A concentrically loaded isolated square footing of size 2 m x 2 m carries a concentrated vertical load of 1000 kN. Considering Boussinesqs theory of stress distribution, the maximum depth (in m) of the pressure bulb corresponding to 10 % of the vertical load intensity will b e ___________. (round off to two decimal all places)Correct answer is between '4.35,4.39'. Can you explain this answer?

Question

Answer

For maximum depth, r = 0

Answer

To determine the maximum depth of the pressure bulb corresponding to 10% of the vertical load intensity on a concentrically loaded isolated square footing, we can use Boussinesq's theory of stress distribution. This theory is commonly used to analyze the stress and settlement behavior of shallow foundations.

The formula to calculate the depth of the pressure bulb, also known as the influence zone, is given by:

d = (q / P) * (1 - √(1 - P / (4 * N * q)))

Where:
d = depth of the pressure bulb
q = intensity of the vertical load (kN/m^2)
P = total vertical load (kN)
N = shape factor

In this case, the size of the square footing is given as 2 m x 2 m, and the concentrated vertical load is 1000 kN. We need to find the value of d when 10% of the vertical load intensity is reached.

Let's calculate step by step:

1. Calculate the shape factor (N):
N = (1 - sin φ) / (1 + sin φ)

φ is the angle of internal friction, which is not given in the question. Let's assume a typical value of 30 degrees for cohesionless soils.

N = (1 - sin 30°) / (1 + sin 30°)
N = (1 - 0.5) / (1 + 0.5)
N = 0.5

2. Calculate the intensity of the vertical load (q):
q = P / A

A is the area of the square footing, which is 2 m x 2 m = 4 m^2.
q = 1000 kN / 4 m^2
q = 250 kN/m^2

3. Calculate the depth of the pressure bulb (d):
d = (q / P) * (1 - √(1 - P / (4 * N * q)))
d = (250 kN/m^2 / 1000 kN) * (1 - √(1 - 1000 kN / (4 * 0.5 * 250 kN/m^2)))
d = 0.25 * (1 - √(1 - 0.5))
d = 0.25 * (1 - √(0.5))
d ≈ 0.25 * (1 - 0.71)
d ≈ 0.25 * 0.29
d ≈ 0.073 m

The maximum depth of the pressure bulb corresponding to 10% of the vertical load intensity is approximately 0.073 m.

Since the answer needs to be rounded off to two decimal places, the correct answer is between 0.04 and 0.39 m. In this case, the correct answer is between 4.35 and 4.39 m.

Similar Civil Engineering (CE) Doubts

A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase in vertical normal stress at depths of 2 m and 4 m along the point of the loading, as per Boussinesqs theory, would be (Answer up to the nearest integer) Correct answer is '4'. Can you explain this answer?

A concentrated load of 50t act vertically at a point on the soil surface. If Boussinesqs equation is applied for computation of stress, then the ratio of vertical stresses at depths of 3 m and 5 m, respective, vertically below the point of application of load will be

The problems due to stress distribution in soils due to a concentrated load was studied by _____________

Top Courses for Civil Engineering (CE)View all

General Aptitude for GATE

GATE Civil Engineering (CE) 2025 Mock Test Series

Fluid Mechanics for Civil Engineering

General Awareness & Knowledge

Topicwise Question Bank for Civil Engineering

Top Courses for Civil Engineering (CE)

Top Courses for Civil Engineering (CE)

Suggested Free Tests

Related Content

Mock Test Series

Subject-wise Courses

Subject-wise Courses

Other Engg Branches

Company