Special Structures Model

7/29/2019 Special Structures Model

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Technical University Gh. Asachi from Iasi

Faculty of Civil Engineering and Building Services

Master of Structural Engineering

Student: Coordinator:

Irimia Cristian Radu Prof. Dr. ing. Gosav Ionel


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1. Project themeIt is required to design a digester.

There are given the following data:

- The digester is located in Bucuresti city- The height is 12 m, with the diameter 9.5 m, the foundation is situated at -0.5 m, with

the center diameter of 1 m, the roof has a height of 0.3 m and a center diameter of 1

m.

- The foundation mat has the thickness of 0.4 m, the concrete class used for thefoundation is C20/25

- The thickness of the wall is 0.35 m, the concrete class used for the wall is C25/30- The thickness of the roof is 0.25 m, the concrete class used is C25/30

2. Static computation2.1.Load cases

A. Permanent load- The self weights of the elements are automated generated by the analysis program. It

will be used the following specific weight B. Action of the water

Nr crt

H

(m)

(kN/m3)

pa

(kN/m2)

1 2 3=1*2

1 12

10

120

2 10 100

3 8 80

4 6 60

5 4 40

6 2 20

7 0 0

C. Snow load

Where:

- form factor for flat roofs

- exposure factor

- thermal coefficient for roofs with usual thermo-insulation


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characteristic value for snow load from the soil level (CR 1-1-32005)D. Seismic load

ps=p

i+p

w+p

c(kN/m

2)

piimpulsive pressure

pwpressure from the wall inertia

pcconvective pressure

Hthe height (m)

Rradius (m)

r = R for loading the reservoir wall (m)

zthe distance on vertical direction from the base to the center of the discretised surface (m)

the angle between the horizontal and the center of the discretised surface

=1000 kg/m3water density

n=1 number of vibration modes

I1(x)modified Bessel function of degree 15


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a. Loads from impulsive seismic actionAg(t)=0ag/qdesign acceleration

0=2.75dinamic amplifying factor

ag =0,2gthe ground acceleration (P100/2006)

q=1impulsive behavior factor

s=2500 kg/m3 reinforced concrete density

s() =0.35 mwall thickness

prseismic loading from the snow and roof weight (kN/m2)

hp =0.25 mthickness of the roof

pzsnow load (kN/m2)

b. Loads from the convective seismic action

n =1.841correction coefficient for one mode of vibration

Acn (t)= cn0 ag/q if TcnTc

Acn (t)=cn0Tc/ Tcn/q if TcTd

Tc=1.6 scorner period (P100/2006)

( 0.4 ) ( )r s p z g p h p A t

7 / (2 )cn cn 2

cn

cn

T


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Td=2 scorner period (P100/2006)

cn=0,5% - fratiune from convective critical damping

q=1.5convective behavior factor

J1(x)Bessel function of degree 1

Point z Angle Pi (kN/m2) Pc (kN/m2)

P

(kN/m2)

1 0

0

36.84 0.64 42.88

2 2 35.59 0.75 41.74

3 4 31.91 1.1 37.73

4 6 26.05 1.82 32.6

5 8 18.42 3.14 26.286 10 9.54 5.49 19.75

7 12 0 9.66 14.38

8 0

20

34.62 0.61 40.3

9 2 33.44 0.71 39.22

10 4 29.98 1.04 35.46

11 6 24.48 1.71 30.63

12 8 17.31 2.95 24.7

13 10 8.96 5.16 18.56

14 12 0 9.08 13.51

15 0

40

28.22 0.49 32.85

16 2 27.26 0.58 31.97

17 4 24.44 0.85 28.91

18 6 19.96 1.4 24.97

19 8 14.11 2.41 20.13

20 10 7.3 4.21 15.13

21 12 0 7.4 11.02

22 0

60

18.42 0.32 21.78

23 2 17.79 0.38 21.2

24 4 15.95 0.55 18.87

25 6 13.03 0.91 16.3

26 8 9.21 1.57 13.14

27 10 4.77 2.75 9.88

28 12 0 4.83 7.19

29 0

80

6.4 0.11 7.45

30 2 6.18 0.13 7.25

31 4 5.54 0.19 6.55

32 6 4.52 0.32 5.66

33 8 3.2 0.55 4.56

34 10 1.66 0.95 3.4335 12 0 1.68 2.5


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36 0

100

-6.4 -0.11 -7.45

37 2 -6.18 -0.13 -7.25

38 4 -5.54 -0.19 -6.55

39 6 -4.52 -0.32 -5.66

40 8 -3.2 -0.55 -4.56

41 10 -1.66 -0.95 -3.43

42 12 0 -1.68 -2.5

43 0

120

-18.42 -0.32 -21.44

44 2 -17.79 -0.38 -20.87

45 4 -15.95 -0.55 -18.87

46 6 -13.03 -0.91 -16.3

47 8 -9.21 -1.57 -13.14

48 10 -4.77 -2.75 -9.88

49 12 0 -4.83 -7.19

50 0

140

-28.22 -0.49 -32.8551 2 -27.26 -0.58 -31.97

52 4 -24.44 -0.85 -28.91

53 6 -19.96 -1.4 -24.97

54 8 -14.11 -2.41 -20.13

55 10 -7.3 -4.21 -15.13

56 12 0 -7.4 -11.02

57 0

160

-34.62 -0.61 -40.3

58 2 -33.44 -0.71 -38.58

59 4 -29.28 -1.04 -35.46

60 6 -24.48 -1.71 -30.63

61 8 -17.31 -2.95 -24.7

62 10 -8.96 -5.16 -16.56

63 12 0 -9.08 -13.51

64 0

180

-36.84 -0.64 -42.88

65 2 -35.59 -0.75 -41.74

66 4 -31.91 -1.1 -37.73

67 6 -26.05 -1.82 -32.6

68 8 -18.42 -3.14 -26.28

69 10 -9.54 -5.49 -19.7570 12 0 -9.66 -14.38

71 0

200

-34.62 -0.61 -40.3

72 2 -33.44 -0.71 -39.22

73 4 -29.98 -1.04 -35.46

74 6 -24.48 -1.71 -30.63

75 8 -17.31 -2.95 -24.7

76 10 -8.96 -5.16 -18.56

77 12 0 -9.08 -13.51

78 0

220

-28.22 -0.49 -32.85

79 2 -27.26 -0.58 -31.97

80 4 -24.44 -0.85 -28.91


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81 6 -19.96 -1.4 -24.97

82 8 -14.11 -2.41 -20.13

83 10 -7.3 -4.21 -15.13

84 12 0 -7.4 -11.02

85 0

240

-18.42 -0.32 -21.44

86 2 -17.79 -0.38 -20.87

87 4 -15.95 -0.55 -18.87

88 6 -13.03 -0.91 -16.3

89 8 -9.81 -1.57 -13.14

90 10 -4.77 -2.75 -9.88

91 12 0 -4.83 -7.19

92 0

260

-6.4 -0.11 -7.45

93 2 -6.18 -0.13 -7.25

94 4 -5.54 -0.19 -6.55

95 6 -4.52 -0.32 -5.6696 8 -3.2 -0.55 -4.56

97 10 -1.66 -0.95 -3.43

98 12 0 -1.68 -2.5

99 0

280

6.4 0.11 7.45

100 2 6.18 0.13 7.25

101 4 5.54 0.19 6.55

102 6 4.52 0.32 5.66

103 8 3.2 0.55 4.56

104 10 1.66 0.95 3.43

105 12 0 1.68 2.5

106 0

300

18.42 0.32 21.44

107 2 17.79 0.38 20.87

108 4 15.95 0.55 18.87

109 6 13.03 0.91 16.3

110 8 9.21 1.57 13.14

111 10 4.77 2.75 9.88

112 12 0 4.83 7.19

113 0

320

28.22 0.49 32.85

114 2 27.26 0.58 31.97115 4 24.44 0.85 28.91

116 6 19.96 1.4 24.97

117 8 14.11 2.41 20.13

118 10 7.3 4.21 15.13

119 12 0 7.4 11.02

120 0

340

34.62 0.61 40.3

121 2 33.44 0.71 39.22

122 4 29.98 1.04 35.46

123 6 24.48 1.71 30.63

124 8 17.31 2.95 24.7

125 10 8.96 5.16 18.56


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126 12 0 9.08 13.51

127 0

360

36.84 0.64 42.88

128 2 35.59 0.75 41.74

129 4 31.91 1.1 37.73

130 6 26.05 1.82 32.6

131 8 18.42 3.14 26.28

132 10 9.54 5.49 19.75

133 12 0 9.66 14.38

Shell PointPp

(kN/m2)

Ps

(kN/m2)Shell Point

Pp

(kN/m2)

Ps

(kN/m2)

1

1 42.88

41.035 28

32 5.66

02 41.74 33 4.56

8 40.3 39 -5.66

9 39.22 40 -4.56

2

2 41.74

38.5375 29

33 4.56

03 37.73 34 3.43

9 39.22 40 -4.56

10 35.46 41 -3.43

3

3 37.73

34.105 30

34 3.43

04 32.6 35 2.5

10 35.46 41 -3.43

11 30.63 42 -2.5

4

4 32.6

28.5525 31

36 -7.45

-14.25255 26.28 37 -7.25

11 30.63 43 -21.44

12 24.7 44 -20.87

5

5 26.28

22.3225 32

37 -7.25

-13.3856 19.75 38 -6.55

12 24.7 44 -20.87

13 18.56 45 -18.87

6

6 19.75

16.55 33

38 -6.55

-11.8457 14.38 39 -5.66

13 18.56 45 -18.8714 13.51 46 -16.3

7

8 40.3

36.085 34

39 -5.66

-9.9159 39.22 40 -4.56

15 32.85 46 -16.3

16 31.97 47 -13.14

8

9 39.22

33.89 35

40 -4.56

-7.752510 35.46 41 -3.43

16 31.97 47 -13.14

17 28.91 48 -9.889 10 35.46 29.9925 36 41 -3.43 -5.75


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11 30.63 42 -2.5

17 28.91 48 -9.88

18 24.97 49 -7.19

10

11 30.63

25.1075 37

43 -21.44

-26.782512 24.7 44 -20.8718 24.97 50 -32.85

19 20.13 51 -31.97

11

12 24.7

19.63 38

44 -20.87

-25.15513 18.56 45 -18.87

19 20.13 51 -31.97

20 15.13 52 -28.91

12

13 18.56

14.555 39

45 -18.87

-22.262514 13.51 46 -16.3

20 15.13 52 -28.91

21 11.02 53 -24.97

13

15 32.85

26.95 40

46 -16.3

-18.63516 31.97 47 -13.14

22 21.78 53 -24.97

23 21.2 54 -20.13

14

16 31.97

25.2375 41

47 -13.14

-14.5717 28.91 48 -9.88

23 21.2 54 -20.13

24 18.87 55 -15.13

15

17 28.91

22.2625 42

48 -9.88

-10.80518 24.97 49 -7.19

24 18.87 55 -15.13

25 16.3 56 -11.02

16

18 24.97

18.635 43

50 -32.85

-35.92519 20.13 51 -31.97

25 16.3 57 -40.3

26 13.14 58 -38.58

17

19 20.13

14.57 44

51 -31.97

-33.7320 15.13 52 -28.91

26 13.14 58 -38.58

27 9.88 59 -35.46

18

20 15.13

10.805 45

52 -28.91

-29.992521 11.02 53 -24.97

27 9.88 59 -35.46

28 7.19 60 -30.63

19

22 21.78

14.42 46

53 -24.97

-25.107523 21.2 54 -20.13

29 7.45 60 -30.63

30 7.25 61 -24.7


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20

23 21.2

13.4675 47

54 -20.13

-19.1324 18.87 55 -15.13

30 7.25 61 -24.7

31 6.55 62 -16.56

21

24 18.87

11.845 48

55 -15.13

-14.05525 16.3 56 -11.02

31 6.55 62 -16.56

32 5.66 63 -13.51

22

25 16.3

9.915 49

57 -40.3

-40.87526 13.14 58 -38.58

32 5.66 64 -42.88

33 4.56 65 -41.74

23

26 13.14

7.7525 50

58 -38.58

-38.377527 9.88 59 -35.46

33 4.56 65 -41.74

34 3.43 66 -37.73

24

27 9.88

5.75 51

59 -35.46

-34.10528 7.19 60 -30.63

34 3.43 66 -37.73

35 2.5 67 -32.6

25

29 7.45

0 52

60 -30.63

-28.552530 7.25 61 -24.7

36 -7.45 67 -32.6

37 -7.25 68 -26.28

26

30 7.25

0 53

61 -24.7

-21.822531 6.55 62 -16.56

37 -7.25 68 -26.28

38 -6.55 69 -19.75

27

31 6.55

0 54

62 -16.56

-16.0532 5.66 63 -13.51

38 -6.55 69 -19.75

39 -5.66 70 -14.38

Shell PointPp

(kN/m2)

Ps

(kN/m2)Shell Point

Pp

(kN/m2)

Ps

(kN/m2)

55

64 -42.88

-41.035 82

95 -5.66

065 -41.74 96 -4.56

71 -40.3 102 5.66

72 -39.22 103 4.56

56

65 -41.74

-38.5375 83

96 -4.56

066 -37.73 97 -3.4372 -39.22 103 4.56


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73 -35.46 104 3.43

57

66 -37.73

-34.105 84

97 -3.43

067 -32.6 98 -2.5

73 -35.46 104 3.43

74 -30.63 105 2.5

58

67 -32.6

-28.5525 85

99 7.45

14.252568 -26.28 100 7.25

74 -30.63 106 21.44

75 -24.7 107 20.87

59

68 -26.28

-22.3225 86

100 7.25

13.38569 -19.75 101 6.55

75 -24.7 107 20.87

76 -18.56 108 18.87

60

69 -19.75

-16.55 87

101 6.55

12.067570 -14.38 102 6.55

76 -18.56 108 18.87

77 -13.51 109 16.3

61

71 -40.3

-36.085 88

102 6.55

10.137572 -39.22 103 4.56

78 -32.85 109 16.3

79 -31.97 110 13.14

62

72 -39.22

-33.89 89

103 4.56

7.7525

73 -35.46 104 3.43

79 -31.97 110 13.14

80 -28.91 111 9.88

63

73 -35.46

-29.9925 90

104 3.43

5.7574 -30.63 105 2.5

80 -28.91 111 9.88

81 -24.97 112 7.19

64

74 -30.63

-25.1075 91

106 21.44

26.782575 -24.7 107 20.87

81 -24.97 113 32.85

82 -20.13 114 31.97

65

75 -24.7

-19.63 92

107 20.87

25.15576 -18.56 108 18.87

82 -20.13 114 31.97

83 -15.13 115 28.91

66

76 -18.56

-14.555 93

108 18.87

22.262577 -13.51 109 16.3

83 -15.13 115 28.91

84 -11.02 116 24.97

67 78 -32.85 -26.7825 94 109 16.3 18.63579 -31.97 110 13.14


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85 -21.44 116 24.97

86 -20.87 117 20.13

68

79 -31.97

-25.155 95

110 13.14

14.5780 -28.91 111 9.88

86 -20.87 117 20.1387 -18.87 118 15.13

69

80 -28.91

-22.2625 96

111 9.88

10.80581 -24.97 112 7.19

87 -18.87 118 15.13

88 -16.3 119 11.02

70

81 -24.97

-18.635 97

113 32.85

36.08582 -20.13 114 31.97

88 -16.3 120 40.3

89 -13.14 121 39.22

71

82 -20.13

-14.57 98

114 31.97

33.8983 -15.13 115 28.91

89 -13.14 121 39.22

90 -9.88 122 35.46

72

83 -15.13

-10.805 99

115 28.91

29.992584 -11.02 116 24.97

90 -9.88 122 35.46

91 -7.19 123 30.63

73

85 -21.44

-14.2525 100

116 24.97

25.107586 -20.87 117 20.13

92 -7.45 123 30.63

93 -7.25 124 24.7

74

86 -20.87

-13.385 101

117 20.13

19.6387 -18.87 118 15.13

93 -7.25 124 24.7

94 -6.55 125 18.56

75

87 -18.87

-11.845 102

118 15.13

14.555

88 -16.3 119 11.02

94 -6.55 125 18.56

95 -5.66 126 13.51

76

88 -16.3

-9.915 103

120 40.3

41.03589 -13.14 121 39.22

95 -5.66 1 42.88

96 -4.56 2 41.74

77

89 -13.14

-7.7525 104

121 39.22

38.537590 -9.88 122 35.46

96 -4.56 2 41.74

97 -3.43 3 37.7378 90 -9.88 -5.75 105 122 35.46 34.105


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91 -7.19 123 30.63

97 -3.43 3 37.73

98 -2.5 4 32.6

79

92 -7.45

0 106

123 30.63

28.552593 -7.25 124 24.799 7.45 4 32.6

100 7.25 5 26.28

80

93 -7.25

0 107

124 24.7

22.322594 -6.55 125 18.56

100 7.25 5 26.28

101 6.55 6 19.75

81

94 -6.55

0 108

125 18.56

16.5595 -5.66 126 13.51

101 6.55 6 19.75

102 5.66 7 14.38

2.2.Combinations

- SLU1: 1.35P+1.5A+1.05Z- SLU2: 1.35P+1.05A+1.5Z- SLU3: P+0.4Z+S2.3.Results

2.3.1. Modal analysisTABLE: Modal Periods And Frequencies

OutputCase StepType StepNumPeriod Frequency CircFreq Eigenvalue

Sec Cyc/sec rad/sec rad2/sec2

MODAL Mode 1 0.0665 15.039 94.49 8928.4

MODAL Mode 2 0.0608 16.447 103.34 10680

MODAL Mode 3 0.0362 27.597 173.4 30066

MODAL Mode 4 0.0335 29.874 187.7 35232

MODAL Mode 5 0.0333 30.071 188.94 35700

MODAL Mode 6 0.0266 37.662 236.63 55996

MODAL Mode 7 0.0261 38.376 241.12 58141

MODAL Mode 8 0.0248 40.29 253.15 64084

MODAL Mode 9 0.0242 41.251 259.19 67180

MODAL Mode 10 0.0233 42.896 269.53 72645

MODAL Mode 11 0.0224 44.555 279.95 78372

MODAL Mode 12 0.0222 45.045 283.03 80104


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The representation of principal modes of vibration:

Mode 1

Mode 2


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Mode 3


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3. Horizontal prestressing3.1.Geometrical characteristics

r=R+20.105=9.5+20.105=9.71 m

Lr=r+0.17=9.71+0.17=30.57 m

r-the radius of the fascicle

Lr- the fascicle length between anchorages

3.2. Design of the pre-stressed reinforcement

Where:

nithe number of fascicles on height hi (min 8/m and max 20/m)

hi=2 mthe height of the zone with constant distance between fascicles

Nxxi maximum horizontal axial force on zone i (kN/m)

NP1

NP2 NP4

NP3

Pozitia I(se aplica la randurile impare)

Pozitia II(se aplica la randurile pare)

Nervurade ancorare

85

85

Lr

r

2R

17,5

DET. A

7

4,5 5 25,5

28

DET. A

35

17,5

7

10,5

17,5


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A1iarea of one fascicle in zone i (mm2)

fpk=1660 N/mm2 (the characteristic resistance for the pre-stressed reinforcement)

Apithe pre-stressed reinforcement area for zone i (mm2)

Impose A1=462 mm2, 127 mm

For H=0-2 m

Nxx1=1175.05 kN/m

For H=2-4 m

Nxx2=964.91 kN/m

For H=4-6

Nxx3=1120 kN/m

For H=6-8

Nxx4=621.02 kN/m

For H=8-10

Nxx5=500 kN/m

12 5 mm 12 7 mm 24 7 mm 48 7 mm

Section mm2

(A1) 235 462 924 1846

FascicleCharacteristics


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For H=10-12

Nxx6=949.23 kN/m

3.3.Tensions in concrete and reinforcement during transfer

3.3.1. Control tension

3.3.2. Tension lossesa. losses due to successive stretching of the reinforcement

Ep=180000 (N/mm2) elastic modulus for the pre-stressed reinforcement Ecm(t)=33500 (N/mm2)the elastic modului for the concrete at time t nthe number of reinforcement that is stretched succesive c(t)1 (N/mm2)the tension variation in concrete at the level of the gravity center

point of the pre-stressed reinforcement

b. Tension losses due to friction and slipping inside the anchorages


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=0.12 friction coefficient for polyethilene

k=0.01 m-1

1, 2elongation at the ends 1 = 0, 2 = 5mm

{


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3.3.3. Tensions in reinforcement during transfer

3.3.4. Tensions in concrete during transfer

3.4.Tensions in concrete and reinforcement during exploitation

3.4.1. Tension lossa. Tension loss due to relaxation, creep and contraction

[ ]

()

()


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() ()

* + * +

[

] * +

[]

Where:

cs total deformation due to contraction () cd(t)total deformation due to concrete hardening


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ca (t)total deformation due to endogen contraction t=90 zilethe concrete age when the checking in performed Ac=A1+A2+A3the area of the concrete section Uthe concrete section perimeter cd,0=0,52 nominal value of hardening contraction fck =35 N/mm2 (C35/45)characteristic strenght prtension loss due to reinforcement relaxation potension in reinforcement during transfer 1000 =8%tension loss at 1000 hours from tensioning Ecm=36000 (N/mm2)concrete elastic modulus (t,t0)-creep coefficient RHfactor that takes into account the influence of humidity RH=50% - humidity t0 =28 zile the age of the concrete at the checking moment fcm =43 N/mm2 (C35/45)compressive mean strenght Ic=I1+I2+I3moment of inertia for the concrete section zcpthe distance from the center of gravity of the reinforcement to the center of

gravity of the section

c,QP=530 kN/mconcrete tension on reinforcement direction from combinationP+0.4Z

3.4.2. Tension in reinforcement during service


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3.4.3. Tension in concrete during service

3.5.Checking the transmition zones

3.5.1. Checking to local compresion

a=b=350 mm a0=b0=280 mm fyd= fyk/s=235/1,15=204.4 (N/mm2) OB37 fcd=fck/b=35/1.5 = 23.33 N/mm2 (C35/45) s=50 mm Aa1=Aa2=410 OB37=314 mm2


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3.5.2. Checking the cracking in plane

3.5.3. Checking the resistance to the friction forces during transfer

Np1min> Nf Np1min=pp,min Ap1=83.336462=38501.232 N=38.5 kN Nf= nfr =8.75 6.71=58.71(kN) nf=vf=17.50.5=8.75 v=0.35hiba=0.35225=17.5(kN/m) ba =25(kN/m3) f=0.5friction coefficient between concrete and

neopren


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4. Vertical pre-stressing4.1.Geometrical characteristics

nithe number of fascicles on height h=1m(between 4 and 10)

Nyyi vertical axial effort (kN/m)

A1fascicle area (mm2)

fpk=1660 N/mm2

Impose A1=235 mm2, 125 mm

4.2.Tension in concrete and reinforcement during transfer

4.2.1. Control tension

4.2.2. Tension lossa. Tension loss due to succesive stretch of the reinforcement


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b. Tension loss due to friction and slipping inside anchorages

=0.12 friction coefficient for polyethilene; k=0.01 m-1

1, 2elongation at the ends 1 = 0, 2 = 5mm

,


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4.3.Tension during transfer in concrete and reinforcement

4.3.1. Tension during transfer in reinforcement

4.3.2. Tension during transfer in concrete

4.4.Tension in concrete and reinforcement during service

4.4.1. Tension lossa. Tension loss due to creep and contraction

[ ]


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() ()

() ()

* + * + [ ]

* +


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4.4.2. Tension in reinforcement during service

4.4.3. Tension in concrete during service

mxx =64.19 kNm/mthe bending moment with respect to the horizontal local axis4.5.Checking the transmition zones

4.5.1. Checking to local compresion a=b=350 mm a0=b0=280 mm fyd= fyk/s=235/1,15=204.4

(N/mm2) OB37

fcd=fck/b=35/1.5 = 23.33 N/mm2(C35/45)

s=50 mm Aa1=Aa2=410 OB37=314 mm2


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4.5.2. Checking the cracking in plane

4.5.3. Checking the resistance to the friction forces during transfer

Np1min> Nf

Np1min=pp,min Ap1=908.493462=419723.8 N=419.7 kN

Nf= nfr =4.375 6710=29356 (N) nf=vf=8.750.5=4.375 v=0.35hiba=35010002510-6=8.75(N/mm) ba =25(kN/m3) f=0.5friction coefficient between concrete and

neopren

Special Structures Model

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