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A square footing of 2m sides rests on the surface of a homogeneous soil bed having the properties: cohesion c = 24 kPa, angle of internal friction ϕ = 25°, and unit weight γ = 18 kN/m3. Terzaghi’s bearing capacity factor ϕ = 25° are Nc = 25.1, Nq = 12.7, Nγ = 9.7, N’c = 14.8, N’q = 5.6, and N’γ = 3. The ultimate bearing capacity of the foundation (in kPa, round off to 2 decimal places) is ______.
Correct answer is '353.92'. Can you explain this answer?
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A square footing of 2m sides rests on the surface of a homogeneous soi...
Here, ϕ < 29o
Footing rests on the ground
Hence, q = 0
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A square footing of 2m sides rests on the surface of a homogeneous soi...
°, unit weight of soil γ = 18 kN/m³. Determine the ultimate bearing capacity of the footing using Terzaghi's bearing capacity theory.
Solution:
Given:
Side of the square footing (B) = 2m
Cohesion of soil (c) = 24 kPa
Angle of internal friction (φ) = 25°
Unit weight of soil (γ) = 18 kN/m³
To determine the ultimate bearing capacity of the footing using Terzaghi's bearing capacity theory, we need to calculate the following:
1. Depth factors:
The depth factors are calculated using the following expression:
Z = [(B/2) / tan(45 + φ/2)] / B
For φ = 25°, Z = 0.44
2. Shape factors:
The shape factors are calculated using the following expression:
S = 1 + 0.2(Z - 1) = 1.08
3. Unit base resistance:
The unit base resistance (q_b) is calculated using the following expression:
q_b = c*N_c*S + 0.5*γ*B*N_q*S + 0.5*γ*B*N_γ*Z*S
where N_c, N_q, and N_γ are the bearing capacity factors for cohesion, surcharge, and unit weight, respectively. These factors are determined from the bearing capacity chart for strip footing.
For a square footing, the values of N_c, N_q, and N_γ are:
N_c = 5.14, N_q = 1.22, N_γ = 0.75
Substituting the values, we get:
q_b = 24*5.14*1.08 + 0.5*18*2*1.22*1.08 + 0.5*18*2*0.75*0.44*1.08
q_b = 142.42 kPa
4. Ultimate bearing capacity:
The ultimate bearing capacity (q_u) is given by:
q_u = q_b*N_γ*S
Substituting the values, we get:
q_u = 142.42*0.75*1.08
q_u = 115.31 kPa
Therefore, the ultimate bearing capacity of the square footing is 115.31 kPa.
Solution:
Given:
Side of the square footing (B) = 2m
Cohesion of soil (c) = 24 kPa
Angle of internal friction (φ) = 25°
Unit weight of soil (γ) = 18 kN/m³
To determine the ultimate bearing capacity of the footing using Terzaghi's bearing capacity theory, we need to calculate the following:
1. Depth factors:
The depth factors are calculated using the following expression:
Z = [(B/2) / tan(45 + φ/2)] / B
For φ = 25°, Z = 0.44
2. Shape factors:
The shape factors are calculated using the following expression:
S = 1 + 0.2(Z - 1) = 1.08
3. Unit base resistance:
The unit base resistance (q_b) is calculated using the following expression:
q_b = c*N_c*S + 0.5*γ*B*N_q*S + 0.5*γ*B*N_γ*Z*S
where N_c, N_q, and N_γ are the bearing capacity factors for cohesion, surcharge, and unit weight, respectively. These factors are determined from the bearing capacity chart for strip footing.
For a square footing, the values of N_c, N_q, and N_γ are:
N_c = 5.14, N_q = 1.22, N_γ = 0.75
Substituting the values, we get:
q_b = 24*5.14*1.08 + 0.5*18*2*1.22*1.08 + 0.5*18*2*0.75*0.44*1.08
q_b = 142.42 kPa
4. Ultimate bearing capacity:
The ultimate bearing capacity (q_u) is given by:
q_u = q_b*N_γ*S
Substituting the values, we get:
q_u = 142.42*0.75*1.08
q_u = 115.31 kPa
Therefore, the ultimate bearing capacity of the square footing is 115.31 kPa.
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A square footing of 2m sides rests on the surface of a homogeneous soil bed having the properties: cohesion c = 24 kPa, angle of internal friction ϕ = 25°, and unit weight γ = 18 kN/m3. Terzaghi’s bearing capacity factor ϕ = 25° are Nc = 25.1, Nq = 12.7, Nγ = 9.7, N’c = 14.8, N’q = 5.6, and N’γ = 3. The ultimate bearing capacity of the foundation (in kPa, round off to 2 decimal places) is ______.Correct answer is '353.92'. Can you explain this answer?
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A square footing of 2m sides rests on the surface of a homogeneous soil bed having the properties: cohesion c = 24 kPa, angle of internal friction ϕ = 25°, and unit weight γ = 18 kN/m3. Terzaghi’s bearing capacity factor ϕ = 25° are Nc = 25.1, Nq = 12.7, Nγ = 9.7, N’c = 14.8, N’q = 5.6, and N’γ = 3. The ultimate bearing capacity of the foundation (in kPa, round off to 2 decimal places) is ______.Correct answer is '353.92'. 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 2m sides rests on the surface of a homogeneous soil bed having the properties: cohesion c = 24 kPa, angle of internal friction ϕ = 25°, and unit weight γ = 18 kN/m3. Terzaghi’s bearing capacity factor ϕ = 25° are Nc = 25.1, Nq = 12.7, Nγ = 9.7, N’c = 14.8, N’q = 5.6, and N’γ = 3. The ultimate bearing capacity of the foundation (in kPa, round off to 2 decimal places) is ______.Correct answer is '353.92'. 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 2m sides rests on the surface of a homogeneous soil bed having the properties: cohesion c = 24 kPa, angle of internal friction ϕ = 25°, and unit weight γ = 18 kN/m3. Terzaghi’s bearing capacity factor ϕ = 25° are Nc = 25.1, Nq = 12.7, Nγ = 9.7, N’c = 14.8, N’q = 5.6, and N’γ = 3. The ultimate bearing capacity of the foundation (in kPa, round off to 2 decimal places) is ______.Correct answer is '353.92'. Can you explain this answer?.
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