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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 2m and 4m along the point of the loading, as per Boussinesq’s theory, would be _______.
Correct answer is '4'. Can you explain this answer?
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A concentrated load of 500 kN is applied on an elastic half space. The...
Boussinesq’s theory 
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A concentrated load of 500 kN is applied on an elastic half space. The...
The Boussinesq equation can be used to calculate the increase in vertical normal stress at different depths along the point of loading on an elastic half space. The equation is:
Δσ = (q / π) * [(z2 - z1) / r^2]
Where:
Δσ = Increase in vertical normal stress
q = Applied load
z1 = Depth 1
z2 = Depth 2
r = Distance from the point of loading to the point of interest
In this case, the applied load is 500 kN, the depth at 2m is z1 = 2m, the depth at 4m is z2 = 4m, and the distance from the point of loading to the point of interest is r.
To find the ratio of the increase in vertical normal stress at depths of 2m and 4m, we can divide the equation for depth 4m by the equation for depth 2m:
(Δσ2m / Δσ4m) = [(q / π) * (z2 - z1) / r^2] / [(q / π) * (z4 - z1) / r^2]
The π, r^2, and q cancel out, so the equation simplifies to:
(Δσ2m / Δσ4m) = (z2 - z1) / (z4 - z1)
Plugging in the values, we get:
(Δσ2m / Δσ4m) = (4m - 2m) / (4m - 2m)
(Δσ2m / Δσ4m) = 2m / 2m
(Δσ2m / Δσ4m) = 1
Therefore, the ratio of the increase in vertical normal stress at depths of 2m and 4m along the point of loading, as per Boussinesq, is 1.
Δσ = (q / π) * [(z2 - z1) / r^2]
Where:
Δσ = Increase in vertical normal stress
q = Applied load
z1 = Depth 1
z2 = Depth 2
r = Distance from the point of loading to the point of interest
In this case, the applied load is 500 kN, the depth at 2m is z1 = 2m, the depth at 4m is z2 = 4m, and the distance from the point of loading to the point of interest is r.
To find the ratio of the increase in vertical normal stress at depths of 2m and 4m, we can divide the equation for depth 4m by the equation for depth 2m:
(Δσ2m / Δσ4m) = [(q / π) * (z2 - z1) / r^2] / [(q / π) * (z4 - z1) / r^2]
The π, r^2, and q cancel out, so the equation simplifies to:
(Δσ2m / Δσ4m) = (z2 - z1) / (z4 - z1)
Plugging in the values, we get:
(Δσ2m / Δσ4m) = (4m - 2m) / (4m - 2m)
(Δσ2m / Δσ4m) = 2m / 2m
(Δσ2m / Δσ4m) = 1
Therefore, the ratio of the increase in vertical normal stress at depths of 2m and 4m along the point of loading, as per Boussinesq, is 1.
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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 2m and 4m along the point of the loading, as per Boussinesq’s theory, would be _______.Correct answer is '4'. Can you explain this answer?
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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 2m and 4m along the point of the loading, as per Boussinesq’s theory, would be _______.Correct answer is '4'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about 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 2m and 4m along the point of the loading, as per Boussinesq’s theory, would be _______.Correct answer is '4'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 2m and 4m along the point of the loading, as per Boussinesq’s theory, would be _______.Correct answer is '4'. Can you explain this answer?.
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 2m and 4m along the point of the loading, as per Boussinesq’s theory, would be _______.Correct answer is '4'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about 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 2m and 4m along the point of the loading, as per Boussinesq’s theory, would be _______.Correct answer is '4'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 2m and 4m along the point of the loading, as per Boussinesq’s theory, would be _______.Correct answer is '4'. Can you explain this answer?.
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