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 225x10mm, initial stress in steel is 400N/mm², modular ratio is 8. Estimate the percentage loss?

Answer 1

Nos of Solution Part 7 Guen: - width of beam= 100mm Depth of blom= 400 mm cables=03 Area of cable = somm? Initial stress = 1200 N/mm2 To be find out Stress in concrete at level level of steel Jets assume eccentricity Ce) - somm (P) load - 50x1200 =GOKN * when the (1) bar is tensioned there is no loss in firat bar. * When the (2) bar is tensioned the loss will occur in i bar * when (3) bar is tensioned, there will be loss in bar (1) and (2)

Aug. Stress at the level of Ist bar cuhen 2nd bar is being tonsioned to feat support a po to- =60x10² =1.5N/mm2 100x400 fe at mich spana P + Pexe A 1 = Goxlo? + Goxlo²x50x50 100x400 to x 100x4003 1.5+ 0.281 1.78 N/mm² Av. stress at the level of barco) 23 [1.78-1.5 = 1.68 N/mm2 -lost 2

when the third baris tensioned and anchored At support P.e.so to A =%.5-0.00028 =1.40 N/mm2 mid span Eft Pet = 1.78 N/mm2 Aug. stress at the level of bar (3) =1.49+8 [1678-1.49 = 1.68 N/mm² when the third bar is tensioned and anchored. at support = lisamma At mid span= 1078

ugibtress = 1.68N) mm2 Hence from above calculation the stress in concrete at level of steel is 1.68 N/mm2

force solution D (Part 2 Given in width of beam= 100 mm Depth bcom = 300 mm Initial I SIN Eccentricity - 50 1910) MOI = 225x108 mm Initial stress = 4000/unit Percentage lass=? modular Ratio = 8 beam = 100X300 = 3x104mm te= Stress in concrete te 3 1 Sono 1 50810 x soyse 3x104 2058100 to= 6.66 N/mm² loss of stress due to elastic deformation of concrete = mte = 8x6.66 - 53.28 N) mm2

Percentage loss of stress in steel 53.28X100 800/2 53.28 X100 400 % loss = 13.32% Conclusion :- The result of above the value of eccentricity in question question de reliable and 2 is assumel Somm. Honce the results are as follows 0 = 1.68 nlmm2 = 13.32%