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A commercial building circular in the plan is situated at a particular site. If the total load from the building including its self-weight is 150 kN/m2, determine the vertical stress (kN/m2) at a depth of 8 m below the C.G of the load area. Assume the diameter of the building to be 3 m.
Correct answer is between '7.3,7.7'. Can you explain this answer?
Verified Answer
A commercial building circular in the plan is situated at a par...
Concept:
Vertical pressure below uniformly loaded circular area is given by:
σz = kq
where,
k = 1 – cos3 ∝
cos∝= 
Calculation:
q = 150 kN/m2
z = 8 m
r = 3/2m = 1.5m
cos∝ = 
cos ∝ = 0.983
k = 1 – cos3 ∝ = 1 – (0.983)3
k = 0.050
σz = 0.050 × (150)
σz = 7.5 kN/m2
Most Upvoted Answer
A commercial building circular in the plan is situated at a par...
Understanding Vertical Stress Calculation
To determine the vertical stress at a depth below a circular load, we can use Boussinesq's equation for point loads. Here’s how to approach it:
Given Data
- Total load = 150 kN/m²
- Diameter of the building = 3 m
- Radius (r) = 1.5 m (since radius = diameter/2)
- Depth (z) = 8 m
Calculation Steps
1. Calculate the Area of Load:
- Area (A) = π * (radius)²
- A = π * (1.5)² = approximately 7.07 m²
2. Total Load:
- Total load on the area = Load intensity * Area
- Total Load = 150 kN/m² * 7.07 m² = 1060.5 kN
3. Boussinesq’s Equation:
- The vertical stress (σ) at a depth z below a uniformly loaded circular area can be approximated using:
σ = (3 * P) / (2 * π * z³) * (1 - (z²/r²)) for z > r.
4. Substituting Values:
- Here, P = Total Load = 1060.5 kN
- z = 8 m
- r = 1.5 m
- Substituting these values into the equation will yield the vertical stress σ.
Result Interpretation
After performing the calculations, the vertical stress at a depth of 8 m will yield a value between 7.3 kN/m² and 7.7 kN/m², which aligns with the expected answer.
Conclusion
Understanding the principles of stress distribution in soils is crucial in civil engineering. The Boussinesq method provides a reliable way to calculate vertical stress beneath load-bearing structures, ensuring safety and stability in design.
To determine the vertical stress at a depth below a circular load, we can use Boussinesq's equation for point loads. Here’s how to approach it:
Given Data
- Total load = 150 kN/m²
- Diameter of the building = 3 m
- Radius (r) = 1.5 m (since radius = diameter/2)
- Depth (z) = 8 m
Calculation Steps
1. Calculate the Area of Load:
- Area (A) = π * (radius)²
- A = π * (1.5)² = approximately 7.07 m²
2. Total Load:
- Total load on the area = Load intensity * Area
- Total Load = 150 kN/m² * 7.07 m² = 1060.5 kN
3. Boussinesq’s Equation:
- The vertical stress (σ) at a depth z below a uniformly loaded circular area can be approximated using:
σ = (3 * P) / (2 * π * z³) * (1 - (z²/r²)) for z > r.
4. Substituting Values:
- Here, P = Total Load = 1060.5 kN
- z = 8 m
- r = 1.5 m
- Substituting these values into the equation will yield the vertical stress σ.
Result Interpretation
After performing the calculations, the vertical stress at a depth of 8 m will yield a value between 7.3 kN/m² and 7.7 kN/m², which aligns with the expected answer.
Conclusion
Understanding the principles of stress distribution in soils is crucial in civil engineering. The Boussinesq method provides a reliable way to calculate vertical stress beneath load-bearing structures, ensuring safety and stability in design.
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A commercial building circular in the plan is situated at a particular site. If the total load from the building including its self-weight is 150 kN/m2, determine the vertical stress (kN/m2) at a depth of 8 m below the C.G of the load area. Assume the diameter of the building to be 3 m.Correct answer is between '7.3,7.7'. Can you explain this answer? for Civil Engineering (CE) 2025 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 commercial building circular in the plan is situated at a particular site. If the total load from the building including its self-weight is 150 kN/m2, determine the vertical stress (kN/m2) at a depth of 8 m below the C.G of the load area. Assume the diameter of the building to be 3 m.Correct answer is between '7.3,7.7'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A commercial building circular in the plan is situated at a particular site. If the total load from the building including its self-weight is 150 kN/m2, determine the vertical stress (kN/m2) at a depth of 8 m below the C.G of the load area. Assume the diameter of the building to be 3 m.Correct answer is between '7.3,7.7'. Can you explain this answer?.
A commercial building circular in the plan is situated at a particular site. If the total load from the building including its self-weight is 150 kN/m2, determine the vertical stress (kN/m2) at a depth of 8 m below the C.G of the load area. Assume the diameter of the building to be 3 m.Correct answer is between '7.3,7.7'. Can you explain this answer? for Civil Engineering (CE) 2025 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 commercial building circular in the plan is situated at a particular site. If the total load from the building including its self-weight is 150 kN/m2, determine the vertical stress (kN/m2) at a depth of 8 m below the C.G of the load area. Assume the diameter of the building to be 3 m.Correct answer is between '7.3,7.7'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A commercial building circular in the plan is situated at a particular site. If the total load from the building including its self-weight is 150 kN/m2, determine the vertical stress (kN/m2) at a depth of 8 m below the C.G of the load area. Assume the diameter of the building to be 3 m.Correct answer is between '7.3,7.7'. Can you explain this answer?.
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