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A pre tensioned concrete beam 100mm wide and 300mm deep, initial force of 150kn at an eccentricity of 50mm, moment of inertia is 225×106mm4, initial stress in steel is 400n/mm2, modular ratio is 8. Estimate the percentage loss?

A pre tensioned concrete beam 100mm wide and 300mm deep, initial force of 150kn at an eccentricity of 50mm, moment of inertia is 225×106mm4, initial stress in steel is 400n/mm2, modular ratio is 8. Estimate the percentage loss? Correct Answer 14%

P = 150kn, y = d/6 = 300/6 = 50mm, a = (100×300) = 3×104, I = 225×106, αe = 8, initial stress = 400n/mm2, Stress in concrete, fc = (150×103/3×104)+(150×103×50×50/225×106) = 6.66n/mm2, Loss of stress due to elastic deformation of concrete = αefc = (8×6.66) = 53n/mm2, Percentage of loss of stress in steel = (53×100/400) = 13.25% = 14%.

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