Traffic load

The Traffic Load feature is a specialized load pattern designed to determine the most unfavourable load system and its position for road and railway bridges according to EN 1991-2. The primary goals of this feature are:

• Facilitating parametric/variable vehicle definition
• Assisting in Eurocode's Load model definition
• Aiding in determining the dynamic load multiplier and managing uneven loading on rails
• Supporting multiple lane alignment definition
• Providing solution for both road and railway bridges
• Handling scenarios with multiple road lanes/railways
• Displaying maximal values and the associated actual load system
• Handling arbitrary geometry with inclined lines/surfaces
• Facilitating the creation of multiple traffic loads with various options

Load patterns are seamlessly integrated into the load cases, similar to other load items. It's important to note that this type of load comes with a high computational demand, and for optimal performance, see the Performance tips section.

Contents

• Definition steps
• Settings
• Load system display and load case generation
• Theory
• Recommendation
• Limitations

Definition steps

Basics

Traffic load patterns are objects associated with the Moving loads. A new traffic load creates one or more new Moving loads with a Unit load, and with different Load cases. The position of Moving loads can be freely edited. To minimize the number of new Moving loads (and consequently load cases), use the Wizard and Mass-generation tools, which will employ the same Moving loads.

Advantages: the details of the Influence graphs can be easily controlled, and the calculation time can be significantly reduced when multiple traffic loads use the same moving load object.

Disadvantages: editing/moving/copying traffic loads' geometry is restricted, as modifications to connected moving loads may conflict with other coupled traffic loads. In such cases, redefinition may be necessary. To solve this problem more efficiently, use the Pick and Copy properties (Tools menu) of the original object.

Simple line model

Both carriageway and railway load patterns can be defined as a simple line model, specifically designed for the pre-design phase using single bar models. The definition process only requires the stake-out line.

Complex models

Carriageway

For carriageway vehicles, it is necessary to have one or multiple carriageway regions, which can be nearly arbitrary in space (except close to vertical). Slopes are allowed in both longitudinal and transversal directions. Surface moving loads will be generated on each selected/defined carriageway region, required for influence graph creation. The load system of the vehicle can only be placed in these regions during the calculation. All region parts not included in the lane alignment can be referred to as Remaining areas.

Carriageway vehicle definition process:

1. Select the regions of the carriageway.
2. Define the stake-out line.

Railway

Railway models are specially designed to handle complex rail geometry and superelevation. Therefore, during the definition process, the geometry of each rail or underlying girder must be defined.

Note: Multiple regions can be selected as a carriageway part using the selection sub-option.

Railway vehicle definition process:

1. Set the number of railways.
2. Define the polyline of each track.
3. Define the stake-out line.

Load positioning during the calculation: one railway contains two rails, and the influence lines of these rails are summed during the calculation. However, they may have different lengths. If the rails can be matched with the stake-out line (its segments are parallel pairwise with the stake-out line), the longer segments could be paired exactly, and the curving parts of the track will be paired by ratio. Otherwise, the track will be paired by ratio along the entire length.

Wizard

The Wizard is a specialized tool designed for creating a new load pattern based on an existing one. If you require a new load pattern with the same geometry but different properties, this tool should be used.

Usage:

1. Select an existing load pattern.
2. Modify the properties.
3. Click the Create button to generate a new load pattern.

Mass-generation of Traffic load patterns

A single Traffic load pattern item could manage only one Load model and has certain limitations regarding component selection. With this tool, you can define multiple Traffic loads, each with different Load models and components, based on a selected load pattern (prototype). The Generate load patterns function will generate the Load cases for Components grouped in Subgroups of load models within the selected Load group.

Settings

General

On the General tab, internal force/displacement components can be selected for the calculation. The dominant load system is determined through the maximization process of the chosen component.

If the model is configured with limit state-dependent materials (e.g. Creep settings), four different calculations would be required. To reduce the calculation time, three major options are available for all selected components:

1. [Limit state] clone (e.g. “U clone”): Calculate the selected limit state, and all results will be cloned to the others.
2. [Limit state] resultset (e.g. “U resultset”): Calculate the dominant load system by the selected limit state, then calculate all results individually by this load system.
3. U/Sq/Sf/Sc: All limit states will be calculated individually.
    

If the Calculate simultaneous results option is checked, the related simultaneous internal force components will be calculated (e.g.: selected Bar/N+ will also calculate Ty, Tz, Mt, My, Mz).

All newly generated Moving loads will be placed in one Load group, named after the Comment field.
 

Load model

The Load model tab is designed for creating/selecting/adjusting Eurocode (EN 1991-2)-defined load models.

Vehicles can be selected from the Vehicle library (available when clicking on a Vehicle filed). The Factor is a versatile tool: if the vehicle is defined as a unit, it can be used as a load factor, or it can consider the code-defined alpha values. The Lane option allows adjusting vehicle relationships. The 1st lane represents the most unfavourable lane, the 2nd lane is the second most unfavourable, and so on. For all lanes above the 3rd, Other lanes should be used (e.g., if the bridge has 8 lanes, LM1 UDL Unit with Other lanes selection means the vehicle could be placed simultaneously on all 5 remaining “other” lanes). The Remaining areas option is for surface-type loads, like crowd load, and represents the outer areas of the lane system. The load model will be applied according to the Lane alignments  for Road vehicles. The vehicles on the same lane are placed in the order of their Priority parameter.

Notes

• The number of lanes does not have to match in the Load model and the Lane alignments tab, any load model can be applied to any Lane alignments.
• EN 1991-2 4.3.2. defined adjustment factors (alpha) can be easily applied in the Factor column.
• With one load pattern, only one load model can be considered. If the model requires it, use the Wizard or the Mass generation tool to create multiple load patterns with the same geometry but different load models.

Vehicle library

A Load model handles multiple vehicles, and the Vehicle library is developed to provide these. A vehicle could be Road or Rail type, aiding usability for different Traffic load objects. Nominal width is the width of the vehicle, which is significant if it is less than the width of the designated lane (in Lane alignment): the vehicle will also be tested on multiple transversal positions within the lane during the maximum search.

A Vehicle could be defined with the following elements in a proper order:

• Axle load: Point load representation (e.g. LM1 Tandem System). The load intensity is the summation of all-wheel loads. It can be applied on a lane.
• Line load: Line load representation (e.g. SW/2 load system) for a Vehicle with wheels. The load intensity is the summation of the all-wheel loads. It could be parametric by length by setting different Min. and Max. lengths. It can be applied on a lane.
• Surface load: it can be applied on arbitrary geometry (e.g. Crowd load). This is a mutually exclusive load item, it cannot be applied with other load items (Surface-type vehicle).
• Distance: The distance between the load elements. It could be variable.

If one of these sub-elements is variable, that means the vehicle is parametrical, and this is a Vehicle parameter. The vehicles can also be used on a single line model in a simplified mode. For example, Tandem System will be simplified to one point load, surface load will be simplified to one line load calculated by the notional width.

Load modifier

Load modifiers have multiple use-cases, such as dynamic amplification or national annex defined design factors, therefore, it is developed to be as versatile as possible.

• If the whole Load model should be multiplied, a constant value could be appropriate.
• If the model requires uneven load level along the stake-out line, variable load multiplier should be used. For example, additional dynamic amplification in the vicinity of expansion joints, EN 1991-2 4.3.3 (3).

Variable load multipliers are constant outside the handled length domain, and linear interpolation is applied between the sample points.

Note: The Variable load modifier is not applied to surface-type vehicles.
 

Wheel load ratio between the tracks is available for trains, and this is the exact implementation of EN 1991-2 6.3.5.(1).
 

Lane alignments

Lane alignments are possible lane configurations during the structural lifetime, which are parallel to the stake-out line, and the user-defined left/right boundaries are measured from it. As the stake-out line could be an almost arbitrary polyline, the lane system could handle turning road design with a good approximation.

To create a lane, its Lane name, Left and Width properties must be defined, and the Right will be filled out automatically. The New button creates a new Lane alignment from the current settings of the dialog.

In the case of the simple line model, the position of the lane has no significance, but the load level can be determined by the number of the lanes. For carriageway types, three fill options are available to aid work: Left, Right, Middle alignment.

Using the Applied checkbox, lane alignment could be inactivated. Multiple lane alignment could increase the calculation time; for pre-evaluation of structure, it could be worth temporarily reducing the active alignments.

Note: Load model reference of the "1^st” lane means the most unfavourable Lane and is unrelated to the order of the Lanes in a Lane alignment.

Calculation options

Load pattern calculation has a high calculation demand and involves a complex optimization process that allows for adjustment. The maximum search uses two different strategies:

Brute force: This method systemically tests all discrete positions and values of vehicle parameters based on given settings. Advantage: if the discretization is set properly, it finds the maximum solution, or at least, the closest discrete values. Disadvantage: if the number of the parameters is high, it could be very slow, and the exact position of the maximum is usually not found, only the closest discrete value set. The Number of positions along the stakeout line parameter controls the longitudinal load positioning. Division number of vehicle parameters is used in case of vehicles that contain Line load or Distance with varying length. The possible discrete length parameters will be generated based on the minimum and maximum length and the division number.

Multistart optimization: This method is based on an optimization algorithm for convex functions, making it possible to get stuck in a local maximum position when used on an arbitrary function. To reduce the chance of getting stuck, it is started multiple times with different initial values. Advantage: it is continuous, allowing it to find the exact maximum place. For multiparametric systems, it is usually much faster. Disadvantage: it may not find the maximum. A higher number of Number of restart increases the likelihood of identifying the extreme traffic load position but extends calculation time. Conversely, a lower value accelerates calculations.

The Maximal step within the lane parameter controls the transversal load positioning when vehicle width and lane width differ.

Load system display and load case generation

For more advanced usage, such as non-linear FEA calculations, the Load pattern cannot be directly used. Therefore, the Load case generation by Load patterns tool was implemented to create the corresponding load system for the examined point in a specific result.

After opening this edit tool, more inspections can be executed:

• On the mouse hover event over the structure, the corresponding load system of the examined point is displayed.
• On the mouse click event, this load case be added to the Load case generation list, which will be applied for Tab change (e.g. Loads tab).

In the List of requested load cases, the basic properties of a load case can be overviewed, the names can be set, or any request can be deleted.

Theory

The Maximal graph generation in a finite element node is based on the Influence graph of the node. Parameter optimization is applied to find the most unfavourable positions, and load parameters.

Calculations steps:

1. Influence line and surface generation
2. Load pattern resultset calculation (position, vehicle parameter calculation)
   • For all lane alignments.
   • For all permutations of lane alignments.
   • For all transversal steps in lane if the lane width is wider than the nominal width of the vehicle.
   • The vehicles are applied one by one, in the Load model defined order.
   • Probe the vehicle in the reverse direction if it is asymmetrical.
   • For Point- and Line-load based vehicle loads, the influence surface will be reduced to an influence line on the stake-out line of the lane. The reducing algorithm transversally integrates the influence graph under the wheel area.
   • Surface loads are only constrained by the designated area in Load model settings. The area of the surface loads can be calculated trivially by the sign of the influence graph.
3. Requested simultaneous component calculation by the influence graph of the component and the previously determined load systems.

Each of these steps is executed for all requested components in all structural nodes.

The load system contribution is only calculated on the domain. That means, if the unfavourable load position is outside of the carriageway/rails/stake-out line, only the overlapping load system part will be considered.

In a Load combination, Load pattern results are linearly added to the results after any non-linear calculated Load combinations during the post-processing. If any load system of the Load pattern results is wanted to be involved in a non-linear FEA calculation, the Load case generation by Load patterns should be used.

Recommendation

Usage tips

The Traffic load item has high computational demand; therefore, a prototype calculation is advised before any mass-generation. Using a prototype load item, the proper settings could be found iteratively, inspecting the most significant results. After the prototype load item is finalized, the Wizard and Mass-generation tools could be used to create load items for the other result components. This process could be repeated for different Load models.

One load model can be applied to multiple Traffic load items (in different Load cases). For example, using EN 1991-2, the complex psi value settings of LM1 can be set in the Load combination dialog by separating the UDL and Tandem System part.

Performance tips

Object

• Edit the moving load for fewer but more relevant load positions.
   

General

• Using multiple creep coefficients for materials could lead to multiple calculations (maximum four) for highlighted limit states (U, Sq, Sc, Sf). It would mean 4 times calculation of each traffic load as well. To avoid this:
  • calculate only one limit state and then clone it to the others (fastest, 4x faster overall), or
  • calculate the result set for the selected limit state and then apply it for the four limit states’ simultaneous components (4x faster resultset calculation).

Load model

• Apply symmetrical vehicles if the model allows (2x faster resultset calculation).
• Reduce the number of vehicle parameters if the model allows.
• If simultaneous results are not necessary, uncheck it (for 6-8x faster influence graph generation and simultaneous result calculation).
• Prefer to use one lengthy line with allowed discontinuity rather than multiple line loads with variable lengths and distances, if the model allows.
• Surface-type vehicle calculation requires surface topology build during influence graph generations, and its simultaneous component calculation has high demand. If the model allows, it can be replaced by a one-wheel line-load based vehicle with the equivalent width of the lane. These types of vehicles have “Resultant” suffix.
• Lane alignments options affect the resultset calculation phase only
  • Calculation time is linear with the applied lane alignments.
  • The permutations of the Lanes could be high ((No. Lane)! / (No. Lane-3)!)
     

Calculation options

• Brute-force method’s calculation time is exponential with the number of parameters:
  • Time complexity: “No. of position along the stake-out line” * (“Div. of Vehicle parameters” ^ “No. of Vehicle parameters”).
  • A certain optimization is applied, which greatly reduces the time complexity of the implementation, but the exponential characteristic still remains.
• Calculation time is linear with the number of restarts of the Multistart optimization.
• Calculation time is linear with transversal load positions.

Limitations

• The stake-out line is not allowed to intersect itself in the top-plane view.
• Line and surface moving loads of the Traffic load are not allowed to overlap in the top-plane view.
• Three vehicles are allowed per lane.
• Line/point-based vehicles are only placed within the lane alignment system, following the stake-out line (e.g. LM2 cannot be placed with arbitrary rotation).
• The simple line model considers a centrical load system because it does not apply torsional influence graph to calculate torsional maximal graph.
• Eurocode-defined horizontal forces, like Braking/Acceleration/Centrifugal/etc. effects, are not implemented in this feature.
• The major edit functions are disabled because of the coupled Moving loads. The creation process is aided by the Pick and Copy properties functions.