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Two footings, one circular and the other square, are founded on the surface of a purely cohensionless soil. The diameter of the circular footing is same as that of the side of the square footing. The ratio of their ultimate bearing capacities is
- a)3 / 4
- b)4 / 3
- c)1.0
- d)1.3
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Two footings, one circular and the other square, are founded on the su...
Ratio = strength of circular section / Strength of Square section.
If We assumed Side or Dia. Is 4 cm.
And Load P is the same,
Then Ratio of ultimate stresses of circular to the square is;
= (P/12.56) / (P/16).
= P .16/P. 12.56.
= 1.3.
Most Upvoted Answer
Two footings, one circular and the other square, are founded on the su...
Solution:
Given:
Diameter of circular footing = Side of square footing
To find: Ratio of their ultimate bearing capacities
Let the diameter of circular footing be D and side of square footing be S.
Area of circular footing, A1 = π(D/2)² = πD²/4
Area of square footing, A2 = S²
From soil mechanics, the ultimate bearing capacity of a footing is given by:
qult = cNc + qNq + 0.5γBNγ
where c is the cohesion of soil, Nc and Nq are bearing capacity factors, q is the effective overburden pressure, γ is the unit weight of soil, B is the width of the footing and Nγ is another bearing capacity factor.
Assuming that both footings are founded at the same depth and subjected to the same effective overburden pressure, we can compare their bearing capacities by comparing the first two terms of the above equation, since they depend only on the soil properties and the shape of the footing.
For circular footing,
qult1 = cNc + qNq
For square footing,
qult2 = cNc + qNq
where Nc and Nq are different for circular and square footings.
Let the ratio of bearing capacity factors be:
Nq/Nc = k
Then,
qult1/qult2 = (Nc + kNq)/(Nc + kNq) = 1
Therefore, the ratio of ultimate bearing capacities of circular and square footings is 1.
However, in practice, the third term of the above equation (γBNγ/2) also plays a role in determining the ultimate bearing capacity, and the shape and size of the footing can affect the value of B and Nγ. Therefore, the ratio of ultimate bearing capacities may not be exactly 1 in all cases, but can be slightly greater or less than 1.
Hence, the correct answer is option (D) 1.3.
Given:
Diameter of circular footing = Side of square footing
To find: Ratio of their ultimate bearing capacities
Let the diameter of circular footing be D and side of square footing be S.
Area of circular footing, A1 = π(D/2)² = πD²/4
Area of square footing, A2 = S²
From soil mechanics, the ultimate bearing capacity of a footing is given by:
qult = cNc + qNq + 0.5γBNγ
where c is the cohesion of soil, Nc and Nq are bearing capacity factors, q is the effective overburden pressure, γ is the unit weight of soil, B is the width of the footing and Nγ is another bearing capacity factor.
Assuming that both footings are founded at the same depth and subjected to the same effective overburden pressure, we can compare their bearing capacities by comparing the first two terms of the above equation, since they depend only on the soil properties and the shape of the footing.
For circular footing,
qult1 = cNc + qNq
For square footing,
qult2 = cNc + qNq
where Nc and Nq are different for circular and square footings.
Let the ratio of bearing capacity factors be:
Nq/Nc = k
Then,
qult1/qult2 = (Nc + kNq)/(Nc + kNq) = 1
Therefore, the ratio of ultimate bearing capacities of circular and square footings is 1.
However, in practice, the third term of the above equation (γBNγ/2) also plays a role in determining the ultimate bearing capacity, and the shape and size of the footing can affect the value of B and Nγ. Therefore, the ratio of ultimate bearing capacities may not be exactly 1 in all cases, but can be slightly greater or less than 1.
Hence, the correct answer is option (D) 1.3.
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Two footings, one circular and the other square, are founded on the surface of a purely cohensionless soil. The diameter of the circular footing is same as that of the side of the square footing. The ratio of their ultimate bearing capacities isa)3 / 4b)4 / 3c)1.0d)1.3Correct answer is option 'D'. Can you explain this answer?
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Two footings, one circular and the other square, are founded on the surface of a purely cohensionless soil. The diameter of the circular footing is same as that of the side of the square footing. The ratio of their ultimate bearing capacities isa)3 / 4b)4 / 3c)1.0d)1.3Correct answer is option 'D'. 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 Two footings, one circular and the other square, are founded on the surface of a purely cohensionless soil. The diameter of the circular footing is same as that of the side of the square footing. The ratio of their ultimate bearing capacities isa)3 / 4b)4 / 3c)1.0d)1.3Correct answer is option 'D'. 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 Two footings, one circular and the other square, are founded on the surface of a purely cohensionless soil. The diameter of the circular footing is same as that of the side of the square footing. The ratio of their ultimate bearing capacities isa)3 / 4b)4 / 3c)1.0d)1.3Correct answer is option 'D'. Can you explain this answer?.
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