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Nonlinear buckling analysis of network arch bridges

Adrian Błonka

Adrian Błonka

Wroclaw University of Science and Technology, Doctoral School, Faculty of Civil Engineering, Discipline of Civil Engineering and Transport, Department of Structural Mechanics and Urban EngineeringWroclaw, Poland
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Błonka, Adrian
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Łukasz Skrętkowicz

Łukasz Skrętkowicz

Wroclaw University of Science and Technology, Faculty of Civil Engineering, Department of Building StructuresWroclaw, Poland
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Skrętkowicz, Łukasz
  
26 apr 2022
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Categoria dell'articolo: Original Study
Pubblicato online: 26 apr 2022
Pagine: 123 - 137
Ricevuto: 02 ott 2021
Accettato: 11 gen 2022
DOI: https://doi.org/10.2478/sgem-2022-0007
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© 2022 Adrian Błonka et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1

Comparison of sample equilibrium paths for different types of analyses (B – bifurcation point, L – limit point).
Comparison of sample equilibrium paths for different types of analyses (B – bifurcation point, L – limit point).

Figure 2

Comparison of sample equilibrium paths with the snap-through instability (B – bifurcation point, L – limit point).
Comparison of sample equilibrium paths with the snap-through instability (B – bifurcation point, L – limit point).

Figure 3

The model of von Mises truss.
The model of von Mises truss.

Figure 4

Equilibrium paths for von Mises truss from different types of analysis. The vertical axe represents applied force and the horizontal axe represents the displacement of the point where the load is applied. FEA TH3 with displacement results (continuous) match exactly the analytical results with force load (dotted).
Equilibrium paths for von Mises truss from different types of analysis. The vertical axe represents applied force and the horizontal axe represents the displacement of the point where the load is applied. FEA TH3 with displacement results (continuous) match exactly the analytical results with force load (dotted).

Figure 5

Instability forms: (a) structure without deformation, (b) form after snap-through, (c) first buckling form.
Instability forms: (a) structure without deformation, (b) form after snap-through, (c) first buckling form.

Figure 6

Sample geometry of columns with the lowest (a) and highest (b) elevation with initial loads.
Sample geometry of columns with the lowest (a) and highest (b) elevation with initial loads.

Figure 7

Midpoint equilibrium paths for TH2 (a) and TH3 (b) analyses and corresponding displacements (c) of 40-m-long column with a 1/300 elevation (equivalent imperfection e0 = 0.133 m).
Midpoint equilibrium paths for TH2 (a) and TH3 (b) analyses and corresponding displacements (c) of 40-m-long column with a 1/300 elevation (equivalent imperfection e0 = 0.133 m).

Figure 8

The geometry of the beam with initial uniform loads.
The geometry of the beam with initial uniform loads.

Figure 9

Scaled deformation forms from buckling and TH3 analysis.
Scaled deformation forms from buckling and TH3 analysis.

Figure 10

Photos of network arch bridge over Vistula River in Cracow (own source).
Photos of network arch bridge over Vistula River in Cracow (own source).

Figure 11

Side view of the numerical model.
Side view of the numerical model.

Figure 12

Detail view of the skewback.
Detail view of the skewback.

Figure 13

Load Model 71 and characteristic value for vertical load from Eurocode [19].
Load Model 71 and characteristic value for vertical load from Eurocode [19].

Figure 14

The LM 71 positions along the span.
The LM 71 positions along the span.

Figure 15

Resultant ranges of the critical load factors for the LBA and ULTI analysis.
Resultant ranges of the critical load factors for the LBA and ULTI analysis.

Figure 16

Resultant ranges of critical load factor ratios. NT – no tension, LT – low tension (1 kN), MT – middle tension (500 kN), HT – high tension (1000 kN), NP – no prestress, AP – all prestress cases (10, 15, 20 MN).
Resultant ranges of critical load factor ratios. NT – no tension, LT – low tension (1 kN), MT – middle tension (500 kN), HT – high tension (1000 kN), NP – no prestress, AP – all prestress cases (10, 15, 20 MN).

Figure 17

Deformations form: LBA (a), last ULTI step (b), and PUSH after 50 steps (c).
Deformations form: LBA (a), last ULTI step (b), and PUSH after 50 steps (c).

Figure 18

Scaled deformation forms of the arch between skewbacks from LBA and TH3 analysis.
Scaled deformation forms of the arch between skewbacks from LBA and TH3 analysis.

Figure 19

Ranges of ULTI-to-LBA critical load factor ratios for various elevations and predicted trends.
Ranges of ULTI-to-LBA critical load factor ratios for various elevations and predicted trends.

Figure 20

The numeration scheme of hangers’ arrangement.
The numeration scheme of hangers’ arrangement.

Figure 21

The range of ULTI-to-LBA critical load factor ratios for breaking one hanger at once.
The range of ULTI-to-LBA critical load factor ratios for breaking one hanger at once.

Figure 22

Examples of rupturing two nearest hangers.
Examples of rupturing two nearest hangers.

Figure 23

The range of ULTI-to-LBA critical load factor ratios for breaking two nearest hangers at once. The first number in brackets on the horizontal axis corresponds to the right-skewed hanger and the second number to the left-skewed hanger.
The range of ULTI-to-LBA critical load factor ratios for breaking two nearest hangers at once. The first number in brackets on the horizontal axis corresponds to the right-skewed hanger and the second number to the left-skewed hanger.

Figure 24

Scaled, exampled deformations of instability forms of the arch between skewbacks from LBA and TH3 analysis: rupturing the leftmost hanger (a), rupturing the hanger in one-fourth of the span (b), and rupturing the hanger in the midspan (c).
Scaled, exampled deformations of instability forms of the arch between skewbacks from LBA and TH3 analysis: rupturing the leftmost hanger (a), rupturing the hanger in one-fourth of the span (b), and rupturing the hanger in the midspan (c).
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