CALDINTAV V.2.0 : USER’S GUIDE

Madrid, November 9, 2013

Technical University of MadridJose M. Goicolea, Teresa Ancochea, Pablo Antolın, J.Domınguez

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Contents

1 Introduction 31.1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Basic concepts for structural dynamics . . . . . . . . . . . . . . . . . . 31.3 Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Tutorial 5

3 Advanced options 11

4 Define new trains 114.1 Create new train . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114.2 Upload a train already created . . . . . . . . . . . . . . . . . . . . . . . 12

5 Validation examples 125.1 Example 1: Single load response on a simply supported bridge . . . . . 135.2 Example 2: AVE-S103 response on a simply supported bridge . . . . . 155.3 Example 3: Continuous double span bridge . . . . . . . . . . . . . . . . 15

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1 Introduction

CALDINTAV is a program for dynamic analysis of railway bridges developed by theComputational Mechanics Group at the Civil Engineering School (Technical Universityof Madrid)

1.1 Scope

The objective of this program is to provide the user a fast and simple tool to analysedynamic effects on simply supported and continuous bridges of up to 6 spans.

The main measures of dynamic performance for the design of the bridge may beobtained by CALDINTAV. For instance, dynamic impact factor, acceleration and dis-placement on the deck of the bridge... etc.

A wide database with real trains of European network is provided, as well as theHSLM defined in Eurocodes. Additionally, the user can define additional trains forperforming the calculations.

Real trains Max. running speed.AVE-S103 (ICE-3) 420

AVE-S112 (Talgo 350) 420AVE-S100 (TGV) 420

CAF-TEMD 250ETR-Y 420

EUROSTAR-373 420THALYS 420

Table 1: Real trains provided with the program and maximum running speed

1.2 Basic concepts for structural dynamics

The actions to which a railway bridge is subjected are dynamic. Their effects can behigher than those due to static actions. This is due to:

• The mobile nature of the loads, which produces increases or decreases in theequivalent static load

• Repeated application of the loads which can lead to resonance.

• The irregularities of the track and wheels.

To evaluate the dynamic effects, all trains which could run on the line should beconsidered, and all possible running speeds.

For each structural element, the maximum dynamic stress envelope is defined bythe impact factor, regardless the dynamic calculation procedure chosen. The dynamicimpact factor is defined as:

Φ =maxSdin,max

Sest,maximo

Where maxSdin,real is the maximum dynamic solicitation due to all possible trainsand running speeds, and Sest,tipo is the maximum static solicitation due to the train.

For simply supported bridges CALDINTAV obtains this impact factor as the quo-tient between the maximum displacements at centre of span:

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Φ =maxδdin,max

δest,maximo

Generally, the available dynamic analysis methods are:

1. Methods based on direct integration

2. Methods based on modal decomposition

3. Simplified methods for simply supported bridges based on train signature.

CALDINTAV uses the second type. As default, for simply supported bridges, twovibration symmetric modes are considered, as the antisymmetric modes are zero at thecentre of span (see figure 1). The vibration modes of an simply supported bridge couldbe described as follow:

φi(x) = sin( iπxL

)

Where i is the considered mode, L is the span length and x is the bridge localcoordinate.

2ρLω2 = 4π2E IρL4

x

x

x

ω1 = π2E IρL4

φ1(x) = sen(πx/ L)

φ2(x) = sen(2πx/L)

M3 = 12ρLω3 = 9π2

E IρL4

φ3(x) = sen(3πx/L)

Figure 1: Three first vibration modes of a simply supported beam

Load distribution between sleepers.Considering load distribution means that the vertical load of each axle of the train,

which is acting on the rail, is divided among three consecutive sleepers with a ratio of14, 1

2y 1

4(Figure 2).

It is known that considering the load as concentrated, without distribution betweenthe sleepers, causes higher accelerations in the deck of the bridge than if the load isdistributed. Therefore, not considering load distribution, is the most conservativeassumption, and consequently is more often used in dynamic analysis.

CALDINTAV allow to choose between considering load distribution or not.4

Figure 2: Load distribution schema

Figure 3: Moving and concentrated load schema

1.3 Installation

CALDINTAV is a tool developed in MATLAB. For running is not necessary to haveinstalled MATLAB, only a MATLAB set of libraries that are freely distributed, calledMATLAB Compiler Runtime (MCR). These libraries are incorporated in the providedpackage.

For installation on WINDOWS is necessary to follow the next steps:

1. Extract CALDINTAV.zip file

2. Inside the extracted file, execute CALDINTAV pgk which is a self-extracting filethat will extract all the necessary files and run the MCRInstaller. Follow thesteps and complete the installation of the MCR library.

Once done, to run the program, double click on the file called Caldintav.exe. De-pending on your computer this can last few minutes, please wait.

NOTE: In case that when running the file CALDINTAV.exe the next message errorappears: ’Could not find version 7.14 of the MCR. Attempting to load mcl ...’ weshould repeat the installation of the MCR module (running again MCRInstaller.exe).By repeating this operation the computer will solve its problem to detect the path of thisfile and we will be able to run de program correctly.

2 Tutorial

We are going to introduce the use of the program by a simple example.A continuoustwo span bridge with the following characteristic is considered:

• L = 15 m (each span)

• m = 15.000 kg/m

• EI= 7.6941 e+09

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• ζ = 2%

Lets calculate the dynamic response of a bridge under train ICE-3 (AVE S-103) fordifferent running speeds, varying from 250 to 280 km/h. The steps are:

1. Running the program and name the projectIf we are working in WINDOWS, double click on the icon CALDINTAV. It will

start the interface, and then click on START.Then, we are asked to introduce project name. We type a name, which could contain

spaces, but should not contain symbols or accents, as our output files are going to besaved with this name. We write, for example, ’ejemplo’ and then click on Accept.

2. Bridge properties definition.To introduce the bridge properties we click on Define properties button of the

main window. On the upper part of the new window a table can be shown (see figure 4.Each row of the table correspond to each span. For introducing the different propertiesthere are two options:

• Load a text file in which the chacteristics of the bridge are gathered. For doingthis, we go to the menu bar Load. In the bridges folder we will select the bridge.In this case, we choose puente2vanos.dat.

• The bridge properties can be writen manually in the table. After that, if we wantto save this bridge, in order to be able to load it in a future, we click on Saveas, select the bridges folder and introduce the name of the file.

After that, damping has to be introduced in the section Damping. In this case adamping of 2% will be introduced. Thus, we type 0.02 (see figure 4). Then we click onShow. A bridge schema will appear, as well as the possible output points for request.

In our case, we want to know the acceleration and displacement in both spans, andthe bending moment in the first span and the support. We will select this points in thelist of available request, and we will add to the selected points by the Add button (seefigure 4. The selected points will turn red in the bridge schema as we choose them.

3. Choosing trains and speeds.In this case, we want to perform our analysis with one of the trains included in

the program library, the AVE-S103. Thus, we only have to select it form the list ofavailable trains (Available trains) and pass it through the button Add to the list oftrains that we are going to use for the analysis (Selection) (see figure 5).

This program allows the analysis with several trains at the same time, simply byincluding them in analogous manner as described. It also allows to define new trainsor load the ones that we have already defined (see section 4).

We write the minimum running speed, in our case 250 km/h, and the maximumrunning speed, 280 km/h. By default, the program carries out speed increments of 5km/h. We can modify this increment if desired, and therefore the different speeds atwhich calculation is going to be made.

4.Choosing type of analysisIf we want to consider load distribution we should check the box Load distribu-

tion. In this case, we are not going to consider load distribution so we are leaving thisbox without check.

5. ResultsTo perform the calculation we click on the button Submit of the main window. A

window that inform us about the progress of the calculation will appear. At any timewe can cancel the analysis we have sent by clicking on button Cancel of this window.

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Figure 4: Defining bridge properties

Figure 5: Select trains and running speeds

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When the calculation is finished, two graphs will appear on the right of the mainwindow, in the panel of results (Results). The graph on the top shows the maximumaccelerations for each calculated speed. The lower graph shows the maximum dynamicimpact factor for each running speed. Below this, maximum value of the accelerationand impact factor is shown, as well as the speed at which occurs. If you have carriedout the analysis using several trains, there it will appear the value of the train whichinvolves higher dynamic effects.

To facilitate the interpretation of the results, some buttons under each graph areprovided. This buttons allow to plot different limits. In this case, we will plot themaximum limit of acceleration, defined in the IAPF-2007, by selecting the type of track,for example ballast track (Ballast) and then clicking on the button Max.Accel.Limit.

In the figure 6 maximum limit of accelerations is shown for a ballast track. It canbe seen that this limit is overpassed for speeds higher than 300 km/h.

Analogously for the impact factor graph it is available a limit which gives an ideaof when significant dynamic phenomena are appearing. This limit is defined by theUIC-776 and we can plot it by clicking in the button 1 + ϕ′

UIC.In the figure 7 it can be seen that there are certain points in which value 1 + ϕ′

UIC

is overpassed, that approximately coincide with the ones that produce higher values ofthe acceleration.

Figure 6: Maximum accelerations vs speed and limit for ballast track.

The point at which the results are displayed appear in pink color on the bridgeschema located on the left part of the main window (see figure 9).

In order to change the visualization point, we click with the right button of themouse in the result graphs. A context menu will appear and allow us to move to thenext or the previous point.

In order to understand what is happening at 300 km/h, we can obtain the historyof acceleration at this point. For this, we shall go to the menu bar: Results −→ Timehistories −→ Accelerations. A new window will appear. Enter the speed at whichyou want to see the history of acceleration, for instance 300 km/h, and push intro inthe same field in which we have edited the speed (see figure ??). In order to see theresults in the centre of the second span we need to click on the button Next

Analogously, the history of displacement for the output requested points could beshown. Additionally, history of bending moments can be shown if we go to Results−→ Time histories −→ Bending moments. To see the bending moment at 300 km/h

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Figure 7: Maximum dynamic impact factor vs speed and limit defined by the UIC-776

Figure 8: Bridge schema shown after the calculation. Requested output points appearmarked with a circle. The point of which the results are being shown is always pink.

Figure 9: History of acceleration for the train ICE-3 at 300 km/h at the first centre ofspan. In order to change the visualization point use the next and previous buttons.

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we write 300 in the corresponding field and push intro in the same field. By defaultthe results are shown for the supports (see figure 10). If we want to see the results atthe centre of the span we should activate the Centre of span box and push intro inthe speed field (see figure 12).

Figure 10: History of bending moment for the train ICE-3 at 300 km/h at the centralsupport. In order to change the visualization point use the next and previous buttons.To see the positive bending moments at the centre of the spans use the button on theright ’Centre of span’ and push intro in the speed field.

Figure 11: History of bending moment for the train ICE-3 at 300 km/h at the firstcentre of span. In order to change the visualization point use the next and previousbuttons. To see the negative bending moments at the supports use the button on theright ’Supports’ and push intro in the speed field.

Finally, if we want to see the modes that have been used in the analysis and itscorresponding frequencies we click on Results −→Modes. To change the visualization

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mode, click on the right pop-up menu (see figure ??)

Figure 12: First bending mode and its corresponding frequency. To change the visual-ization mode, click on the right pop-up menu.

3 Advanced options

The user can specify the number of modes and the time step to be considered in theanalysis. The time step indicates at which times is the problem going to be solved.Thus, the smaller the time step the more accurate the solution will be, but also themore time the calculation will take.

For simply supported bridges the program only considers symmetric modes of vi-bration, as the mode shape in the centre of span for anti-symmetric modes vanishes.By default the number of modes considered is 2. If we want to modify them, we shallgo to Options −→ Advanced.

In figure 13 we have changed the number of considered modes to 3 and we haveaccepted the default time step (1e-3). To confirm we click on Accept.

Figure 13: Modifying number of modes and/or time step

4 Define new trains

4.1 Create new train

To create a new train we click on Options −→ Train −→ New.A new window will open, in which we can define the value of the load per axle in

tons (Axle Load (ton)) and the distance from that axis to the first one. The distance11

from the first axis to itself is always zero (see 14). If our train has more than 20 axeswe can increase the number of rows writing the desired number on the field Numberof rows and push enter button. Finally we must specify the name we want to give toour new train in the field Name and click on Save. This way, a data file is created inthe folder trenes, in which we kept this train saved. (This files can be also modified byusing any text editor).

Figure 14: Create new train

4.2 Upload a train already created

For achieving that an already created train appears in the list of available trains forthe calculation, and therefore, we can use it in the analysis, we should go to Options−→ Train −→ Load. We must enter in the folder trenes and load the file of our train(with extension .dat) by clicking on Open. The train will appear the last in the listof available trains and we can select it for the analysis by clicking on Add.

5 Validation examples

The first two validation examples are based on the ones gathered in [1] national annex.Thus, the results obtained can be compared with the ones of the mentioned document.Both examples are for a simply supported bridge. Additionally, an example with acontinuous bridge is gathered.

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5.1 Example 1: Single load response on a simply supportedbridge

In this example, the bridge properties are the following:

• L = 15m

• f1 = 7Hz

• EI=12064000 kNm2

• ρ = 12000 kg/m

• ξ = 1.85%

A single load of 20 tons is considered. Thus the static deflection at centre span forthis load P , is:

u(L

2) =

PL3

48EI= 1.16 mm

In figure 5.1 it can be seen that for a speed of 180 km/h the maximum deflectionis 1.38 mm. Therefore, the impact factor at 180 km/h is 1 + ϕ′ = 1.38/1.16 = 1.19.This is gathered in figure 5.1, in which the values of ϕ are shown vs the speed. Finally,figure 15 shows the maximum values of the displacement obtained for each speed.

0 0.2 0.4 0.6 0.8 1 1.2 1.4−1.5

−1

−0.5

0

0.5

Time (s)

Dis

pla

cem

ent

(mm

)

Static displacement

Figure 15: Maximum displacement at centre span for v = 180km/h. 15 m span simplysupported bridge. ξ = 1.85. Only the first bending mode has been considered.

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100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400

1.2

1.4

1.6

1.8

Speed (km/h)

Dis

pla

cem

ent

(mm

)

Figure 16: Maximum displacement at centre span vs train speed for a single load of 20tons. 15 m span simply supported bridge. ξ = 1.85. Only the first bending mode hasbeen considered.

100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 4001

1.2

1.4

1.6

Speed (km/h)

1+ϕ′

Figure 17: Maximum impact factor 1 + ϕ′ at centre span vs train speed for a singleload of 20 tons. 15 m span simply supported bridge. ξ = 1.85. Only the first bendingmode has been considered.

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5.2 Example 2: AVE-S103 response on a simply supportedbridge

The same bridge used in example 1 is applied for this case. The difference is that nowa train load (AVE-S103) is passing over the bridge. The train axle load distributionis gathered in [1]. Figure 5.2 shows the maximum displacement at centre span for arange of speeds varying from 100 km/h to 400 km/h. Analogously in figure 5.2 themaximum accelerations for this case are presented.

100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 4000

5

10

15

Speed (km/h)

Dis

pla

cem

ent

(mm

)

Figure 18: Maximum displacement at centre span vs train speed for the train AVE-S103. 15 m span simply supported bridge. ξ = 1.85. Only the first bending mode hasbeen considered.

100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 4000

5

10

15

Speed (km/h)

Acc

eler

atio

n(m

/s2

Figure 19: Maximum impact acceleration at centre span vs train speed for a singleload of 20 tons. 15 m span simply supported bridge. ξ = 1.85. Only the first bendingmode has been considered.

5.3 Example 3: Continuous double span bridge

A continuous bridge with two spans of 15 m is considered (see 20). This bridge hasthe following properties:

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• m = 15.000 kg/m

• EI= 7.6941 e+09

• ζ = 2%

A train with 10 loads of 195 kN passing over the bridge at 200 km/h is used forthis example. The results obtained with CALDINTAV are compared with the resultsobtained with a finite element program (FEAP [2]).

Figure 20: Example 3 schema: bridge and train

Figure 5.3 shows the hogging moment in the middle support using two modes.Figure 5.3 presents the sagging moment at the centre span. In both cases the resultsobtained with FEAP and CALDINTAV are very similar.

0 0.5 1 1.5 2 2.5 3 3.5

−6

−4

−2

0

2

·105

Tiempo (s)

Mom

ento

(N·m

)

FEAP CALDINTAV

Figure 21: Bending moment at the middle support for a train with 10 loads of 195 kNpassing over the bridge at 200 km/h. Two modes has been considered

Finally, in figure 5.3 acceleration at the centre span are gathered. The resultsobtained with the two programs are very similar, and the differences are due to aslightly different discretization.

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0 0.5 1 1.5 2 2.5 3 3.5−4

−2

0

2

4

6

·105

Tiempo (s)

Mom

ento

(N·m

)

FEAP CALDINTAV

Figure 22: Bending moment at the centre span for a train with 10 loads of 195 kNpassing over the bridge at 200 km/h. Two modes has been considered

0 0.5 1 1.5 2 2.5 3 3.5

−0.5

0

0.5

1

Tiempo (s)

Ace

lera

cion

(m/s

)

FEAP Caldintav

Figure 23: Aceleracion en el primer centro de vano con 2 modos

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References

[1] Ministerio de Fomento. Universidad Politecnica de Madrid. J.MGoicolea, P. Antolın, T. Ancochea. NCCI: Calculo Dinamico dePuentes para las Acciones de Trafico Ferroviario. Informacion com-plementaria no contradictoria (NCCI) a los Eurocodigos de ac-ciones de trafico y criterios de diseno para estructuras ferroviariasEN1990/A1 EN1991-2. Madrid, 2012

[2] Robert L. Taylor. Department of Civil and Enviromental Engineer-ing. University of California at Berkeley. FEAP: A Finite ElementProgram. Version 8.3 User Manual. March 2011.

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