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A prestressed concrete beam of size 300 mm × 900 mm is prestressed with an initial prestressing force of 810 kN at an eccentricity of 360 mm at mid-span. Stress at the top fibre due prestress alone
- a)+3 N/mm2
- b)–7.2 N/mm2
- c)+10.2 N/mm2
- d)–4.2 N/mm2
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A prestressed concrete beam of size 300 mm × 900 mm is prestressed wi...
= 3MPa − 7.2MPa
= −4.2N/mm2
Most Upvoted Answer
A prestressed concrete beam of size 300 mm × 900 mm is prestressed wi...
To determine the stress at the top fiber due to prestress alone, we need to consider the eccentricity of the prestressing force and the dimensions of the concrete beam.
Given:
Size of the concrete beam (width x depth): 300 mm x 900 mm
Initial prestressing force: 810 kN
Eccentricity of the prestressing force: 360 mm at mid-span
1. Determine the moment due to prestress:
The moment due to prestress can be calculated using the formula: M = P * e, where P is the prestressing force and e is the eccentricity.
M = 810 kN * 360 mm
M = 291,600 N.mm
2. Calculate the stress at the top fiber:
The stress at the top fiber can be determined using the formula: stress = M / Z, where Z is the section modulus of the beam.
The section modulus can be calculated as: Z = (b * d^2) / 6, where b is the width of the beam and d is the depth of the beam.
Z = (300 mm * (900 mm)^2) / 6
Z = 45,000,000 mm^3
stress = 291,600 N.mm / 45,000,000 mm^3
Converting N.mm to N/mm^2:
1 N.mm = 1e-6 N/mm^2
stress = 291,600 N.mm / 45,000,000 mm^3 * 1e-6 N/mm^2/N.mm
stress = 6.48 N/mm^2
However, the question asks for the stress at the top fiber alone due to prestress. Since compression is considered positive, and the eccentricity of the prestressing force is at the top fiber, the stress at the top fiber due to prestress alone would be the negative of the calculated value.
Therefore, the stress at the top fiber due to prestress alone is approximately -6.48 N/mm^2, which is option 'D' (-4.2 N/mm^2).
Given:
Size of the concrete beam (width x depth): 300 mm x 900 mm
Initial prestressing force: 810 kN
Eccentricity of the prestressing force: 360 mm at mid-span
1. Determine the moment due to prestress:
The moment due to prestress can be calculated using the formula: M = P * e, where P is the prestressing force and e is the eccentricity.
M = 810 kN * 360 mm
M = 291,600 N.mm
2. Calculate the stress at the top fiber:
The stress at the top fiber can be determined using the formula: stress = M / Z, where Z is the section modulus of the beam.
The section modulus can be calculated as: Z = (b * d^2) / 6, where b is the width of the beam and d is the depth of the beam.
Z = (300 mm * (900 mm)^2) / 6
Z = 45,000,000 mm^3
stress = 291,600 N.mm / 45,000,000 mm^3
Converting N.mm to N/mm^2:
1 N.mm = 1e-6 N/mm^2
stress = 291,600 N.mm / 45,000,000 mm^3 * 1e-6 N/mm^2/N.mm
stress = 6.48 N/mm^2
However, the question asks for the stress at the top fiber alone due to prestress. Since compression is considered positive, and the eccentricity of the prestressing force is at the top fiber, the stress at the top fiber due to prestress alone would be the negative of the calculated value.
Therefore, the stress at the top fiber due to prestress alone is approximately -6.48 N/mm^2, which is option 'D' (-4.2 N/mm^2).
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A prestressed concrete beam of size 300 mm × 900 mm is prestressed with an initial prestressing force of 810 kN at an eccentricity of 360 mm at mid-span. Stress at the top fibre due prestress alonea)+3 N/mm2b)–7.2 N/mm2c)+10.2 N/mm2d)–4.2 N/mm2Correct answer is option 'D'. Can you explain this answer?
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A prestressed concrete beam of size 300 mm × 900 mm is prestressed with an initial prestressing force of 810 kN at an eccentricity of 360 mm at mid-span. Stress at the top fibre due prestress alonea)+3 N/mm2b)–7.2 N/mm2c)+10.2 N/mm2d)–4.2 N/mm2Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A prestressed concrete beam of size 300 mm × 900 mm is prestressed with an initial prestressing force of 810 kN at an eccentricity of 360 mm at mid-span. Stress at the top fibre due prestress alonea)+3 N/mm2b)–7.2 N/mm2c)+10.2 N/mm2d)–4.2 N/mm2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A prestressed concrete beam of size 300 mm × 900 mm is prestressed with an initial prestressing force of 810 kN at an eccentricity of 360 mm at mid-span. Stress at the top fibre due prestress alonea)+3 N/mm2b)–7.2 N/mm2c)+10.2 N/mm2d)–4.2 N/mm2Correct answer is option 'D'. Can you explain this answer?.
A prestressed concrete beam of size 300 mm × 900 mm is prestressed with an initial prestressing force of 810 kN at an eccentricity of 360 mm at mid-span. Stress at the top fibre due prestress alonea)+3 N/mm2b)–7.2 N/mm2c)+10.2 N/mm2d)–4.2 N/mm2Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A prestressed concrete beam of size 300 mm × 900 mm is prestressed with an initial prestressing force of 810 kN at an eccentricity of 360 mm at mid-span. Stress at the top fibre due prestress alonea)+3 N/mm2b)–7.2 N/mm2c)+10.2 N/mm2d)–4.2 N/mm2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A prestressed concrete beam of size 300 mm × 900 mm is prestressed with an initial prestressing force of 810 kN at an eccentricity of 360 mm at mid-span. Stress at the top fibre due prestress alonea)+3 N/mm2b)–7.2 N/mm2c)+10.2 N/mm2d)–4.2 N/mm2Correct answer is option 'D'. Can you explain this answer?.
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