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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?
    Verified Answer
    A pre-tensioned rectangular concrete beam 150 mm wide and 300 mm depth...
    Stress = 1200 N / mm2
    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
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    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.
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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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