The numbers in the horizontal column, T. P., are found thus: The-S., 11.399, is obtained from the first position of the instrument by the reading of the rod on T. P. 21.512 32.911 11.399. The + S., 2.243, is the reading of the rod from the new position of the instrument. 23.775 21.512+ 2.243. The cutting or filling is the difference of S. H. and G. H. 347. Profile of Section and Grade. 11.5 348. Remarks. 1. The grade height at 0, minus the grade at 6, which the descent from 0 to 6. 18÷ is 29.5 11.5 18 2. The establishment of the grade is influenced by the object of the work, economy, the balance of cuttings and fillings, the points desirable for termini, etc. 3. The method exhibited above may be extended to any distance. 349. Example. Fill out the notes of the following table, and make a profile of section and grade from S. H. at 0 to S. H. at 5. Excavations and embankments are constructed with sloping sides, in order to prevent the sliding of earth down the surface. The ratio of slope is the vertical distance divided by the horizontal, and is therefore the tangent of the angle which the sloping surface makes with a horizontal plane. The usual ratio of slope is, and the angle 33° 41'. Slope stakes are driven to mark where the sloping sides, whether of cutting or filling, will intersect the surface, and thus indicate the boundaries of the work. The rod used in cross-section leveling is 15 feet long, graded and plainly marked to feet and tenths, and is read by the leveler at the instruments. The assistants of the leveler are the rodman, axman, and two tapemen. The Field book is ruled into four columns, headed D. for distance; L. for left; C. C. for center-cut; R. for right. The numbers in the columns D. and C. C. are, respectively, the distance and the corresponding cut, or fill marked minus cut, taken from the field book for section leveling. The fractions in the columns L. and R. have for their numerators the vertical distances of the cross-section, and for their denominators, the corresponding horizontal distances, from the center or from the vertex of the angle of slope, according as the vertical distance is taken within or without the limits of the horizontal portion of the road. 351. Cross-Section Excavations. We give the following profile of cross-section, the method of performing the field operations and recording the notes. Let us suppose the cross-section to be taken at the distance 3 of the field notes of article 343, where the center cut is 8.3; that the road bed is 20 feet wide, that the ratio of slope is, and that both horizontal and vertical distances are plotted to the scale of 20 feet to 1 inch. Take AA' for the datum line, and suppose the reading at the center stake to be 7.4. The height of the instrument above the datum line is therefore 8.3 + 7.4 15.7. The reading of the rod at the depression F, between the center and the angle A, is 8.5; hence, the cut is 15.78.57.2. The horizontal distance, CF, is 4 feet; hence, the record in the field notes, as seen in the next article in the column L, is 72 4 The reading of the rod, at the temporary stake E, is 8.3 7.4; hence, the cut is 15.7-7.48.3, and the entry, Α The point S, where the slope intersects the surface, is found by trial. Since the vertical distance of the slope is of the horizontal, then ES, if horizontal, would be of EA, which is 12.4; but, on account of the inclination of the surface, ES will be less, say 10 feet. Setting the rod 10 feet out from E, the reading is 8.3, and hence the cut 15.7-8.3 7.4. Now, 3 of 7.4 is 11.1; hence, the assumed distance, 10 feet, is too small. For a second trial, take 11 feet out from E, at which the reading of the rod is 8.4, and the cut 7.3. Now, 3 of 7.3 10.9, which lacks but .1 of 11, and is sufficiently accurate. The record for the slope stake, in the column L, is 7.3 The reading of the rod at the stake D is 6.9; hence, the cut is 8.8, and the record in the column R is 8.8 The reading at the elevation G is 5.1; hence, the cut is 10.6. The horizontal distance, DG, is 9 feet; 10.6 9 hence, the record is To find S' where the slope intersects the surface, since, on account of the rising of the surface, it is more than of 8.8, which is 13.2, take, for a first trial, 18 feet out from D, at which point the reading of the rod is 4.5, and hence the cut 15.7 4.5 11.2. Now, 3 of 11.2 16.8; hence, 18 feet is too far out. For a second trial, take 17 feet out from D. The reading of the rod is 4.3, and the cut 15.7-4.3 11.4. Now, of 11.4 17.1, which is sufficiently accurate; hence, the record for the slope stake S', in the column 11.4 R, is 17.1 352. Field Notes. The following is the profile of the cross section drawn to a scale of 20 feet to 1 inch, taken at the distance 5 of the field notes of article 346, where the filling is 3.2, now called a minus cut, and written — 3.2. Take AA', which is the horizontal top of the embankment 20 feet wide, for the datum line. |