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fundamentals of engineering supplied-reference handbook - Ventech!

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EARTHWORK FORMULAS<br />

Average End Area Formula, V = L(A1 + A2)/2<br />

Prismoidal Formula, V = L (A1 + 4Am + A2)/6, where Am = area <strong>of</strong> mid-section<br />

Pyramid or Cone, V = h (Area <strong>of</strong> Base)/3<br />

where L = distance between A1 and A2<br />

AREA FORMULAS<br />

Area by Coordinates: Area = [XA (YB – YN) + XB (YC – YA) + XC (YD – YB) + ... + XN (YA – YN–1)] / 2<br />

⎛ h1<br />

+ hn<br />

⎞<br />

Trapezoidal Rule: Area = w ⎜ + h2<br />

+ h3<br />

+ h4<br />

+ … + hn−1<br />

⎟ w = common interval<br />

⎝ 2<br />

⎠<br />

⎡ ⎛ n−2<br />

⎞ ⎛ n−1<br />

⎞ ⎤<br />

Simpson's 1/3 Rule: Area = w⎢h1<br />

+ 2⎜<br />

∑ hk<br />

⎟ + 4⎜<br />

∑ hk<br />

⎟ + hn<br />

⎥ 3<br />

⎣ ⎝ k = 3,<br />

5,<br />

… ⎠ ⎝ k = 2,<br />

4,<br />

… ⎠ ⎦<br />

142<br />

CIVIL ENGINEERING (continued)<br />

n must be odd number <strong>of</strong> measurements<br />

w = common interval

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