Handbook of Civil Engineering Calculations

H = Ks COS^2 Ct + C cos a (11)

V=y 2 Kssm2a + Csma (12)

Elevation of N= elevation of O + OM + V-NQ (13)

where K = stadia interval factor; C = distance from center of instrument to principal
focus.

2. Substitute numerical values in the above equations
   The results obtained are shown:

Point H, ft(m) ^,ft(m) Elevation, ft (m)

1 544.8(166.06) 25.4 (7.74) 505.6(154.11)

2 622.0(189.59) 34.8 (10.61) 520.0(158.50)

3 482.5(147.07) -15.7 (-4.79) 468.5(142.80)

VOLUME OF EARTHWORK

Figure 10« and b represent two highway cross sections 100 ft (30.5 m) apart. Compute the
volume of earthwork to be excavated, in cubic yards (cubic meters). Apply both the aver-
age-end-area method and the prismoidal method.

Calculation Procedure:

1. Resolve each section into an isosceles trapezoid and a triangle;
   record the relevant dimensions
   Let A 1 and A 2 denote the areas of the end sections, L the intervening distance, and V the
   volume of earthwork to be excavated or filled.
   Method 1: The average-end-area method equates the average area to the mean of the
   two end areas. Then

L(A 1 ^-A 2 )

V= \ (14)

Figure 1Oc shows the first section resolved into an isosceles trapezoid and a triangle,

along with the relevant dimensions.

2. Compute the end areas, and apply Eq. 14
   Thus: A 1 = [24(40 + 64) + (32 - 24)64]/2 = 1504 ft
   2
   (139.72 m
   2
   ); A 2 = [36(40 + 76) + (40

• 36)76]/2 - 2240 ft
  2
  (208.10 m
  2
  ); V= 100(1504 + 2240)/[2(27)] = 6933 yd
  3
  (5301.0 m
  3
  ).

3. Apply the prismoidal method
   Method 2: The prismoidal method postulates that the earthwork between the stations is a
   prismoid (a polyhedron having its vertices in two parallel planes). The volume of a pris-
   moid is

y=_±_lL(A «^1 + 4Am 27 + A^2 ) (15)

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