02 tinh toan do gian dai DUL v2

tính toán độ giãn dài các bó cáp 12.7 mm
elongation Calculation of cable 12.7 mm

Cầu / Bridge: LRB08
Quang Nam
Thi công dầm I 33

Dự án/ Project
Vị trí/ Location
Hạng mục/ Item

Da Nang - Quang Ngai Expressway
Project:

Pr. Time

- Công thức tính độ dãn dài/ Formula of elongation computation:
L = P*L/(Ap*Ep)
- Trong đó/ With:
P
(kN) Lực kéo bình quân/ Average force
Ep

(kPa) Môđuyn đàn hồi của tao cáp/ Modulus of elasticity

Ap

(m2) Diện tích của bó cáp/ Nominal area
(m) Chiều dài tao cáp đã tính cả phần ôm kích/

L

Length of cable include part in jack.
Lneo =

(mm) Độ tụt nêm khi đóng neo (Lấy theo thí nghiệm)
Displacement when fixed anchorage(according to test results).

P = Ptk * (1 e ( Kx + à ) )
Ptk

(kN) Lực kéo thiết kế/ Design force

x

(m) Chiều dài bó cáp DUL đo từ đầu kích đến điểm bất kỳ đang xét.
Tendon length from the head of Jack to the point being considered

K

(1/m) Hệ số ma sát lắc của bó cáp/ Coefficient of friction

à

Hệ số ma sát/ Coefficient of friction



Tổng giá trị tuyệt đối của thay đổi góc của đờng trục cáp DUL từ đầu kích
Absolute total value of the angle changing of line cable from the head jack
hoặc từ đầu kích gần nhất (nếu căng hai đầu) đến điểm đang xem xét (Rad)

or from the nearest jack head to the point being considered (if tension two ends)

e

:Cơ số logarit tự nhiên/ Natural logarithm

- Kết quả / Result:

Tên cáp/
Cable No.

C1
C2
C3
C4
C5
main contractor

Độ tụt Giãn dài tt/
neo /
Actual
Anchor elongation
sliding
DL

C. dài/
length

Giãn dài tk/
Design elongation

L

(m)

(mm)

(mm)

mm

(%)

32.790
32.762
32.739
33.940
32.704

216.6
217.5
218.4
217.7
219.1

6
6
6
6
6

222.6
223.5
224.4
223.7
225.1

0.66
0.66
0.67
0.67
0.67

Consultant

L/L


calculation of elongation
Block name:
Cable name:
Type tension :
Type
0.5"-15

Point
1
2
3
4
5

6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

Cable 01
C1
A head
2

Ap (m )
0.001485
Xi
(m)
0.000
1.000
2.350
3.350
4.350

5.350
6.350
7.350
8.350
9.350
10.350
11.350
12.350
13.350
14.350
15.350
16.350
17.350
18.350
19.350

Yi
(m)
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0

0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0

Total length of cable
Designed Elongation

x Two head

Ep (MPa)

Ptk (kN)

197000

1927.6

Zi
(m)
1.440
1.315
1.160
1.054
0.956
0.865

0.783
0.708
0.641
0.582
0.531
0.488
0.453
0.425
0.406
0.394
0.390
0.394
0.406
0.425

∆x
(m)
0.000
1.000
1.350
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000

1.000
1.000
1.000
1.000
1.000
1.000
1.000

µ
0.25

K(1/m)
0.00066
∆β
(rad.)

∆Y
(m)

∆z
(m)

∆Li
(m)

0.000
0.000
0.000
0.000
0.000

0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

0.125
0.155
0.106
0.098
0.091
0.082
0.075
0.067
0.059
0.051
0.043
0.035
0.028
0.019
0.012

0.004
0.004
0.012
0.019

1.008
1.359
1.006
1.005
1.004
1.003
1.003
1.002
1.002
1.001
1.001
1.001
1.000
1.000
1.000
1.000
1.000
1.000
1.000

0.000
0.000
0.000
0.000
0.000

0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

L = 32.790 (m)
∆1 = 207.6 (mm)
∆2 =
9.0
(mm)
∆L = 216.6 (mm)
∆L/L= 0.661 (%)

Elongation cable of OVM jack
Total elongation
Elongation percentage
∆α
(rad.)
0.000
-0.010

-0.009
-0.008
-0.007
-0.009
-0.007
-0.008
-0.008
-0.008
-0.008
-0.008
-0.007
-0.009
-0.007
-0.008
0.000
0.008
0.007

∆(α+β)
(rad.)
0.000
0.010
0.009
0.008
0.007
0.009
0.007
0.008
0.008
0.008

0.008
0.008
0.007
0.009
0.007
0.008
0.000
0.008
0.007

Σ∆(α+β)
(rad.)

0.010
0.019
0.027
0.034
0.043
0.049
0.057
0.065
0.073
0.081
0.089
0.096
0.105
0.112
0.120
0.120
0.128

0.135

Σµ*α

0.003
0.005
0.007
0.008
0.011
0.012
0.014
0.016
0.018
0.020
0.022
0.024
0.026
0.028
0.030
0.030
0.032
0.034

ΣK*x
0.001
0.002
0.002
0.003
0.004
0.004

0.005
0.006
0.006
0.007
0.008
0.008
0.009
0.010
0.010
0.011
0.011
0.012
0.013

Σ(µ*α+
K*x)
0.001
0.004
0.007
0.010
0.012
0.015
0.017
0.020
0.023
0.025
0.028
0.031
0.033
0.036

0.038
0.041
0.042
0.044
0.047

Px
(KN)
1927.60
1926.32
1919.77
1914.32
1909.27
1904.70
1899.19
1894.64
1889.62
1884.61
1879.61
1874.63
1869.65
1865.16
1859.74
1855.26
1850.33
1849.11
1844.20
1839.76

Pav

(KN)
1926.96
1923.04
1917.04
1911.79
1906.98
1901.94
1896.91
1892.13
1887.11
1882.11
1877.12
1872.14
1867.4
1862.45
1857.5
1852.8
1849.72
1846.66
1841.98

∆
(mm)
6.638
8.933
6.590
6.566
6.546
6.523
6.502

6.482
6.462
6.442
6.422
6.403
6.386
6.368
6.350
6.333
6.323
6.313
6.298


21
22
23
24
25
26
27
28
29
30
31
32
33

20.350
21.350

22.350
23.350
24.350
25.350
26.350
27.350
28.350
29.350
30.350
31.700
32.700

0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0

0.453
0.488
0.531
0.582

0.641
0.708
0.783
0.865
0.956
1.054
1.160
1.315
1.440

1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.350
1.000

0.000
0.000
0.000
0.000
0.000
0.000

0.000
0.000
0.000
0.000
0.000
0.000
0.000

0.028
0.035
0.043
0.051
0.059
0.067
0.075
0.082
0.091
0.098
0.106
0.155
0.125

1.000
1.001
1.001
1.001
1.002
1.002
1.003
1.003

1.004
1.005
1.006
1.359
1.008

0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

0.009
0.007
0.008
0.008
0.008
0.008
0.008
0.007
0.009
0.007

0.008
0.009
0.010

0.009
0.007
0.008
0.008
0.008
0.008
0.008
0.007
0.009
0.007
0.008
0.009
0.010

0.144
0.151
0.159
0.167
0.175
0.183
0.191
0.198
0.207
0.214
0.222
0.231

0.241

0.036
0.038
0.040
0.042
0.044
0.046
0.048
0.050
0.052
0.054
0.055
0.058
0.060

0.013
0.014
0.015
0.015
0.016
0.017
0.017
0.018
0.019
0.019
0.020
0.021
0.022

0.050
0.052
0.055
0.057
0.060
0.063
0.065
0.068
0.071
0.073
0.076
0.079
0.082

1834.42
1830.01
1825.15
1820.31
1815.48
1810.67
1805.87
1801.54
1796.33
1792.03
1787.30
1781.81
1776.17

1837.09
1832.21

1827.58
1822.73
1817.89
1813.07
1808.27
1803.71
1798.94
1794.18
1789.67
1784.56
1778.99

6.282
6.267
6.253
6.239
6.225
6.211
6.199
6.186
6.175
6.162
6.152
8.289
6.128


calculation of elongation
Block name:
Cable name:

Type tension :
Type
0.5"-15

Point
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21

Cable 01
C1
A head

2

Ap (m )
0.001485
Xi
(m)
0.000
1.000
2.350
3.350
4.350
5.350
6.350
7.350
8.350
9.350
10.350
11.350
12.350
13.350
14.350
15.350
16.350
17.350
18.350
19.350
20.350

Yi
(m)

0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0

Total length of cable
Designed Elongation

x Two head

Ep (MPa)

Ptk (kN)

197000

1928

Zi
(m)
1.130
1.027
0.898
0.810
0.729
0.654
0.585
0.524
0.468
0.419
0.377
0.341
0.312
0.289
0.273
0.263
0.260
0.263
0.273
0.289
0.312

∆x

(m)
0.000
1.000
1.350
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000

µ
0.25

K(1/m)
0.00066
∆β
(rad.)

∆Y
(m)

∆z
(m)

∆Li
(m)

0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

0.103
0.129
0.088
0.081
0.075
0.069
0.061
0.056
0.049
0.042
0.036
0.029
0.023
0.016
0.010
0.003
0.003
0.010
0.016
0.023

1.005
1.356
1.004
1.003
1.003
1.002
1.002
1.002

1.001
1.001
1.001
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000

0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

0.000
0.000
0.000

Elongation cable of OVM jack
Total elongation
Elongation percentage
∆α
(rad.)
0.000
-0.007
-0.007
-0.007
-0.006
-0.006
-0.008
-0.005
-0.007
-0.007
-0.006
-0.007
-0.006
-0.007
-0.006
-0.007
0.000
0.007
0.006
0.007

∆(α+β)
(rad.)
0.000
0.007
0.007
0.007
0.006
0.006
0.008
0.005
0.007
0.007
0.006
0.007
0.006
0.007
0.006
0.007
0.000
0.007
0.006
0.007

Σ∆(α+β)
(rad.)

0.007
0.015
0.022
0.028

0.034
0.042
0.047
0.054
0.061
0.067
0.074
0.080
0.087
0.093
0.100
0.100
0.107
0.113
0.120

Σµ*α

0.002
0.004
0.005
0.007
0.008
0.010
0.012
0.013
0.015
0.017
0.018
0.020

0.022
0.023
0.025
0.025
0.027
0.028
0.030

ΣK*x
0.001
0.002
0.002
0.003
0.004
0.004
0.005
0.006
0.006
0.007
0.008
0.008
0.009
0.009
0.010
0.011
0.011
0.012
0.013
0.013

Σ(µ*α+
K*x)
0.001
0.003
0.006
0.008
0.010
0.013
0.015
0.017
0.020
0.022
0.024
0.027
0.029
0.031
0.033
0.036
0.036
0.039
0.041
0.043

L = 32.762 (m)
∆1 = 208.5 (mm)
∆2 =
9.0
(mm)
∆L = 217.5 (mm)
∆L/L= 0.664 (%)

Px
(KN)
1927.600
1926.321
1921.054
1916.189
1911.597
1907.486
1903.382
1898.339
1894.723
1890.170
1885.626
1881.561
1877.034
1872.986
1868.479
1864.448
1859.960
1858.733
1854.259
1850.258
1845.805

Pav
(KN)
1926.96
1923.69
1918.62
1913.89

1909.54
1905.43
1900.86
1896.53
1892.45
1887.9
1883.59
1879.3
1875.01
1870.73
1866.46
1862.2
1859.35
1856.5
1852.26
1848.03

∆
(mm)
6.622
8.918
6.584
6.564
6.546
6.529
6.510
6.493
6.477
6.459
6.443

6.427
6.411
6.396
6.380
6.366
6.356
6.346
6.332
6.319


22
23
24
25
26
27
28
29
30
31
32
33

21.350
22.350
23.350
24.350
25.350
26.350

27.350
28.350
29.350
30.350
31.700
32.700

0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0

0.341
0.377
0.419
0.468
0.524
0.585
0.654
0.729
0.810
0.898

1.027
1.130

1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.350
1.000

0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

0.029

0.036
0.042
0.049
0.056
0.061
0.069
0.075
0.081
0.088
0.129
0.103

1.000
1.001
1.001
1.001
1.002
1.002
1.002
1.003
1.003
1.004
1.356
1.005

0.000
0.000
0.000
0.000
0.000

0.000
0.000
0.000
0.000
0.000
0.000
0.000

0.006
0.007
0.006
0.007
0.007
0.005
0.008
0.006
0.006
0.007
0.007
0.007

0.006
0.007
0.006
0.007
0.007
0.005
0.008
0.006
0.006

0.007
0.007
0.007

0.126
0.133
0.139
0.146
0.153
0.158
0.166
0.171
0.177
0.184
0.192
0.199

0.031
0.033
0.035
0.036
0.038
0.039
0.041
0.043
0.044
0.046
0.048
0.050

0.014
0.015
0.015
0.016
0.017
0.017
0.018
0.019
0.019
0.020
0.021
0.022

0.046
0.048
0.050
0.052
0.055
0.057
0.059
0.062
0.064
0.066
0.069
0.071

1841.824
1837.393
1833.432
1829.024

1824.628
1821.152
1816.326
1812.418
1808.520
1804.184
1799.197
1794.693

1843.81
1839.61
1835.41
1831.23
1826.83
1822.89
1818.74
1814.37
1810.47
1806.35
1801.69
1796.95

6.305
6.292
6.279
6.267
6.254
6.243
6.232
6.219

6.209
6.198
8.352
6.175


L=
P=
E=
A=
Dta =

32.762 m
1927.60 kN
197000
1.97E+08
0.001485
0.215868

Mpa
KN/m
m2
(m)

215.8684 mm
Chieu dai dau kich va nem nem
Độ giãn dài 1 đầu là

680.00 mm
0.00 m

4.48 mm


calculation of elongation
Block name: Cable 01
Cable name: C1
Type tension :
A head
Type
0.5"-15

Point
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18

19
20
21

2

Ap (m )
0.001485
Xi
(m)
0.000
1.000
2.350
3.350
4.350
5.350
6.350
7.350
8.350
9.350
10.350
11.350
12.350
13.350
14.350
15.350
16.350
17.350
18.350
19.350

20.350

Yi
(m)
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0

Total length of cable
Designed Elongation

x Two head

Ep (MPa)

Ptk (kN)

197000

1928

Zi
(m)
0.820
0.738
0.636
0.566
0.502
0.442
0.388
0.339
0.295
0.256
0.223
0.195
0.171
0.153
0.140
0.133
0.130
0.133
0.140

0.153
0.171

∆x
(m)
0.000
1.000
1.350
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000

Elongation cable of OVM jack
Total elongation
Elongation percentage

K(1/m)
µ
0.25 0.00066

∆Y
(m)

∆z
(m)

∆Li
(m)

0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

0.000
0.000
0.000
0.000

0.082
0.102
0.070
0.064
0.060
0.054
0.049
0.044
0.039
0.033
0.028
0.024
0.018
0.013
0.007
0.003
0.003
0.007
0.013
0.018

1.003
1.354
1.002
1.002

1.002
1.001
1.001
1.001
1.001
1.001
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000

∆β
(rad.)
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

L=
∆1 =
∆2 =

∆α
(rad.)
0.000
-0.006
-0.006
-0.006
-0.004
-0.006
-0.005
-0.005
-0.005
-0.006
-0.005
-0.004
-0.006
-0.005

-0.006
-0.004
0.000
0.004
0.006
0.005

∆(α+β)
(rad.)
0.000
0.006
0.006
0.006
0.004
0.006
0.005
0.005
0.005
0.006
0.005
0.004
0.006
0.005
0.006
0.004
0.000
0.004
0.006
0.005

Σ∆(α+β)
(rad.)

0.006
0.012
0.018
0.022
0.028
0.033
0.038
0.043
0.049
0.054
0.058
0.064
0.069
0.075
0.079
0.079
0.083
0.089
0.094

Σµ*α

0.002
0.003
0.004
0.005
0.007

0.008
0.009
0.011
0.012
0.013
0.014
0.016
0.017
0.019
0.020
0.020
0.021
0.022
0.023

ΣK*x
0.001
0.002
0.002
0.003
0.004
0.004
0.005
0.006
0.006
0.007
0.008
0.008
0.009
0.009

0.010
0.011
0.011
0.012
0.013
0.013

∆L =
∆L/L=

Σ(µ*α+K
*x)
0.001
0.003
0.005
0.007
0.009
0.011
0.013
0.015
0.017
0.019
0.021
0.023
0.025
0.027
0.029
0.031
0.031
0.033

0.035
0.037

Px
(KN)
1927.600
1926.324
1921.524
1917.602
1913.475
1910.306
1906.192
1902.559
1898.933
1895.312
1891.226
1887.619
1884.489
1880.424
1876.836
1872.787
1869.681
1868.447
1865.348
1861.323
1857.772

32.739 (m)
209.4 (mm)
9.0

218.4
0.667
Pav
(KN)
1926.962
1923.924
1919.563
1915.539
1911.891
1908.249
1904.376
1900.746
1897.123
1893.269
1889.422
1886.054
1882.456
1878.63
1874.812
1871.234
1869.064
1866.898
1863.336
1859.548

(mm)
(mm)
(%)
∆
(mm)

6.609
8.904
6.578
6.561
6.547
6.532
6.517
6.504
6.490
6.475
6.461
6.449
6.436
6.422
6.409
6.396
6.389
6.382
6.370
6.357


22
23
24
25
26
27
28
29

30
31
32
33

21.350
22.350
23.350
24.350
25.350
26.350
27.350
28.350
29.350
30.350
31.700
32.700

0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0

0.195
0.223
0.256
0.295
0.339
0.388
0.442
0.502
0.566
0.636
0.738
0.820

1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.350
1.000

0.000
0.000
0.000

0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

0.024
0.028
0.033
0.039
0.044
0.049
0.054
0.060
0.064
0.070
0.102
0.082

1.000
1.000
1.001
1.001
1.001
1.001
1.001

1.002
1.002
1.002
1.354
1.003

0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

0.006
0.004
0.005
0.006
0.005
0.005
0.005
0.006
0.004
0.006
0.006

0.006

0.006
0.004
0.005
0.006
0.005
0.005
0.005
0.006
0.004
0.006
0.006
0.006

0.100
0.104
0.109
0.115
0.120
0.125
0.130
0.136
0.140
0.146
0.151
0.158

0.025
0.026

0.027
0.029
0.030
0.031
0.032
0.034
0.035
0.036
0.038
0.039

0.014
0.015
0.015
0.016
0.017
0.017
0.018
0.019
0.019
0.020
0.021
0.022

0.039
0.041
0.043
0.045
0.047
0.049

0.051
0.053
0.054
0.056
0.059
0.061

1853.765
1850.691
1847.161
1843.178
1839.663
1836.157
1832.657
1828.710
1825.681
1821.751
1817.611
1813.502

1855.768
1852.228
1848.926
1845.169
1841.421
1837.91
1834.407
1830.683
1827.195
1823.716

1819.681
1815.556

6.345
6.334
6.324
6.312
6.301
6.290
6.280
6.269
6.259
6.249
8.421
6.227


L=
P=
E=
A=
Dta =

32.739 m
1927.60 kN
197000
1.97E+08
0.001485
0.215718

Mpa
KN/m
m2
(m)

215.718 mm
Chieu dai dau kich va nem nem
Độ giãn dài 1 đầu là

680.00 mm
0.00 m
4.48 mm


calculation of elongation
Block name:
Cable name:
Type tension :
Type
0.5"-15

Point
1
2
3
4
5
6
7
8

9
10
11
12
13
14
15
16
17
18
19
20
21

Cable 01
C1
A head
2

Ap (m )
0.001485
Xi
(m)
0.000
1.000
2.350
3.350
4.350
5.350
6.350

7.350
8.350
9.350
10.350
11.350
12.350
13.350
14.350
15.350
16.350
17.350
18.350
19.350
20.350

Yi
(m)
0.000
0.000
0.000
0.000
-0.025
-0.050
-0.075
-0.100
-0.125
-0.150
-0.150
-0.150
-0.150

-0.150
-0.150
-0.150
-0.150
-0.150
-0.150
-0.150
-0.150

x Two head

Ep (MPa)

Ptk (kN)

197000

1928

Zi
(m)
0.510
0.465
0.409
0.370
0.335
0.302
0.272
0.245
0.221

0.200
0.181
0.166
0.153
0.143
0.136
0.131
0.130
0.131
0.136
0.143
0.153

Total length of cable
Designed Elongation

∆x
(m)
0.000
1.000
1.350
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000

1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000

Elongation cable of OVM jack
Total elongation
Elongation percentage

K(1/m)
µ
0.25 0.00066

∆Y
(m)

∆z
(m)

∆Li
(m)

0.000
0.000
0.000

0.025
0.025
0.025
0.025
0.025
0.025
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

0.045
0.056
0.039
0.035
0.033
0.030
0.027
0.024
0.021
0.019
0.015
0.013

0.010
0.007
0.005
0.001
0.001
0.005
0.007
0.010

1.001
1.351
1.001
1.001
1.001
1.001
1.001
1.001
1.001
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000

∆β
(rad.)
0.000
0.000
0.000
0.025
0.000
0.000
0.000
0.000
0.000
-0.025
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

∆α
(rad.)
0.000
-0.004
-0.002
-0.004
-0.002

-0.003
-0.003
-0.003
-0.003
-0.002
-0.004
-0.002
-0.003
-0.003
-0.002
-0.004
0.000
0.004
0.002
0.003

∆(α+β)
(rad.)
0.000
0.004
0.002
0.025
0.002
0.003
0.003
0.003
0.003
0.025
0.004
0.002

0.003
0.003
0.002
0.004
0.000
0.004
0.002
0.003

Σ∆(α+β)
(rad.)

0.004
0.006
0.031
0.033
0.036
0.039
0.042
0.045
0.070
0.074
0.076
0.079
0.082
0.084
0.088
0.088
0.092
0.094

0.097

Σµ*α

0.001
0.001
0.008
0.008
0.009
0.010
0.011
0.011
0.018
0.019
0.019
0.020
0.021
0.021
0.022
0.022
0.023
0.024
0.024

ΣK*x

Σ(µ*α+
K*x)

0.001

0.002
0.002
0.003
0.004
0.004
0.005
0.006
0.006
0.007
0.007
0.008
0.009
0.009
0.010
0.011
0.011
0.012
0.013
0.013

0.001
0.002
0.004
0.011
0.012
0.013
0.015
0.016
0.017
0.024

0.026
0.027
0.029
0.030
0.031
0.033
0.034
0.035
0.036
0.038

L = 32.715 (m)
∆1 = 208.7 (mm)
∆2 =
9.0
(mm)
∆L = 217.7 (mm)
∆L/L= 0.665 (%)
Px
(KN)
1927.60
1926.33
1922.92
1920.46
1907.09
1904.88
1902.19
1899.51
1896.84
1894.16

1881.08
1877.97
1875.79
1873.15
1870.51
1868.34
1865.24
1864.01
1860.92
1858.76
1856.14

Pav
(KN)
1926.96
1924.62
1921.69
1913.77
1905.98
1903.53
1900.85
1898.17
1895.50
1887.62
1879.52
1876.88
1874.47
1871.83
1869.42
1866.79

1864.62
1862.46
1859.84
1857.45

∆
(mm)
6.594
8.889
6.574
6.548
6.521
6.512
6.502
6.492
6.483
6.454
6.425
6.416
6.408
6.399
6.390
6.381
6.374
6.366
6.358
6.350


22

23
24
25
26
27
28
29
30
31
32
33

21.350
22.350
23.350
24.350
25.350
26.350
27.350
28.350
29.350
30.350
31.700
32.700

-0.150
-0.150
-0.150
-0.125
-0.100

-0.075
-0.050
-0.025
0.000
0.000
0.000
0.000

0.166
0.181
0.200
0.221
0.245
0.272
0.302
0.335
0.370
0.409
0.465
0.510

1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000

1.000
1.350
1.000

0.000
0.000
0.000
0.025
0.025
0.025
0.025
0.025
0.000
0.000
0.000
0.000

0.013
0.015
0.019
0.021
0.024
0.027
0.030
0.033
0.035
0.039
0.056
0.045

1.000
1.000
1.000
1.001
1.001
1.001
1.001
1.001
1.001
1.001
1.351
1.001

0.000
0.000
0.000
0.025
0.000
0.000
0.000
0.000
-0.025
0.000
0.000
0.000

0.003
0.002
0.004
0.002

0.003
0.003
0.003
0.003
0.002
0.004
0.002
0.004

0.003
0.002
0.004
0.025
0.003
0.003
0.003
0.003
0.025
0.004
0.002
0.004

0.100
0.102
0.106
0.131
0.134
0.137
0.140
0.143

0.169
0.172
0.175
0.178

0.025
0.026
0.027
0.033
0.034
0.034
0.035
0.036
0.042
0.043
0.044
0.045

0.014
0.015
0.015
0.016
0.017
0.017
0.018
0.019
0.019
0.020
0.021
0.022

0.039
0.040
0.042
0.049
0.050
0.052
0.053
0.055
0.062
0.063
0.065
0.066

1853.52
1851.38
1848.31
1835.54
1832.96
1830.37
1827.80
1825.22
1812.62
1809.61
1806.88
1804.10

1854.83
1852.45
1849.84

1841.92
1834.25
1831.67
1829.08
1826.51
1818.92
1811.11
1808.25
1805.49

6.341
6.333
6.324
6.300
6.274
6.265
6.257
6.249
6.221
6.196
8.352
6.178


L=
P=
E=
A=
Dta =

32.715 m
1927.60 kN
197000
1.97E+08
0.001485
0.215563

Mpa
KN/m
m2
(m)

215.5627 mm
Chieu dai dau kich va nem nem
Độ giãn dài 1 đầu là

680.00 mm
0.00 m
4.48 mm


calculation of elongation
Block name:
Cable name:
Type tension :
Type
0.5"-15

Point
1

2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21

Cable 01
C1
A head
2

Ap (m )
0.001485
Xi
(m)

0.000
1.000
2.350
3.350
4.350
5.350
6.350
7.350
8.350
9.350
10.350
11.350
12.350
13.350
14.350
15.350
16.350
17.350
18.350
19.350
20.350

Yi
(m)
0.000
0.000
0.000
0.000
0.025
0.050

0.075
0.100
0.125
0.150
0.150
0.150
0.150
0.150
0.150
0.150
0.150
0.150
0.150
0.150
0.150

Total length of cable
Designed Elongation

x Two head

Ep (kPa)

Ptk (kN)

197000

1928

Zi

(m)
0.200
0.192
0.181
0.174
0.168
0.162
0.156
0.151
0.147
0.143
0.139
0.137
0.134
0.132
0.131
0.130
0.130
0.130
0.131
0.132
0.134

∆x
(m)
0.000
1.000
1.350
1.000
1.000

1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000

µ
0.25

K(1/m)
0.00066
∆β
(rad.)

∆Y
(m)

∆z
(m)

∆Li
(m)

0.000
0.000
0.000
0.025
0.025
0.025
0.025
0.025
0.025
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

0.008
0.011
0.007
0.006
0.006

0.006
0.005
0.004
0.004
0.004
0.002
0.003
0.002
0.001
0.001
0.000
0.000
0.001
0.001
0.002

1.000
1.350
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000

1.000
1.000
1.000
1.000
1.000
1.000

0.000
0.000
0.000
0.025
0.000
0.000
0.000
0.000
0.000
-0.025
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

Elongation cable of OVM jack
Total elongation

Elongation percentage
∆α
(rad.)
0.000
0.000
-0.001
-0.001
0.000
0.000
-0.001
-0.001
0.000
0.000
-0.002
0.001
-0.001
-0.001
0.000
-0.001
0.000
0.001
0.000
0.001

∆(α+β)
(rad.)
0.000
0.000
0.001
0.025

0.000
0.000
0.001
0.001
0.000
0.025
0.002
0.001
0.001
0.001
0.000
0.001
0.000
0.001
0.000
0.001

Σ∆(α+β)
(rad.)

0.000
0.001
0.026
0.026
0.026
0.027
0.028
0.028
0.053
0.055

0.056
0.057
0.058
0.058
0.059
0.059
0.060
0.060
0.061

Σµ*α

0.000
0.000
0.007
0.007
0.007
0.007
0.007
0.007
0.013
0.014
0.014
0.014
0.015
0.015
0.015
0.015
0.015
0.015

0.015

ΣK*x
0.001
0.002
0.002
0.003
0.004
0.004
0.005
0.006
0.006
0.007
0.007
0.008
0.009
0.009
0.010
0.011
0.011
0.012
0.013
0.013

Σ(µ*α+
K*x)
0.001
0.002
0.003
0.009

0.010
0.011
0.012
0.013
0.013
0.020
0.021
0.022
0.023
0.024
0.025
0.026
0.026
0.027
0.028
0.029

L = 32.704 (m)
∆1 = 210 (mm)
∆2 =
9.0 (mm)
∆L = 219.1 (mm)
∆L/L= 0.670 (%)
Px
(KN)
1927.60
1926.33
1924.54
1922.72
1909.47

1908.21
1906.95
1905.22
1903.48
1902.23
1889.13
1886.94
1885.22
1883.51
1881.80
1880.55
1878.84
1877.60
1875.90
1874.66
1872.95

Pav
(KN)
1926.96
1925.43
1923.63
1916.10
1908.84
1907.58
1906.08
1904.35
1902.86
1895.68
1888.04

1886.08
1884.37
1882.65
1881.18
1879.70
1878.22
1876.75
1875.28
1873.81

∆
(mm)
6.587
8.886
6.576
6.552
6.527
6.523
6.518
6.512
6.507
6.480
6.454
6.447
6.441
6.435
6.430
6.425
6.420
6.415

6.410
6.405


22
23
24
25
26
27
28
29
30
31
32
33

21.350
22.350
23.350
24.350
25.350
26.350
27.350
28.350
29.350
30.350
31.700
32.700

0.150
0.150
0.150
0.125
0.100
0.075
0.050
0.025
0.000
0.000
0.000
0.000

0.137
0.139
0.143
0.147
0.151
0.156
0.162
0.168
0.174
0.181
0.192
0.200

1.000
1.000
1.000
1.000

1.000
1.000
1.000
1.000
1.000
1.000
1.350
1.000

0.000
0.000
0.000
0.025
0.025
0.025
0.025
0.025
0.000
0.000
0.000
0.000

0.003
0.002
0.004
0.004
0.004
0.005
0.006
0.006

0.006
0.007
0.011
0.008

1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.350
1.000

0.000 0.001
0.000 -0.001
0.000 0.002
0.025 0.000
0.000 0.000
0.000 0.001
0.000 0.001
0.000 0.000
-0.025 0.000
0.000 0.001
0.000 0.001
0.000 0.000

0.001
0.001
0.002
0.025
0.000
0.001
0.001
0.000
0.025
0.001
0.001
0.000

0.062
0.063
0.065
0.090
0.090
0.091
0.092
0.092
0.117
0.118
0.119
0.120

0.016
0.016
0.016

0.023
0.023
0.023
0.023
0.023
0.029
0.030
0.030
0.030

0.014
0.015
0.015
0.016
0.017
0.017
0.018
0.019
0.019
0.020
0.021
0.022

0.030
0.031
0.032
0.039
0.039
0.040
0.041

0.042
0.049
0.050
0.051
0.051

1871.25
1869.55
1867.38
1854.52
1853.30
1851.61
1849.93
1848.71
1835.98
1834.31
1832.15
1830.87

1872.10
1870.40
1868.46
1860.95
1853.91
1852.46
1850.77
1849.32
1842.34
1835.15
1833.23

1831.51

6.399
6.394
6.387
6.363
6.339
6.334
6.329
6.324
6.298
6.273
8.460
6.261


L=
P=
E=
A=
Dta =

32.704 m
1927.60 kN
197000
1.97E+08
0.001485
0.215488

Mpa

KN/m
m2
(m)

215.4879 mm
Chieu dai dau kich va nem nem
Độ giãn dài 1 đầu là

680.00 mm
0.00 m
4.48 mm


Phụ lục / Appendix
Bảng theo dõi các bớc căng cáp và đo độ dãn dài của từng bó cáp
Table of PRESTRESSING CABLE step and measure the elongation of each tendon
dầm I BTCT DƯL 33.0M - Dầm số - Dầm giữa hay biên
PCI girder 33.0M - Girder No.
Thứ tự
Tên bó
căng /
/
Sequence
Cable
tension

Đầu đo /
Measure at
girder end
forward to

Bớc căng lực /
Prestressing cable step
(mm)
0,0xP 0,1xP

Bó 1

1

2

3

4

5

1,0xP

0,2xP

0,4xP

0,6xP

0,8xP

1,0xP

0,2xP

0,4xP

0,6xP

0,8xP

1,0xP

0,6xP

0,8xP

1,0xP

Quang Ngai
Da Nang
Quang Ngai
- Trong đó:

0,4xP

0,6xP

0,8xP

1,0xP

205.78

227.44

217.46

206.59

228.34

218.36

207.44

229.28

217.69

206.80

228.57

219.07

208.12

230.03

0,1xP

Da Nang

0,2xP

216.61

L1

0,1xP

Quang Ngai
0,4xP

Max
(1.05Ltk)

0,1xP

Da Nang
0,2xP

Min
(0.95Ltk)

Độ dãn dài thực tế / Actual
elongation
Ltt=L1+L2 (mm)

0,1xP

Quang Ngai

0,0xP 0,1xP
Bó 5

0,8xP

Da Nang

0,0xP 0,1xP
Bó 4

0,6xP

Quang Ngai

0,0xP 0,1xP
Bó 3

0,4xP

Da Nang
0,0xP 0,1xP

Bó 2

0,2xP

Độ dãn dài cho phép /
allow elongation
Lcp (mm)

Độ dãn dài
thiết kế /
Design
elongation
Ltk (mm)

0,1xP

+ L1: Trị số dãn dài thực đo từ lực kéo ban đầu đến lực căng kéo lớn nhất
Elongation values observed from initial traction to greatest tension
+ L2: Trị số dãn dài tính đổi của lực kéo ban đầu để so dây L2 = 0.1 * L1 tại cấp lực 1,0xP
Change elongation values of initial traction for equalizing strings L2 = 0.1 * L1 at force level 1,0xP

L2

Ltt


- §é vång cña dÇm ngay sau khi c¨ng kÐo theo thiÕt kÕ:

41.4 (mm)

Design deflection of girder just after anchor set is:
- §é vång cña dÇm ngay sau khi c¨ng kÐo theo thùc tÕ:

(mm)

Actual deflection of girder just after anchor set is:
§¹i diÖn TVGS / Consultant

§¹i diÖn nhµ thÇu chÝnh / Main contractor

§¹i diÖn nhµ thÇu phô / sub contractor