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A pre-tensioned rectangular concrete beam 150 mm wide and 300 mm depth is prestressed with three straight tendons, each having a cross-sectional area of 50 mm2, to an initial stress of 1200 N/mm2. The tendons are located at 100 mm from the soffit of the beam. If the modular ratio is 6, the loss of prestressing force (in kN, up to one decimal place) due to the elastic deformation of concrete only is ______.
Correct answer is '4.8'. Can you explain this answer?
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Verified Answer
A pre-tensioned rectangular concrete beam 150 mm wide and 300 mm depth...
Stress = 1200 N / mm2
P/4 = 1200
P/4 = 1200
Loss due to elastic deformation = m.fc = 6 × 5.33 = 31.98
Prestress force = 31.98 × 3 × 50 = 4797 N = 4.8 KN
Prestress force = 31.98 × 3 × 50 = 4797 N = 4.8 KN
Most Upvoted Answer
A pre-tensioned rectangular concrete beam 150 mm wide and 300 mm depth...
Given data:
Width of the beam (b) = 150 mm
Depth of the beam (h) = 300 mm
Cross-sectional area of each tendon (A) = 50 mm2
Initial stress in tendons (σp) = 1200 N/mm2
Distance of tendons from the soffit (d) = 100 mm
Modular ratio (n) = 6
Calculation:
1. Calculate the lever arm (z) using the formula:
z = h - (d + A/n)
= 300 - (100 + 50/6)
= 300 - (100 + 8.33)
= 300 - 108.33
= 191.67 mm
2. Calculate the loss of prestressing force due to the elastic deformation of concrete only using the formula:
ΔPc = A × σp × z
= 50 × 1200 × 191.67
= 11500200 N
≈ 11.5 kN
Therefore, the loss of prestressing force due to the elastic deformation of concrete only is approximately 11.5 kN, which rounded to one decimal place is 11.5 kN.
Width of the beam (b) = 150 mm
Depth of the beam (h) = 300 mm
Cross-sectional area of each tendon (A) = 50 mm2
Initial stress in tendons (σp) = 1200 N/mm2
Distance of tendons from the soffit (d) = 100 mm
Modular ratio (n) = 6
Calculation:
1. Calculate the lever arm (z) using the formula:
z = h - (d + A/n)
= 300 - (100 + 50/6)
= 300 - (100 + 8.33)
= 300 - 108.33
= 191.67 mm
2. Calculate the loss of prestressing force due to the elastic deformation of concrete only using the formula:
ΔPc = A × σp × z
= 50 × 1200 × 191.67
= 11500200 N
≈ 11.5 kN
Therefore, the loss of prestressing force due to the elastic deformation of concrete only is approximately 11.5 kN, which rounded to one decimal place is 11.5 kN.
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A pre-tensioned rectangular concrete beam 150 mm wide and 300 mm depth is prestressed with three straight tendons, each having a cross-sectional area of 50 mm2, to an initial stress of 1200 N/mm2. The tendons are located at 100 mm from the soffit of the beam. If the modular ratio is 6, the loss of prestressing force (in kN, up to one decimal place) due to the elastic deformation of concrete only is ______.Correct answer is '4.8'. Can you explain this answer?
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A pre-tensioned rectangular concrete beam 150 mm wide and 300 mm depth is prestressed with three straight tendons, each having a cross-sectional area of 50 mm2, to an initial stress of 1200 N/mm2. The tendons are located at 100 mm from the soffit of the beam. If the modular ratio is 6, the loss of prestressing force (in kN, up to one decimal place) due to the elastic deformation of concrete only is ______.Correct answer is '4.8'. 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 pre-tensioned rectangular concrete beam 150 mm wide and 300 mm depth is prestressed with three straight tendons, each having a cross-sectional area of 50 mm2, to an initial stress of 1200 N/mm2. The tendons are located at 100 mm from the soffit of the beam. If the modular ratio is 6, the loss of prestressing force (in kN, up to one decimal place) due to the elastic deformation of concrete only is ______.Correct answer is '4.8'. 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 pre-tensioned rectangular concrete beam 150 mm wide and 300 mm depth is prestressed with three straight tendons, each having a cross-sectional area of 50 mm2, to an initial stress of 1200 N/mm2. The tendons are located at 100 mm from the soffit of the beam. If the modular ratio is 6, the loss of prestressing force (in kN, up to one decimal place) due to the elastic deformation of concrete only is ______.Correct answer is '4.8'. Can you explain this answer?.
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