Theoretical derivation was conducted for the stability of axial compression bars with inter-bar torsional constraints. A theoretical model was established by simplifying engineering examples, the stability bearing capacity of compression bars with fixed ends was solved, and the relationship formula between buckling load and torsional spring stiffness of inter-bar was put forward. According to the theoretical model, the torsional spring was replaced by a beam, and then the buckling test was carried out using the beam as the support of the compression bar. The torsional stiffness of the beam was altered through changing its cross section. Six groups of compression bars having different torsional stiffness were tested to verify the correctness of the theoretical solution. A finite element model was also established, and its reliability was verified by the test results. Based on the verified finite element model, the analysis of twelve cases was carried out, and compared with the theoretical curve. The correctness of the theoretical solution was demonstrated by experiments and finite element analysis, and a promising calculation formula was put forward for engineering design.
Fig.1Local force model of simplified steel tower structure
Fig.2Theoretical model of compression bar
Fig.3Partial member below torsional spring constraint
Fig.4Partial member containing torsional spring constraint
Fig.5Relation curve between stable bearing capacity of compression bar and torsional spring stiffness
Fig.6Compression bars used in experiment
Fig.7Cross beam support between bars
Fig.8Two-end fixed compression bar with cross beam support between bar
Fig.9Theoretical model corresponding to test model of two-end fixed compression bar with cross beam support between bar
Fig.10Tensile experiment of compression bar
试验编号
E/GPa
$ \nu $
G/GPa
1
202
0.306
77
2
204
0.298
79
3
206
0.301
79
平均值
204
0.302
78
Tab.1Tensile experimental result of compression bar
Fig.11Instability pattern of model MX-1
Fig.12Torsion of beam of MX-1
Fig.13Load-displacement curve of MX-1
模型编号
横梁截面尺寸/mm
GJ/（N·m）
Pe/kN
n=1
n=2
n=3
平均值
MX-1
Φ10×1
274
18.47
18.52
18.59
18.53
MX-2
Φ22×1
3 446
23.56
23.25
22.82
23.21
MX-3
Φ22×2
6 000
24.99
25.76
25.78
25.51
MX-4
Φ26×2
10 336
26.97
27.63
28.27
27.62
MX-5
Φ26×4
16 336
29.07
29.35
29.35
29.26
MX-6
Φ26×8
20 744
30.51
29.99
31.10
30.53
Tab.2Stability bearing capacities of compression bar specimens with different experimental models
模型编号
$ \gamma $
$ \eta $
Pe/kN
Pt/kN
e/%
MX-1
0.07
2.90
18.53
20.61
+11.2
MX-2
0.88
3.22
23.21
25.42
+9.5
MX-3
1.53
3.37
25.51
27.84
+9.1
MX-4
2.64
3.54
27.62
30.72
+11.2
MX-5
4.17
3.67
29.26
33.01
+12.8
MX-6
5.29
3.73
30.53
34.10
+11.7
Tab.3Comparison between experimental values and theoretical values of stability bearing capacities with different experimental models
Fig.14Ultimate load capacities of six experimental models
Fig.15Compression bars with cross beam support between bars
试验编号
Pe/kN
Pt/kN
Pf /kN
ef /%
et /%
MX-1
18.53
20.61
20.82
+12.4
+11.2
MX-2
23.21
25.42
25.95
+11.8
+9.5
MX-3
25.51
27.84
28.62
+12.2
+9.1
MX-4
27.62
30.72
31.50
+14.0
+11.2
MX-5
29.26
33.01
33.74
+15.3
+12.8
MX-6
30.53
34.10
34.75
+13.8
+11.7
Tab.4Comparison between experimental values, theoretical values and finite element values of compression bar capacities with different experimental models
c/（N·m）
$\gamma $
Pt/kN
Pf/kN
e/%
0.000 1
0
20.29
20.25
?0.2
1 984
0.5
23.66
23.59
?0.3
3 968
1
26.19
26.12
?0.3
7 936
2
29.66
29.56
?0.3
11 904
3
31.82
31.71
?0.3
15 872
4
33.26
33.14
?0.4
23 808
6
35.02
34.89
?0.4
35 712
9
36.41
36.27
?0.4
51 584
13
37.35
37.20
?0.4
79 360
20
38.12
37.97
?0.4
3 968 000
1 000
39.66
39.48
?0.5
3 968 000 000
1 000 000
39.68
39.51
?0.4
Tab.5Comparison between theoretical solutions and finite element solutions of compression bar capacities under different stiffness of spring
Fig.16Comparison between theoretical curve and finite element curve of compression bar capacities
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