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123456789_123456789_1123456789Concrete Bridge Software 

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Case study




Technical University of Denmark ♦ DTU Ballerup Campus

Exam project 2015/2016 ♦ Answer Book & Case Study


Motorway Bridge over Savstrup Stream in Jutland Denmark

Terrain  -  Geometry  - Analysis 1 2 3 





Analysis model (2 of 3)



Deformations & natural mode shapes 


First at all in a FEM analysis is to check deformation figure of the bridge at deadload.

Then animation of natural mode shapes for the first 7 modes (and more if needed).

Deformation figure and the natural mode shapes will confirm the correctness of the

static system. Especially animation of the natural mode shapes will reveal often the

forgot lateral fixation of the bridge deck through bearings.   


Deformations and the natural mode shapes performed in LUSAS Analysis 1 have
only deadload and prestressing. I.e. you will get the results within a few seconds for

a normal PC/Laptop.

Once the deformation and vibrations are as expecting, you can continue to run Analysis
2 with thousands of variable load cases and load combinations for further verifications.


In this context, LUSAS allow you to run a selected particular load case(s) at any Analysis

when you want to check the results for that case(s) only.


Note that in railway bridge the natural frequencies can lead to the need of changes in

dimensions and thicknesses of the deck. Thus, do not start the Analysis 2 to save

the time, if you later found out the changes already needed at Analysis 1.


Tablenatural mode shapes of Savstrup bridge.

Mode 1: 1st longitudinal, 0.579Hz

Mode 2: 1st asymmetric vertical, 1.998Hz

Mode 3: 1st symmetric vertical, 2.563Hz

Mode 4: 1st torsion, 3.002Hz

Mode 5: 2nd asymmetric vertical, 3.355Hz

Mode 6: 1st lateral (rotation about vertical axes), 3.465Hz

Mode 7: 2nd symmetric vertical, 3.713Hz


Below are descriptions of the natural mode shapes. Click on the image for animations in 3000 pixels. 


The 1st longitudinal mode the bridge oscillates in longitudinal direction.

The centre pier deforms with oscillation as the deck is fixed to top of pier here, but not the other piers.

Animation mode 1, 1st longitudinal, 0.579Hz

The 1st asymmetric vertical mode the first two spans are oscillated in opposite direction of
the last two spans. 
Rotation of the deck in the centre forces the centre pier to deform as it is
fixed to the deck, but not the other piers (bearings)

Animation mode 2, 1st asymmetric vertical, 1.998Hz

The 1st symmetric vertical mode the first two spans are oscillated in the same direction of the
last two spans.
This mode has a frequency 1.28 times the 1st asymmetric and is often used in
further dynamic analysis. 

Animation mode 3, 1st symmetric vertical, 2.563Hz

The 1st torsion mode the deck twists over the centre pier and force the centre pier in deformation.

Animation mode 4, 1st torsion, 3.002Hz

The 2nd asymmetric vertical mode the oscillation's amplitudes are dominant in the first and the last span.
Unlike the 1st asymmetric vertical mode where all the four spans are oscillated with the same amplitude.

Animation mode 5, 2nd asymmetric vertical, 3.355Hz

The 1st lateral mode the deck rotate about the vertical axes at the centre pier and force the centre
pier in deformation.

Animation mode 6, 1st lateral (rotation about vertical axes), 3.465Hz

The 2nd vertical symmetric vertical mode the all four spans are oscillated in the same direction.
Unlike the 1st vertical symmetric vertical mode the two centre span are oscillated in opposite direction
of the two end spans.

Animation mode 7, 2nd symmetric vertical, 3.713Hz

  Terrain  - Geometry  - Analysis 1 2 3   Savstrup Bridge

123456789_123456789_1123456789ICDAS  •  Hans Erik Nielsens Vej 3  •  DK-3650 Ølstykke  •   E-mail: th@icdas.dk   •  Tel.: +45 60 53 83 79  •  CVR no.: 34436169