Question

1. A post tensioned concrete beam, 100mm wide and 400mm deep is prestressed by three cables, each with a cross sectional area of 50mm², initial stress of 1200N/mm². Calculate the stress in concrete at level of steel? 2. A pre tensioned concrete beam 100mm wide and 300mm deep, initial force of 150kN at an eccentricity of 50mm, moment of inertia is 225*10mm, initial stress in steel is 400N/mm², modular ratio is 8. Estimate the percentage loss? 3. A pretensioned concrete beam, 100mm wide and 300mm deep in prestressed by straight wires and modulus of elasticity of steel and concrete are 210 and 35N/mm². Find modular ratio? 4. A concrete beam is prestressed by a cable carrying an initial prestressing force of 300kN, area is 300mm”. Calculate the percentage of loss of stress due to shrinkage in pretensioned members?

Answer 1

Irage NO:1) Dool: Given Post tensioned beam beam width, b= loomm Depth, d = poomm Arca, A-bd 2 4x104 mm Initial stress = 1200 N/mm² Area of cables = 3x50 2 force, p= - 150 mm Initial 1 200 X 150 = 180KN Stress in concrete at level of steel P A 3 180 X10 4x104 = 4.5 N/mm stress in concrete af level of steel = 4.5 N/mm²

: 2 P.NO: loomm lwidth of pre-tensioned concrete beom, ba Depth, d = 300mm Initial force, P = 150KN Eccentricity, - 50 mm Moment of Inestia, I = 225 x 10 mm Initial stress in steel = 400 N/mm² e / Modular Ratio , de = 8 2 Cross-sectional Arca , А 100 X 300 3x104 Stress in concrete at the level of steel, f - P A + Pe Z c . 150x1000 t (150x1000 X 500x50 225 X 106 3x104 5 t 1667 f = 6.667 N/mm2 - 2- Losses ☺ loss of stress due to elastic deformation of concrete = de for 8 X 6.667 = 53.33 6 N/mm (ii) Loss due to creep of concrete Assuming creep co-efficient, d = 16 Loss = 16X6.667 x 8 =85:337 N/mm2 = 85.33 tN/mm² de foto

X Es 3 (nig loss due to shrinkage of concrete = 6gx Fas Ess = 360x10 cits for pare-tersioned beam Assume Es = 210 kw (inmi? 3 Loss 6 - 300 X 10 °x 8210 X10 = 63 N/mm² civ) loss due to relax ation of stress in steel 54. of initical pre stress 5 400 = 20 N/mm² X 100 S.NO of loss Type Loss (N/mm²) of stress 53.336 Elostic deformation of concrete 85.337 (ii) creep of concrete 63 shrinkage of concocte stress 20 (۱۷) Relaxation of loss 221-673 Total 221.673 x 100 Percentage loss 400 - 55.42% Percentage loss : 55:42)

3.Sol 1Pg. NO:4 Given Modulus of elasticity of steel, Es= 210 warm Modulus of elasticity of concrete, &,= 35 N/mm Modular Ratio, xe = ES Ec 210 35 = 6 Modular Ratio - 6 4 stelle 2 Given Pre stressing fooce, P = 300 KN Area, A = 300 mm :. Initial stress in wines, f, P 300 X 1000 f 300 N/mm² 1000 total Loss of stress due to shrinkage in Pre - tensioned member = Ecs x Es where Eis residual shrinkage strain Es = Modulus of elasticity of steel As the beam is pre-tensioned, Ees= 300x106 units Assuming Es= 210kN/mm² - loss of stress = 300x10 * 210x10 mm 6 63 63 Percentage loss of stressa X100 = 6.3% Торо