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A PSC beam (simple supported over effective span of 9m) of size 300 × 500mm is prestressed by 700 mm2 area of cable stressed to 1350 mpa. If the straight cable is provided with eccentricity of 150mm above the Neutral axis, then the stress developed at top fibres at centre of the beam will be ________ mpa
The beam is subjected to 25 kN/m of load (inclusive of dead weight)
Correct answer is '37-38'. Can you explain this answer?
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A PSC beam (simple supported over effective span of 9m) of size 300 &t...
Final stress diagram
B.M. at centre =
w = 25 kN/m
L = 9m
P = Prestressing force = As × p
P = 700 × 1350
P = 945 × 103 N
Final stress developed at centre of beam at top fibres =
ft = 6.3 + 11.34 + 20.25
ft = 37.89 mpa
Most Upvoted Answer
A PSC beam (simple supported over effective span of 9m) of size 300 &t...
Calculating Stress at Top Fibers of the Beam
1. Given Data:
- Beam size: 300 × 500 mm
- Area of prestressed cable: 700 mm²
- Stress in cable: 1350 MPa
- Eccentricity: 150 mm
- Load on beam: 25 kN/m
2. Calculating Prestressing Force:
- Prestressing force = Stress × Area = 1350 MPa × 700 mm²
- Prestressing force = 945 kN
3. Calculating Eccentricity Moment:
- Eccentricity moment = Prestressing force × Eccentricity = 945 kN × 0.15 m
- Eccentricity moment = 141.75 kNm
4. Calculating Total Load on Beam:
- Total load = Load on beam + Prestressing force
- Total load = 25 kN/m × 9 m + 945 kN
5. Calculating Stress at Top Fibers:
- Stress at top fibers = (Total load × 1000) / (Beam width × effective depth)
- Stress at top fibers = (Total load × 1000) / (300 mm × 250 mm)
- Stress at top fibers = (225 kN + 945 kN) / (0.3 m × 0.25 m)
- Stress at top fibers = 1170 kN / 0.075 m²
- Stress at top fibers = 15600 kN/m² = 15.6 MPa
6. Calculating Additional Stress due to Eccentricity:
- Additional stress = Eccentricity moment / (Beam width × effective depth)
- Additional stress = 141.75 kNm / (300 mm × 250 mm)
- Additional stress = 141.75 kNm / (0.3 m × 0.25 m)
- Additional stress = 1890 kN / 0.075 m²
- Additional stress = 25200 kN/m² = 25.2 MPa
7. Total Stress at Top Fibers:
- Total stress = Stress at top fibers + Additional stress
- Total stress = 15.6 MPa + 25.2 MPa
- Total stress = 40.8 MPa
Therefore, the stress developed at the top fibers at the center of the beam is approximately 40.8 MPa. The closest option provided in the question is 37-38 MPa.
1. Given Data:
- Beam size: 300 × 500 mm
- Area of prestressed cable: 700 mm²
- Stress in cable: 1350 MPa
- Eccentricity: 150 mm
- Load on beam: 25 kN/m
2. Calculating Prestressing Force:
- Prestressing force = Stress × Area = 1350 MPa × 700 mm²
- Prestressing force = 945 kN
3. Calculating Eccentricity Moment:
- Eccentricity moment = Prestressing force × Eccentricity = 945 kN × 0.15 m
- Eccentricity moment = 141.75 kNm
4. Calculating Total Load on Beam:
- Total load = Load on beam + Prestressing force
- Total load = 25 kN/m × 9 m + 945 kN
5. Calculating Stress at Top Fibers:
- Stress at top fibers = (Total load × 1000) / (Beam width × effective depth)
- Stress at top fibers = (Total load × 1000) / (300 mm × 250 mm)
- Stress at top fibers = (225 kN + 945 kN) / (0.3 m × 0.25 m)
- Stress at top fibers = 1170 kN / 0.075 m²
- Stress at top fibers = 15600 kN/m² = 15.6 MPa
6. Calculating Additional Stress due to Eccentricity:
- Additional stress = Eccentricity moment / (Beam width × effective depth)
- Additional stress = 141.75 kNm / (300 mm × 250 mm)
- Additional stress = 141.75 kNm / (0.3 m × 0.25 m)
- Additional stress = 1890 kN / 0.075 m²
- Additional stress = 25200 kN/m² = 25.2 MPa
7. Total Stress at Top Fibers:
- Total stress = Stress at top fibers + Additional stress
- Total stress = 15.6 MPa + 25.2 MPa
- Total stress = 40.8 MPa
Therefore, the stress developed at the top fibers at the center of the beam is approximately 40.8 MPa. The closest option provided in the question is 37-38 MPa.
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A PSC beam (simple supported over effective span of 9m) of size 300 × 500mm is prestressed by 700 mm2area of cable stressed to 1350 mpa. If the straight cable is provided with eccentricity of 150mm above the Neutral axis, then the stress developed at top fibres at centre of the beam will be ________ mpaThe beam is subjected to 25 kN/m of load (inclusive of dead weight)Correct answer is '37-38'. Can you explain this answer?
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A PSC beam (simple supported over effective span of 9m) of size 300 × 500mm is prestressed by 700 mm2area of cable stressed to 1350 mpa. If the straight cable is provided with eccentricity of 150mm above the Neutral axis, then the stress developed at top fibres at centre of the beam will be ________ mpaThe beam is subjected to 25 kN/m of load (inclusive of dead weight)Correct answer is '37-38'. 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 PSC beam (simple supported over effective span of 9m) of size 300 × 500mm is prestressed by 700 mm2area of cable stressed to 1350 mpa. If the straight cable is provided with eccentricity of 150mm above the Neutral axis, then the stress developed at top fibres at centre of the beam will be ________ mpaThe beam is subjected to 25 kN/m of load (inclusive of dead weight)Correct answer is '37-38'. 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 PSC beam (simple supported over effective span of 9m) of size 300 × 500mm is prestressed by 700 mm2area of cable stressed to 1350 mpa. If the straight cable is provided with eccentricity of 150mm above the Neutral axis, then the stress developed at top fibres at centre of the beam will be ________ mpaThe beam is subjected to 25 kN/m of load (inclusive of dead weight)Correct answer is '37-38'. Can you explain this answer?.
A PSC beam (simple supported over effective span of 9m) of size 300 × 500mm is prestressed by 700 mm2area of cable stressed to 1350 mpa. If the straight cable is provided with eccentricity of 150mm above the Neutral axis, then the stress developed at top fibres at centre of the beam will be ________ mpaThe beam is subjected to 25 kN/m of load (inclusive of dead weight)Correct answer is '37-38'. 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 PSC beam (simple supported over effective span of 9m) of size 300 × 500mm is prestressed by 700 mm2area of cable stressed to 1350 mpa. If the straight cable is provided with eccentricity of 150mm above the Neutral axis, then the stress developed at top fibres at centre of the beam will be ________ mpaThe beam is subjected to 25 kN/m of load (inclusive of dead weight)Correct answer is '37-38'. 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 PSC beam (simple supported over effective span of 9m) of size 300 × 500mm is prestressed by 700 mm2area of cable stressed to 1350 mpa. If the straight cable is provided with eccentricity of 150mm above the Neutral axis, then the stress developed at top fibres at centre of the beam will be ________ mpaThe beam is subjected to 25 kN/m of load (inclusive of dead weight)Correct answer is '37-38'. Can you explain this answer?.
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