SSC JE Civil Engineering 30-Oct-2020 Shift 2 Paper

Concept:

Gradient:
A gradient is the rate of rise or falls along the length of the road with respect to horizontal. It is expressed as ‘1' vertical unit to 'N' horizontal units. Tan θ = $\frac{\mathrm{h}}{\mathrm{I}}$
$\frac{\mathrm{h}}{\mathrm{I}}$ = $\frac{\mathrm{1}}{\mathrm{N}}$
Area of trapezoidal:
According to the trapezoid area formula, the area of a trapezoid is equal to half the product of the height and the sum of the two bases.
Area = $\frac{1}{2}$ × (Sum of parallel sides) × (perpendicular distance between the parallel sides).
Calculation: Road embankment = 10 m
Average height = 5 m
Difference in elevation(h) = 280 - 220 = 60 m
Average gradient = $\frac{1}{40}$
$\frac{\mathrm{h}}{\mathrm{l}}=\frac{1}{40}$
$\frac{60}{1}=\frac{1}{40}$
L = 2400 m Average cross-sectional area(A) = 12×(10+30)×5
A = 100 ${\mathit{m}}^2$
Volume of earthwork = A × L
Volume of earthwork = 100 × 2400
∴ Volume of earthwork = 2,40,000 ${\mathrm{m}}^3$