Question
Download Solution PDFCalculate the quantity of the earthworks in the cubic meter for a canal embankment of 100 m long having heights of 3 m and 5 m at the two extreme edges. Top widths of the embankment are 2 m and 4 m at the two extreme edges and the side slope is 2 : 1. Use the trapezoidal method.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The trapezoidal formula is given as,
\(V=\frac{L}{2}\left[ \left( {{A}_{1}}+{{A}_{n}} \right)+2\left( {{A}_{2}}+{{A}_{3}}+\ldots +{{A}_{n-1}} \right) \right]\)
Calculation:
The section across the embankment would be trapezoidal in shape.
For extreme edge (1): Top Width = 2 m, Heigth = 3, and
Bottom width = 2 + 2 × 3 + 2 × 3 = 14 m
\(⇒ A_1 = \frac{Top\;width+Bottom\;width}{2}× h=\frac{2+14}{2}× 3=24\;m^2\)
For extreme edge (2): Top Width = 4 m, Heigth = 5,
Bottom width = 4 + 2 × 5 + 2 × 5 = 24 m
\(⇒ A_2 = \frac{Top\;width+Bottom\;width}{2}× h=\frac{4+24}{2}× 5=70\;m^2\)
The volume of earthwork \(\Rightarrow V = \frac{L}{2}\left[ {\left( {{A_1} + {A_2}} \right)} \right]=\frac{100}{2}\left[ {\left( {{24} + {70}} \right)} \right]=4700\) m3.
Last updated on May 28, 2025
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