Consider that a force P is acting on the surface of a half-space (Boussinesq’s problem). The expression for the vertical stress (σz) at any point (r, z), within the half-space is given as, \sigma _{z} = \frac{3P}{2\pi } {z^{3}}/{_{(r^{2} + z^{2})}\frac{5}{2}} where, r is the radial distance, and z is the depth with downward direction taken as positive. At any given r, there is a variation of σ z along z, and at a specific z, the value of σz will be maximum. What is the locus of the maximum σz ?

GATE Civil Engineering (CE) 2023 Shift 1 Solved Paper

Question : 41 of 65

Marks: +1, -0

Consider that a force P is acting on the surface of a half-space (Boussinesq’s problem). The expression for the vertical stress (σz) at any point (r, z), within the half-space is given as,

σ _{z} = \;{3P}/{2π\;}\;{z^{3}}/{_{(r^{2} + z^{2})}\;{5}/{2}}

where, r is the radial distance, and z is the depth with downward direction taken as positive. At any given r, there is a variation of σ_z along z, and at a specific z, the value of σz will be maximum. What is the locus of the maximum σz ?

$z^{2} = \;{3}/{2}r^{2}$
$z^{3} = \;{3}/{2}r^{2}$
$z^{2} = \;{5}/{2}r^{2}$
$z^{3} = \;{5}/{2}r^{2}$

Validate

Go to Question:

Prev Question

Next Question