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AREA  OF  FIVE-LEVEL  OR  IRREGULAR SECTION - 14070_207
Table 10-1.Soil Conversion Factors

Engineering Aid 1 - Advanced Structural engineering guide book
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determine the area of sections of this kind, you should use a method of determining area by coordinates. For explanation purpose, let’s consider station 305 (fig. 10-6). First, consider the point where the center line intersects the grade line as the point of origin for the  coordinates.  Vertical  distances  above  the  grade  line are positive Y coordinates; vertical distances below the grade line are negative Y coordinates. A point on the grade line itself has a  Y coordinate  of  0.  Similarly, horizontal distances to the right of the center line are positive  X coordinates; distances to the left of the center line  are  negative  X coordinates;  and  any  point  on  the center line itself has an X coordinate of 0. Plot the cross section, as shown in figure 10-7, and be sure that the X and Y coordinates  have  their  proper signs. Then, starting at a particular point and going successively in a clockwise direction, write down the coordinates, as shown in figure 10-8. After writing down the coordinates, you then mul- tiply each  upper term by the algebraic difference  of the following lower term and the  preceding  lower  term, as  indicated  by  the  direction  of  the  arrows  (fig.  10-8). The  algebraic  sum  of  the  resulting  products  is  the double  area of the cross section. Proceed with the computation  as  follows: Since  the  result  (1,080.70  square  feet)  represents the double area, the area of the cross section is one half of that amount, or 540.35 square feet. By similar method, the area of the cross section at station 306 (fig. 10-7) is 408.40 square feet. EARTHWORK   VOLUME.—   As   discussed previously,  when  you  know  the  area  of  two  cross sections,  you  can  multiply  the  average  of  those cross-sectional  areas  by  the  known  distance  between them to obtain the volume of earth to be cut or filled. Consider  figure  10-9  that  shows  the  plotted  cross sections of two sidehill sections. For this figure, when you multiply the average-end area (in fill) and the average-end area (in cut) by the distance between the two  stations  (100  feet),  you  obtain  the  estimated amount of cut and fill between the stations. In this case,  the  amount  of  space  that  requires  filling  is computed to be approximately 497.00 cubic yards and the amount of cut is about 77.40 cubic yards. MASS DIAGRAMS.— A  concern  of  the  highway designer  is  economy  on  earthwork.  He  wants  to  know exactly  where,  how  far,  and  how  much  earth  to  move in a section of road. The ideal situation is to balance the cut and fill and limit the haul distance. A technique for  balancing  cut  and  fill  and  determining  the Figure 10-9.—Plots of two sidehill sections. Figure  10-8.—Coordinates  for  cross-section  station  305  shown  in  figure  10-7. 10-10







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