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A foundation in a loose sand is 4 m wide, 6 m long and 1.5 m deep. The soil weighs 16 kN/m3 and has an effective angle of internal friction of 22.6°. Compute the safe bearing capacity of soil (in kN/m2), adopting a factor of safety of 2.
[for ϕ=22.6∘,
Nc = 21.55.Nq
= 10.16 and Nγ = 7.44]
- a)350
- b)450
- c)225.1
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A foundation in a loose sand is 4 m wide, 6 m long and 1.5 m deep. The...
B = 4, L = 6m, Df = 1.5m
Since Df < b,="" it="" is="" a="" shallow="" footing.="" moreover,="" it="" is="" a="" rectangular="" footing="" with="" b/l="" />
Now, for rectangular footing, these factors must be corrected by multiplying with shape factors as:
(∵ c = 0 for loose and)
= 450.2 kN/m2
Safe bearing capacity,
qa = (Ultimate bearing capacity)/FOS
= 450.2/2
= 225.1 kN/m2
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A foundation in a loose sand is 4 m wide, 6 m long and 1.5 m deep. The...
We can start by finding the weight of the soil within the foundation:
Volume of soil = 4 m x 6 m x 1.5 m = 36 m3
Weight of soil = 36 m3 x 16 kN/m3 = 576 kN
Next, we can calculate the vertical and horizontal forces acting on the foundation due to the soil:
Vertical force = weight of soil = 576 kN
Horizontal force = vertical force x tan(22.6°) = 576 kN x 0.461 = 265.14 kN
Finally, we can check if the foundation is stable against overturning and sliding:
Overturning:
Moment due to vertical force = vertical force x (1.5 m/2) = 576 kN x 0.75 m = 432 kNm
Moment due to horizontal force = horizontal force x (1.5 m/2) = 265.14 kN x 0.75 m = 198.86 kNm
Total moment = 432 kNm + 198.86 kNm = 630.86 kNm
Resisting moment = weight of foundation x distance to centroid = (4 m x 6 m x 1.5 m) x (1.5 m/2) = 81 kNm
Since the resisting moment is less than the total moment, the foundation is not stable against overturning.
Sliding:
Sliding force = horizontal force = 265.14 kN
Resisting force = weight of foundation = 4 m x 6 m x 16 kN/m3 x 1.5 m = 576 kN
Since the resisting force is greater than the sliding force, the foundation is stable against sliding.
To make the foundation stable against overturning, we can either increase the weight of the foundation or increase the size of the foundation. One option could be to increase the depth of the foundation to 2 m, which would increase the weight of the foundation and provide more stability against overturning.
Volume of soil = 4 m x 6 m x 1.5 m = 36 m3
Weight of soil = 36 m3 x 16 kN/m3 = 576 kN
Next, we can calculate the vertical and horizontal forces acting on the foundation due to the soil:
Vertical force = weight of soil = 576 kN
Horizontal force = vertical force x tan(22.6°) = 576 kN x 0.461 = 265.14 kN
Finally, we can check if the foundation is stable against overturning and sliding:
Overturning:
Moment due to vertical force = vertical force x (1.5 m/2) = 576 kN x 0.75 m = 432 kNm
Moment due to horizontal force = horizontal force x (1.5 m/2) = 265.14 kN x 0.75 m = 198.86 kNm
Total moment = 432 kNm + 198.86 kNm = 630.86 kNm
Resisting moment = weight of foundation x distance to centroid = (4 m x 6 m x 1.5 m) x (1.5 m/2) = 81 kNm
Since the resisting moment is less than the total moment, the foundation is not stable against overturning.
Sliding:
Sliding force = horizontal force = 265.14 kN
Resisting force = weight of foundation = 4 m x 6 m x 16 kN/m3 x 1.5 m = 576 kN
Since the resisting force is greater than the sliding force, the foundation is stable against sliding.
To make the foundation stable against overturning, we can either increase the weight of the foundation or increase the size of the foundation. One option could be to increase the depth of the foundation to 2 m, which would increase the weight of the foundation and provide more stability against overturning.
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A foundation in a loose sand is 4 m wide, 6 m long and 1.5 m deep. The soil weighs 16 kN/m3 and has an effective angle of internal friction of 22.6°. Compute the safe bearing capacity of soil (in kN/m2), adopting a factor of safety of 2.[for =22.6,Nc = 21.55.Nq= 10.16 and Nγ = 7.44]a)350b)450c)225.1d)None of theseCorrect answer is option 'C'. Can you explain this answer?
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A foundation in a loose sand is 4 m wide, 6 m long and 1.5 m deep. The soil weighs 16 kN/m3 and has an effective angle of internal friction of 22.6°. Compute the safe bearing capacity of soil (in kN/m2), adopting a factor of safety of 2.[for =22.6,Nc = 21.55.Nq= 10.16 and Nγ = 7.44]a)350b)450c)225.1d)None of theseCorrect answer is option 'C'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A foundation in a loose sand is 4 m wide, 6 m long and 1.5 m deep. The soil weighs 16 kN/m3 and has an effective angle of internal friction of 22.6°. Compute the safe bearing capacity of soil (in kN/m2), adopting a factor of safety of 2.[for =22.6,Nc = 21.55.Nq= 10.16 and Nγ = 7.44]a)350b)450c)225.1d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A foundation in a loose sand is 4 m wide, 6 m long and 1.5 m deep. The soil weighs 16 kN/m3 and has an effective angle of internal friction of 22.6°. Compute the safe bearing capacity of soil (in kN/m2), adopting a factor of safety of 2.[for =22.6,Nc = 21.55.Nq= 10.16 and Nγ = 7.44]a)350b)450c)225.1d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
A foundation in a loose sand is 4 m wide, 6 m long and 1.5 m deep. The soil weighs 16 kN/m3 and has an effective angle of internal friction of 22.6°. Compute the safe bearing capacity of soil (in kN/m2), adopting a factor of safety of 2.[for =22.6,Nc = 21.55.Nq= 10.16 and Nγ = 7.44]a)350b)450c)225.1d)None of theseCorrect answer is option 'C'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A foundation in a loose sand is 4 m wide, 6 m long and 1.5 m deep. The soil weighs 16 kN/m3 and has an effective angle of internal friction of 22.6°. Compute the safe bearing capacity of soil (in kN/m2), adopting a factor of safety of 2.[for =22.6,Nc = 21.55.Nq= 10.16 and Nγ = 7.44]a)350b)450c)225.1d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A foundation in a loose sand is 4 m wide, 6 m long and 1.5 m deep. The soil weighs 16 kN/m3 and has an effective angle of internal friction of 22.6°. Compute the safe bearing capacity of soil (in kN/m2), adopting a factor of safety of 2.[for =22.6,Nc = 21.55.Nq= 10.16 and Nγ = 7.44]a)350b)450c)225.1d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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