Question

If a uniformly loaded circular area is divided into 44 sectors, then the influence value if is given by ___________

(a) \(\frac{1}{44} \left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^\frac{3}{2}\right] \)

(b) \(44\left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^\frac{3}{2}\right] \)

(c) \(44\left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^\frac{5}{2}\right] \)

(d) \(\frac{1}{44} \left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^\frac{5}{2}\right] \)

This question was posed to me during an interview.

Origin of the question is Stress Distribution topic in portion Stress Distribution of Geotechnical Engineering I

Answer 1

The correct option is (a) \(\frac{1}{44} \left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^\frac{3}{2}\right] \)

Best explanation: Let a uniformly loaded circular area is divided into 44 sectors.

q=load

σz=vertical stress at depth z

The stress at each unit area will be \(\frac{σ_z}{44} \)

∴ \(\frac{σ_z}{44}=\frac{q}{44}\left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^\frac{3}{2}\right] \)

The influence factor is given by \(i_f=\frac{1}{44} \left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^\frac{3}{2}\right] \).