L8: Earthwork Quantities Flashcards
Why is the study of areas and volumes important for engineering projects?
It is often necessary to:
Make accurate assumption/calculation about the volume of materials to be transported or the area to be worked on
Estimate time and cost of work, form basis of payment for conducted work
Areas may be required in connection with purchase/sale of land or subdivision thereof
How is area defined in plane surveying?
The orthographic projection of the surface onto a horizontal plane
List a few methods for calculating area (both from field measurements and from maps)
Field measurement (more accurate):
1) division of tract into simple figures
2) offsets from a straight line
3) coordinates
4) double-meridian distances
From map:
1) counting coordinate squares
2) dividing area into regular geometric shapes
3) digitizing coordinates
4) planimeter
Discuss the graphical method for determining area
Use transparent overlay of squared paper over drawing/plan
Count number of squares and parts of squares to calculate the area
Accuracy depends on size of grid
Discuss the method of calculating areas from triangles
Area = sqrt[s(s-a)(s-b)(s-c)]
Where:
a,b,c - side lengths
s = 1 / 2(a+b+c)
OR
Area = 0.5ab*sinC
Where:
a,b - side lengths
C - angle between a and b
Subdivide area into triangles and work from there
Describe the method of calculating area from coordinates
The total area enclosed by a traverse can be expressed in terms of the areas of individual traverses
Formula (for three points but it follows the same pattern):
2(area) = XaYb + XbYc + XcYa - YaXb - YbXc - YcXa
Use the criss-cross table visualization
Define meridian distance
The perpendicular distance from the midpoint of a traverse course to the reference meridian (the first point)
Define double-meridian distance (DMD)
Twice the meridian distance
What are the three rules of computing the DMD for each course of a traverse?
1) The DMD of the first course is equal to its departure
2) The DMD of any other course is equal to the DMD of the preceding course plus the departure of the preceding course plus the departure of the course itself
3) The DMD of the last course is of the same magnitude but opposite direction of its departure
Discuss how to calculate area using the DMD method
For each course, the DMD is multiplied by the latitude (signs important here)
The sum of the multiplications will be equal to twice the area of the traverse (so divide by 2 to get the actual area)
What is the trapezoid rule applied to and what is its formula?
Applied to get the area of a profile
A = 0.5L12(O1 + O2) + 0.5L23(O2+O3) + …
Where:
A - area
L - length of an interval
O - offset at that point (negative elevation)
What is Simpson’s rule?
Similar to trapezoid but assumes that the boundary is a series of parabolic arcs rather than straight lines (more accurate)
Considers offsets in sets of three
The area between offset 1 and 3:
A = L/3(O1 + 4O2 + O3)
If there is an even number of offsets, the last offset is omitted and the trapezoid rule must be used to find that area
Describe planimeters
Devices that trace over the perimeter of an object and therefore calculate the angle
Work similar to an odometer but also consider angle switch ups
