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Influence of Permanent Deflections on The Vibrations of Bridge Spans in Operating Conditions

Mieszko Kużawa

Mieszko Kużawa

Department of Civil Engineering, Wroclaw University of Science and TechnologyPoland
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Kużawa, Mieszko
, 
Aleksander Mróz

Aleksander Mróz

Department of Civil Engineering, Wroclaw University of Science and TechnologyPoland
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Mróz, Aleksander
 et 
Jan Bień

Jan Bień

Department of Civil Engineering, Wroclaw University of Science and TechnologyPoland
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Bień, Jan
  
02 mars 2022
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Catégorie d'article: Original Study
Publié en ligne: 02 mars 2022
Pages: 97 - 113
Reçu: 03 juil. 2021
Accepté: 15 déc. 2021
DOI: https://doi.org/10.2478/sgem-2022-0004
Mots clés
© 2022 Mieszko Kużawa et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1

View of selected spans of the bridge structure.
View of selected spans of the bridge structure.

Figure 2

View of the support zone of the span structure.
View of the support zone of the span structure.

Figure 3

Basic dimensions of a single structure of a bridge span – cross section.
Basic dimensions of a single structure of a bridge span – cross section.

Figure 4

Permanent deflections of the girders of the main spans.
Permanent deflections of the girders of the main spans.

Figure 5

Scheme of the spans’ geometry model – the three-span system was analysed; for the purpose of analyses, the spans were marked as 1, 2 and 3
Scheme of the spans’ geometry model – the three-span system was analysed; for the purpose of analyses, the spans were marked as 1, 2 and 3

Figure 6

Numerical model of the structure developed in the SOFiSTiK program – side view with spans marked
Numerical model of the structure developed in the SOFiSTiK program – side view with spans marked

Figure 7

Axonometric views of the numerical model of the structure developed in the SOFiSTiK program.
Axonometric views of the numerical model of the structure developed in the SOFiSTiK program.

Figure 8

Cross sections of the bar elements of the model of the superstructure: (a) cross section – type 1 (near the support), (b) cross section – type 2 (in the middle of the span)
Cross sections of the bar elements of the model of the superstructure: (a) cross section – type 1 (near the support), (b) cross section – type 2 (in the middle of the span)

Figure 9

Typical five-axle vehicle weighing 40 t: (a) wheelbase and loads of the vehicle’s axle, (b) general view of the vehicle passing through the considered facility
Typical five-axle vehicle weighing 40 t: (a) wheelbase and loads of the vehicle’s axle, (b) general view of the vehicle passing through the considered facility

Figure 10

The scheme of the suspension modelled as viscoelastic oscillators connected by a bar of considerable stiffness – modelling structure of vehicle.
The scheme of the suspension modelled as viscoelastic oscillators connected by a bar of considerable stiffness – modelling structure of vehicle.

Figure 11

The average acceleration value method (left); the linear acceleration change method (right).
The average acceleration value method (left); the linear acceleration change method (right).

Figure 12

Changes in the displacements of the cross section located in the middle of span 3, which were caused by the passage of a vehicle (vehicle speed 23 m/s = 82.8 km/h; permanent deflections: 0–150 mm): (a) Model A (elastic suspension), (b) Model B (rigid suspension).
Changes in the displacements of the cross section located in the middle of span 3, which were caused by the passage of a vehicle (vehicle speed 23 m/s = 82.8 km/h; permanent deflections: 0–150 mm): (a) Model A (elastic suspension), (b) Model B (rigid suspension).

Figure 13

Changes in the displacements of the cross section located in the middle of span 3, which were caused by the passage of a vehicle (vehicle speed 26.8 m/s = 96.5 km/h; permanent deflections: 0–150 mm): (a) Model A (elastic suspension), (b) Model B (rigid suspension).
Changes in the displacements of the cross section located in the middle of span 3, which were caused by the passage of a vehicle (vehicle speed 26.8 m/s = 96.5 km/h; permanent deflections: 0–150 mm): (a) Model A (elastic suspension), (b) Model B (rigid suspension).

Figure 14

Changes in the displacements of the cross section located in the middle of span 3, which were caused by the passage of a vehicle (vehicle speed 30 m/s = 108 km/h; permanent deflections: 0–150 mm): (a) Model A (elastic suspension), (b) Model B (rigid suspension).
Changes in the displacements of the cross section located in the middle of span 3, which were caused by the passage of a vehicle (vehicle speed 30 m/s = 108 km/h; permanent deflections: 0–150 mm): (a) Model A (elastic suspension), (b) Model B (rigid suspension).

Figure 15

Changes in the vibration accelerations of the cross section located in the middle of span 3, which were caused by the passage of a vehicle (vehicle speed 23 m/s = 82.8 km/h; permanent deflections: 0–150 mm): (a) Model A (elastic suspension), (b) Model B (rigid suspension)
Changes in the vibration accelerations of the cross section located in the middle of span 3, which were caused by the passage of a vehicle (vehicle speed 23 m/s = 82.8 km/h; permanent deflections: 0–150 mm): (a) Model A (elastic suspension), (b) Model B (rigid suspension)

Figure 16

Changes in the vibration accelerations of the cross section located in the middle of span 3, which were caused by the passage of a vehicle (vehicle speed 26.8 m/s = 96.5 km/h; permanent deflections: 0–150 mm): (a) Model A (elastic suspension), (b) Model B (rigid suspension).
Changes in the vibration accelerations of the cross section located in the middle of span 3, which were caused by the passage of a vehicle (vehicle speed 26.8 m/s = 96.5 km/h; permanent deflections: 0–150 mm): (a) Model A (elastic suspension), (b) Model B (rigid suspension).

Figure 17

Changes in the vibration accelerations of the cross section located in the middle of span 3, which were caused by the passage of a vehicle (vehicle speed 30 m/s = 108 km/h; permanent deflections: 0–150 mm): (a) Model A (elastic suspension), (b) Model B (rigid suspension).
Changes in the vibration accelerations of the cross section located in the middle of span 3, which were caused by the passage of a vehicle (vehicle speed 30 m/s = 108 km/h; permanent deflections: 0–150 mm): (a) Model A (elastic suspension), (b) Model B (rigid suspension).

Figure 18

The maximum deflections of the cross section located in the middle of spans 1–3 as a function of the vehicle speed and the value of permanent deflections (0 and 100 mm, respectively): Model A (elastic suspension; left), Model B (rigid suspension; right).
The maximum deflections of the cross section located in the middle of spans 1–3 as a function of the vehicle speed and the value of permanent deflections (0 and 100 mm, respectively): Model A (elastic suspension; left), Model B (rigid suspension; right).

Figure 19

The maximum vibration accelerations of the cross section located in the middle of spans 1–3 as a function of the vehicle speed and the value of permanent deflections (0 and 100 mm, respectively): Model A (elastic suspension; left), Model B (rigid suspension; right).
The maximum vibration accelerations of the cross section located in the middle of spans 1–3 as a function of the vehicle speed and the value of permanent deflections (0 and 100 mm, respectively): Model A (elastic suspension; left), Model B (rigid suspension; right).

Figure 20

Changes in the DAF imposed by the passage of the vehicle (which were read in the cross sections located in the middle of spans 1–3) as a function of the value of the permanent deflections of the spans and the determined value of the vehicle speed equal to 23 m/s: (a) Model A (elastic suspension), (b) Model B (rigid suspension).
Changes in the DAF imposed by the passage of the vehicle (which were read in the cross sections located in the middle of spans 1–3) as a function of the value of the permanent deflections of the spans and the determined value of the vehicle speed equal to 23 m/s: (a) Model A (elastic suspension), (b) Model B (rigid suspension).

Selected results of linear modal analysis using FEM_

The first group of natural forms of vibrations
The second group of natural forms of vibrations
The third group of natural forms of vibrations

Parameters of the numerical models of the considered vehicles_

Vehicle model Model A Model B
Basic natural frequencies 2.3 Hz 7.5 Hz
Number of generalised nodal displacements 5 5
Concentrated masses in the place of the axles M1=1.265 t M1=1.265 t
M2=2.415 t M2=2.415 t
M3–5=1.840 t M3–5=1.840 t
Suspension rigidity k1=263.9 kN/m k1=2806.0 kN/m
k2=503.8 kN/m k2=5357.0 kN/m
k3–5=383.9 kN/m k3–5==4082.0 kN/m
Suspension damping c1=3.654 kN/(m·s) c1==11.920 kN/(m·s)
c2=6.976 kN/(m·s) c2=22.750 kN/(m·s)
c3–5=5.315 kN/(m·s) c3–5=17.330 kN/(m·s)

Summary of material parameters of the steel and reinforced concrete parts of the bar elements of the FEM model_

Material characteristics Steel girder Reinforced concrete slab
Self-weight (volumetric weights additionally take into account the weight of the span's bracings and the spans’ equipment) γ 82.6 (kNm3) \left({{{{\rm{kN}}} \over {{{\rm{m}}^3}}}} \right) 29.6 (Nmm2) \left({{{\rm{N}} \over {{\rm{m}}{{\rm{m}}^2}}}} \right)
Young's modulus E 210,000.0 (Nmm2) \left({{{\rm{N}} \over {{\rm{m}}{{\rm{m}}^2}}}} \right) 36000.0 (Nmm2) \left({{{\rm{N}} \over {{\rm{m}}{{\rm{m}}^2}}}} \right)
Shear modulus G 80,769.0 (Nmm2) \left({{{\rm{N}} \over {{\rm{m}}{{\rm{m}}^2}}}} \right) 15000.0 (Nmm2) \left({{{\rm{N}} \over {{\rm{m}}{{\rm{m}}^2}}}} \right)
Poisson ratio μ 0.3 ( - ) 0.2 ( - )
Langue:
Anglais
Périodicité:
4 fois par an
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