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A square footing of 4m side is placed at 1 m depth in a sand deposit. The dry unit weight (γ) of sand is 15 kN/m3. This footing has an ultimate bearing capacity of 600 kPa. Consider the depth factors; dq = dγ = 1.0 and the bearing capacity factor: Nγ = 18.This footing is placed at a depth of 2m in the same soil deposit. For a factor of safety of 3.0 per Terzaghi’s theory, the safe bearing capacity (in kPa) of this footing would be ________
Correct answer is '270'. Can you explain this answer?
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Verified Answer
A square footing of 4m side is placed at 1 m depth in a sand deposit. ...
Side of square footing = 4 m
Depth of footing = 1 m
Unit weight of soil = 15 KN/m3
Ultimate bearing capacity = 600 KPa
Depth factors, dq = dγ = 1
Nγ = 18.75
According to terzaghi, the ultimate bearing capacity of square footing is given as
At depth of footing = 1 m
qu = 1.3CNC + qNqdq + 04BγNγdγ
For sand, C = 0, q = γDf = 15 × 1 = 15KN m2
600 = 0 + 15 × Nq × 1 + 0.4 × 4 × 15 × 18.75 × 1
⇒ Nq = 10
Now at depth of footing at 2m
qu = 1.3 CNC + qNq + 0.4BγNγdγ
qu = 0 + (2 × 15)10 × 1 + 0.4 × 4 × 15 × 18.75 × 1
qu = 750 KPa
∵ We know that
qnu = qu - γDf
qnu = 750 – 15 × 2
qnu = 720 KPa
and safe bearing capacity qsafe
Depth of footing = 1 m
Unit weight of soil = 15 KN/m3
Ultimate bearing capacity = 600 KPa
Depth factors, dq = dγ = 1
Nγ = 18.75
According to terzaghi, the ultimate bearing capacity of square footing is given as
At depth of footing = 1 m
qu = 1.3CNC + qNqdq + 04BγNγdγ
For sand, C = 0, q = γDf = 15 × 1 = 15KN m2
600 = 0 + 15 × Nq × 1 + 0.4 × 4 × 15 × 18.75 × 1
⇒ Nq = 10
Now at depth of footing at 2m
qu = 1.3 CNC + qNq + 0.4BγNγdγ
qu = 0 + (2 × 15)10 × 1 + 0.4 × 4 × 15 × 18.75 × 1
qu = 750 KPa
∵ We know that
qnu = qu - γDf
qnu = 750 – 15 × 2
qnu = 720 KPa
and safe bearing capacity qsafe
Most Upvoted Answer
A square footing of 4m side is placed at 1 m depth in a sand deposit. ...
Γd) of the sand is 18.5 kN/m3 and the angle of internal friction (ϕ) is 30°. Determine the ultimate bearing capacity of the footing using Terzaghi's bearing capacity theory.
Solution:
The ultimate bearing capacity of the footing can be determined using the following equation:
Qu = cNc + qNq + 0.5γBNγ
where,
Qu = ultimate bearing capacity
c = cohesion
Nc, Nq, Nγ = bearing capacity factors
q = surcharge
γ = unit weight of soil
B = width of the footing
First, we need to determine the values of the bearing capacity factors.
Nc = [(Nq-1)tan^2(ϕ)] / [1 + tan^2(ϕ)]
Nq = 1 + 0.4Df/B(1 - sinϕ)
Nγ = 0.5Df/B(1 + sinϕ)
where,
Df = depth of the footing
Plugging in the values, we get:
Nc = [(1.4-1)tan^2(30)] / [1 + tan^2(30)] = 0.98
Nq = 1 + 0.4(1)(1/4)(1 - sin30) = 1.2
Nγ = 0.5(1)(1/4)(1 + sin30) = 0.31
Next, we need to determine the values of the cohesion and surcharge.
Since the sand deposit is assumed to be cohesionless, the cohesion (c) is zero.
The surcharge (q) is also zero since there are no additional loads acting on the soil.
Finally, we can determine the ultimate bearing capacity:
Qu = cNc + qNq + 0.5γBNγ
Qu = 0 + 0 + 0.5(18.5)(4)(0.31)
Qu = 2.87 kN/m2
Therefore, the ultimate bearing capacity of the footing is 2.87 kN/m2.
Solution:
The ultimate bearing capacity of the footing can be determined using the following equation:
Qu = cNc + qNq + 0.5γBNγ
where,
Qu = ultimate bearing capacity
c = cohesion
Nc, Nq, Nγ = bearing capacity factors
q = surcharge
γ = unit weight of soil
B = width of the footing
First, we need to determine the values of the bearing capacity factors.
Nc = [(Nq-1)tan^2(ϕ)] / [1 + tan^2(ϕ)]
Nq = 1 + 0.4Df/B(1 - sinϕ)
Nγ = 0.5Df/B(1 + sinϕ)
where,
Df = depth of the footing
Plugging in the values, we get:
Nc = [(1.4-1)tan^2(30)] / [1 + tan^2(30)] = 0.98
Nq = 1 + 0.4(1)(1/4)(1 - sin30) = 1.2
Nγ = 0.5(1)(1/4)(1 + sin30) = 0.31
Next, we need to determine the values of the cohesion and surcharge.
Since the sand deposit is assumed to be cohesionless, the cohesion (c) is zero.
The surcharge (q) is also zero since there are no additional loads acting on the soil.
Finally, we can determine the ultimate bearing capacity:
Qu = cNc + qNq + 0.5γBNγ
Qu = 0 + 0 + 0.5(18.5)(4)(0.31)
Qu = 2.87 kN/m2
Therefore, the ultimate bearing capacity of the footing is 2.87 kN/m2.
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A square footing of 4m side is placed at 1 m depth in a sand deposit. The dry unit weight (γ) of sand is 15 kN/m3. This footing has an ultimate bearing capacity of 600 kPa. Consider the depth factors; dq = dγ = 1.0 and the bearing capacity factor: Nγ = 18.This footing is placed at a depth of 2m in the same soil deposit. For a factor of safety of 3.0 per Terzaghi’s theory, the safe bearing capacity (in kPa) of this footing would be ________Correct answer is '270'. Can you explain this answer?
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A square footing of 4m side is placed at 1 m depth in a sand deposit. The dry unit weight (γ) of sand is 15 kN/m3. This footing has an ultimate bearing capacity of 600 kPa. Consider the depth factors; dq = dγ = 1.0 and the bearing capacity factor: Nγ = 18.This footing is placed at a depth of 2m in the same soil deposit. For a factor of safety of 3.0 per Terzaghi’s theory, the safe bearing capacity (in kPa) of this footing would be ________Correct answer is '270'. 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 square footing of 4m side is placed at 1 m depth in a sand deposit. The dry unit weight (γ) of sand is 15 kN/m3. This footing has an ultimate bearing capacity of 600 kPa. Consider the depth factors; dq = dγ = 1.0 and the bearing capacity factor: Nγ = 18.This footing is placed at a depth of 2m in the same soil deposit. For a factor of safety of 3.0 per Terzaghi’s theory, the safe bearing capacity (in kPa) of this footing would be ________Correct answer is '270'. 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 square footing of 4m side is placed at 1 m depth in a sand deposit. The dry unit weight (γ) of sand is 15 kN/m3. This footing has an ultimate bearing capacity of 600 kPa. Consider the depth factors; dq = dγ = 1.0 and the bearing capacity factor: Nγ = 18.This footing is placed at a depth of 2m in the same soil deposit. For a factor of safety of 3.0 per Terzaghi’s theory, the safe bearing capacity (in kPa) of this footing would be ________Correct answer is '270'. Can you explain this answer?.
A square footing of 4m side is placed at 1 m depth in a sand deposit. The dry unit weight (γ) of sand is 15 kN/m3. This footing has an ultimate bearing capacity of 600 kPa. Consider the depth factors; dq = dγ = 1.0 and the bearing capacity factor: Nγ = 18.This footing is placed at a depth of 2m in the same soil deposit. For a factor of safety of 3.0 per Terzaghi’s theory, the safe bearing capacity (in kPa) of this footing would be ________Correct answer is '270'. 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 square footing of 4m side is placed at 1 m depth in a sand deposit. The dry unit weight (γ) of sand is 15 kN/m3. This footing has an ultimate bearing capacity of 600 kPa. Consider the depth factors; dq = dγ = 1.0 and the bearing capacity factor: Nγ = 18.This footing is placed at a depth of 2m in the same soil deposit. For a factor of safety of 3.0 per Terzaghi’s theory, the safe bearing capacity (in kPa) of this footing would be ________Correct answer is '270'. 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 square footing of 4m side is placed at 1 m depth in a sand deposit. The dry unit weight (γ) of sand is 15 kN/m3. This footing has an ultimate bearing capacity of 600 kPa. Consider the depth factors; dq = dγ = 1.0 and the bearing capacity factor: Nγ = 18.This footing is placed at a depth of 2m in the same soil deposit. For a factor of safety of 3.0 per Terzaghi’s theory, the safe bearing capacity (in kPa) of this footing would be ________Correct answer is '270'. Can you explain this answer?.
Solutions for A square footing of 4m side is placed at 1 m depth in a sand deposit. The dry unit weight (γ) of sand is 15 kN/m3. This footing has an ultimate bearing capacity of 600 kPa. Consider the depth factors; dq = dγ = 1.0 and the bearing capacity factor: Nγ = 18.This footing is placed at a depth of 2m in the same soil deposit. For a factor of safety of 3.0 per Terzaghi’s theory, the safe bearing capacity (in kPa) of this footing would be ________Correct answer is '270'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
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A square footing of 4m side is placed at 1 m depth in a sand deposit. The dry unit weight (γ) of sand is 15 kN/m3. This footing has an ultimate bearing capacity of 600 kPa. Consider the depth factors; dq = dγ = 1.0 and the bearing capacity factor: Nγ = 18.This footing is placed at a depth of 2m in the same soil deposit. For a factor of safety of 3.0 per Terzaghi’s theory, the safe bearing capacity (in kPa) of this footing would be ________Correct answer is '270'. Can you explain this answer?, a detailed solution for A square footing of 4m side is placed at 1 m depth in a sand deposit. The dry unit weight (γ) of sand is 15 kN/m3. This footing has an ultimate bearing capacity of 600 kPa. Consider the depth factors; dq = dγ = 1.0 and the bearing capacity factor: Nγ = 18.This footing is placed at a depth of 2m in the same soil deposit. For a factor of safety of 3.0 per Terzaghi’s theory, the safe bearing capacity (in kPa) of this footing would be ________Correct answer is '270'. Can you explain this answer? has been provided alongside types of A square footing of 4m side is placed at 1 m depth in a sand deposit. The dry unit weight (γ) of sand is 15 kN/m3. This footing has an ultimate bearing capacity of 600 kPa. Consider the depth factors; dq = dγ = 1.0 and the bearing capacity factor: Nγ = 18.This footing is placed at a depth of 2m in the same soil deposit. For a factor of safety of 3.0 per Terzaghi’s theory, the safe bearing capacity (in kPa) of this footing would be ________Correct answer is '270'. Can you explain this answer? theory, EduRev gives you an
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