Download the following files
Moving load analysis as per EN1991-2.zip
0. Contents
| 1. Overview | |
|---|---|
| 2. Lane Definition |
2-1 Notional Lane and Remaining Area 2-2 Location and Numbering of the Lanes |
| 3. Vehicle Load |
3-1 Load Model 1 3-2 Load Model 2 3-3 Load Model 3 3-4 Moving Load Analysis Settings |
| 4. Perform Structural Analysis |
|
| 5. Result Evaluation |
5-1 Shear Force Diagram 5-2 Shear Force Tables 5-3 Shear Force Tables (Concurrent Forces) 5-4 Bending Moment Diagram 5-5 Reactions 5-6 Influence Lines 5-7 Moving Load Tracer 5-8 Converting the Moving Load into a Static Load 5-9 Check Beam Reactions due to the Converted Static Load 5-10 Check Reactions Table due to the Static Load |
1. Overview
| Bridge Overview |
2-span continuous composite girder bridge |
|---|---|
|
Bridge type: Straight Bridge |
|
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Span length: 2@24m |
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| Carriageway width: 9.3m | |
| Spacing of cross beams: 4.8m | |
| Unit system: kN, m |
Analysis Model
Plan View
Cross Section
2. Lane Definition
2-1 Notional Lanes and Remaining Area
Number and width of notional lanes
| Carriageway width w | w = 9.3m |
|---|---|
| Number of notional lanes | n1 = Int(w/3) =3 |
| Width of a notional lane w1 | w1 = 3m |
| Width of the remaining area | w - 3 x n1 = 0.3m |
2-2 Location and Numbering of the Lanes
For each individual verification, the number of lanes to be taken into account as loaded, their locations on the carriageway and their numbering should be so chosen that the effects from the load models are the most adverse. (EN 1991-2:2003, 4.2.4(2)).
In midas CIVIL, the user directly defines the locations of lanes, and the numbering of the lanes for design is automatically performed. In this tutorial, the locations of the lanes are shown below.
Location of different lanes
Step 1 Open the Model File
First, double-click the midas CIVIL icon in the relevant directory.
Main Menu > File > Open Project
1. Select 'Eurocode Moving Load.mcb'
2. Click the button
Open model file
Model file
This tutorial is intended to introduce the functions of Moving load analysis. Therefore the procedures of creating elements, assigning static loads and boundary conditions are omitted here. Please refer to the online manual for the detailed usage.
Step 2 Define Moving Load Code
Main Menu > [Load] Tab > [Load Type] Group > Moving Load
1. Moving Load Code: EUROCODE
Step 3-1 Define Traffic Line Lane (Lane_A)
Main Menu > [Load] Tab > [Load Type] Group > Moving Load > [Moving Load Analysis Data] Group > Traffic Line Lanes
Display Node Numbers (Toggle on),
1. Click the button
2. Enter Lane Name: Lane_A
3. Enter Eccentricity: -0.9m
4. Select Vehicular Load Distribution: Cross Beam
5. Select Cross Beam Group: Cross Beam
6. Select Selection by: 2 Points
7. Click at node number '42' (0,0,0,).
8. Click at node number '82' (48,0,0).
9. Click the button
Dialogue box for Lane_A
Location of Lane_A
Depending on the design members, Lane_A could be notional lane No. 1,2 or 3. The number of lanes is determined when performing analysis.
For detailed information on Vehicular load Distribution, refer to the tip mentioned below.
For the calculation of the eccentricity, refer to Step 3-2 in this tutorial.
Cross Beam Group comprises of all the transverse elements.
Tip 1. Vehicular Load Distribution
- Lane Element: Apply loads to the traffic line lane elements reflecting the eccentricity.
When defining lanes by the lane element type, the vertical load components (vehicle loads) and the moments due to the eccentricity are assigned only to the line lane elements. Even though the lanes can be located on cross-beam elements, if the lane element type is selected, then the distribution of the loads onto the cross beams will not be considered. - Cross Beam: Apply the traffic loads to the cross beams.
When using the Cross Beam type, the eccentricity is used only for locating the lanes from the line lane elements. The vehicle loads are distributed to the girders via cross-beam elements defined as a Cross Beam Group. If the user is modeling a bridge having multiple girders, the Cross Beam type is recommended for vehicular load distribution.
For example, an axle load of 100kN is located as shown below. Then, concentrated loads, 25kN and 75kN, are applied to point A and point B respectively. The cross beams themselves are loaded.
Step 3-2 Define Traffic Line lane (Lane_B)
Main Menu > [Load] Tab > [Load Type] Group > Moving Load > [Moving Load Analysis Data] Group > Traffic Line Lanes
1. Click the button
2. Enter Lane Name: Lane_B
3. Enter Eccentricity: -3.9m
4. Select Vehicular Load Distribution: Cross Beam
5. Select Cross Beam Group: Cross Beam
6. Select Selection by: 2 Points
7. Click at node number '42' (0,0,0,).
8. Click at node number '82' (48,0,0).
9. Click the button
Dialogue box for Lane_B
Eccentricity of All the lanes
Location of Lane_B
Enter the eccentricity of a traffic line lane relative to a traffic line lane element. Traffic line lane elements are defined as the reference frame elements from which the eccentricity is measured.
In this tutorial, the eccentricities are calculated as shown in the above figure.
Step 3-3 Define Traffic Line Lane (Lane_C)
Main Menu > [Load] Tab > [Load Type] Group > Moving Load > [Moving Load Analysis Data] Group > Traffic Line Lanes
1. Click the button
2. Enter Lane Name: Lane_C
3. Enter Eccentricity: -6.9m
4. Select Vehicular Load Distribution: Cross Beam
5. Select Cross Beam Group: Cross Beam
6. Select Selection by: 2 Points
7. Click at node number '42' (0,0,0,).
8. Click at node number '82' (48,0,0).
9. Click the button
Dialogue box for Lane_C
Location of Lane_C
Step 3-4 Define Remaining Area
Main Menu > [Load] Tab > [Load Type] Group > Moving Load > [Moving Load Analysis Data] Group > Traffic Line Lanes
1. Click the button
2. Enter Lane Name: RA
3. Enter Lane Width: 0.3m
4. Enter Eccentricity: -8.55m
5. Enter Wheel Spacing: 0m
6. Select Vehicular Load Distribution: Cross Beam
7. Select Cross Beam Group: Cross Beam
8. Select Selection by: 2 Points
9. Click at node number '42' (0,0,0,).
10. Click at node number '82' (48,0,0).
11. Click the button
Dialogue box for Remaining Area
Location of RA
3. Vehicle Load
3-1 Load Model 1
Define Vehicular Load (Case 1. Check Load Model 1)
Main Menu > [Load] Tab > [Load Type] Group > Moving Load > [Moving Load Analysis Data] Group > Vehicles
1. Click the button
2. Select Standard Name: EN 1991-2:2003 - RoadBridge
3. Select Vehicular Load Type: Load Model 1
4. Click the button
Definition of Load Model 1
Load Model 1(LM1): Concentrated and uniformly distributed loads, which cover most of the effects of the traffic of lorries and cars.
The user can directly change the Adjustment Factor given in the National Annex.
Recommended values of Ψ factors for road bridge.
| Symbol | Ψ0 | Ψ1 | Ψ2 | |
|---|---|---|---|---|
|
gr1a (LM1+pedestrian or cycle-track loads) |
TS | 0.75 | 0.75 | 0 |
| UDL | 0.40 | 0.40 | 0 | |
|
Pedestrian + cycle-track loads |
0.40 | 0.40 | 0 | |
| gr1b(Single axle) | 0 | 0.75 | 0 | |
| gr2 (Horizontal forces) | 0 | 0 | 0 | |
| gr3 (Pedestrian loads) | 0 | 0 | 0 | |
| gr4 (LM4-Crowd loading) | 0 | 0.75 | 0 | |
| gr5 (LM3-Special vehicles) | 0 | 0 | 0 | |
Define Moving load case (Case 1. Check Load Model 1)
Main Menu > [Load] Tab > [Load Type] Group > Moving Load > [Moving Load Analysis Data] Group > Moving Load Cases
1. Click the button
2. Enter Load Case Name: MV-LM1
3. Select Load Model: LM1, FLM1
4. Select Vehicle: Load Model 1
5. Select Lane_A, Lane_B, Lane_C and RA
6. Click the button of Selected Lanes
7. Select RA
8. Click the button of Remaining Area
9. Click the button
10. Click the button
Load Model 1 should be applied to each notional lane and to the remaining area. Load Model 1 is applied only to the unfavorable parts of the influence line, longitudinally and transversally.
3-2 Load Model 2
Define Vehicular Load (Case 2. Check Load Model 2)
Main Menu > [Load] Tab > [Load Type] Group > Moving Load > [Moving Load Analysis Data] Group > Vehicles
1. Click the button
2. Select Standard Name: EN 1991-2:2003 - RoadBridge
3. Select Vehicular Load Type: Load Model 2
4. Click the button
Definition of Load Model 2
Load Model 2 (LM2): A single axle load applied to specific type contact areas which covers the dynamic effects of the normal traffic on short structural members.
The user can directly change the Adjustment Factor given in the National Annex.
Additional dynamic amplification factor near expansion joints are not taken into account.
Define Moving load case (Case 2. Check Load Model 2)
Main Menu > [Load] Tab > [Load Type] Group > Moving Load > [Moving Load Analysis Data] Group > Moving Load Cases
1. Click the button
2. Enter Load Case Name: MV-LM2
3. Select Load Model: LM2,3,4 / FLM2,3,4 / Footbridge
4. Loading Effect: Select Independent
5. Sub-Load Cases: Click the button
6. Select Vehicle Class: VL:Load Model 2
7. Max. Number of Loaded Lanes : 1
8. Select Lane_A, Lane_B, Lane_C and RA
9. Click the button
10. Click the button
11. Click the button
Load Model 2 Should be applied to any location on the carriageway.
3-3 Load model 3
Define Vehicular Load (Case 3. Check Load Model 3 with the simultaneous presence of Load Model 1)
Main Menu > [Load] Tab > [Load Type] Group > Moving Load > [Moving Load Analysis Data] Group > Vehicles
1. Click the button
2. Select Standard Name: EN 1991-2:2003 - RoadBridge
3. Select Vehicular Load Type: Load Model 3(3600/200)
4. Click the button
Definition of Load Model 3
Load Model 3(LM3): A set of assemblies of axle loads representing special vehicles which can travel on routes permitted for abnormal loads.
A dynamic amplification for Load Model 3 is taken into account automatically.
In this tutorial, special vehicle is assumed to move at normal speed.
Applicable Axle-lines in midas CIVIL
| Axle-lines of 150kN | Axle-lines of 200kN | Axle-lines of 240kN |
|---|---|---|
| Available | Available | Not Available |
Define Moving load case (Case 3. Check Load Model 3 with the simultaneous presence of Load Model 1)
Main Menu > [Load] Tab > [Load Type] Group > Moving Load > [Moving Load Analysis Data] Group > Moving Load Cases
1. Click the button
2. Enter Load Case Name: MV-LM3
3. Select Load Model: LM1 & 3 Multi
4. Select LM1: Load Model 1
5. Select LM3: Load Model 3 (3600/200)
6. Select Lane_A, Lane_B, Lane_C and RA
7. Click the button of Selected Lanes
8. Select RA
9. Click the button of Remaining Area
10. Click the button
11. Click the button
Load Model 3 is applied to Lane_A, Lane_B or Lane_C.
Tip 2. Simultaneity of Load Model 1 and special vehicle
Where special vehicles are assumed to move at normal speed, a pair of special vehicles should be used in the lane(s) occupied by these vehicles. On the other lanes and the remaining area, the bridge deck should be loaded by Load Model 1 with its frequent values.
3-4 Moving Load Analysis Settings
Main Menu > [Analysis] Tab > [Analysis Control] Group > Moving Load
1. Select Frame: Normal + Concurrent Force and Combined Stress
2. Select Displacements Group: Results
3. Select Forces/Moments Group: Results
4. Click the button
Moving load analysis control
Number/Line Element: Assign the number of reference points on a line element for moving loads and drawing influence line in an influence line analysis. The accuracy of results increases with the increase in the number, but the analysis time may become excessive.
Normal+Concurrent Force: If the output of concurrent forces for max and min values is required for moving load analysis, select [Normal+Concurrent Force]. Concurrent forces are not calculated for LM1 & 3(Multi) model.
Select the specific group for which analysis results need to be checked in order to reduce analysis time. [Structure Group: Results]
4. Perform Structural Analysis
Perform the structural analysis of the structure attributed to boundary conditions and load cases.
Main menu > [Analysis] Tab > [Perform] Group > Perform Analysis
5. Result Evaluation
5-1 Shear Force Diagram
Main Menu > [Results] Tab > [Results] Group > Forces > Beam Diagrams
1. Select Load Cases/Combinations: MVall:MV-LM1
2. Select Components: Fz
3. Select Display Options: Solid Fill
4. Check on Contour and Legend in Type of Display
5. Click the button
Shear force diagram
MVmin: The minimum force resulting from the vehicle load applied to the structure.
MVmax: The maximum force resulting from the vehicle load applied to the structure.
MVall: Both maximum and minimum force resulting from the vehicle load applied to the structure.
5-2 Shear Force Table
Main Menu > [Results] Tab > [Results] Group > Forces > Beam Diagrams
1. Click the button
2. Check on: MV-LM1(MV:all)
3. Click the button
5-3 Shear Force Table (Concurrent Forces)
From the Beam Force table
1. Right-click on the Beam Force table.
2. Select View by Max Value Item...
3. Check on Shear-z
4. Click the button
Calculate the corresponding member forces under the conditions where the maximum and minimum member forces occur at each position.
5-4 Bending Moment Diagram
Main Menu > [Results] Tab > [Results] Group > Forces > Beam Diagrams
1. Select Load Cases/Combinations: MVall:MV-LM1
2. Select Components: My
3. Select Display Options: Solid Fill
4. Check on Contour and Legend in Type of Display
5. Click the button
Bending moment diagram
5-5 Reactions
Main Menu > [Results] Tab > [Results] Group > Reactions > Reaction Forces/Moments
1. Select Load Cases/Combinations: MVall:MV-LM1
2. Select Components: Fz
3. Check on Values in Type of Display
4. Check on Legend in Type of Display
5. Click the button
Reaction forces
5-6 Influence Lines
Main Menu > [Results] Tab > [Moving Load] Group > Influ. Lines > Beam Forces/Moments
1. Select Line/Surface Lanes: LANE All
2. Enter Key Element: 101
3. Select Parts: j
4. Select Components: My
5. Check on Legend in Type of Display
6. Click the button
Key Element: 101
5-7 Moving Load Tracer
Display moving load location that results in the minimum moment at the j-end of the element no. 101 due to the “MV-LM2” load case.
Main Menu > [Results] Tab > [Moving Load] Group > Moving Tracer > Beam Forces/Moments
1. Select Moving Load Cases: MVmin:MV-LM2
2. Enter Key Element: 101
3. Select Parts: j
4. Select Components: My
5. Check on Contour, Lengend and Applied Loads in Type of Display
6. Click the button
Trace and graphically display the vehicle loading condition (corresponding moving load case and location) that results in the maximum/minimum force of a beam element. The loading condition is converted into a static loading and produced as a model file of the MCT type by clicking [Write Min/Max Load to File] button.
Display moving load location that results in the minimum moment at the j-end of the element no. 101 due to the “MV-LM3” load case.
Main Menu > [Results] Tab > [Moving Load] Group > Moving Tracer > Beam Forces/Moments
1. Select Moving Load Cases: MVmin:MV-LM3
2. Enter Key Element: 101
3. Select Parts: j
4. Select Components: My
5. Check on Contour, Lengend and Applied Loads in Type of Display
6. Click the button
Display moving load location that results in the maximum reaction of node no. 103 due to the “MV-LM1” load case.
Main Menu > [Results] Tab > [Moving Load] Group > Moving Tracer > Reactions
1. Select Moving Load Cases: MVmax:MV-LM1
2. Enter Key Element: 103
3. Select Components: Fz
4. Check on Contour, Lengend and Applied Loads in Type of Display
5. Click the button
Key Node: 103
6. Click the button
7. Click button
8. Go to File>Exit in the Midas/Text Editor
Where moving load analysis has been carried out, the moving load case, which produces the maximum or minimum results, is converted into a static loading and produced as the MCT type.
5-8 Converting the Moving Load into a Static Load
Main Menu > [Tools] Tab > MCT Command Shell
1. Click
2. Select the file name "MVmaxMV-LM1Fz103.mct"
3. Click the button
4. Click the button
5. Click the button
6. Click the button
7. Click Perform Analysis
5-9 Check Beam Reactions due to the Converted Static Load
Main Menu > [Results] Tab > [Results] Group > Reactions > Reaction Forces/Moments
1. Select Load Cases/Combinations: ST:MVmaxMV-LM1Fz103
3. Select Components: Fz
4. Check on Values and Legend in Type of Display
5. Click the button
5-10 Check Reactions Table due to the Static Load
Main Menu > Results] Tab > [Results] Group > Reactions > Reaction Forces/Moments
1. Click the button
2. Check on : MVmaxMV-LM1Fz103
3. Click the button
Reaction table due to static load case ‘MVmaxMV-LM1Fz103’ displays the concurrent reactions due to the moving load case ‘MV-LM1’ when the reaction of the node no. 103 is maximum.