The vertical stress at point P1 due to the point load Q on the ground surface as shown in figure is - z- According to Boussinesq-s equation- the vertical stress at point P2 Shown in figure will be

Vertical stress at P_1' σ _z_1=3Q2π z^2 [ 11+r^2z^2 ]^5/2 Vertical stress at P_2' σ _z_2=3Q2π ( z2 )^2 [ 11+ ( r/2z/2 )^2 ]^5/2 σ _z_2=4·3Q2π z^2 [ 11+r^2z^ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Other

Foundation Engineering

Boussinesq's Formula

The vertical ...

Question

The vertical stress at point $P_{1}$ due to the point load Q on the ground surface as shown in figure is $σ_{z}$ . According to Boussinesq's equation, the vertical stress at point $P_{2}$ Shown in figure will be

σ_{z} / 2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

σ_{z}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 σ_{z}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4 σ_{z}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $4 σ_{z}$
Vertical stress at $P_{1^{'}}$

$σ_{z_{1}} = \frac{3 Q}{2 π z^{2}} {⎡ ⎢ ⎢ ⎢ ⎣ \frac{1}{1 + \frac{r^{2}}{z^{2}}} ⎤ ⎥ ⎥ ⎥ ⎦}^{5 / 2}$

Vertical stress at $P_{2^{'}}$

$σ_{z_{2}} = \frac{3 Q}{2 π {(\frac{z}{2})}^{2}} {⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ \frac{1}{1 + {(\frac{r / 2}{z / 2})}^{2}} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦}^{5 / 2}$

$σ_{z_{2}} = 4 \cdot \frac{3 Q}{2 π z^{2}} {⎡ ⎢ ⎢ ⎢ ⎣ \frac{1}{1 + \frac{r^{2}}{z^{2}}} ⎤ ⎥ ⎥ ⎥ ⎦}^{5 / 2}$

$= 4 σ_{z_{1}}$

Suggest Corrections

Similar questions

Q. Consider a square-shaped area ABCD on the ground with this centre at M as shown in the figure. Four concentrated vertical loads of P = 5000 kN are applied on this area, one at each corner.

The vertical stress increment (in kPa up to one decimal place) due to these loads according to the Boussinesq's equation at a point 5m right below M is

σ_{z}

is the vertical stress at a depth equal to Z in the soil mass due to a surface point load Q. The vertical stress at depth equal to 2Z will be

Q. A concentrated load of 50 t acts vertically at a point on the soil surface.If Boussinesq's equation is applied for computation of stress, then the ratio of vertical stresses at depths of 3 m and 5 m respectively vertically below the point of application of load will be

Q. A concentrated load of 500kN is applied on an elastic half space. The ratio of the increase in vertical normal stress at depth of 2m and 4m along the point of the loading, as per Boussinesq's theory, would be .

Q. A uniformly distributed line load of 500kN/m is acting on the ground surface. Based on Boussinesq's theory, the ratio of vertical stress at a depth 2 m to that at 4 m right below the line of loading is

Join BYJU'S Learning Program

The vertical stress at point P1 due to the point load Q on the ground surface as shown in figure is σz. According to Boussinesq's equation, the vertical stress at point P2 Shown in figure will be

The correct option is D 4σzVertical stress at P1′ σz1=3Q2πz2⎡⎢ ⎢ ⎢⎣11+r2z2⎤⎥ ⎥ ⎥⎦5/2 Vertical stress at P2′ σz2=3Q2π(z2)2⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣11+(r/2z/2)2⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦5/2 σz2=4⋅3Q2πz2⎡⎢ ⎢ ⎢⎣11+r2z2⎤⎥ ⎥ ⎥⎦5/2 =4σz1

The vertical stress at point $P_{1}$ due to the point load Q on the ground surface as shown in figure is $σ_{z}$ . According to Boussinesq's equation, the vertical stress at point $P_{2}$ Shown in figure will be