123456789_123456789_1123456789Case Study and Research
123456789_123456789_123456789_123456789_123456789_123456789_123456789_123456789_1234567
Page 1  2  3  4  5  6  7  8  9  10


123456789_123456789_1123456789 
Cable-stayed bridge during construction

Cable-stayed Bridge
Model Examples



Model description



Input



BIM model



Analysis model



Landscape model



ICDAS Basis of Design



Workflow of Software



Additional features



Rendering, Animation &
Vitural Reality
  


Case Study and 
Research




 


 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 Natural mode shapes and frequencies

Natural mode shapes and frequencies of bridge at deadload

Natural mode shapes and frequencies (nmf) of bridge are fundamental to the solution of its dynamic responses 

due to seismic, wind and traffic loads. The nmf is depended on the particularities and characteristics of the bridge

such as the bending and torsional stiffness of the stiffening girder, the pylon, the hanger's distance between the

two cables (in transverse and longitudinal direction) and the support conditions. By changing nmf, one will get a

significant change in results of the dynamic analysis.

 

However, the eigenvalues (frequencies) and the eigenvectors (mode shapes) of a bridge are obtained already after

Loadcase1 Initial Forces and Loadcase2 Deadload has been convergent successfully. I.e. the nmf are depended on

the initial tensions of the cables, the structural weight of the bridge's elements, but not on the vehicle weighs.

 

Thus, optimization of the nmf should be done before the analysis of the live loads on bridge because the eigenvalue

analysis can lead to the necessary changes of structural dimensions. The case a static analysis lead to the changes

of structural dimensions, a new eigenvalue analysis should be performed again. In LUSAS 15.0-* we can solve a

selected analysis so we can perform the analysis we need.

 

Vibrations of a cable-stayed bridge can be distinguished on the global and local modes. The global modes are where

the pylons, the girder and all cables are vibrated in the same frequency, typically identified by the motions of the

pylons and the deck. In these modes the non-vibration cables just follow the motions of the pylons and the deck.

The local modes are referred to vibrations of some single cables, with significant bigger amplitudes than the pylons

and the deck. However, there are also some modes where the dominant vibrations of the cables occur in the same frequency of visible vibrations of the deck and the pylons, as shown in mode 9 to 11 below.

 

It should be noted that mode shapes of the cables are most realistic when they are fine division in many elements (which need more time to reach convergence). The model below has the longest and the shortest cables of 160.2m

and 37.9m, respectively. They are all modeled in 2m element, i.e. there are 19 elements (of thick nonlinear beam)

in the shortest cable. Finally, solution for the mode shapes below allow the cables to be shorter and longer, as shown

in mode 9 below for the short cables at the pylon.

 

The following abbreviations are used with respect to the vibrations of the deck

 

Symmetric Lateral (SL)

Asymmetric Lateral (AL)


Symmetric Vertical (SV)

Asymmetric Vertical (AV)


Symmetric Torsional (ST)

Asymmetric Torsional (AT)
Updated 31-01-2015

 

123456789_123456789_1123456789 
  

Mode 1, f = 0.017 Hz

 

is the 1st asymmetric rotation mode of the deck about vertical axes at the pylon. Note that during

construction the bridge is assumed free support at the deck ends.


150+302+150 



Mode 2, f = 0.051 Hz

 

is the 1st longitudinal mode combining with a vertical motion of the deck. The one end of deck

is moving up in turns with the other moving down.


150+302+150


Mode 3, f = 0.119 Hz

 

is the 2nd longitudinal mode of the deck combined slightly with asymmetric vertical mode of

the deck, and clearly bending mode of the pylon about the axes perpendicular to the deck.

Note that a short blue line below the deck connected to the pylon. It is the "master-slave"

connection fixing the deck to the pylon leg in the lateral direction. It is also an easy coupling

in reality to prevent the deck oscillate lateral and hit the pylon legs. 


150+302+150

  

123456789_123456789_1123456789 
  

Mode 4, f = 0.149 Hz

is the 1st symmetric lateral mode (1st SL) where the pylon and the deck are oscillated to the

same side.


150+302+150 


Mode 5, f = 0.282 Hz

 

is the 1st bending mode of the pylon about the bridge axes. This mode can be prevented by a

cross beam located between the two pylon legs above the deck.


150+302+150


Mode 6, f = 0.378 Hz

 

is the 2nd symmetric lateral mode (2nd SL) where the pylon and the deck are oscillated to

the opposite side.


150+302+150

 

123456789_123456789_1123456789 
  

Mode 7, f = 0.412 Hz

is the 1st symmetric vertical mode of the deck (1st SV). The motions of the deck ends will decrease

and increase the cable sags of the longest cables. Note that during construction the bridge is assumed

free support at the deck ends.


150+302+150 


Mode 8, f = 0.896 Hz

 

is the 1st asymmetric vertical mode of the deck (1st AV). The motion is combining with a bending

mode of the pylon about axes perpendicular to the deck.


150+302+150


Mode 9, f = 1.052 Hz

 

is the 2nd symmetric vertical mode of the deck (2nd SV). Vibration of the longest cables become

violent. Amplitude of this mode can be reduced by fixing the deck vertical to the cross beam between

the two pylon legs.


150+302+150




Mode 10, f = 1.072 Hz

 

is the 1st symmetric rotation mode of the deck about vertical axes at the pylon. Note that in

this modes the longest cables are oscillated out of plan and in the opposite side of the deck

motion.


150+302+150



Mode 11, f = 1.211 Hz

 

is the 1st symmetric torsional mode of the deck (1st ST). This mode occurs by violent vibrations of

the two longest cables on one leg of the pylon, by turns with the other two cables on the other leg

of the pylon. Note that the cables are also vibrated out of the cable plan. This mode can be changed

by fixing the deck vertical to the cross beam between the two pylon legs.


150+302+150

When the wind start a small motion of the cables and then the bridge deck, the entire bridge can oscillate

with its lowest natural frequencies with corresponding mode shapes. The most dangerous mode (flutter) is

the one that couple two or many natural modes, especially the vertical and the torsional modes. Prediction

of such coupled mode shape needed the layouts of many natural mode shapes and frequencies of the bridge.

Normally the first 10 - 30 modes or more depended on the construction of the bridge. In terms of flutter in

frequency domain, the ratio fST / fSV (symmetric torsional-to-vertical bending frequency) is the critical

parameter of interest. This ratio is ideally above 2.5. In this case the torsional mode 11 and the vertical

mode 7 are of interest, where

 
fT11 / fV7 = 1.211/0.412 = 2.939

Note that not any two torsional-, vertical modes should be coupled in flutter analysis, [00,0]. The above frequency

ratio is the case of construction stage in a short period, where both ends of deck are free for supports. The case

the finish bridge is also a cantilever bridge (of a single pylon) the above ratio will be changed because the bridge

is supported at the deck ends.


 Page 1  2  3  4  5  6  7  8  9  10 

 

123456789_123456789_1123456789
ICDAS   •    Hans Erik Nielsens Vej 3   •    DK-3650 Ølstykke   •    E-mail: th@icdas.dk    •   Tel.: +45 20 20 33 78   •   CVR no.: 34436169 
  123456789_123456789_123456789_123456789_123456789_123456789_123456789_123456789_123456789_123456789_123456789_123456789_123456789_123456789_12345