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

B. Concrete PropertiesC30/37fck 30 MpaEcm 33 Gpa

C.Prestressing CablesLow relaxationfpk (Charateristic Strength) 1770 Mpau 0.19

k 0.005

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:

7.71 + 0 =7.71 + 16.57 =7.71 + 0 =7.71 + 7.76 =7.71 + 0 =7.71 + 16.57 =

Average stress in the concrete adjacent to the tendon over its length:

Centeroid (m) from Bottom

Eccentrcity of tendon from centeroid (mm)

Length(m)9.95 = 15.99 Mpa

10.14 = 15.99 Mpa7.91 = 11.58 Mpa8.93 = 11.58 Mpa

12.57 = 15.99 Mpa

Calculation of the average stress in the conceret adjacent to the tendon over its length

Prestress Diagram after loss of prestress from elastic deformation of concrete:

3.27 %

2 Calculation of the prestress losses

Loss

0 2000 4000 6000 8000 10000 120000.7

0.8

0.9

1

1.1

Pmax Pel

0 P(x)/Pmax 1.0009.95 P(x)/Pmax 0.9919.95 P(x)/Pmax 0.9557.06 P(x)/Pmax 0.9583.08 P(x)/Pmax 0.9613.08 P(x)/Pmax 0.9307.91 P(x)/Pmax 0.9267.91 P(x)/Pmax 0.8938.93 P(x)/Pmax 0.8928.93 P(x)/Pmax 0.863

12.57 P(x)/Pmax 0.834Prestress Diagram after loss of prestress due to friction

Wedge draw-in of the anchorage devices

Reduction of the area in the prestressing diagram due to the draw in:

25.50 x 2 =

0 2000 4000 6000 8000 10000 120000

0.2

0.4

0.6

0.8

1

1.2

Pmax Pel Pel+fr

Fast

Drying shrinkage (assuming three days curing period)

Table 3.2 For RH=80% 2.70E-04Table 3.3 For ho>=500 h0=2*Ac/U 776.03

Ac 12.855U 33.13

Total Shrinkage to consider for prestress loss

0 2000 4000 6000 8000 10000 120000.7

0.75

0.8

0.85

0.9

0.95

1

Pmax Pel Pel+fr Pel+fr+sl

Phie(infinity,30) 1.8

Stress in the concrete at the tendon level (calculated in elastic shortening above)

Steel Relaxation under Tension

2.50 % Assuming Class 2 wire or strand:Low realaxation

Value of the initial prestress Sigma pi = sigma pmo

Value of the relaxation losses of the prestress

Losses due to simultaneous effects

Time-dependent losses due to shrinkage, creep and relaxation

Immediate Loss(kN)%loss Pu %loss Psl

3.27% 7619.85 0.00% 500.95

3.27% 7548.16 0.94% 500.953.27% 7053.86 7.43% 0.003.27% 6794.51 10.83% 0.00

3.27% 6357.43 16.57% 0.00

<75% yield strength of steel < 1125

Considering half of the whole span since it is symmetrical about the center of mid span

NoteEnd Support

Pier

Center of mid Span

780010

7.71 Mpa24.28 Mpa

7.71 Mpa15.46 Mpa

7.71 Mpa24.28 Mpa

0 10 20 30 40 50 600

500

1000

Eccentrcity of tendon from centeroid (mm)

Avg over its length159.11162.15

91.63103.45201.01

717.36

x(m) Pel Pmax0 0.967 1

9.95 0.967 19821.30 0.967 1

20.09 0.967 128 0.967 1

36.93 0.967 149.5 0.967 1

Calculation of the prestress losses

Pel+frPrestress force after loss

0 2000 4000 6000 8000 10000 120000.7

0.8

0.9

1

1.1

Pmax Pel

0.000 0.9670.009 0.9580.045 0.9220.042 0.9250.039 0.9290.070 0.8970.074 0.8930.107 0.8600.108 0.8590.137 0.8300.166 0.802

9821.30 mm

mm

C.Sectional Aream Perimeter m2

0 2000 4000 6000 8000 10000 120000.7

0.75

0.8

0.85

0.9

0.95

1

Pmax Pel Pel+fr Pel+fr+sl

Assuming Class 2 wire or strand:Low realaxation

%loss Total % Loss6.57% 9.85%

6.57% 10.79%6.57% 17.27%6.57% 20.68%

6.57% 26.41%

Mpa From EN-1991-1-1 , Section 7

0 10 20 30 40 50 600

500

1000

Eccentrcity of tendon from centeroid (mm)