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The rectangular beam of width, 250 mm is having an effective depth of 317 mm. The concrete grade is M20 and the grade of reinforcing steel is Fe415. The moment capacity of the section due to concrete as per limit state method is:
- a)47.88 kNm
- b)53.28 kNm
- c)69.395 kNm
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
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The rectangular beam of width, 250 mm is having an effective depth of...
(i) Characteristics strength of concrete, fck=20N/mm2
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(ii) Characteristics strength of reinforcing steel, fy=415N/mm2
(iii) Width, b=250mm
(iv) Effective depth, d=317mm
(v) Neutral axis factor, xub/d
=ϵc/ϵc+ϵs
=0.0035/0.0035+0.0038
=0.48
(vi) Coefficient, Qub
=k1(xub/d)(1−k2(xub/d))
=0.36×0.48×(1−0.42×0.48)
=0.138
(vii) Moment of resistance due to concrete,
Muab =Qubfckbd2
=0.138×20×250×3172
=69.395kNm
Hence, the correct option is (c).
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The rectangular beam of width, 250 mm is having an effective depth of...
To determine the moment capacity of the rectangular beam, we need to consider the contribution of both concrete and reinforcing steel. The moment capacity is calculated based on the limit state method.
Given data:
Width of the beam (b) = 250 mm
Effective depth of the beam (d) = 317 mm
Concrete grade (fck) = M20
Reinforcing steel grade (fy) = Fe415
1. Calculation of Modular Ratio (m):
The modular ratio (m) is the ratio of the modulus of elasticity of steel (Es) to the modulus of elasticity of concrete (Ec). It is given by the formula:
m = Es / Ec
For Fe415 steel, Es = 200 GPa (Giga Pascal)
For M20 concrete, Ec = 5000 √fck = 5000 √20 = 10,000 N/mm²
Therefore, m = 200 / 10,000 = 0.02
2. Calculation of Moment Capacity due to Concrete (Mcc):
The moment capacity due to concrete is given by the formula:
Mcc = 0.36 * fck * b * (d^2) / (m + 1)
Substituting the given values:
Mcc = 0.36 * 20 * 250 * (317^2) / (0.02 + 1)
Mcc = 0.36 * 20 * 250 * 100489 / 1.02
Mcc ≈ 69.395 kNm
3. Calculation of Moment Capacity due to Steel (Mcs):
The moment capacity due to steel is given by the formula:
Mcs = 0.87 * fy * Ast * (d - a/2)
Where:
Ast = Area of steel reinforcement
a = Lever arm distance (distance from the centroid of the steel reinforcement to the extreme compression fiber)
To find the area of steel reinforcement, we need to determine the percentage of steel reinforcement (ρ) first. For Fe415 steel, ρ = 0.415%.
Therefore, Ast = ρ * b * d
Ast = 0.415% * 250 * 317
Ast ≈ 329.36 mm²
Now, the lever arm distance (a) is given by the formula:
a = Ast * fy / (0.87 * fck * b)
Substituting the given values:
a = 329.36 * 415 / (0.87 * 20 * 250)
a ≈ 49.352 mm
Finally, substituting the values of Ast and a into the formula for Mcs:
Mcs = 0.87 * 415 * 329.36 * (317 - 49.352) / 10^6
Mcs ≈ 9.806 kNm
4. Calculation of Total Moment Capacity (M):
The total moment capacity is the sum of the moment capacities due to concrete and steel:
M = Mcc + Mcs
M ≈ 69.395 + 9.806
M ≈ 79.201 kNm
Therefore, the moment capacity of the section due to concrete as per the limit state method is approximately 69.395 kNm, which corresponds to option C.
Given data:
Width of the beam (b) = 250 mm
Effective depth of the beam (d) = 317 mm
Concrete grade (fck) = M20
Reinforcing steel grade (fy) = Fe415
1. Calculation of Modular Ratio (m):
The modular ratio (m) is the ratio of the modulus of elasticity of steel (Es) to the modulus of elasticity of concrete (Ec). It is given by the formula:
m = Es / Ec
For Fe415 steel, Es = 200 GPa (Giga Pascal)
For M20 concrete, Ec = 5000 √fck = 5000 √20 = 10,000 N/mm²
Therefore, m = 200 / 10,000 = 0.02
2. Calculation of Moment Capacity due to Concrete (Mcc):
The moment capacity due to concrete is given by the formula:
Mcc = 0.36 * fck * b * (d^2) / (m + 1)
Substituting the given values:
Mcc = 0.36 * 20 * 250 * (317^2) / (0.02 + 1)
Mcc = 0.36 * 20 * 250 * 100489 / 1.02
Mcc ≈ 69.395 kNm
3. Calculation of Moment Capacity due to Steel (Mcs):
The moment capacity due to steel is given by the formula:
Mcs = 0.87 * fy * Ast * (d - a/2)
Where:
Ast = Area of steel reinforcement
a = Lever arm distance (distance from the centroid of the steel reinforcement to the extreme compression fiber)
To find the area of steel reinforcement, we need to determine the percentage of steel reinforcement (ρ) first. For Fe415 steel, ρ = 0.415%.
Therefore, Ast = ρ * b * d
Ast = 0.415% * 250 * 317
Ast ≈ 329.36 mm²
Now, the lever arm distance (a) is given by the formula:
a = Ast * fy / (0.87 * fck * b)
Substituting the given values:
a = 329.36 * 415 / (0.87 * 20 * 250)
a ≈ 49.352 mm
Finally, substituting the values of Ast and a into the formula for Mcs:
Mcs = 0.87 * 415 * 329.36 * (317 - 49.352) / 10^6
Mcs ≈ 9.806 kNm
4. Calculation of Total Moment Capacity (M):
The total moment capacity is the sum of the moment capacities due to concrete and steel:
M = Mcc + Mcs
M ≈ 69.395 + 9.806
M ≈ 79.201 kNm
Therefore, the moment capacity of the section due to concrete as per the limit state method is approximately 69.395 kNm, which corresponds to option C.
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The rectangular beam of width, 250 mm is having an effective depth of 317 mm. The concrete grade is M20 and the grade of reinforcing steel is Fe415. The moment capacity of the section due to concrete as per limit state method is:a)47.88 kNmb)53.28 kNmc)69.395 kNmd)None of the aboveCorrect answer is option 'C'. Can you explain this answer?
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The rectangular beam of width, 250 mm is having an effective depth of 317 mm. The concrete grade is M20 and the grade of reinforcing steel is Fe415. The moment capacity of the section due to concrete as per limit state method is:a)47.88 kNmb)53.28 kNmc)69.395 kNmd)None of the aboveCorrect answer is option 'C'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about The rectangular beam of width, 250 mm is having an effective depth of 317 mm. The concrete grade is M20 and the grade of reinforcing steel is Fe415. The moment capacity of the section due to concrete as per limit state method is:a)47.88 kNmb)53.28 kNmc)69.395 kNmd)None of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The rectangular beam of width, 250 mm is having an effective depth of 317 mm. The concrete grade is M20 and the grade of reinforcing steel is Fe415. The moment capacity of the section due to concrete as per limit state method is:a)47.88 kNmb)53.28 kNmc)69.395 kNmd)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.
The rectangular beam of width, 250 mm is having an effective depth of 317 mm. The concrete grade is M20 and the grade of reinforcing steel is Fe415. The moment capacity of the section due to concrete as per limit state method is:a)47.88 kNmb)53.28 kNmc)69.395 kNmd)None of the aboveCorrect answer is option 'C'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about The rectangular beam of width, 250 mm is having an effective depth of 317 mm. The concrete grade is M20 and the grade of reinforcing steel is Fe415. The moment capacity of the section due to concrete as per limit state method is:a)47.88 kNmb)53.28 kNmc)69.395 kNmd)None of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The rectangular beam of width, 250 mm is having an effective depth of 317 mm. The concrete grade is M20 and the grade of reinforcing steel is Fe415. The moment capacity of the section due to concrete as per limit state method is:a)47.88 kNmb)53.28 kNmc)69.395 kNmd)None of the aboveCorrect answer is option 'C'. Can you explain this answer?.
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