A. Geometric Properties Section properties Area (m2) Inertia m4 End Support 12.855 5.395 At a distance 9.95 meter 12.855 5.395 Pier 12.855 5.395 Ceneter of middel span 12.855 5.395 B. Concrete Properties C30/37 fck 30 Mpa Ecm 33 Gpa C.Prestressing Cables Low relaxation fpk (Charateristic Strength) 1770 Mpa u 0.19 k 0.005 Ap Area of one tendon 6150 No. of tendons 13 Sigma p 0.7 x fpk 1239 Ep 200 Gpa Prestress 7 days after pouring Drawn in achorageat Delta 2 mm Pmax (one tendon) 7619.85 kN 1 Elastic Deformation of concret 1 Calculation of the stresses in the concrete a Distance (m) 0 Sigma c = 9.95 Sigma c = 20.09 Sigma c = 28 Sigma c = 36.93 Sigma c = 49.5 Sigma c = 2 Average stress in the concrete adjacent to t m -1 mm 2
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A. Geometric Properties
Section properties Area (m2) Inertia m4End Support 12.855 5.395At a distance 9.95 meter 12.855 5.395Pier 12.855 5.395Ceneter of middel span 12.855 5.395
Ap Area of one tendon 6150No. of tendons 13Sigma p 0.7 x fpk 1239Ep 200 GpaPrestress 7 days after pouring Drawn in achorageat Delta 2 mmPmax (one tendon) 7619.85 kN
1Elastic Deformation of concrete
1 Calculation of the stresses in the concrete at the level of the tendon centeroids:
Distance (m)0 Sigma c =
9.95 Sigma c =20.09 Sigma c =
28 Sigma c =36.93 Sigma c =
49.5 Sigma c =
2 Average stress in the concrete adjacent to the tendon over its length:
m-1
mm2
0 to 9.959.95 to 20.09
20.09 to 2828 to 36.93
36.93 to 49.5
3 Calculation of the average stress in the conceret adjacent to the tendon over its length
Sigma c 14.49 Mpa
4 Calculation of the elastic prestress losses
Ap 6150 mm2Ep 200000 MpaEcm(t) 33000 Mpaj 0.4615384615
Delta Pel 249.30 kN
5 Prestress Diagram after loss of prestress from elastic deformation of concrete:
Pmax 7619.85 kNP(x) 249.30 kNLoss 0.033 orPrestress force after loss 0.967
2Friction
1 Calculation of angular deviation
x(m) Delta theta (radians)Delta theta (degrees)
0 2000 4000 6000 8000 10000 120000.7
0.8
0.9
1
1.1
Pmax Pel
0 0 0.0009.95 0 0.0009.95 11 0.192
17.01 11 0.19220.09 11 0.19220.09 21 0.367
28 21 0.36728 32 0.559
36.93 32 0.55936.93 42 0.733
49.5 51 0.8903 Prestress Diagram after loss of prestress due to friction
3Wedge draw-in of the anchorage devices
1 Reduction of the area in the prestressing diagram due to the draw in:
Asl 2460 kN-mf
2 Estimation of the draw in length
Xsl 1.23E+09 /
3 Loss due to wedge draw in anchorage
Delta Psl 500.95 kNDelta Psl /Pmax or Loss 0.0657430598Pmo 7369.37 kN
0 2000 4000 6000 8000 10000 120000
0.2
0.4
0.6
0.8
1
1.2
Pmax Pel Pel+fr
x(m) Pel+fr+sl0 0.902
9.95 0.8929.95 0.857
9821.30 0.85920.09 0.92920.09 0.897
28 0.89328 0.860
36.93 0.85936.93 0.830
49.5 0.802
4Shrinkage of Concrete
1 Autogenous shrinkage
for t = infinity Eca(Infinity) 5.0E-05for t = 7 days transfer of prestress Eca(t=7) 2.1E-05
2 Drying shrinkage (assuming three days curing period)
For t=infinity Ecdo 2.50E-04Kh 0.7
Ecd(infinity) 1.75E-04
For t=7days Ecd(t=7) 8.06E-07
3 Total Shrinkage to consider for prestress loss
Es(Infinity,7) 2.5E-04
4 Prestress loss due to shrinkage of concrete
Delta Ps 3939.14 kN
5Creep of concrete
1 Final creep coefficentC(30/37)
From Fig3.1RH=80%
2 Stress in the concrete at the tendon level (calculated in elastic shortening above)Sigma c 14.49 Mpa
3 Prestress loss due to creep of concrete
Ecc(infinity,7) 7.53E-04
Delta Pc 12037.84 kN
6Steel Relaxation under Tension
1 Value of roh1000Low relaxation-->
2 Value of the initial prestress Sigma pi = sigma pmo
Pmo(x=1.7m) from anchorage draw in 7369.37 kN
Sigma pmo 1198.27 Mpa
3 Value of the relaxation losses of the prestress
U 0.68Sigmapr/sigma pmo 0.0165045816
Sigma Pr 19.78 Mpa
4 Prestress loss due to relaxation of steel
Delta Pr 1581.17 kN
7Losses due to simultaneous effects
t=7days Prestress transfer
1 Time-dependent losses due to shrinkage, creep and relaxation
17558.15 kN
8Summary of the Losses
x(m) Location Immediate Loss(kN)Pel
0 Abutment 249.30
9.95 249.3028 At Pier 249.30
36.93 249.30
49.5 249.30
Long Term Loss 17558.15 kNPrestressing Force at jacking 61762.50 kN
28.43%
Total Loss at 49.5 meter 54.84%Prestress force after loss 27890.67 kNStress in all tendons 348.85 Mpa
Alpha 0.79Beta 0.45
Center of Side Span at a distance 9 meter
Center of central span
Considering half of the whole span since it is symmetrical about the center of mid span
x(m)1240 0 01240 9.95 9501240 20.09 01240 28 650
36.93 0
49.5 950
Cylindrical Strength
Coefficient of Friction
Wobbel factor
12 Strands in one tendon each having 150mm2 area
Mpa
Elastic Deformation of concrete
Calculation of the stresses in the concrete at the level of the tendon centeroids: