STUDY ON THE OPTIMUM HOISTING PROJECT
OF “DOUBLE-CRANE AND DOUBLE-ROPE SYSTEM” FOR LARGE-SCALE
SLENDER R.C. COLUMNS
Fu, Bing
Chen, Longzhu
Chen, Xiangdu
School of Structure Engineering, Zhejiang University, P.R. China
School of Civil Engineering & Mechanics, Shanghai Jiaotong University,
Department of Civil Engineering, North-east China Institute of Electric Power
Introduction
In the construction of a Large or middle-scale plant or factory, slender R.C. columns are cut into pieces
beforehand to prevent them being broken in the hoisting ,but it makes the process more complicated and
destroys the integrity of the structure.
That problem can be resolved by applying double cranes, two rope systems and proper hoisting points. In
Fig. 1, R n 1 and R n2 denote two binding forces offered by two cranes. The left rope system can be
represented by “ (n  1)  1  s ”, and “ (n  2)  ( s  1)  n ” represents the right one. The left and right rope
systems have s and n  s fixed points respectively , n denotes the total number of hoisting points. m ri ( r =
n+1, n+2 ; i = 1, 2, …, n ) means the multiple of distance between each fixed and movable pulley that a
rope passed by.
Presently, articles about this problem are few. Some authors’ opinions are only applied to brief
columns[2].Some authors didn’t consider minus moments and the influence of the form of rope
systems[3].
In this paper, the optimal hoisting points of rope systems are computed by optimization methods. All
kinds of the rope systems drafted having one array of optimum hoisting points of their own, by comparing
the inner forces a column hoisted with them receives in the process , the best rope systems can be
determined to reduce the values of the inner forces further.
Figure 1 Double-crane and Double-rope system
Determination of Optimum Hoisting Points
The column receives maximal or minimal bending moment when there is some angle between its body
and ground. Because the angle is changing, the restraint reacting forces that the ropes offer generate
favorable or unfavorable change to the column. So every angle in the erecting should be consider.
The optimum hoisting points can be determined by optimization. In this method, the maximal bending
moment in each span and minus bending moment at each hoisting point are called controlling moments.
The target function is the maximal absolute value of the controlling moments from 0 0 to 90 0 . The object
49
of optimization is finding the minimum of the target function. Hoisting points’ positions are elements of
vectors to be optimized. The model of optimization can be
searching
[ l i ]T ( i =1, 2, …, n )
max M k ( , li )
min
s. t.
0  li  li 1  l
In the model, l i , n and l denote the position of a hoisting point, its total number, and the length of the
column respectively. M denotes one controlling moment. k denotes its no..  denotes the angle.
By “ Grid optimization ”, the value of the target function is searched out. That is the maximum among the
maximal absolute values of the controlling moments at all angles from 0 0 to 90 0 by each array of hoisting
points. The minimum of the function is found by “Simplex optimization”, and the elements of the
corresponding vector are the optimum hoisting points’ positions.
Analysis of Inner Forces for the Column Hoisted
For a uniform column to be hoisted, let l, q, G denote its length , uniform load , and gross weight. The
calculation diagram is shown in Fig. 2 . In the diagram, n+1 and n+2 denote the two movable points,
their loci are like ovum. The tangents of them lie in level when the directions of the two binding forces,
R n 1 , R n2 are upright. These lead to
F ( xr , yr )  mrs ( xr  l s cos ) 2  ( yr  l s sin  ) 2  Lr  0
and
(1)
f ( xr , y r )  mrs cos  rs  0
(2)
where
 xr  ls cos 

 yr  ls sin  
 rs  c tan 1 
(3)
In the equations, r, s denote the no. of a movable and fixed point resp.. mrs denotes a multiple. Lr denotes a
rope’s length. When r = n+1, s = 1, 2,…, s ; when r = n+2, s = s  1 , s  2 , …, n. The meanings of s and n
are the same as the ones in Fig.1. .If s appears two times in a product, it implies sum of the products
owning tabs that s denotes. The following equations obey those rules.




Figure 2 Calculation diagram
50
The binding forces are
Rr 
G ( xr  0.5l cos  )
xr  xt
(4)
where
t = n  1, n  2 , t  r .
The constraint reacting forces at static points are
Rs 
sin(  rs   ) R r
mrs sin  rs
(5)
Let e denotes the no. of spans, the positions where shearing force is zero in each span are
i
l0e 
R
j 1
j
q  cos 
(6)
where
i =1, 2, …, n ; e = i+1, e  n  1.
Let k denotes one controlling moment’s no. ,
when k  e ,
i
M k ( , li )   R j (l0e  l j )  0.5q  cos   (l0e ) 2
j 1
when k  i ,
i
M k ( , li )   R j (li  l j )  0.5q  cos   (li ) 2 (7)
j 1
After analysis of inner forces, the results can be programmed and applied to the optimization of hoisting
points. The flow chart of calculation is shown in appendix.
Study on the Optimum Hoisting Project of “ Four -Hoisting- Point ”
To be convenient and save material, four hoisting points are needed. As application examples of the above mentioned
method, the project of Four-hoisting point is computed. The parameters for the column are l = 32 m, q = 9 k N / m; for
the rope systems, n = 4, r = 5, 6 , s =2, because the multiples’ change of the right rope has little influence to the
project, m63  m64  1 , m51  m52 , but the difference between them can’t be large, L5  30m . The optimum rope
systems are determined by comparison among the computation results of several rope systems drafted. They are
shown in Tables 1-5.
The absolute value of every controlling moment reaches its maximum at some degree, and tend to be zero
when the angle approaches to 90 0 . This is shown in the tables.
51
l1 = 3. 295
l2 = 12. 315
l3 = 19. 338
l4 = 28. 789
sections in spans and at hoisting points

1
1—2
2
2—3
3
3—4
4
0
-48. 853
48. 040 -38. 274
18. 615 -35. 501
59. 598 -46. 407
10 -48. 111
39. 542 -53. 112
20. 122 -18. 659
67. 233 -45. 702
20 -45. 907
29. 932 -66. 882
20. 784 -5. 017
71. 091 -43. 608
30 -42. 308
20. 527 -77. 074
20. 436 4. 515
70. 615 -40. 190
40 -37. 424
12. 419 -81. 416
19. 020 9. 911
65. 829 -35. 550
50 -31. 403
6. 283
-78.386
16. 585 11. 746
57. 217 -29. 830
60 -24. 427
2. 321
-67. 535
13. 261 10. 870
45. 517 -23. 204
Table 1 The controlling moments by optimum hoisting points from 0 0→600 when m51= m52=1, l5
=30m
l1 = 3. 980
l2 = 12. 241
l 3 = 18. 681
l 4 = 28. 132
sections in spans and at hoisting points
1
1—2
2
2—3
3
3—4
4
0
-71. 289
70. 206 38. 522
54. 633 -38. 420
48. 148 -67. 320
10 -70. 206
68. 111 36. 419
60. 519 -14. 251
60. 408 -66. 297
20 -66. 990
61. 873 30. 113
62. 509 5. 503
68. 691 -63. 260
30 -61. 738
52. 361 20. 707
60. 268 19. 019
71. 686 -50. 301
40 -54. 611
41. 071 10. 202
54. 201 25. 869
69. 004 -51. 570
50 -45. 824
29. 695 0. 971
45. 268 26. 810
61. 120 -43. 272
60 -34. 645
19. 604 -4. 983
34. 609 23. 272
49. 087 -33. 660
Table 2 The controlling moments by optimum hoisting points from 0 0→600 when m51=2, m52=1, l5
=45m


0
10
20
30
40
50
60
1
-81. 744
-80. 503
-76. 815
-70. 793
-62. 620
-52. 544
-40. 872
l1 =44. 262
l2 = 12. 063
l3 = 18. 666
l4 = 27. 589
sections in spans and at hoisting points
1—2
2
2—3
3
3—4
4
78. 175 62. 941
71. 042 -53. 483
19. 856 -87. 573
79. 485 65. 240
78. 133 -28. 120
33. 425 -86. 243
76. 136 62. 631
80. 714 -6. 225
44. 210 -82. 292
68. 366 55. 377
78. 179 9. 980
50. 578 -75. 841
57. 226 44. 716
20. 758 19. 556
51. 698 -67. 085
44. 334 32. 601
59. 432 22. 844
47. 651 -56. 291
31. 382 21. 131
45. 592 21. 106
39. 261 -43. 787
Table 3 The controlling moments by optimum hoisting points from 0 0→600 when m51=3, m52=1, l5
=60m

0
10
20
30
40
50
60
1
-65. 034
-64. 046
-61. 112
-56. 321
-49. 819
-41. 803
-32. 517
l1 = 3. 802
l2 = 12. 513
l3 = 18. 961
l4 = 28. 337
sections in spans and at hoisting points
1—2
2
2—3
3
3—4
59. 552 5. 991
34. 400 -43. 186
47. 303
53. 998 -1. 872
34. 235 -22. 978
57. 031
45. 451 -12. 179
34. 604 -6. 592
62. 959
35. 224 -22. 992
32. 536 4. 698
64. 220
24. 889 -31. 832
28. 506 10. 842
60. 742
15. 836 -36. 355
23. 225 12. 684
53. 113
8. 923
-35. 037
17. 379 11. 468
42. 280
4
-60. 389
-59. 471
-56. 747
-52. 298
-46. 260
-38. 817
-30. 194
Table 4 The controlling moments by optimum hoisting points from 0 0→600 when m51=3, m52=2, L5
=75m
52
m51 m52
L6
1 1
m63 m64
30
L5
1
1
30
2
3
3
1
1
2
45
60
75
Table 5
Figure
5
l1
l2
l3
l4
inatial positions
3. 380 12. 618 19. 380 28. 620
positions after optimization
3. 295 12. 315 19. 338 28. 789
3. 980 12. 241 18. 681 28. 132
4. 262 12. 063 18. 666 27. 589
3. 802 12. 513 18. 961 28. 337
maxim
um
percentage
of decrease
95. 481
_____
81. 462
15 %
71. 687
87. 573
65. 034
25 %
8%
32 %
Comparison of the projects drafted
shows
that
the
parameters
of
the
optimum
project
for
this
column
are
T
T
m51  3 , m52  2 , m63  m64 =1, L5  75m , L6  30m , [ li ] = [ 3. 802 12. 513 18. 916 28. 377 ] , i = 1~ 4.
There is linear relation between inner forces and uniform load, so the optimum hoisting points’ positions
are determined by the length of the column and ropes. For columns of different length, determination of
hoisting points and rope systems drafted by optimization is necessary.
Conclusions
1.
2.
3.
Double-crane and Double-rope system are practice means for hoisting slender R.C. columns.
Selection of hoisting points’ positions and rope systems drafted is important after determination of
the total number of hoisting points, which can lessen inner forces and convenience hoisting.
“Grid optimization” and “Simplex optimization” are effective methods for determination of hoisting
points. They are easy but feasible.
Reference
[1] Xiangdu Chen, Mechanics of Binding Systems of Ropes and Pulleys, Huazhong University of
Technology Press, 1995.
[2] Xiangdu Chen, Chengjie Xu, and Yansong Zhao. ,the Mechanics Problem Existed Long of Hoisting
Slender R.C. Columns, Journal of Harbin university of Architecture 29(1996) 2.
[3] Binghua Zhang, Chang Hou, Design of Architectural Structure by Optimization, Tongji University
Press, 1995.
53
Appendix
begin
read q, l, Ln+1, Ln+2,
read mrs, li (i=1,...n
(0)
X = [l1, l2, ....ln]
T
(j)
X = [...li-1+q, li+p, li+1+q...]
T
M[j]=0
compute (xr, yr)
compute Mk(,li)
if |Mk(,li)|>M[j] |Mk(,li)| implies M[j]
proceed Simple
Optimization to
search new X
(j)
|max M - min M| < 
write min M, li
end
54