake... Stake FIG. 185. MANNER OF SETTING STAKES FOR STRUC TURES. 939. Two stakes, at a sufficient distance apart upon the land, will fix any line upon the water; and two sets of stakes, upon different lines upon the shore, will by their intersection fix any point upon the water with accuracy sufficient for many purposes. For exact work, however, a transit should be employed to fix a line; and two angular instruments, in well-chosen positions, will determine any point. 940. Bench Marks.—A permanent bench or reference mark for levels should be established with care, in the immediate neighborhood of any proposed structure, from which the elevations of the various parts may be obtained. Such bench marks should also be fixed at the commencement of long cuttings, and generally at intervals of from 500 to 1000 feet along the works, a list of such elevations being entered in the engineer's note-book. CHAPTER XXII. SPECIFICATIONS AND CONTRACTS. 941. Specifications.-A specification or detailed description of the various works to be carried out is always attached to a contract, and is prepared before estimates are called for. The prominent points in connection with specifications are as follows: (1) Description of the work. (2) Extent of the work. (3) Quality of the materials. (4) Testing of the materials. (6) Character of the workmanship. (9) Time of completion. (10) Manner and times of payment. (12) Such general instructions and stipulations as may be found necessary in each case. Attention to these points and a clear and accurate description of each detail (leaving nothing to be imagined) will not only materially contribute to the rapid and efficient execution of the work, but will avoid all future misunderstandings. 942. Concerning Tests of Materials.—While proper tests should always be stipulated, yet if they are carried to an extreme degree, as frequently happens, they defeat their own object. When it becomes impossible to carry out certain unreasonable demands, the alternative is to evade them as much as possible; and it must always be borne in mind that the more stringent the demand, the greater the difficulty in enforcing it. |