Moving Load Train Analysis#

The SSD task task_moving_load_train_analysis_small Moving Load Train Analysis allows for the dynamic analysis of railway bridges under predefined load models. By specifying a set of load models, relevant train passage information, and bridge and analysis parameters, a complete set of load effects from a dynamic analysis is determined.

Load Trains#

Specify load models to be used in the analysis.

This tab allows to add load trains to the analysis and edit their properties, if applicable. A comprehensive list of Eurocode load models is available to choose from, or a user-defined load train can be manually created.

Important

When defining a user-defined load train it is important to build up the load pattern against the direction of travel.

The Distance to Previous Load has to be input as negative value.

../../../_images/direction_of_travel.png

Note

For the user-defined load trains it is possible to copy the loading definition data from the Excel spreadsheet directly.

Train Passages#

Define the information regarding the movement of the train model and the distribution of load on the bridge structure.

Track#

Moving Load Train Analysis - Train Passages Tab (click on image to enlarge)#

Reference line#

To define an axis of movement for the load model, a reference line must be indicated. A geometric axis or a structural line can be used, provided that it aligns with the structure to ensure correct load transfer. Additionally, by specifying a second reference line, a more precise simulation of the two train rails is possible.

The horizontal eccentricity of the entire load train in relation to the reference line can also be specified. In case a second reference line is defined along with the horizontal eccentricity, the effective torsional load is applied as a pair of forces acting on the reference lines:

Moving Load Train Analysis - Load application in the case of a second reference line — Load application in the case of a second reference line (click on image to enlarge)#

Longitudinal distribution of loads#

The longitudinal distribution of a point force or wheel load by the rail (See EN 1991-2, 6.3.6.1) can be activated and adjusted by specifying the LDA and LDB distances:

Moving Load Train Analysis - Longitudinal distribution of a point force — Longitudinal distribution of a point force or wheel load by the rail (click on image to enlarge)#

Directions and speeds of trains#

In order to include previously defined train models in the dynamic analysis additional information about their movement must be provided. A complete analytical task can be created by assigning a travel direction, minimum and maximum speeds along with the required speed increment and the ID. The resulting speeds for the analysis and the number of speed steps are calculated automatically.

Note

The number of speed steps per 1 task is currently limited to 99. If the analysis of a load train requires more than 99 speed steps, then it is recommended to define the train load multiple times, with a desired speed range divided into intervals.

For a specific load train the speeds that lead to resonant effects can be estimated based on the eigenfrequencies of the structure, the coach length and the bogie axle distance of the train. These critical speeds are calculated as v_crit = f * d / i, where f is the investigated eigenfrequency, d the coach length or bogie axle distance and i is an integer. The task provides the option to add these critical speeds to the investigated speeds by selecting the relevant eigenfrequencies and providing a range for i. For coach length and bogie axle distance the values specified in the tab Load Trains are used.

Note

In order to use this feature the eigenfrequencies of the structure must be calculated beforehand with the SSD-Task Dynamic Eigenmodes.

Analysis#

Define the numerical and material parameters for a time history analysis.

Damping, Stiffness, Mass#

Moving Load Train Analysis - Analysis Tab (click on image to enlarge)#

For all primary and secondary groups of the structure a set of material and analytical parameters must be established. These include the material-dependent modal (Lehr’s) damping coefficient, a relevant frequency range for an automated Rayleigh damping computation, and the percentage of stiffness and mass activation for the given group.

Note

The values provided by default may not be relevant to the analysis and may need to be checked and adjusted for the specific case.

Time stepping#

The numerical integration scheme type has to be defined. A range of different numerical methods for implicit analysis is available, with the Newmark method and the Generalised-α method being available to choose from in the graphical interface as the most versatile and recommended ones.

Note

More numerical scheme types for advanced and custom applications are available for selection in TEDDY format. Refer to the FEABENCH manual for more information.

The appropriate time step size depends on the frequency of the expected response. A smaller time step interval allows for a higher degree of definition and can capture higher frequency events, but it comes with increased computational cost. On the other hand, a larger time step size reduces computational cost but may dampen out components with smaller periods. The total running time for a time history analysis and the time step size can be provided explicitly or computed automatically.

In the case of selecting an automatic time step size, a convergence study is performed to find the optimal step size for the analysis.

Automatic time step selection using a convergence study#

The convergence study is carried out to automatically determine the maximum possible time step for the analytical task, with the goal of minimizing computational effort while preserving result accuracy. This is achieved by calculating a specified result (such as nodal vertical acceleration or displacement) multiple times using different time step sizes until convergence or meeting the abort criterion.

The algorithm by default investigates time step sizes smaller or equal to the start value ts=0.05/fmax. If time step sizes larger than the start value are to be checked, then the Allow for larger time step function should be activated.

Results#

Post-processing of the time history analysis to generate result envelopes and histograms.

Result envelopes of individual train passages#

Moving Load Train Analysis - Results Tab (click on image to enlarge)#

To define a result envelope, it is necessary to specify the result type and the type of envelope. Additionally, it is possible to directly assign an action type for further superpositions.

Time histories#

It is also possible to create a histogram for a specific element and result type. While the Moving Load Train Analysis task stores the necessary data in the database, it can be further accessed by the SOFiSTiK Result Viewer to generate visual plots.

Note

Refer to the Moving Load Train Analysis tutorial for detailed instructions on configuring and creating histogram plots: https://docs.sofistik.com/2025/en/tutorials/railway-bridges/dynamic-moving-loads/dynamic-moving-loads.html#dynamic-moving-load-train-analysis

Store all time step results for a train passage#

For detailed checks it is possible to store all time step results of a selected train passage. In this case also the loads that are applied at the time steps are stored and can be displayed in GRAPHIC.

Note

Storing all time step results for a train passage may increase the computation time significantly. We recommend to use this feature with care and reduce the amount of stored results by an appropriate storage intervall at Store every n-th time step.