Question

If a uniformly loaded circular area is divided into 20 sectors, then the influence value if is given by ___________

(a) \(\frac{1}{20}\left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^\frac{3}{2}\right]\)

(b) \(20\left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^\frac{3}{2}\right]\)

(c) \(20\left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^\frac{5}{2}\right]\)

(d) \(\frac{1}{20}\left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^\frac{5}{2} \right]\)

This question was addressed to me during an online exam.

Question is from Stress Distribution in division Stress Distribution of Geotechnical Engineering I

Answer 1

The correct option is (a) \(\frac{1}{20}\left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^\frac{3}{2}\right]\)

The best explanation: Let a uniformly loaded circular area is divided into 20 sectors.

q=load

σz=vertical stress at depth z

The stress at each unit area will be \(\frac{σ_z}{20}\)

∴ \(\frac{σ_z}{20}=\frac{q}{20}\left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^\frac{3}{2}\right]\)

The influence factor is given by \(i_f=\frac{1}{20}\left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^\frac{3}{2} \right]\).