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LimitState:RING User Manual

1. c Support block rotation Figure 9 1 Identifying the causes of pre existing cracks using the support movement feature LimitState Ltd CHAPTER 9 USING OTHER LIMITSTATE RING FEATURES TO INVESTIGATE BRIDGE 76 BEHAVIOUR 9 3 Modelling bridge spans with intermediate supports Assessment engineers are sometimes required to analyse a masonry arch bridge which con tains spans which have been propped Whilst such propping is not in general recommended as a remedial measure if these are present then LimitState RING can model the likely effects of this For example suppose that the crown of an arch was propped This can be modelled by specifying that one or more blocks at the crown are restrained in the vertical y direction The failure mechanism is altered accordingly Figure 9 2 A LUS a unpropped failure mechanism Prop at crown b differing failure mechanism when propped Figure 9 2 Using LimitState RING to mimic the effect of a midspan prop LimitState Ltd Chapter 10 Interpreting output from LimitState RING 10 1 Adequacy factor The output from a standard LimitState RING analysis is the adequacy factor AF see Section 5 3 1 Possible outcomes are indicated in Table 10 1 Outcome Scenario Explanation The structure is unstable action of dead loads i AF lt 0 it would require the applied live loads to be negative i e acting upwards to stand Bri
2. 42 Following an analysis 44 na de ee eee e dos ee ee ew AS MUU TOM analysis lt lt LE LE sh NS as dE Ed NRA as Le eee dus 4 4 Modifying properties with the property editor 5 13 15 15 15 16 17 17 17 18 18 18 18 18 19 19 19 19 20 20 20 21 21 21 6 CONTENTS ll Theory 31 5 Theoretical basis of LimitState RING 33 5 1 Background erre IR 33 5 2 Analysis methods used by LimitState RING 34 5 3 Output from a LimitState RING analysis 37 5 3 1 Identification of the adequacy factor 37 5 3 2 Bridge behaviour when subjected to support movements 37 5 4 Range of applicability of LimitState RING 39 SAT ABS 5 000 dos e e e A OA A A 39 E AI 39 5 4 3 Stress related failures 39 5 4 4 Filldepth lt lt 62 ms A A SRS RRS 40 DAG OU a ee e Be as E ARA O me 40 5 4 6 Range of collapse modes identifiable 41 5 5 Use OF reinforcement 2 2 bead ee bk els a SESE Ree EG BX 41 5 6 Finite masonry strength 622 6 eee cion Be RRS RE ee Be es 43 5 7 Sliding failures iria RE See eee te Se ewe Peek ee ee eS 44 Bi PAO oe 2000 ek ora ee BO oa 45 DD AA 2 14252 CR AREER SEO Hh GREE WHEELS 45 5 8 2 Dispersion of live loads 42 4e 4 44 eo e444 44465 dote 8 45 5 8 3 Passive restraint gt io Se E es eS Se
3. 0 5m 0 5 0 5m 0 5m be l0 46m gt 0 58m l0 46m e Figure D 5 BD86 SVTT loading vehicle note direction of travel LimitState Ltd 204 APPENDIX D STANDARD LOADING MODELS D 2 10 BD91 AXLE WEIGHTS AND SPACING VEHICLE 01 w1 A1 w2 A2 w3 A3 Wa A4 W5 A5 W6 02 m KN m KN m kN m KN m KN m KN m 32 tonne 4 Axle Rigid 1 00 63 77 1 20 63 77 3 90 112 82 1 30 73 58 1 00 88 tonne 4 Axle 2 2 Artic 1 00 63 77 3 00 112 82 5 10 98 10 1 80 98 10 1 00 40 tonne 5 Axle 2 3 Arctic 1 00 58 86 3 00 112 82 4 20 73 58 1 35 73 58 1 35 73 58 1 00 40 tonne 5 Axle 3 2 Artic 1 00 58 86 2 80 112 82 1 30 63 77 5 28 78 48 1 02 78 48 1 00 40 tonne 5 Axle 3 2 Artic 1 00 58 86 2 80 63 77 1 30 112 82 5 28 78 48 1 02 78 48 1 00 40 tonne 5 Axle 3 2 Artic 10 5 tonne drive axle 1 00 49 05 2 80 103 01 1 30 44 15 4 80 98 10 1 80 98 10 1 00 40 tonne 5 Axle 3 2 Artic 10 5 tonne drive axle 1 00 49 05 2 80 44 15 1 30 103 01 4 80 98 10 1 80 98 10 1 00 41 tonne 6 Axle 3 3 Artic 1 00 49 05 2 80 103 01 1 30 49 05 4 18 67 00 1 35 67 00 1 35 67 00 1 00 41 tonne 6 Axle 3 3 Artic 1 00 49 05 2 80 49 05 1 30 103 01 4 18 67 00 1 35 67 00 1 35 67 00 1 00 44 tonne 6 Axle
4. LimitState Ltd CHAPTER 20 DISPLAY OPTIONS 145 20 3 5 Tools menu Bridge5 ring LimitState RING File Edit Select View Tools Analysis Help a ul o Project Details Ctrl 1 S it bJ Geometry Ctrl 2 Partial Factors Ctrl 3 g Materials Ctri 4 Y Loads Ctrl 5 Support Movement Wizard Preferences Figure 20 6 The LimitState RING Tools menu Function Description Project Details Open the Project details dialog box Geometry Open the Geometry dialog box Materials Open the Materials dialog box Partial Factors Open the Partial factors dialog box Loads Open the Loading dialog box Support Movement Wizard Open the Support Movement Wizard Preferences Modify General Report preferences Table 20 5 Tools menu functions 20 3 6 Analysis menu State RING N Tools Analysis Help a Solve F5 a w a Unlock Report Figure 20 7 The LimitState RING Analysis menu Function Shortcut Description Solve F5 Analyse the current problem Unlock Unlock the project for editing Report View the analysis report Table 20 6 Analysis menu functions LimitState Ltd CHAPTER 20 DISPLAY OPTIONS 20 3 7 Help menu RING 3 Analysis Help vj Help Fi Ly License Information sj About Figure 20 8 The LimitState RING Help menu Function Shortcut Description Help License Information About F1 Enter the Help sys
5. This is a fictitious bridge with details taken from several real bridges 205 206 APPENDIX E WORKED EXAMPLES GENERAL Figure E 1 Photograph of Example 1 bridge Commentary When undertaking an initial assessment of a bridge there will often be question marks over certain dimensions internal constructional details and material properties A prudent strategy is to use best guess values for the relevant parameters initially but to subsequently undertake parametric studies to determine the sensitivity of the analysis to the assumptions made This ensures that a subsequent detailed dimensional survey and or intrusive investigation can focus in on the features of the bridge which have been identified to be most important Other issues specifically relevant to this bridge e The influence of the mortar loss should be considered separately to see whether re pointing is an immediate priority e The presence of longitudinal cracks in the arch barrel will be likely to limit the effective bridge width to 3 1m The first step in the assessment is to assemble the data necessary in order to undertake an analysis LimitState Ltd APPENDIX E WORKED EXAMPLES GENERAL 207 E 1 2 Assessment data Parameter Value Notes Span 5480mm Rise 2105mm Measured values arch thickness confirmed by drillings at the crown and springings Thickness 340mm Depth of fill amp ballast below the un 1155mm
6. 40 Tonne 5 Axle 3 2 Artic 10 5 Tonne Driv 41 Tonne 6 Axle 3 3 Artic 41 Tonne 6 Axle 343 Artic 44 Tonne 6 Axle Artic 44 Tonne 6 Axle Artic HHH a EE 44Tonne 5 Axle 3 2 Artic 40ft ISO Container il Project vehides Standard vehicles must be renamed before properties can be edited Default 1kN Single Axle 3x 7 Tonne Triple Axle 1 3m Axle Spacing Rename Vehicle Delete vehide Force kN Local Position mm Width mm Loaded length mm 1 68 67 0 1800 300 2 68 67 1800 300 3 68 67 1800 300 Figure 15 2 Vehicle database dialog box 15 2 1 Importing existing vehicles The current vehicles in the database are categorized by family To import one of these for use in the project 1 Choose a vehicle from the list on the left by expanding the tree you will be able to view the properties for each one before importing 2 Import the vehicle into the project by clicking on the vehicle and using the Import arrow button the vehicle details are displayed in the right hand window 3 Click OK The vehicle is now available for use in any load case although it will not have been specifically allocated to any one LimitState Ltd CHAPTER 15 LOADING 115 You may also export vehicles e g user defined from the project by selecting them and clicking the Export arrow button 15 2 2 Defining a new vehicle using properties saved in a file Click on Import vehicl
7. It is not possible to paste numerical data into a cell containing drop down options and vice versa Itis not possible to select copy or paste data to and from more than one feature at a time e g in the Block explorer you cannot copy data from an abutment and a span at the same time It is not possible to overwrite object ID s using the Copy Paste details functions al though the standard Copy Paste will allow this py and paste from a spreadsheet To change the contents of many cells at the same time it can be convenient to use a spread sheet open such as Microsoft Excel Firstly making sure that you have your spreadsheet software highlight all the data that you wish to copy then Copy as described above Navigate to your spreadsheet and Paste the data You can then edit the data as required To move the data back into LimitState RING the reverse process is carried out A convenient way to select all the data in the current branch which is useful for exporting to a sprea dsheet is to use the Copy all function in a similar manner LimitState Ltd 138 CHAPTER 19 VIEWING AND MODIFYING ATTRIBUTES LimitState Ltd Chapter 20 Display options 20 1 General 20 1 1 Language specific variations It should be noted that the different language options in LimitState RING can cause the display to alter according to the prevailing direction of reading Here it is assumed that the
8. AXLE WEIGHTS AND SPACING VEHICLE w1 A1 w2 A2 W3 A3 W4 A4 w5 A5 W6 kN m kN m kN m kN m kN m kN Single Axle 112 82 EJ na 78 48 1 00 78 48 ee ee ieee 88 29 1 30 88 29 En o Air 93 20 1 30 93 20 ER aa 98 10 1 80 98 10 aes 68 67 1 30 68 67 1 30 68 67 E 78 48 1 40 78 48 1 40 78 48 Ee E 68 67 3 90 11282 1 30 73 58 r er 68 67 3 90 73 58 1 30 112 82 oe ee 63 77 1 20 63 77 3 90 73 58 1 30 112 82 A eS 63 77 1 20 63 77 3 90 112 82 1 30 73 58 e a 68 67 3 90 112 84 1 30 73 58 260 68 67 2 90 68 67 dyes A 68 67 3 90 73 58 1 30 112 82 260 68 67 2 90 68 67 rte 68 67 3 90 112 84 1 30 73 58 3 60 58 86 1 20 58 86 1 20 58 86 D ias 68 67 3 90 73 58 1 30 112 82 3 60 58 86 1 20 58 86 1 20 58 86 Overhang Overhang W1 W2 W3 W4 W5 Table D 8 European Union load vehicles Key W1 W2 etc axle weights kN A1 A2 etc axle spacings m axle weights reversed LimitState Ltd APPENDIX D STANDARD LOADING MODELS 197 D 2 4 BD21 Annex A AW Schedule 3 AXLE WEIGHTS AND SPACING VEHICLE Wi Al w2 A2 W3 KN m kN m kN 11 5 Tonne Single Axle 112 82 2x 8 Tonne Double Axle 1m Axle Spacing 78 48 1 0 78 48 2x 9 Tonne Double Axle 1 3m Axle Spacing 2x 9 5 Tonne Double Axle 1 3m Axle Spa
9. Alternatively if in the case of ii the brittle response stems from shear failure at masonry joints it may alternatively be assumed that the initial bond strength at these joints is zero and that LimitState Ltd 40 CHAPTER 5 THEORETICAL BASIS OF LIMITSTATE RING only compressive and frictional forces may be transmitted In this case LimitState RING may be used and can normally be expected to provide lower bound conservative results Unfortunately the decision as to when cases i and ii might apply is complicated by the fact that both are dependent on stress levels If stresses are very low in comparison to the elastic modulus and or bond strength of the masonry then brittle fracture of the bond between rings for example is unlikely to be an important issue Since it can be shown that stresses increase with the size of structure being considered this implies that brittle fracture of the bond between rings may not be of great concern in the case of very short span bridges Readers are referred to Section 7 8 2 for further discussion on modelling multi ring arch bridges 5 4 4 Fill depth Additionally since LimitState RING has been calibrated in situations when fill depths are rela tively small in comparison to the arch span for bridges with relatively small fill depths at the crown or with no fill LimitState RING can be expected to provide reasonable results Con versely when the fill depth at the crown is large e g
10. EX show Hide Contacts EX show Hide Blocks El Show Hide Fill v Property Editor 98659 820 6 V output Explorers 3D View gt Toolbars K Figure 20 5 The LimitState RING View menu Function Description Zoom All View the extents of the bridge and loading Save Camera Remember the current camera viewpoint for later use Load Camera Load the previously saved camera viewpoint Show Hide Contacts Toggle the display of the contact surfaces Show Hide Blocks Toggle the display of the blocks Show Hide Fill Toggle the display of the fill bar elements Show Hide Thrust Toggle the display of the thrust zone Show Hide Hinges Toggle the display of the hinges Show Hide Moment Diagram Toggle the display of the moment diagram Show Hide Normal Force Diagram Toggle the display of the normal force diagram Show Hide Shear Force Diagram Toggle the display of the shear force diagram Property Editor Toggle the display of the Property Editor pane default position right of screen Output Toggle the display of the Output pane default position bottom of screen Explorers Toggle the display of the Block Contact Vehicle and Load case explorers see Section 19 2 3D View Choose from a variety of pre defined camera viewpoints Toolbars Toggle the display of default and non default toolbars Table 20 4 View menu functions post solve only
11. Here the user must specify whether the bridge under consideration is of a fixed width or alter natively if a calculated width will be used Loading from vehicles will tend to spread transversely as it passes through the underlying fill material This means that a 1 8m wide load on the surface may for example be spread across a 3m width at arch level By default LimitState RING assumes a constant specified effective bridge width of 2500mm However if the user selects the option to Auto compute LimitState RING 3 2 a can automat ically calculate the effective width of a bridge according to the width of loading at the base of the fill as follows effective width specified axle sleeper width amount of load spread at the loaded axle sleeper with minimum fill depth extra distance to account for distribution within the arch By default the effective bridge widths are calculated assuming full spread of load to both sides of the loading vehicle using the values in Table 12 1 see also Chapter 8 Highway bridge auto compute defaults The Highway bridge auto compute defaults are given in Table 12 1 Parameter Default value Maximum effective width 5000mm Transverse angle of distribution through surface fill 26 6 Transverse angle of distribution through backfill 26 6 Additional transverse width of arch to include 1500mm Table 12 1 Default values for calculation of effective highway bridge width
12. Railway bridge auto compute defaults The Railway bridge auto compute defaults are given in Table 12 2 LimitState Ltd CHAPTER 12 PROJECT DETAILS 91 Parameter Default value Maximum effective width 5000mm Transverse angle of distribution through surface fill 15 Transverse angle of distribution through backfill 30 Additional transverse width of arch to include Omm Table 12 2 Default values for calculation of effective railway bridge width 12 1 3 Model reinforcement Here the user must specify whether reinforcement is to be modelled in the bridge The choice made will determine whether reinforcement information is required displayed during modelling and analysis By default the option to model reinforcement is not selected 12 2 Optional details Useful details that the user may wish to specify are e Bridge name e Reference No e Location Map reference e Assessor name Assessor organization e Comments These attributes are displayed in the Property Editor Section 19 1 and also in the Summary section of the Report Output Chapter 23 LimitState Ltd 92 CHAPTER 12 PROJECT DETAILS LimitState Ltd Chapter 13 Bridge geometry The bridge geometry can be specified in geometry section of the Wizard Section 4 1 3 or by clicking on Geometry in the Tools menu Section 20 3 5 Alternatively the command may be accessed via the keyboard shortc
13. Data in the explorers is presented in a convenient tabulated form with objects grouped together in a logical manner To begin using simply expand the desired sections of the project tree on the left hand side of the explorer window using the and buttons Some of the columns may not be visible as the tables can be quite wide for this reason you may wish to widen the explorer window After using the mouse to select an object group of objects or their properties in the explorer the corresponding objects will be highlighted in the modeller window This allows the user to determine precisely which parts of the bridge are being considered Similarly objects selected in the modeller window will be highlighted in the relevant explorer window The columns currently shown on a given explorer can be changed by right clicking with a mouse on the explorer title bar selecting View and then selecting and deselecting attributes as required 19 2 3 Editing data Editing data can be done in one of three ways 1 By changing individual cells within the explorer 2 By copying and pasting cells within the explorer 3 By copying and pasting from a spreadsheet 1 Changing individual cells To change the contents of an individual cell in an explorer double click with the mouse If the data is numerical you will now be able to enter a new value using the keyboard Alternately if the data is an option e g true false a drop down list will a
14. If the vertical road alignment is very sharply curved e g in the case of a hump back bridge then there is also a need to consider the possibility of axle lift off This means that the axles which remain in contact with the bridge apply greater loading than normal In this scenario standard vehicles can be renamed and individual axle loads edited as appropriate by the user LimitState Ltd CHAPTER 8 LOADING MODELS a Automatically computed effective width using default parameters based on axle width minimum fill depth below axle and load distribution parameters Rs ma cracks Effective width b Possible reduced user specified effective width due to longitudinal cracks Spandrel Effective width c Possible reduced user specified effective width due to proximity of adjacent lane and edge of bridge Figure 8 5 Transverse dispersal and effective bridge widths highway LimitState Ltd Chapter 9 Using other LimitState RING features to investigate bridge behaviour 9 1 Identifying the causes of observed cracks using the Support Movement feature The option to model support movements in LimitState RING opens up a range of possibilities including the capability to investigate the likely causes of observed cracks in an existing bridge structure By imposing support movements and comparing the actual and modelled deformed shapes it is possible to get a sense for the various possible underlyi
15. 500mm Default surface profile assumed to be level Height of surface fill layer y distance between left hand intrados springing and base of surface fill layer Height of surface fill layer 2000mm Table C 2 Geometry default properties 185 186 APPENDIX C DEFAULT PARAMETERS C 3 Transverse properties only used with auto computed bridge width Parameter Default Notes Transverse sleeper length 2400mm Railway underline bridges only Transverse axle spacing 1800mm Highway bridges only a Railway bridges UIC 774 2R a Omm Auto computed extra width b Highway bridges UK Highways Agency b 1500mm Standard BD21 01 Rail j IC 774 2R Transverse angle of disper 5 a ei rO Pa ale i a 15 b Highway bridges equivalent to 2 1 sion of live loads ballast 3 b 26 6 as recommended in UK Highways Agency surface fill Standard BD21 01 a Railway bridges Transverse angle of disper a 30 b Highway bridges equivalent to 2 1 sion of live loads backfill b 26 6 as recommended in UK Highways Agency Standard BD21 01 Table C 3 Transverse default properties only used with auto computed bridge width LimitState Ltd APPENDIX C DEFAULT PARAMETERS 187 C 4 Material properties Parameter Default Notes Unit weight masonry 20kN m Coefficient of friction radial 0 6 From BS5628
16. In order that users may manually replicate RING 1 5 settings in LimitState RING 3 2 a and also understand how the import facility has represented RING 1 5 models this section provides direct guidance on how to replicate RING 1 5 settings The RING 1 5 backfill properties tab is given in Figure B 5 Properties Materials Load dispersion SE SN TE C Uniform Boussinesq Limiting fill barel angle of fricton rads 10 524 Limiting angle rads 0 524 Horizontal pressure type None Uniform Classical Position Present LHS RHS DK Cancel Figure B 5 RING 1 5 backfill properties tab B 6 1 Unit weight In LimitState RING 3 2 a enter this value under Unit Weight B 6 2 Limiting fill barrel angle of friction This requires an angle of friction to have been set in the LimitState RING 3 2 a dialog see the section on B 6 4 for guidance on setting this value Let the required limiting backfill arch barrel angle of friction be 6 In LimitState RING 3 2 a click on Advanced and in the section Soil arch interface properties set the Friction multiplier on value to 9 4 Also set the Adhesion multiplier on c value to zero LimitState Ltd 182 APPENDIX B ADDITIONAL NOTES ON THE BACKFILL MODEL B 6 3 Load dispersion type In LimitState RING 3 2 a click on Advanced The settings in the section Live load dispersion details are directly equivalent to the RING 1 5 settings Note that cut o
17. Material masonry friction Ymmf 1 0 Table C 5 Default partial factors C 6 Track parameters Parameter Default Notes eiasnarepaen 500mm Conservative value less than stan p p 9 dard 600mm Sleeper breadth 250mm Standard see Network Rail 2006 Sleeper length transverse 2400mm Standard sleeper length Track weight incl sleep ers rails and ballast between 2 0kN m sleepers Table C 6 Default track properties LimitState Ltd 189 190 APPENDIX D STANDARD LOADING MODELS Appendix D Standard loading models D 1 Railway loading models D 1 1 UIC Description Loading Q yx 250kN 250kN 250kN 250 kN dx 80 kN m 80 kN m Load model 71 dle limitati 0 8 1 6 1 6 16 0 8 limitati UIC776 1R q 8 16m 16m 16m o ro imitation UIC702 distributed load components are not included in the LimitState RING database 22 5t 22 5t 22 5t 22 5t Load train D4 UIC700 Load train C3 UIC700 Load train E4 UIC700 25t 25t 25t 25t Load train E5 LE 1 8 4 75 1 8 1 5 UIC700 4 qui d 11 35 gt e distributed load components are not included in the LimitState RING database Table D 1 Standard UIC railway loading in LimitState RING LimitState Ltd APPENDIX D STANDARD LOADING MODELS 191 D 1 2 BD37 Description Loading 250 250 250 250 kN 80kN m 80kN m __NO io
18. Model sliding excluding inter ring sliding Standard friction coeff u 0 6 V Model inter ting sliding Inter ring friction coeff use 0 5 Figure 14 1 Material properties dialog box 14 1 Masonry 14 1 1 Specify properties for The Specify properties for drop down box on the Masonry tab allows the user to change the properties of different masonry features within the project 101 102 CHAPTER 14 MATERIAL PROPERTIES All masonry This is the default option and changes made here will affect the material properties of all ma sonry objects The tab for all masonry remains on show whichever option is chosen in the drop down This allows the user to get an overview of the project and make wholesale changes if this is required Spans vs piers abutments Selecting this option generates three further tabs in the properties box 1 All spans alterations made here affect all spans in the project 2 All piers alterations made here affect all piers in the project 3 All skewbacks alterations made here affect all skewbacks in the project All bridge parts Selecting this option generates tabs in the properties box which correspond to each individual part of the bridge In addition tabs for All masonry All spans All piers and All skewbacks are also generated so that the user can make changes to all similar features in the project without the need to alter each individual tab 14 1 2
19. Predicted LimitState RING failure mechanism of retro reinforced TRL Arch bridge LimitState Ltd Appendix H Comparison with previous versions H 1 Version history Table H 1 shows the various versions of ring which have existed since its original inception in 1992 Version Operating Release Publicly system year available comments Original research version programmed in BASIC RING DOS 1992 No Output published in papers appearing in the Struc tural Engineer Windows user interface added to original DOS ver sion program converted to Visual Basic Boussi RING10 Winga 1993 ne nesq distribution model multiple axle loads amp user defined arch profile capabilities added RING1 1 Win32 2001 Yes Backfill elements added Limit analysis kernel re programmed in C and RING1 5 Win32 2004 Yes linked to existing Visual Basic user interface More efficient solution of multi ring arch problems LimitState RING 2 0 2007 Yes Entire program re written from scratch in C Win32 Numerous features added Arch profile entry updated to include new types including interpolated spline fit Solver upgraded LimitState RING Win32 2011 Yes Improved user interface implemented Reinforce ment and moment force diagrams made avail able Table H 1 LimitState RING version history H 2 Comparison of results between versions As part of the validation process for LimitState RING
20. be realised This approach is also used in LimitState RING According to vertical retaining wall theory the horizontal passive restraining stress c applied to the back of a smooth wall is LimitState Ltd CHAPTER 5 THEORETICAL BASIS OF LIMITSTATE RING 47 Oh Kyo Kpce 5 1 Where Kp 1 tan 45 6 2 0 is the vertical stress Kpc 2 Kp and where is the effective angle of friction of the fill material and c is the cohesion of the fill material For a frictional backfill drained strength properties and c would be used In LimitState RING equation 5 1 is used in modified form Th MpKpOv Mpe K pee 5 2 where mp and my are modification factors designed to account for additional effects not repre sented by simple vertical retaining wall theory Determination of m Consider a wall which retains a frictional soil In the case of a vertical wall which rotates at failure full passive pressures will not be mobilised until rotations are very large Figure 5 8 a In practice a reduced earth pressure coefficient is often used to limit rotations to acceptable levels Figure 5 8 b If the wall is actually curved i e part of an arch then the coefficient can be assumed to be further reduced Figure 5 8 c a 1 0 Kp b Kp c Y Kp Figure 5 8 Commonly used horizontal earth pressure coefficients a large wall rotation b small wall rotation 0 5 c arch segment rotation into s
21. derside of the sleepers above the crown Effective width of bridge 3100mm Governed by the presence of longi tudinal cracks in arch barrel Intrados shape Segmental First approximation in the absence of a comprehensive dimensional survey Number of units per ring 23 Actual number of voussoirs Number of rings Single ring of voussoirs Table E 1 Bridge geometry Parameter Value Notes Depth of ballast below sleeper 300mm Estimated value Sleeper breadth 250mm Typical value timber sleeper Sleeper length 2400mm Typical value timber sleeper Table E 2 Track geometry Parameter Value Notes Unit weight masonry 26 kN m Estimated value limestone Coefficient of friction radial 0 6 Estimated value Crushing strength 20 N mm a es POKS Unit weight backfill 18 kN m Estimated value Angle of friction backfill 300 Default value Cohesion backfill 0 kN m Default value Unit weight ballast 18 kN m Estimated value Track weight incl sleepers rails 2 ASSUMING Z AIKA IGNO taren 2 40kN m from NR GN CIV 025 assuming and ballast between sleepers BH rail and timber sleepers Table E 3 Material properties characteristic values LimitState Ltd 208 APPENDIX E WORKED EXAMPLES GENERAL Parameter Value Notes Distributed part of this load model LM71 no Load model name udi can be ignored for this sho
22. that computed if the outer spans are omitted from the analysis indicating that the presence of stocky piers and backing in this case is no guarantee that the structure can be safely idealized as a series of separate single spans In general users should avoid using such rules of thumb and should where possible model as much of the structure as is practicable refer to Section 7 4 for further advice on modelling multi span bridges 5 5 Use of reinforcement The key assumptions made when modelling bridges containing reinforcement using Limit State RING are as follows e The masonry or concrete arch and the reinforcement are assumed to behave in a rigid plastic manner This means that at a failing contact the reinforcement is assumed to yield at the specified force if it is located away from the neutral axis This idealization means that the software is likely to be most suitable when sections are lightly reinforced using ductile steel bars e Shear failures in reinforced sections can be modelled by specifying a limiting shear force e Anchorage failure of the reinforcement is not considered For details on how to specify reinforcement in a bridge model see Chapter 17 LimitState Ltd CHAPTER 5 THEORETICAL BASIS OF LIMITSTATE RING a single span 4 hinges paced sane HT an Tree TS s Pr TR ere nt SZ Q hh st sane nase Sans OS c single span hinges amp
23. would be 1 54 1 54 100 154kN When the applied load comprises a series of axle loads the adequacy factor is the multiplier which when applied to all axle loads simultaneously leads to collapse For example if a 1400kN rail vehicle comprises four 200KN axles and four 150kN axles and LimitState RING indicates a computed adequacy factor of 3 this means that the loading at failure comprises four 600kN axles and four 450kN axles 8x 200 600KN 3x 150 450kN Full details of the mathematical formulation are provided in Appendix A 1 5 3 2 Bridge behaviour when subjected to support movements Although the usual standard analysis mode goal of a LimitState RING analysis is to identify the adequacy factor LimitState RING can also be used to model the effects of support move ments Movement of a support will lead to formation of hinges and or sliding failures in the same way as when excessive applied loading is applied by a highway or railway vehicle When in support movement analysis mode vehicle loads if present can be pre factored by the user and the critical arrangement of hinges and or sliding failure planes are identified by finding the energy associated by moving the supports The line zone of thrust is also identified Figure 5 3 shows the result of a support movement analysis Full details of the mathematical formulation are provided in Appendix A 2 The adequacy factor may need to be commensurately greater th
24. 0 35m gr 5 D eo 3 E Critical of 2 1 2m r amp or gt 5 0m a or 9 9 0m O Note Overall vehicle width overall track width Figure D 2 BD86 SV100 loading vehicle all permutations included in LimitState RING vehicle database LimitState Ltd APPENDIX D STANDARD LOADING MODELS 203 SV150 146 146 146 146 146 146 146 146 146 146 kN kN kN kN kN kN kN kN kN kN ren 1 2m 1 2m 1 2m 12m 2m ram an 2 Critical of 3 1 2m or s 5 0m T or g 9 0m fe Note Overall vehicle width overall track width Figure D 3 BD86 SV150 loading vehicle all permutations included in LimitState RING vehicle database SV Train SV196 Trailer Tractor 146 146 146 146 146 146 146 146 146 146 180 180 100 N kN kN ki kN kN kN kN kN kN kN kN kN kN 1 2m 1 2m 1 2m 1 2m 1 2m fim 1 2m ram fion 4 4m 4 0m Direction of Travel gt gt 4 0 35m sf at a Critical of 3 E 1 2m z5 or 5 gt 5 0m a or 9 0m fe Note Overall vehicle width overall track width Figure D 4 BD86 SVTrain SV 196 loading vehicle all permutations included in Limit State RING vehicle database SVTT 150 200 200 250 250 kN kN kN kN kN 4 0m 1 5m 8 0m 1 5m lt __ Direction of Travel 0 5m 2 5m Overall Vehicle Width 3 7 pa 0 5m
25. 1 1 25 1 5 Net closing rotation of barrel Figure B 3 Mean horizontal backfill pressure vs net closing barrel rotation of arch barrels A special version of LimitState RING was developed to enable gross displacement analyses to be performed with the experimentally observed build up in pressures back substituted into the analysis The trend shown in Figure B 4 was obtained LimitState Ltd 180 APPENDIX B ADDITIONAL NOTES ON THE BACKFILL MODEL bridge no 3 3 Load kN Gross displacement mechanism solution 10 15 Displacement mm Figure B 4 Experimental and predicted load vs displacement response of single span bridges Thus Figure B 4 indicates that the standard mechanism solution which does not take gross structural movements into account is in error by less than 15 Had the build up in backfill pressures been more gradual then the error would have been greater Nevertheless given the numerous other uncertainties which exist when modelling masonry arch bridges such errors may well be considered acceptable B 5 Unusual failure mechanisms Most bridges tested in the laboratory to date have failed in 4 hinge failure mechanisms and as indicated previously taking m t where the resultant coefficient of lateral earth pressure is calculated as m K permits generally good predictions of carrying capacity to be obtained However it is currently unclear as to whether taking mp i is applicable in all
26. 4 and then saved as a Text Tab Delimited txt file prior to being read in by LimitState RING LimitState Ltd 116 CHAPTER 15 LOADING PJ A B Cc D E 1 1 2 Vehicle 3 3x 7Tonne Triple Axle 1 3m Axle Spacing 4 Axles 5 3 6 Force Position Width loadedLength dynamicFactor 7 68 67 O 1800 300 FALSE 8 68 67 1300 1800 300 FALSE 9 68 67 2600 1800 300 FALSE Figure 15 4 Defining a new vehicle using a spreadsheet 15 2 3 Defining a new vehicle within LimitState RING To define a completely new vehicle within the software click on the Add vehicle button and enter the name of the vehicle to be added Details of the vehicle can then be added to the Vehicle Database as shown in Figure 15 5 Note that if defining a vehicle in this way the Dynamic axle factor is specified in the Loading dialog and not within the Vehicle Database itself Vehicle Database Vehide library Vehides marked with a contain reversed axles amp Construction and Use amp Restricted Construction and Use European Union El BD21 Annex A AW Schedule 3 11 5 Tonne Single Axle 2x 8 Tonne Double Axle im Axle Spacing E 2x 9 Tonne Double Axle 1 3m Axle Spacing 2x 9 5 Tonne Double Axle 1 3m Axle Spacing E Double Axle 11 5 Tonne Driving 1 3m Axle Sp Double Axle 10 5 Tonne Driving 1 3m Axle Sp Es 2x 10 Tonne Double Axle 1 8m Axle Spacing Es 3x 7 Tonne Triple Axle 1 3m Axle Spac
27. 4x200kN 4x1 50kN 4x200kN 4x150kN 2x250kN 65kNIm SHORT LENGTHS Type RA1 Load 20 BSU CEH EE he 1 524 1 524 1 524 2 743 1 829 1 829 1 829 3 962 1 524 1 524 1 524 1 829 1 829 1 829 1 524 2 438 No UDL RA10 2 743 distributed load components are not included in the LimitState RING database Type RA1 Short Lengths See above 20 BSU No UDL RA10 2x250kN 2x250kN Assessment Load Wagon Table D 4 Standard Network Rail railway loading in LimitState RING LimitState Ltd APPENDIX D STANDARD LOADING MODELS 193 D 1 4 Indian Railways 1987 A Description Loading LOCO LOCO AXLE LOADS K o o e e e e TRAINLOAD amp 8 S 8 as a S SN TRANLOAD i i Of80 9kNim TI TT DJ J Of80 9kN m Indian Railways E SUM 4 y y 8 25 Um Modified Broad AXLE fsqotesolieso 6400 _lisso sol 3000 Hhesoliesol_ 6400 165016501500 Gauge Loading sons 16000 16000 distributed load components are not included in the LimitState RING database 1 LOCO AXLE LOADS n n N a no LS E TONNES 222 TRAIN LOAD S 6 ES Of 80 9 kN m rae ee A y Indian Railways 8 25 Um eo ee E AXLE Modified Broad SPACING 70 20501950 5560 1 19500 IN mm Gauge Loading 1987 B o a y 25 0 245 2 N A N N wo wo wo wo x Y A AAA a SA wo l a wo Te S aaa 050 5940 20501950 LOCO 5560 19500 distributed load c
28. 68 67 CU H1 38 Tonne 5 Axle Articulated 57 49 2 45 58 86 1 35 103 01 5 28 76 71 1 02 76 71 CU H1 38 Tonne 5 Axle Articulated 57 49 2 45 103 01 1 35 58 86 5 28 76 71 1 02 76 71 Table D 6 Construction and use Key W1 W2 etc axle weights kN A1 A2 etc axle spacings m axle weights reversed LimitState Ltd APPENDIX D STANDARD LOADING MODELS 195 D 2 2 Restricted construction and use AXLE WEIGHTS AND SPACING VEHICLE Wi Al W2 A2 W3 KN m KN m KN RA 39 83 2 18 79 76 1 02 79 76 20 Tonne 3 Axle Rigid i RB 24 Tonne 3 Axle Rigid 59 84 3 70 89 66 1 20 89 66 RC 24 Tonne 3 Axle Rigid 59 84 3 60 99 67 1 40 79 76 RC 24 Tonne 3 Axle Rigid 59 84 3 60 79 76 1 40 99 67 RD 24 Tonne 3 Axle Rigid 62 69 3 60 103 01 1 40 73 58 RD 62 69 3 60 73 58 1 40 103 01 24 Tonne 3 Axle Rigid i RE 17 Tonne 2 Axle Rigid pasa eee ae RF 7 5 Tonne 2 Axle Rigid 886 ee Wa RG 20 Tonne 3 Axle Rigid 20 60 200 8 89 Overhang Overhang w1 W2 W3 Table D 7 Restricted Construction and Use load vehicles Key W1 W2 etc axle weights KN A1 A2 etc axle spacings m axle weights reversed LimitState Ltd 196 APPENDIX D STANDARD LOADING MODELS D 2 3 European Union vehicles
29. English Language version is being used sections of the LimitState RING window referred to as right and left should be reversed where appropriate 20 1 2 Scrollbars Vertical and horizontal scrollbars allow the display area to be shifted in the vertical and horizon tal sense respectively 20 1 3 Current mouse position The coordinates of the mouse are shown in the bottom right hand corner of the screen This may be useful for determining the global position of various parts of a bridge the datum for all bridges is the left hand springing of span 1 20 1 4 Scrolling wheels Most mice are equipped with a third button that is used for scrolling LimitState RING makes use of this additional feature by allowing the user to pan and zoom the display e To pan simply press and hold the third button whilst in the display window Moving the mouse will now pan the image around the screen 139 140 CHAPTER 20 DISPLAY OPTIONS e To zoom simply roll the wheel up to zoom out and down to zoom in The pan and zoom functions are also accessible via the Table 20 8 20 2 Viewer pane In order to better visualize the model and post analysis failure mechanism it is possible to manipulate the view in a number of ways 20 2 1 Rotating the model The rotate tool The rotate tool allows the user to quickly and easily manipulate the scene in the viewer pane by providing handles to rotate around the major cartesian axes and also freely in 3D
30. In this case the maximum computed adequacy factor approximately corresponds to the segmental arch shape and it is evident that quite significant reductions in adequacy factor are observed as the shape deviates from this span and crown rise fixed but critical load position allowed to vary Indeed it can be considered just as important to accurately record the arch shape and thickness as it would for example to accurately measure the overall depth flange thickness etc of a steel l beam prior to assessing its ability to span a given distance LimitState Ltd CHAPTER 7 DETAILED BRIDGE ASSESSMENTS USING LIMITSTATE RING 55 o o o N 00 o 1 1 Load factor normalised o D 9 a 0 6 0 7 0 8 0 9 1 quarter span crown rise Figure 7 1 Influence of varying 1 4 and 3 4 point rises as ratio of midspan rise It is also important to note that if the arch shape is asymmetrical i e if the quarter and three quarter point rises differ then carrying capacity can be significantly reduced 7 3 Skew bridges Since LimitState RING is 2D analysis software it is most suitable for the analysis of bridges which span squarely between abutments Skew bridges tested in the laboratory Melbourne amp Hodgson 1995 have exhibited distinct 3D failure modes which cannot be replicated using a 2D analysis tool However given the comparative computational expense and lack of availability of mainstream 3D analysis tools
31. Pane This pane displays the current problem geometry It provides access to user editable geometry objects Properties may be edited using the mouse or keyboard or both depending on their nature Specific geometry objects e g Contacts or Solids may be selected by left clicking with the mouse The properties of the objects are then displayed in the Property Editor Section 11 6 Right clicking the mouse in the Viewer Pane brings up the viewer context menu From here amongst other options it is possible to modify the way in which objects are selected manipulate the image e g pan zoom or rotate in 3D space Exit a Select a Pan E Rotate gt wo Zoom gt View b Render Save Image Figure 11 3 The Viewer Pane context menu LimitState Ltd 86 CHAPTER 11 THE GRAPHICAL INTERFACE 11 6 Property Editor The Property Editor provides core access to problem parameters in a direct and intuitive way In general the properties of any material or geometry object may be displayed simply by selecting it in the an Explorer or the Viewer pane In addition global project level parameters may be displayed at any time by left clicking on an empty part of the Viewer pane with the mouse The Property Editor is shown in Figure 11 4 Single clicking on any item in the Property column of the Property Editor gives an expanded explanation of the parameter in the window at the base of the Property Editor A El symbol next to a
32. TA Hem ios eek Be kd AA AA A 88 12 Project details 89 12 1 Reguired details 2 4244 4 die SRS ae de SARA NUE SERRE GRR 89 21 1 Bdge ype 5 6 OA SEAGRASS AA SS ADS EARS 90 12 1 2 Effective bridge width eee ee ee tee eee up eee 90 121 3 Model reinforcement oo mosca mu ee ee 91 12 2 Optional details bee i e so ha tee has Pise II 91 13 Bridge geometry 93 13 1 Geometry dialog oc eta tee eee h net aan arte 93 13 2 ADUIMEMS o so sisp ca ee ewe ee a dis ee eas 94 13 2 1 Default abutment model 94 13 2 2 Modelling abutments explicitly 94 199 SPANS oriana 52 SNS II 95 13 3 1 Number of rings lt td puis Here n po 95 1332 ARIS sea ss a e A E a E 95 13 3 3 Number O Units s e od A Ge de a Pe 96 1334 Ring USERS s L 2 ju dus don re ponte m a des de do 96 1335 inserting aspan sok Lis oea BS AA a BOs 97 1336 Deleting SHANE escrit 97 ISA PIES lt q oo eo a a e eA a a ew ad Y 97 LimitState Ltd 8 CONTENTS 13 4 1 Default pier model 98 13 4 2 Modelling piers explicitly lt lt lt 98 AS EMS Ds a ee NN ae A Ru MD eme ee BO a 98 14 Material properties 101 Wed PASON A A IN eee ee Be SR 101 14 1 1 Specify properties for ua ce date ei du 4 eben a Rd da vs 101 ALE Unitweight lt oe SS eS E A ES Ant 102 14 1 3 Model TUS ge ur ee a Se ee Peak Pee ee 102 14 1 4 Sliding pr
33. Unit weight Here it is possible to specify the unit weight in kN m3 of the masonry features under consid eration 14 1 3 Model crushing By default crushing is modelled with the default crushing strength taken as 5 N mm To model the blocks as being rigid uncheck the Model crushing option and enter a compressive strength for the material under consideration Note 1 When crushing strength is included in the analysis the problem becomes non linear and several iterations will normally be required before a converged solution is obtained This means that the computational effort required to obtain a solution is increased Limit State RING uses a highly robust solution scheme obviating the need to specify conver gence tolerance etc required with LimitState RING 1 x LimitState Ltd CHAPTER 14 MATERIAL PROPERTIES 103 2 In LimitState RING a moment vs normal force failure envelope which assumes ductile response of the masonry is assumed it is assumed that a given hinge in the failure mechanism forms at the edge of a rectangular stress block 3 If crushing strength is included in the analysis LimitState RING will find a solution though see note below even if the structure had been found to be geometrically locked when crushing strength was assumed infinite unlike LimitState RING 1 x which will provide no solution in such circumstances 4 When very low crushing strengths are specified it may be impossible
34. a library on the left 2 Select the vehicle to be used from the library tree and click the Import button to move it across into the Project vehicles section 3 After all the required vehicle types have been imported click OK to return to the Load Case dialog 4 Use the drop down menus to select the required vehicle for the current load case 5 Specify the position of the vehicle whether it is mirrored and if appropriate assign axles to be subject to the dynamic partial factor of safety 4 1 7 Step 6 Choose mode of operation At this point in the Wizard the user should decide upon the way in which they will use Limit State RING Drag and solve If the user wishes to better understand the behaviour of their model it is recommended that the Drag and solve see Section 21 1 mode is used To do this 1 Complete the Wizard by clicking Finish 2 Move the loading vehicle to the required position 3 Click the Solve button a LimitState Ltd 28 CHAPTER 4 QUICK START TUTORIAL If the user finds that they use this method for the majority of their problems the Auto solve feature can be enabled This will cause LimitState RING to automatically solve each time the vehicle is moved To enable this feature check the Solve automatically box in the Prefer ences dialog located in the Tools menu Multiple load cases Alternately a vehicle can be moved incrementally across a bridge by setting up a ser
35. all spans between king piers should be modelled e full scale laboratory tests indicate that significant backfill pressures can be mobilised above the piers between adjacent spans enhancing carrying capacity Melbourne et al 1997 e alternatively backing or internal spandrels are often present between spans and this can play an important role in propping apart adjacent spans e insome cases the presence of strong fill or backing above a pier may mean that adjacent spans can interact in the failure mechanism without movement of the intermediate pier e g see Figure 5 4 f e in cases where intermediate piers are very slender the user should consider separately performing other local checks e g that elastic instability will not limit the vertical load that can be applied no such check is currently done by LimitState RING 7 5 End abutment blocks Abutment blocks at the ends of a bridge can be included in the model However soil pressures are not applied behind end abutment blocks Hence if end abutments are used to model soil backed abutments there is the potential for the resulting failure mode and adequacy factor to be unrealistic e g the skewback may be observed to slide when only a small load is applied to the bridge whereas in reality such movement would be restrained by soil In LimitState RING distributed load which falls beyond an end abutment is assumed to be lost in the same way as distributed load whic
36. allows dynamic axle loading to be specified on a per load case basis When used in an analysis this axle will then be multiplied by whatever Dynamic partial factor is set in the Partial Factors Dialog see Section 16 15 4 Defining new load cases 15 4 1 Adding load cases To add further load cases click on Add Load Case s to obtain the dialog shown in Figure 15 8 LimitState Ltd CHAPTER 15 LOADING 119 Edit Bridge Load Cases Name Load Case 1 m 10f 1 Vehide 1 11 5 Tonne Single Ade 2 2x 8 Tonne Double Axle 1m Axle Spacing 3 3x 7 Tonne Triple Axle 1 3m Axle Spacing fonne Triple Axle 1 4m Axle Spacing i Not applied Delete All Cases Except Current Add Load Case s Vehicle Database Cox Figure 15 8 Adding a new load case Copy an existing load case In most situations it is easiest to create one or more new load cases by incrementing the positions of an existing load case In this case you should choose to Copy an existing load case You may now enter the existing load case number the total number of copies to be made and the spacing offset between each of the new load cases to be generated Creating an empty load case A single new load case can be set up manually by clicking Create an empty load case in the Add new load case s dialog This can then be edited as normal 15 4 2 Deleting a load case Deleting a single case In the Name dropdown menu
37. and Figure 8 3c To address this a maximum cutoff value can be specified When this is set the effective width will be equal to the lesser of the automatically calculated value and the specified cutoff value Refer to Section 12 1 2 for details on how to set the bridge width In addition the vertical effects of nosing and centrifugal action may mean that one rail is more heavily loaded than the other This may mean that a concentrated wheel loading becomes the critical case and hence that a reduced effective width should be selected Users are referred to Section 8 1 6 for further guidance 8 1 5 Dynamic effects Underline bridges must be capable of carrying a given live train load at a given train speed Train speed is important because certain dynamic effects are speed dependent e g due to the effects of track irregularities excitation of the bridge by the rail vehicle etc Thus a so called dynamic factor is applied to constituent loads in a load model However most railway administrations stipulate that the dynamic factor is applied to all loads simultaneously Since the pattern of loading remains unchanged this means that dynamic effects can be considered after a LimitState RING analysis has been completed In cases when different dynamic factors are applied to different axles then clearly the pattern of loading changes This therefore needs to be taken account of in a LimitState RING analysis lt is the responsibility of t
38. cases Limit State RING chooses the critical failure mechanism from a multitude of possible ones and a 4 hinge failure mechanism is by no means always identified as being critical For example Figure 5 4 b shows an alternative failure mode encountered when recently as sessing a short span bridge Here the predicted failure mode involves sliding failures at three joints and translation rather than rotation of a section of arch into the fill However the magni tudes of the passive restraining pressures applied correspond to those mobilized in a 4 hinge mechanism In reality the sliding failure mode predicted would be likely to more rapidly mobilize significant passive zone soil pressures Thus the LimitState RING strength prediction using my 3 may be quite conservative LimitState Ltd APPENDIX B ADDITIONAL NOTES ON THE BACKFILL MODEL 181 In the future it is expected that this issue will be resolved by moving away from the current indirect modelling strategy for the soil towards instead modelling the soil explicitly i e using solid elements to represent the soil material B 6 Backfill Backwards compatibility with RING 1 5 The import facility in LimitState RING will automatically convert RING 1 5 backfill settings to the correct equivalent values so that identical pressure distributions are modelled in Limit State RING 3 2 a The LimitState RING 3 2 a model provides additional capabilities above those provided in RING 1 5
39. cohesion c in kN m of the backfill material LimitState Ltd CHAPTER 14 MATERIAL PROPERTIES 105 Note These soil properties are used by the selected backfill numerical model In the current version of LimitState RING the standard model is provided which is backwards compatible with RING 1 5 and provides good correlation with published experimental data There is a small difference between how RING 1 5 and LimitState RING 3 2 a models Boussinesq load spreading which may have a minor effect on collapse load calculations for a small subset of loading scenarios The import facility in LimitState RING will automatically convert RING 1 5 backfill settings to the correct equivalent values so that identical pressure distributions are modelled in LimitState RING 3 2 a Further details of this process are given in Appendix B 6 14 2 2 Soil Effects Model dispersion of live load Check this box to specify that the backfill model should include dispersion of the live load When unchecked loading on the bridge structure will occur over a longitudinal distance equal to that at the base of the surface layer Where the effective bridge width is set to Auto compute see Section 12 1 2 dispersion through the backfill in the transverse direction is controlled via the Effective bridge width parameters dialog Model horizontal passive pressures Check this box to specify that the backfill model should include modelling of the passive
40. constraints yield constraints and an objective function A 5 1 Equilibrium constraints Consider the equilibrium of block A a shown in Figure A 5 LimitState Ltd APPENDIX A MATHEMATICAL FORMULATION 171 1 1xA KT Si ma N Figure A 5 Block A forces and geometry for formulating equilibrium constraints Resolving forces in the X direction 1 s2 sin 30 n cos 30 0 A 9 8 V3 51 a ns 0 A 10 Resolving forces in the Y direction n s2 cos 30 ngsin30 A 1 0 A 11 3 mt 8 414120 A 12 Taking moments about the block centroid 58 X Y N X TZ M1 s2 X y No X x Mo 0 A 13 lt 4 6625 2 674n mi 4 66289 2 674n2 ma 0 A 14 Clearly similar relationships can readily be derived for blocks B and C in the case of the mo ment equilibrium constraint it is only necessary to change the subscripted numerals LimitState Ltd 172 APPENDIX A MATHEMATICAL FORMULATION A 5 2 Yield constraints Consider the no tension constraints for contact 1 These can be obtained simply by entering the actual arch thickness 1 5 in equation A 3 and re arranging to ensure problem variables are on the left hand side m lt 1 5 0 5n1 A 15 lt 1 5 0 5n1 m1 lt 0 A 16 my gt 1 5 0 5n1 A 17 1 5 0 5n1 m1 lt 0 A 18 Consider the sliding constraints for contact 1 These can be obtained simply by entering the actua
41. ee ede PO eee eee 1 4 AGOULLINUTSING cc cnt amp Se Sh dS HEE EER EEE SSSR ESE Te Using Re LUE pk ie Rae Rie a Hee Duo tdi eck ee 16 SIENTES lt srta Se ek de ds ee Ae 1 7 Progam IIMS ne eee hs ser sed SAS SEE tree ses 1 8 Contact details ce Le Liu Duel owed lu sise sut ESA O Sn a 4 o de 1 8 2 Software SUBNET 84 db 8e EERE ESA dde SEED Et Pe 2 ei sua LEARN moe a opn e TOI F e i 2 What s new in LimitState RING 2 1 More flexible arch profile definition 2 2 Moment normal and shear force diagrams 2 3 Upgraded solver engine 2k es ee ge da eri ea a 2 4 Reinforced MASON lt lt sreca an de don db we we A e a 2 5 Expanded vehicle database 2 6 Enhanced user interface cios ao as etes dose we de A 3 Getting started 3 1 Installation amp licensing lt p 4 408 den pes me bat ae G 3 2 Starting LimitState RING 44 2 6054 2506 2 2A a EGS 4 Quick Start Tutorial 4 1 Using the New bridge wizard n ue due Ra dipl Ra 4 1 1 Introduction to the wizard aoaaa ed 4 1 2 Step 1 General project settings As o su nie needed en Ur OR ORES HERS 4 1 4 Step 3 Partial Factors sais ss fiehes vs bare lame ds SS 4 1 5 Step 4 Materials 4 1 6 Step 5 Add Venice e446 de dw Vi whe Ae CRs ss 4 1 7 Step 6 Choose mode of operation
42. end of the bar To show the hidden icons simply click the arrows with the left mouse button 11 10 Detaching a menu For convenience the menus of the LimitState RING interface can be detached from the main window using the tear off functionality To do this hover the mouse over the dashed tear off line at the top of a menu and click with the left mouse button The menu will then become detached into a separate window The functions of the new menu window can be used as normal and it will remain on top of the main program interface whilst still allowing interaction with it To close the window click the x button in the top right corner 11 11 Calculator The calculator is used to facilitate entry of data into the Property Editor If the mouse is clicked on any Property Editor numeric data entry cell the calculator button E appears in the right hand end of the cell Click on this to display the calculator The calculator see Figure 11 5 has all the normal functionality of a standard calculator and the value that appears in the the results window of the calculator automatically appears in the data entry cell unless it is a locked or read only cell There is no need to copy and paste to the cell in question Calculator Monitor Target Effective bridge width Expression 2500 O Radians Degrees amia Figure 11 5 The calculator window LimitState Ltd Chapter 12 P
43. failure envelope where required is used A 3 1 Algorithm 1 For each contact i initially add three linear constraints i e OA OB amp AB in Figure A 2 2 Obtain a solution to the global LP problem 3 For each contact i substitute n from the last solution into the inequality constraints in equation A 8 If a constraint is violated calculate the violation factor k i e m ki 1 05 2 LimitState Ltd 168 APPENDIX A MATHEMATICAL FORMULATION 4 For each contact with k gt 1 0 i e violation add an additional linear constraint e g in the case of point X in Figure A 2 introduce a new linear constraint tangential to the true non linear constraint at X 5 Repeat from step 2 until the maximum value of k lt 1 tol where tol is taken as a suitably small value A 4 Including reinforcement LimitState RING uses rigorous optimization techniques to find the distribution of internal forces which give rise to the largest possible load factor which can be applied whilst still satisfying equilibrium and yield constraints When reinforcement is involved consider a contact between adjacent rigid blocks In order to model a rectangular crush block of initially unknown depth see Figure A 3 the failure criterion given in Appendix A 3 can still be used providing the normal force neont and moment Meont values used account only for the effects of contact pressures i e which exclude the effects of any rei
44. fition 60 8 unit weight ga ene sa 264 442 82 span 5 1 Omsingle 4709a 1178 1915 111 span 5m single span o 5 2 debonded 500 253 400 80 arch rings Mal aminple op 202 320 100 2 span a The experimental collapse load of this bridge was reduced by the sudden onset of partial ring separation Table G 1 Sample comparison between Bolton laboratory and LimitState RING collapse loads Table G 1 presents LimitState RING analysis results alongside experimental test results from Bolton Institute representative bridges with detached spandrel walls are included since these behave demonstrably in a two dimensional manner To obtain the LimitState RING results measured geometrical and unit weight properties were used together with a measured angle of friction of the soil backfill of 60 The backfill was purely frictional so zero cohesion was specified The computed failure load was found to be relatively insensitive to crushing strength so a value of 20N mm was used in all cases experimentally recorded values for the brickwork used to construct the bridges ranged from 18 1 to 28 2N mm Itis clear from Table G 1 that predictions are quite conservative when the default soil angle of friction is used column A but become much more realistic when the measured value is used column B It should be noted that the over prediction of the strength of bridge 5 1 results from the sudden onset of partial ring se
45. forcement therefore both top and bottom reinforcement are in full tension at failure The beam properties are in Table F 1 Property Value Block size 250mm x 1000mm bridge width Beam span 5000mm 100mm block width 4900mm Applied force 1kN span 2 Top reinforcement 100kN 50mm from top surface Bottom reinforcement 100kN 50mm from bottom surface Concrete crushing strength 5 x 107 kN mm Table F 1 Reinforced beam worked example Case 1 properties 2450mm Reinforcement bars 50mm from top and bottom faces oO OO 4900mm Figure F 1 Reinforced beam dimensions Case 1 217 218 APPENDIX F WORKED EXAMPLES REINFORCEMENT Applied moment Applied Moment Applied force x Span _ 1x4900 1225kNmm Initial assumed concrete force Concrete force 2 x 100 200kN Concrete crushing depth Concrete crushing depth Concrete force Bridge width Concrete crushing strength Concrete crushing depth 200 1000 5 x 107 40mm Hence the assumption that both the top and bottom reinforcement steel are in full tension is correct Moment capacity 1000mm Figure F 2 Reinforced beam stress block Case 1 Taking moments about centre of compression block depth 20mm Moment capacity 30 x 100 180 x 100 21000kNmm Adequacy factor AF Moment capacity Applied moment 21000 1225 17 1429 LimitState RING calculated adequacy factor AF
46. if a line of thrust satisfies the equilibrium and mechanism conditions then the plastic collapse load cannot be higher than the applied load i e it is an upper bound It is possible to perform limit analysis by hand For example an upper bound hand analysis could be carried out by 1 choosing a likely mechanism of collapse 2 using equilibrium or a work method to calculate the collapse load 3 trying other likely collapse mechanisms until the critical one is found However even in the case of a single span single ring arch the curved geometry makes such a hand based procedure extremely laborious and liable to human error LimitState RING effectively automates this process However rather than adopting a trial and error procedure to find the mechanism associated with the absolute minimum collapse load LimitState RING uses rigorous mathematical optimisation techniques to quickly and accurately determine the correct solution refer to Appendix A 1 for details of the mathematical problem formulation Furthermore whilst the above discussion has implied that masonry possesses infinite com pressive strength this is clearly not the case in reality In fact the presence of finite strength masonry means that the line of thrust mentioned previously is better thought of as a zone of thrust which should have sufficient thickness at any point to carry the compressive force with the required thickness depending on the crushing strength
47. mirror a vehicle when setting up the load cases To do this simply select true in the Mirror dropdown box of the Loading Dialog If there are multiple load cases in the problem a secondary dialog will appear asking whether you wish to change the mirror property for all cases or just the one in question 113 114 CHAPTER 15 LOADING 15 2 Adding a vehicle to the project In order to add loading to a bridge vehicles must be either 1 Imported into the project from the existing database 2 Imported from file 3 Newly defined using LimitState RING In all of these cases the Vehicle Database button must be clicked to obtain the Vehicle Database Dialog shown in Figure 15 2 Vehicle Database Vehide library Vehicles marked with a contain reversed axles Construction and Use Et Restricted Construction and Use G European Union El BD21 Annex A AW Schedule 3 11 5 Tonne Single Axle 2x 8 Tonne Double Axle 1m Axle Spacing 2x 9 Tonne Double Axle 1 3m Axle Spacing 2x 9 5 Tonne Double Axle 1 3m Axle Spacing Double Axle 11 5 Tonne Driving 1 3m Axle Sp Double Axle 10 5 Tonne Driving 1 3m Axle Sp 2x 10 Tonne Double Axle 1 8m Axle Spacing 3x 7 Tonne Triple Axle 1 3m Axle Spacing 3x 8 Tonne Triple Axle 1 4m Axle Spacing El BD21 Annex D 32 Tonne 4 Axle Rigid A amp E E w 40 Tonne 5 Axle 3 2 Artic 40 Tonne 5 Axle 3 2 Artic 10 5 Tonne Drive
48. of the user to determine the length of distributed loading which proves to be most onerous 2 the distributed loading part of a model can be introduced by adding an appropriate number of extra axles 8 1 2 Distribution of rail loads through the track In LimitState RING it is assumed that a sleeper is always located under an axle load Half of the load is then distributed to the adjacent sleepers such that the loading follows a 25 50 25 pattern The specified sleeper spacing governs the location of the adjacent axles e g see Figure 8 1 65 66 CHAPTER 8 LOADING MODELS Fy F2 Axle spacing 2 J EN F FES no EE 2 i Fate LH t 0 25F 0 5F 0 25F 0 25F2 0 5F2 0 25F2 Sleeper Sleeper Sleeper Sleeper Spacing spacing spacing spacing Figure 8 1 Dispersal of twin axle loads through track 8 1 3 Longitudinal distribution of load through ballast and fill After distributing the rail loads through the track LimitState RING computes the live load pres sure at the underside of the sleepers By then assuming a simple uniform distribution model this is then spread through the ballast default spread 15 approx corresponding to 4 1 ver tical horizontal as per UIC 774 2R International Union of Railways 1994 Live load is then spread through the fill according to a user specified model uniform or modified Boussinesq distribution refer to Section 5 8 2 Figure 8 2 shows a graphical view of how the loading from a single
49. of a vehicle In this case the pattern of loading changes This needs to be taken account of in a LimitState RING analysis t is the responsibility of the user to apply the dynamic impact factor to axles in turn to determine which loading pattern is most onerous Note that to have any effect the dynamic partial factor in LimitState RING must also be set to an appropriate value by default it is set at unity 8 2 4 Other effects Centrifugal forces On a curved road the vertical effects of centrifugal actions can lead to one wheel being more heavily loaded than the other This action is speed dependent When one wheel is more heavily loaded than the other it is usually considered prudent to consider the single wheel load case separately to determine whether or not it is critical In LimitState RING this requires the use of a suitably reduced effective width see Section 8 2 2 However since the pattern of loading is unaffected then this special load case can if necessary be considered retrospectively i e after an analysis has been performed by modifying the adequacy factor to account for the use of a different effective width and live load intensity Traction braking forces LimitState RING does not apply horizontal forces at road level e g to model traction braking forces However it is possible to apply user specified horizontal forces as pressures directly to blocks within arches and or piers see Section 19 1 2 Axle lift off
50. of some assessment codes Note however that the Boussinesq option is likely to provide a more realistic represen tation of the actual distribution of fill pressures as has been indicated by numerical and experimental studies LimitState Ltd CHAPTER 14 MATERIAL PROPERTIES 107 14 3 2 Soil arch interface properties Friction multiplier on y Specify the multiplier on the soil angle of friction that gives the soil arch interface angle of friction Adhesion multiplier on c Specify the multiplier on the soil cohesion c that gives the soil arch interface adhesion a This multiplier will depend on the nature of the arch extrados masonry Note 1 The friction multiplier on will depend on the nature of the arch extrados masonry How ever in many geotechnical codes for retaining walls 6 is a function of the critical state angle of shearing resistance which will not necessarily be the value of entered for the backfill 2 In the LimitState RING standard backfill model the soil arch interface properties are used to calculate an upper limit on the magnitude of the horizontal backfill pressures that can be applied to a given masonry block without causing the strip of backfill on the block to slide The specified interface properties are only used for the above purpose and are not used to calculate frictional energy dissipation at the backfill arch barrel interface e g for use in the work equation 3 The c
51. of the Loading dialog select the load case to be deleted e g Load Case 1 shown in Figure 15 9 and then click the Delete Current Case button CET SE Vehicle Database Lx Figure 15 9 Deleting a single load case Note There must always be one load case in the analysis LimitState Ltd 120 CHAPTER 15 LOADING Deleting all but one case In the Name dropdown menu of the Loading dialog select the load case to be retained e g Load Case 3 shown in Figure 15 10 and then click the Delete All Cases Except Current button All of the cases except that which is selected will then be removed from the problem Delete Current Case a Delete All Cases Except Current D Add Load Case s Vehicle Database Figure 15 10 Deleting all but the current load case Note There must always be one load case in the analysis 15 5 Moving vehicles across a bridge A common goal when using LimitState RING is to identify the critical position of a loading vehicle on a bridge i e that position that results in the lowest adequacy factor To achieve this the user can follow one of two methods 15 5 1 Method 1 Multiple load cases A vehicle can be moved incrementally across a bridge by setting up a series of load cases see Section 15 4 1 In this way the user can quickly identify the critical load position 1 Determine the range of load positions that will be required to adequately cover th
52. pres sures see Section 5 8 arising when a the arch moves into the backfill 14 3 Backfill Advanced properties 14 3 1 Live load dispersion details Boussinesq Select this option to specify that the magnitude of the pressure exerted on the back of the arch is to be calculated according to the Boussinesq equation This is the default option Normally a cutoff angle will be specified default 30 degrees because experiments have shown that when arch movements become large e g at failure a cone of soil under the applied load tends to punch through When a limiting distribution angle is specified the magnitudes of the pressures calculated using the Boussinesq equation are scaled up so that that the integral of the vertical pressures acting on a length of arch equals the magnitude of the applied force The length of arch assumed to be subject to vertical loading pressures is indicated Figure 14 3 LimitState Ltd 106 CHAPTER 14 MATERIAL PROPERTIES varies Figure 14 3 Cutoffs used with Boussinesq load dispersion model Uniform Select this option to specify that the magnitude of the pressure exerted on the back of the arch is to be constant The length of arch assumed to be subject to vertical loading pressures is controlled by the specified cutoff angle as indicated Figure 14 4 w 2dTan Figure 14 4 Cutoffs used with uniform load dispersion model Note 1 Use the Uniform option to comply with the requirements
53. properties Reinforcement properties see Chapter 17 19 2 Using the explorers In addition to the Property Editor LimitState RING has several explorers that allow the user to quickly check and compare the attributes of similar objects in the current project as shown in Figure 19 2 Block Explorer Suda oteta g D 0 D D o D 0 D o o 0 D 0 D A D D 0 D 0 D 0 o o 0 o AAA Block 31 20 x Output Minimum adequacy factor 1670 91 with se 2 2 of 6 Note the adeque is the multiplier on factored vehicle loads required to cause collapse factors Axle load 1 0 Dynamic 1 0 Analysis run at 09 27 54 on Mon Load Case Name Vehicle s osition s m Effective Width mm Solution Figure 19 2 The LimitState RING Block Explorer 19 2 1 Opening an explorer To access the explorers click on the View menu and highlight the Explorers option There are four explorers to choose from 1 Block explorer displays the attributes of blocks contained in skewbacks spans and piers 2 Contact explorer displays the attributes of contacts in spans and piers 3 Vehicle explorer displays the properties of each axle of every vehicle in the project 4 Load case explorer displays the properties of the vehicles according to their load case LimitState Ltd 136 CHAPTER 19 VIEWING AND MODIFYING ATTRIBUTES 19 2 2 Navigating the explorers
54. set the Factor mp to zero and uncheck the box Keep m K gt 1 0 Let the specified RING 1 5 Earth Pressure Coefficient be E Compute the equivalent soil angle of friction using the following formula p 2 sca z 45 B 11 Mp In the section Soil Properties set to the value calculated in equation B 11 and c to zero The value given in the box m k should be the required value of E Ensure that the correct procedure for replicating the RING 1 5 Limiting fill barrel angle of friction value has been followed using the value of computed here LimitState Ltd APPENDIX B ADDITIONAL NOTES ON THE BACKFILL MODEL 183 B 6 5 Automatic identification of passive zones This is implemented in the same way in LimitState RING 3 2 a as in RING 1 5 Click Advanced in LimitState RING 3 2 a The corresponding check box and table may be found in the section Passive zone parameters LimitState Ltd 184 APPENDIX B ADDITIONAL NOTES ON THE BACKFILL MODEL LimitState Ltd Appendix C Default parameters C 1 General Parameter Default Notes Bridge width 2500mm Specified width selected by default Table C 1 General default properties C 2 Geometry Parameter Default Notes Intrados shape Segmental Common in practice Number of units per ring 40 Number of rings 4 Most European bridges do not use multi ring construction Depth of surface fill ballast
55. single load case is specified the load factor that would when applied to the specified live loading cause the bridge to collapse is calculated and displayed When multiple load cases are set up the collapse load factor associated with each case is calculated in turn However as the majority of the problem remains unchanged the total CPU time required for two load cases say is rather less than twice that required for one load case 21 2 2 Iterative analysis When finite masonry crushing strength is specified the governing contact moment vs normal force failure envelope is non linear which means that an iterative analysis is required In the iterative analysis the failure envelope is progressively refined until the true non linear failure envelope is properly represented by using a series of linear constraints 151 152 CHAPTER 21 ANALYSIS By default the intermediate output from an iterative analysis is suppressed and only the final adequacy factor is shown To override this and display all the iteration data in the output pane check the Display iteration information in output window box in the Preferences dialog as shown in Figure 21 1 Figure 21 1 Analysis details in the output pane Note when multiple load cases are also specified an iterative analysis is now performed for all load cases By default the displayed output from an analysis is restricted to e The load case number e The load case name e The n
56. sliding d single span multi ring f multi span 8 hinges interaction between spans via spandrel zone Figure 5 4 Selection of potential failure modes identifiable using LimitState RING LimitState Ltd CHAPTER 5 THEORETICAL BASIS OF LIMITSTATE RING 43 5 6 Finite masonry strength In LimitState RING it is assumed that in the vicinity of hinges the thrust in the arch is transmitted across joints either 1 through an infinitely thin strip of material lying on an exterior face or if a finite material strength is specified 2 through a rectangular stress block located adjacent to an exterior face For both cases moment vs normal force failure yield envelopes for a contact can be plotted as shown on Figure 5 5 7 Y 7 4 infinite material strength Moment Normal force ii Figure 5 5 Contact surface moment vs normal force failure envelopes for i infinite ii finite masonry crushing strengths It is evident from Figure 5 5 that the envelope for case i is defined by linear constraints whereas in the case of ii these are non linear In LimitState RING the envelope for case ii is approximated using sufficient linear constraints to ensure that any deviation from the true non linear yield envelope is negligible To achieve this linear constraints are adaptively added using an iterative procedure which is described in Appendix A 3 The procedure ensures that conv
57. some codes of practice pragmatically permit the use of 2D analysis methods for skew bridges and obviously LimitState RING can be used in such cases 7 4 Multi span bridges Multi span bridges are modelled in LimitState RING in exactly the same way as single span structures i e in essence as assemblages of interacting rigid blocks and backfill elements Using LimitState RING the most critical failure mode will automatically be identified whether this involves a single or multi span failure mode Multi span failure modes typically although not always involve two adjacent spans The following points are particularly relevant to the analysis of multi span arch bridges 2Note though that for a bridge with slender piers initial failure of one or two spans is likely in practice to quickly precipitate failure of neighbouring spans because of the out of balance thrusts which then act at the tops of piers supporting these LimitState Ltd 56 CHAPTER 7 DETAILED BRIDGE ASSESSMENTS USING LIMITSTATE RING e for a viaduct comprising a large number of identical spans only two representative adja cent spans need normally be modelled initially e large railway viaducts frequently had large king piers at frequent intervals e g every 6 spans These are typically sufficiently massive to ensure that no interaction occurs between the two spans abutting a king pier e for a bridge comprising spans of different geometries ideally
58. span after this 553 54 sz aa Figure 4 2 Wizard Geometry Note 1 Itis not possible to delete the last remaining span or the abutments 2 For more detailed information on editing the geometry of the bridge see Section 13 4 1 4 Step 3 Partial Factors On the Partial Factors tab insert the partial factors relevant to the code of practice being used see Figure 4 3 New Bridge Wizard Partial Factors Factors applied to loads Masonry unit weight fm 1 0 Fill unit weight Yff 11 0 Surface fill ballast unit weight Yf sf 1 0 Trackload Yrt 1 0 Axde load YF 1 0 Dynamic Y dyn 1 0 Partial Factors Matenals Factors applied to materials Masonry strength mms 1 0 112 Masonry friction Ym mf 1 0 55 54 TS Ca Figure 4 3 Wizard Partial Factors Note For more detailed information on editing the partial factors see Section 16 LimitState Ltd 26 CHAPTER 4 QUICK START TUTORIAL 4 1 5 Step 4 Materials On the Masonry tab Figure 4 4 by using the Specify properties for drop down menu it is possible to specify 1 The same properties for all the masonry in the bridge A masonry 2 Different sets of properties for the spans skewbacks and piers abutments Spans vs piers abutments 3 Different properties for each span pier and abutment in the bridge All bridge parts On the Backfill tab clicking on the Advanced button a
59. strip of backfill acting on the block to slide If so then the reduced horizontal stress associated with the sliding failure is used this can be overridden if a user defined pressure is specified Further details are given in Appendix B 2 Finally it should be appreciated that there are several important simplifications inherent in the way LimitState RING treats passive and active restraining horizontal pressures For example i backfill pressures are assumed to be mobilized by infinitesimal structural movements ii the failure mode is assumed not to influence the magnitude of peak pressure mobilized Further background information on these assumptions is provided in Appendix B 3 and Appendix B 4 5 8 4 Backing LimitState RING permits the modelling of backing material above the abutments and piers see Chapter 13 The backing model is a special implementation of the horizontal backfill element where the compressive strength is set to a high value 5MPa by default This allows the software to account for the transfer of compressive forces between or away from spans where strong material is present If desired the resistance offered by the backing can be tailored on an element by element basis allowing the software to represent differing bridge backing conditions Details on how to achieve this are provided in Section 14 4 Where backing exists over a pier two backing elements will be associated with a block one element fr
60. there must be at least one vehicle present at all times 15 2 7 Exporting a vehicle to a file You may wish to save a customized vehicle for use in later LimitState RING projects To do this click on Export vehicle to export details of a vehicle to a tab separated text txt file The contents of this file may subsequently be imported back into LimitState RING or viewed in a spreadsheet 15 3 Adding a vehicle to a load case Once all of the necessary vehicles have been imported into the project they can be allocated to load cases To do this simply return to the Loading dialog select the relevant load case if there is more than one and click the appropriate box in the Vehicle column This will bring up a drop down menu containing all of the available vehicles as shown in Figure 15 6 Load Cases Name Load Case 1 lof 1 Vehicle Position 1 Default 1kN Single Axle M 1250 2 PEASE 3x 7 Tonne Triple Axle 1 3m Axle Spacing 11 5 Tonne Single Axle 2x 8 Tonne Double Axle im Axle Spacing 3x 8 Tonne Triple Axle 1 4m Axle Spacing Figure 15 6 Vehicles available in the current project The relevant vehicle can now be selected Enter its position on the bridge Note It is usually sensible to position the first axle in a vehicle at a position of Omm Axles in the vehicle to the right of this axle are then indicated by positive distances entered in the table In the case of an unsymmetrical bridge crossed by an unsymmetric
61. this formulation the LP problem variables are the contact forces where n gt 0 si m are unrestricted free variables the support reactions in fsup and the support movement energy E A3 Including finite masonry material strength The yield constraints equation A 3 given in Appendix A 1 are valid only if the material is infinitely strong in compression If it is assumed that the masonry possesses finite masonry LimitState Ltd APPENDIX A MATHEMATICAL FORMULATION 167 strength and that the thrust is transmitted through a rectangular crush block then equation A 3 may be replaced with a 0 5 E x ae for each contact i 1 c A 8 mi 2 Ni 0 5t EH Weruand To aid comparison both equation A 3 and equation A 8 are plotted in Figure A 2 m ae i Additional linear constraint SX ES to approximate 5 Ni NS T Non linear constraint 5 s Linear constraint 3 gt md Figure A 2 Contact surface moment vs normal force failure envelopes However the constraints in equation A 8 are non linear Therefore if a Linear Programming LP solver is still to be used to obtain a solution to the global problem then these constraints need to be approximated as a series of linear constraints In order to minimise the number of constraints in the problem and to maximise computational efficiency an iterative solution algorithm which involves only refining the representation of the
62. to obtain a solution 14 1 4 Sliding properties LimitState RING models potential sliding between blocks both within piers and rings and be tween adjacent rings though this feature can be switched off if required Inter block sliding To model sliding between all blocks except between adjacent arch rings ensure that the Model sliding option is checked and enter a value for the standard coefficient of friction Note 1 LimitState RING 3 2 a models friction by assuming that sliding between adjacent blocks is accompanied by separation so called dilatant friction or plastic shearing For most arch problems this assumption has been found not to affect the computed load factor sig nificantly However it should be borne in mind that strictly speaking the computed factor is an upper bound on the exact load factor though this upper bound often coincides with the exact value Refer to Gilbert amp Melbourne 1994 for more details Inter ring sliding To model sliding between rings ensure that the Model inter ring sliding option is checked and enter a value for the coefficient of friction between adjacent rings Note 1 For problems involving several rings it has been found that the modelling of friction by assuming that separation accompanies relative sliding between rings often leads to rea sonable estimates of bridge strength e g computed strengths often found to agree well with Bolton arch and arch bridge st
63. to the View menu and selecting one of the options under 3D View LimitState Ltd 142 CHAPTER 20 DISPLAY OPTIONS 3D and perspective views The scene can be quickly set to a default 3D viewpoint by right clicking in the Viewer pane to bring up the context menu then selecting View gt 3D View The model will then appear viewed from above and to the right at 45 looking toward the origin To view the model in perspective select the Toggle perspective icon a from the View toolbar Alternatively this function can be accessed from the Viewer pane context menu View gt Toggle Perspective Both the 3D View and Toggle Perspective functions can be accessed from the View gt 3D View menu 20 3 Menus 20 3 1 File menu f Bridge5 ring LimitState RING File Edit Select View Tools Analysis Help y Sy New Ctri N It o 3 Open Ctrl 0 Close kij Save Ctrl S Save As Ctrl Shift 5 1H RING_Manual_Worked_Example_2_Analysi 2H RING_Manual_Worked_Example_1_Analysi 3H RING_Manual_Worked_Example_1_Analysi 4H RING_Manual_Worked_Example_1_Analysi 5 H RING_Manual_Worked_Example_2_Analysi Exit Ctri Q FE Figure 20 2 The LimitState RINGFile menu Function Shortcut Description New Ctrl N Create a new bridge project Open Ctrl O Open an existing bridge project Close Close the current bridge project Save Ctrl S Save the current bridge
64. waterproofed masonry arch bridge subject to flooding buoyant unit weights should be specified for the masonry and backfill materials This enables the modelling a bridge which is flooded up to road rail level the most severe flooding scenario When a bridge is waterproofed and flooded from below it is conceivable that the deleterious effects of flooding on load carrying capacity will be even more severe This scenario can be modelled using LimitState RING although the hydrostatic pressures have to be entered manually Hulet et al 2006 LimitState Ltd 64 CHAPTER 7 DETAILED BRIDGE ASSESSMENTS USING LIMITSTATE RING LimitState Ltd Chapter 8 Loading models 8 1 Loading from railway vehicles 8 1 1 Railway loading models For convenience a library containing common railway load models is distributed with Limit State RING see also Appendix D 1 Alternative loading models may also be defined by the user Some standard loading models contain components of distributed loading Given the origins of such load models typically determined from influence lines for simply supported or continuous beams it is debatable as to how appropriate their use is for masonry arch bridges Neverthe less as they are used by some authorities they are listed for completeness However there are two practical issues which must be borne in mind 1 the length of distributed loading may be variable and in this case it is the responsibility
65. will bring up one of several context menus 20 5 1 Viewer pane context menu Right clicking within the viewer pane will bring up the menu shown in Figure 20 9 Bridges ring LimitState RING File Edit Select View Tools Analysis Help 02 USHVUG Cu Exit Select gt Pan Rotate 808989 View Zoom Render Save Image OS 88s ao Figure 20 9 Viewer pane context menu From here you can easily access many of the display related functions of the toolbars as well as several other independent functions listed in Table 20 10 LimitState Ltd 148 CHAPTER 20 DISPLAY OPTIONS Toolbar Functions Exit Exits the context menu Select Access Select menu see Section 20 3 3 functions Pan Pan around the viewing window Rotate Access the Cursor 3D see Section 20 4 1 toolbar functions Zoom Access the View see Section 20 4 1 toolbar functions View Access the View 3D see Section 20 4 2 toolbar functions Render Change the quality of rendering in the viewer window Save image Save the current view as an image png jpg ps or tiff Table 20 10 Viewer pane context menu options 20 5 2 Toolbar property editor context menu Right clicking within any toolbar or at the top of the Property Editor see Section 19 1 will bring up the following menu depicted in Figure 20 10 Property Editor Calculator s Output Block Explorer Contact Explorer Ve
66. 138 137 137 AP 137 135 138 198 96 T4 181 183 182 ae 178 177 nza 18 104 T5 103 104 100 97 95 A T6 A L 130 131 136 136 103 A Active P Passive L Load spreading Table G 2 Results from load spread passive restraint separation tests G 3 Salford laboratory tests full scale To better establish the nature of the soil arch interaction which takes place a series of bridges have recently been tested at the University of Salford UK The model bridges tested to date have been 3m in span and have been housed in a large 8 3m long 2 1m high and extremely stiff test chamber incorporating large frictionless observation windows along one face to permit measurement of the soil and arch movements Figure G 5 shows vectors of soil displacements LimitState Ltd 228 APPENDIX G VALIDATION AGAINST BRIDGE TEST RESULTS LimitState RING analysis kN wv O ES tee 65 pen efault soi Bridge Description BS properties except is bie cae a 8 using maasnrag Soi roperties g in g unit weight prop 3m single 1 il 126 83 7 122 97 limestone fill 3m single 2 span 92 95 5 95 5 104 clay fill Table G 3 Sample comparison between Salford laboratory and LimitState RING collapse loads in the case of Bridge 1 Further details are available elsewhere Gilbert et al 2007 Figure G 5 Bridge 1 arch and backfill remote from the lo
67. 17 1 to 3 significant figures LimitState Ltd APPENDIX F WORKED EXAMPLES REINFORCEMENT 219 F2 Case 2 Bottom reinforcement in full tension top reinforce ment in partial tension In this example the bottom reinforcement is in full tension and the top reinforcement carries a tensile force that must be determined The beam properties are shown in Table F2 Property Value Block size 250mm x 1000mm bridge width Beam span 5000mm 100mm block width 4900mm Applied force 1kN span 2 Top reinforcement 200kN 50mm from top surface Bottom reinforcement 200kN 50mm from bottom surface Concrete crushing strength 5 x 107 kN mm Table F 2 Reinforced beam worked example Case 2 properties 2450mm Reinforcement bars 50mm from top and bottom faces 4900mm Figure F 3 Reinforced beam dimensions Case 2 Applied moment Applied Moment Applied force x Span _ 1x 4900 1225kNmm Initial assumed concrete force Concrete force 2 x 200 400kN Concrete crushing depth Concrete crushing depth Concrete force Bridge width Concrete crushing strength Concrete crushing depth 400 1000 5 x 107 80mm Hence the crushing depth is apparently greater than the depth to the top reinforcement bar which is clearly incorrect To determine the force in the top bar and calculate the moment capacity of the section we must calculate the force in the concrete and t
68. 175 176 APPENDIX B ADDITIONAL NOTES ON THE BACKFILL MODEL stresses factored up to ensure the vertical applied load is equal to the sum of the distributed load stresses multiplied by the areas over which they act However as applied loads are anyway normally placed at numerous positions across the bridge no attempt is made to ensure that the centre of the line of action of an applied load coincides with the centre of the line of action of the distributed loads i e moment equilibrium is not enforced B 2 Limiting horizontal fill stresses The horizontal soil stresses applied to the extrados of a given voussoir are limited in Limit State RING to those which would just cause sliding of the overlying strip of soil The relevant vertical and horizontal stresses and forces together with the normal and shear forces are shown on Figure B 2 Figure B 2 Forces acting on extrados of a block subject to backfill pressures If the specified soil arch interface has friction 6 and adhesion a then the overlying strip of soil will just slide when Smax N tan al B 1 Where Smax Hmax cos 0 V sin 0 B 2 LimitState Ltd APPENDIX B ADDITIONAL NOTES ON THE BACKFILL MODEL 177 N Hmaz sin 0 V cos O B 3 Hence the maximum applied horizontal force can be expressed as al V cos 9 tan sin 0 Hit B 4 cos 0 sin 0 tan BA Now Amax UOh max B 5 V hos B 6 And hence the maximum
69. 1995 The behaviour of multiring brickwork arch bridges The Struc tural Engineer 73 39 47 Melbourne C amp Hodgson J 1995 The behaviour of skewed brickwork arch bridges 1st Int Conf on Arch Bridges Bolton pp 309 320 Network Rail 2006 NR GN CIV 025 The Structural Assessment of Underbridges Issue 3 Net work Rail Page J 1993 Masonry Arch Bridges HMSO UK Sumon S 2005 Innovative retrofitted reinforcement techniques for masonry arch bridges Pro ceedings of the ICE Bridge Engineering 158 BE3 91 99 LimitState Ltd LimitState Ltd The Innovation Centre 217 Portobello Sheffield S1 4DP United Kingdom t 44 0 114 224 2240 e info limitstate com w limitstate com
70. 2 80 103 01 1 30 44 15 4 80 98 10 1 80 98 10 1 00 40 tonne 5 Axle 3 2 Artic 10 5 tonne drive axle 1 00 49 05 2 80 44 15 1 30 103 01 4 80 98 10 1 80 98 10 1 00 41 tonne 6 Axle 3 3 Artic 1 00 49 05 2 80 103 01 1 30 49 05 4 18 67 00 1 35 67 00 1 35 67 00 1 00 41 tonne 6 Axle 3 3 Artic 1 00 49 05 2 80 49 05 1 30 103 01 4 18 67 00 1 35 67 00 1 35 67 00 1 00 44 tonne 6 Axle 3 3 Artic maximum axle 1 00 58 86 2 80 103 01 1 30 49 05 4 70 73 58 1 35 73 58 1 35 73 58 1 00 weight 10 5 tonnes 44 tonne 6 Axle 3 3 Artic maximum axle 1 00 58 86 2 80 49 05 1 30 103 01 4 70 73 58 1 35 73 58 1 35 73 58 1 00 weight 10 5 tonnes 44 tonne 5 Axle 3 2 Artic 1 00 68 67 2 80 112 82 1 30 73 58 7 60 88 29 1 35 88 29 1 00 40ft ISO container 44 tonne 5 Axle 3 2 Artic 1 00 68 67 2 80 73 58 1 30 112 82 7 60 88 29 1 35 88 29 1 00 40ft ISO container 01 A1 A2 A3 A4 02 w1 W2 W3 W4 W5 Table D 10 BD21 Annex D load vehicles Key W1 W2 etc axle weights kN A1 A2 etc axle spacings m axle weights reversed LimitState Ltd APPENDIX D STANDARD LOADING MODELS 199 D 2 6 BD21 Annex E Brose Weight A KN Axle Mak
71. 3 3 Artic maximum axle 1 00 58 86 2 80 103 01 1 30 49 05 4 70 73 58 1 35 73 58 1 35 73 58 1 00 weight 10 5 tonnes 44 tonne 6 Axle 3 3 Artic maximum axle 1 00 58 86 2 80 49 05 1 30 103 01 4 70 73 58 1 35 73 58 1 35 73 58 1 00 weight 10 5 tonnes 44 tonne 5 Axle 3 2 Artic 1 00 68 67 2 80 112 82 1 30 73 58 7 60 88 29 1 35 88 29 1 00 40ft ISO container 44 tonne 5 Axle 3 2 Artic 1 00 68 67 2 80 73 58 1 30 112 82 7 60 88 29 1 35 88 29 1 00 40ft ISO container 01 A1 A2 A3 A4 02 w1 W2 W3 W4 W5 Table D 14 BD91 loading vehicles Key W1 W2 etc axle weights kN A1 A2 etc axle spacings m axle weights reversed LimitState Ltd Appendix E Worked examples general E 1 Example 1 single span stone voussoir underline railway bridge E 1 1 Details Bridge name Case study example 1 Description An initial LimitState RING assessment of a single span stone voussoir underline railway arch bridge is described The bridge spans squarely between abutments and currently carries a single straight track The bridge is in a fair condition with e mortar loss of approx 20mm on average in the vicinity of the arch springings e two longitudinal cracks in the arch barrel underneath the edges of the track approx 3 1m apart Load model LM71 is used in this assessment Photograph
72. 46 er BRNO LR Mace ck OR I ee Vi ere Oe OY 48 lll Modelling 49 6 Preliminary bridge assessments using LimitState RING 51 7 Detailed bridge assessments using LimitState RING 53 7 1 Analysis parameters ici ee PERSE G Eee Lee ee bes 53 7 1 1 Partial factors of safety ociosas ee EES 53 7 2 Modelling the shape of the arch n ocre qu nel ae pue Oh UE 54 Foo OKON y oa da A AAA A A 55 7 4 Multi span bridges 2 4 cies aa E on E oes 55 7 6 EUA bloks lt o ca da a a Peak Pee oe SES 56 7 6 The influence of infill material 56 7 7 Modelling the mechanical properties of masonry 57 7 8 Modelling bridge defects 58 7 8 1 Missing mortar and or localised spalling of masonry units 58 7 8 2 Ring separation in multi ring brickwork arches 59 783 Gracking ie arch barel lt e cosc eG we ee aus ee ee nep yo 61 7 9 Modelling flooded masonry arch bridges 63 8 Loading models 65 8 1 Loading from railway vehicles 65 8 1 1 Railway loading models 4 4 44 da se spas Bee ie ete ant 65 8 1 2 Distribution of rail loads through the track 65 8 1 3 Longitudinal distribution of load through ballast and fill 66 8 1 4 Transverse distribution and effective bridge width 67 8 1 5 Dynamic effects sia rones da DE RGO PRESS amp x 67 8 1 6 Oth
73. 545s 00 175451 O merme oor searar 000 soon simo me 5520 oo searer 000 sosa simple omg e001 oo four 000 60 082 D nie usnngme 224 008 304 186 000 224 10 eto cg 2m as fon 30 000 EE reos 000 ra sos _simple_crushing_geometejocked mg _ LL simple_towriction mg simple mobackflmg 117 015 1 17172 000 117172 Limpie userproflemg ___ simple _userprofile_crushingmg Prose 000 moss ES L__ simple abutment dispersion 2 2059 727 517421 000 317 421 Less conservative results from LimitState RING 2 0 due to improved solver for problems involving multi rings and crushing Due to error in LimitState RING 1 x Boussinesq distribution model when load dispersed onto a bridge containing spans with user defined arch profiles 3From LimitState RING 2 0 the backing height is conservatively always measured above the lowest point of the top surface of a skewback The algorithm used in LimitState RING 1 x prevented prediction of the load carrying capacity of bridges found to be geometrically locked with infinite crushing strength even if finite crushing strength was specified by the user 5 From LimitState RING 2 0 the Boussinesg distribution spreads to the full extent of the specified cutoff cone even if this means that load is applied to blocks with no direct line of sight to the surface load In LimitState RING 1 x dispersion stops once direct line o
74. APTER 7 DETAILED BRIDGE ASSESSMENTS USING LIMITSTATE RING additional reserves of strength for example because of the potential for increasing passive soil restraint to be mobilised as structural movements increase in this case the large struc tural deformations required are such that the structure will anyway fail to meet any meaningful serviceability criteria It may be feasible to point up transverse cracks but if this is not done a conservative Limit State RING analysis may be performed simply by locally reducing the arch thickness at the position of the crack Figure 7 7 it should be noted that LimitState RING is not capable of modelling the presence of cracks which close up completely after finite movement Opening a crack b crack closing under loading c crack opening under loading Figure 7 7 Modelling an existing crack in an arch using the mortar loss feature In square spanning bridges diagonal cracks may often be caused by abutment settlements Whatever the cause when diagonal cracks are present the arch profile should be surveyed at several positions across the width of the bridge with an analysis being performed for each profile Micro cracks Isolated fine cracks may be present in masonry joints or within masonry units When numerous cracks are concentrated in parts of the structure this can be indicative of a major problem especially if there are signs of recent cracks This is because masonry tends to fa
75. Bed joints normal to intrados output Load Case Name Vehicle s Position s mm 1 Load Case 1 Default 1kN Single Axle 1250 Minimum adequacy factor 455 146 Note the adequacy factor is the multiplier on factored vehicle loads required to cause collapse factors Axle load 1 0 Dynamic 1 0 x 3195 y 5921 Figure 7 5 LimitState RING model of multi ring arch It is usually satisfactory to assume that a brickwork arch with a bonding pattern of the form shown in Figure 7 4b effectively behaves as a single ring voussoir arch i e as Figure 7 4a However if very weak bricks are present headers may shear through and the arch should then be modelled as if composed from separate rings e g see Figure 7 6 for a real world example of this b view through core hole showing separation of bottom layer of brickwork Figure 7 6 Arch barrel containing headers which have sheared through LimitState Ltd CHAPTER 7 DETAILED BRIDGE ASSESSMENTS USING LIMITSTATE RING 61 However even when inter ring cracks are not evident the circumferential mortar joints present in the multi ring bonding patterns shown in Figure 7 4c and Figure 7 4d form potential surfaces of weakness and careful consideration should be given to modelling bridges constructed with these types of barrels In fact when multi ring brickwork arch bridges are assessed the general question arises should for the purposes of analysi
76. EORETICAL BASIS OF LIMITSTATE RING 35 e hence the response of the pier can be considered ductile an important requirement in order for limit analysis theory to be applicable As already indicated in masonry structures the moment of resistance effectively varies contin uously and consequentially this can make conventional bending moment diagrams difficult to interpret It is normally more useful to plot the eccentricity of the compressive force or thrust at each cross section where eccentricity moment thrust Figure 5 2 shows the resulting lines of thrust at collapse for two different configurations of masonry blocks and loading types Lines of thrust Hinges Figure 5 2 Thrust line at collapse in a masonry pier and b masonry arch In Figure 5 2 it can be seen that the lines of thrust lie entirely within the masonry and also that hinges form at the locations where the lines of thrust touch the exterior faces of the blocks Formation of a sufficient number of hinges and or planes of sliding leads to collapse In the case of the masonry pier shown in Figure 5 2 a the structure is statically determinate and statics alone may be used to uniquely determine the position of the thrust line both prior to and at ultimate failure In contrast the masonry arch shown in Figure 5 2 b is statically indeterminate and there are many possible positions of the thrust line prior to failure Therefore the actual position can o
77. G has been designed so that it can be used with default settings to rapidly perform a preliminary and generally conservative assessment of load carrying capac ity rapidly with many dialogs in the program being simplified For example refer to Figure 6 1 which shows the Backfill page of the New Bridge Wizard In a preliminary assessment default backfill parameters can be used Figure 6 1 a If the bridge proves to have insufficient load carrying capacity then a follow up assessment can be performed using more realistic values e g informed by trial pit or penetrometer investigations In a second level assessment it may very occasionally be necessary to also adjust other details of the ring soil model Figure 6 1 b 51 52 CHAPTER 6 PRELIMINARY BRIDGE ASSESSMENTS USING LIMITSTATE RING PF New Bridge Wizard Masonry Backfill SurfaceFil Soil Properties Unit weight KN m 18 Angle of friction 4 degrees 30 Cohesion c kN m 0 Basic values Soil Effects Model dispersion of live load Model horizontal passive pressures Cas a 2 2 a FP New Bridge Wizard Masonry Backfill Surface Fill Soil Properties Unit weight kN m 18 Angle of friction 4 degrees 30 Cohesion c 4N m o Advanced settings Live load dispersion details Boussinesq Uniform Cutoff angle degrees 30 Passive zone parameters mK 1 0 os Mae Kc 0 0 ms 2 02 O
78. INST BRIDGE TEST RESULTS 231 G 5 2 TRL laboratory bridge tests A number of reinforced brickwork arch bridges have been constructed and tested in the lab oratory by TRL Sumon 2005 The first 5m span benchmark bridge comprised 3 debonded brickwork rings and granular soil fill material The bridge failed at a load of 200kN Unfortunately some essential details of this bridge were either not made available or are un certain For example angle of friction of the soil fill material is quoted at 40 from manufacturer literature but in fact this value will depend on the site compaction used Also the strength of this bridge is likely to have been increased by test chamber side wall friction and by the con fined nature of the arch fill For these reasons the values of two of the parameters controlling soil arch interaction were adjusted in order to give better agreement between the predicted and experimental results Table G 6 The remaining input parameters were taken from Sumon 2005 or Chen 2004 This includes the inter ring friction value of 1 0 quoted by Chen the origin of which is unclear and which appears rather high Parameter Value Comments Fill angle of friction 60 Measured value in Bolton arch bridge tests Max angle of dispersion of live loads 45 Table G 6 Soil arch interaction parameter values used in TRL tests others taken from Chen 2004 Sumon 2005 The bridge was subsequently retro
79. ORCEMENT Figure 17 4 Radial contacts selected using Contact Select Tool Then in the Property Editor specify the reinforcement position in millimeters limiting compressive and tensile forces and the reinforced shear capacity in kN per metre width On clicking out of the Property Editor the reinforcement will be displayed on the model see Figure 17 5 Figure 17 5 Reinforcement added to radial contacts LimitState Ltd Chapter 18 Support movement analysis 18 1 Background A notable feature in LimitState RING is the ability to model support movements This opens up a range of possibilities for example e The likely causes of observed cracks in an existing structure can be investigated by im posing support movements and comparing actual and modelled deformed shapes e g are these consistent with vertical horizontal or perhaps angular settlement of the base of a pier or abutment e The observed response of a settled bridge can be used to verify the model idealization A settled bridge can be considered to be of almost the same value as load test to collapse because when a bridge undergoes settlements many of the same modes of resistance are mobilized as when a bridge is subjected to excessive live loading Therefore it is very useful to try to correlate actual and modelled behaviour e g if it is necessary to include backing in the numerical model in order to replicate the observed mode of response then t
80. Partial factors B increasing dead load effects Computed adequacy factor 2 98 axles spaced between 3200 and 8000mm from the left springing i e this case is not critical E 1 4 Next steps e Dynamic factors can now be applied to the computed adequacy factor as deemed appro priate e The validity of the assumptions made should where possible be verified e g the shape of the arch should be verified as this can have an important influence on the computed load carrying capacity e If the computed load carrying capacity proves to be insufficient then consideration should be given to carrying out a more detailed investigation of the fill and or backing if present LimitState Ltd 210 APPENDIX E WORKED EXAMPLES GENERAL E 2 Example 2 multi span multi ring brickwork underline railway bridge E 2 1 Details Bridge name Case study example 2 Description An initial LimitState RING assessment of a multi span multi ring brickwork un derline railway arch bridge is described The bridge spans squarely between abutments and piers and currently carries two straight tracks The 8 semicircular spans are nominally identical The bridge was constructed using engineering bricks and lime mortar and is in a reasonably good condition with only isolated instances of loss of mortar from the joints and or minor crack ing A hammer survey indicated no evidence of ring separation Initial intrusive investigations have indicat
81. To access the tool click the Rotate icon on the Cursor toolbar E or open the Viewer pane context menu by right clicking the mouse anywhere within the viewer pane and selecting Rotate gt Rotate This action will overlay the rotate tool on top of the viewer pane Figure 20 1 TS Figure 20 1 The rotate tool Now when hovering in the different areas of the viewer pane rotate cursors are displayed Rotate x Hovering the cursor in the small circles at the top or bottom brings up the rotate x cursor Click with the left mouse button and hold Moving the mouse up and down the screen will now rotate the model around the x axis LimitState Ltd CHAPTER 20 DISPLAY OPTIONS 141 Rotate y Hovering the cursor in the small circles at the left or right brings up the rotate y cursor Click with the left mouse button and hold Moving the mouse left and right across the screen will now rotate the model around the y axis Rotate z Hovering the cursor outside the large central circle brings up the rotate z cursor ZA Click with the left mouse button and hold Moving the mouse up and down the screen will now rotate the model around the z axis Rotate 3D Hovering the cursor inside the large central circle brings up the rotate 3D cursor amp Click with the left mouse button and hold Moving the mouse in any direction keeping within the circle will now rotate the model freely in any direction To exit the Rotate tool select a
82. a load case 117 15 3 1 Assigning dynamic factors lt lt lt lt lt lt lt lt 118 15 4 Defining new load cases aio is A Ja Bu 118 15 41 Adding load cases LL ssa Sue eee READ a a 118 15 4 2 Deleting a load case 2 ebb eee a 119 15 5 Moving vehicles across a bridge 120 15 5 1 Method 1 Multiple load cases 120 15 5 2 Method 2 Drag and solve lt lt eed ieee dw e a 121 15 6 Moving a load in a multiple load case problem 121 15 7 Viewing load cases iw dd A AR A eR 121 16 Partial factors 123 17 Reinforcement 125 EA AAA EIA 125 17 2 Adding reinforcement to the project 126 18 Support movement analysis 129 18 1 Background resarcirse SE MEER S amp S 129 18 2 Support movement wizard 130 LimitState Ltd CONTENTS 9 19 Viewing and modifying attributes 131 19 1 Using the property editor ee tae by ek hab Jared tes Es 131 19 1 1 PSM 22 cw de Ae Gey RK RS Oe 4 ee a OS 132 Wet ec oe ee due 28e eau oe eae ee E 133 19 1 3 SO oe a a eK en RS a Se au 134 19 2 Using the IDR scada Lun a L an a be es 135 19 2 1 Opening an explorer n 2 2 eke ac ee ee EES 135 19 2 2 Navigating the explorers lt lt ee a ee eae a de eos 136 1923 Eding GAA e oe ee I eR Se Oe da doom eS a 136 20 Display options 139 20 1 General ga i
83. ad also showing soil displacement vectors For the LimitState RING analyses measured geometry and unit weight properties were used initially for sake of simplicity the soil unit weight for Bridge 2 which was clay filled with a limestone capping layer was taken as the mean of the limestone and clay unit weights For Bridge 1 the angle of friction of the soil was taken as 54 5 the measured value For Bridge 2 a cohesive strength of 78kPa was used the measured value Finally the masonry crushing strength was taken as 25MPa which is representative of that found for the type of brickwork used Experimental and analysis results are provided in Table G 3 It is clear from Table G 3 that when the measured soil strength parameters are used column B LimitState RING provides a close prediction of load carrying capacity LimitState Ltd APPENDIX G VALIDATION AGAINST BRIDGE TEST RESULTS 229 G 4 Field bridge tests In the late 1980s and early 1990s the Transport and Road Research Laboratory TRRL now TRL in the UK carried out a series of load tests to collapse on redundant arch bridges Most bridges failed in four hinge mechanisms although some of the bridges were reported as failing by three hinge snap through or in compression material failure It was likely that many of the bridges tested were restrained considerably by their attached spandrel walls and or masonry backing Outline information on these bridge tests has been pr
84. ae aa el dae NO LIMITATION __ distributed load components are not included in the LimitState RING database RU loading no UDL RL loading no UDL No image in code single 200KN axle RL loading no UDL No image in code 300kN amp 150KN axles Table D 2 Standard BD37 railway loading in LimitState RING D 1 3 Network Rail NR GN CIV 025 Description Loading 4x200kN 4x150kN 4x200kN 4x150kN 2x250kN 65kN m 7 SHORT LENGTHS Network Rail RA1 J load train 3352825838 g 2222 gF kl 20 units shown T N R GN CIV 025 distributed load components are not included in the LimitState RING database 2x250kN 2x250kN Network Rail Assessment Load Wagon NR GN CIV 025 Table D 3 Standard Network Rail railway loading in LimitState RING LimitState Ltd 192 APPENDIX D STANDARD LOADING MODELS Description Loading Units of load per track N 3 270kN m y i lt _ 9 967kN 7 475kN 7 475kN 7 475kN K 7 475kN ES oS Ed a ik 9 967kN 9 967kN 9 967kN K 7 475kN 7 475kN 7 475kN l 7 475kN k 9 967kN k 9 967kN z B 8 a Type RA1 Load 1 BSU No UDL metres distributed load components are not included in the LimitState RING database Units of load per track N k 12 459kN Type RA Short Lengths l 1 BSU No UDL 1 829 metres
85. al force kN m bridge width shear force kN m bridge width and bending moment kKNmm m bridge width diagrams has been added These can be accessed in a solved model by clicking the moment shear or normal force icons a and a This is illustrated for the case of a beam in Figure 22 2 and in the case of an arch bridge in Figure 22 3 b Moment Figure 22 2 Sample beam shear force and moment diagrams The force diagrams can be displayed by navigating to the relevant options in the View menu or by using the appropriate toolbar buttons to toggle the view of the normal force shear force and moment Note 1 The entities e g thrust and or bending moment diagrams displayed on screen when the report is generated via Analysis gt Report will be those also displayed on the image in the report 2 A given magnitude e g shear force magnitude can be queried by clicking on the part of the contact of interest not obscured by the diagram and referring to the Property Editor 22 2 Quantitative output The contact normal force and bending moment values displayed in the Property Editor Contact Explorer and in the Report Output are combined values that take account of joint stresses and the presence of reinforcement Full details of the reinforcement specifications are also included in the Report Output see Chapter 23 LimitState Ltd CHAPTER 22 POST ANALYSIS FUNCTIONS 157 b Shear forces c Mo
86. al vehicle a mirror can be applied to the vehicle so that it can cross the bridges in both directions Several vehicles can be used to form a load case as shown in Figure 15 7 LimitState Ltd 118 CHAPTER 15 LOADING T Edit Bridge Load Cases Name Load Case 1 m lof 1 Vehicle Position Mirror Dynamic Factor 1 11 5 Tonne Single Axle 0 0 false Not applied 2 2x 8 Tonne Double Axle im Axle Spacing 10 0 false Not applied 3 3x 7 Tonne Triple Axle 1 3m Axle Spacing 0 0 Not applied 4 3x 8 Tonne Triple Axle 1 4m Axle Spacing 0 0 Not applied 5 Add Load Case s Delete All Cases Except Current Vehicle Database Figure 15 7 Multiple vehicles in a load case Note 1 The vehicle positions specified are relative to the assumed bridge datum point which is the left hand intrados springing of span 1 2 When multiple vehicles are specified in a single load case they are assumed to be acting together If you wish to analyse a bridge for several different vehicle types then separate models should be created one for each 15 3 1 Assigning dynamic factors Codes of practice sometimes require the consideration of dynamic or impact loading when assessing the capacity of a bridge structure Often this is implemented via the application of a dynamic load factor to one or more axles maybe the most heavily loaded of the loading vehicle LimitState RING now
87. ames of the vehicle s in the load case e The vehicle position s in mm measured from the left hand springing of the left hand arch e The effective bridge width in mm either fixed or calculated e The solution as an adequacy factor on the applied load e The minimum adequacy factor calculated over all the load cases To enable the display of all iteration data go to the Preferences dialog in Tools see Section 20 3 5 and select the option to Display iteration information in output window 21 3 The solvers A solver is required to find the critical collapse load factor and associated collapse mechanism The internal forces in the structure must satisfy all specified yield constraints these are set up for a particular problem by LimitState RING Version 3 2 a of LimitState RING makes use of two third party solvers Mosek which uses an interior point optimization algorithm and CLP which uses a simplex optimization algorithm Both are powerful linear programming solvers which are called as a subroutine and to maximize efficiency the problem data is passed via memory LimitState Ltd CHAPTER 21 ANALYSIS 153 By default LimitState RING will automatically choose the most appropriate solver for the type of problem being analysed A single ring problem one where all the spans possess a single ring of masonry will be solved using CLP Multi ring problems will be solved using Mosek Should the user wish to override this s
88. an 1 0 for a safe structure if dynamic and or other factors have still to be applied following completion of a LimitState RING analysis LimitState Ltd 38 CHAPTER 5 THEORETICAL BASIS OF LIMITSTATE RING Figure 5 3 Modelling the effects of support movement at the base of a pier LimitState Ltd CHAPTER 5 THEORETICAL BASIS OF LIMITSTATE RING 39 5 4 Range of applicability of LimitState RING 5 4 1 Spans When the adequacy factor is sought LimitState RING is most suited to the analysis of single and multi span masonry arch bridges with short to medium span lengths where foreseeable live loadings are typically non negligible in comparison to structural self weight For spans longer than 20 to 30m foreseeable live loadings are often essentially negligible and other considerations become more important such as long term masonry creep effects due to persistent moderately high stresses Additionally in the case of very long span bridges the presence of high compressive stresses may give rise to non negligible second order deforma tions making the adequacy factors computed by LimitState RING potentially non conservative 5 4 2 Block shape LimitState RING provides a realistic model of bridges comprising single or multi ring arch bar rels constructed using regular stone blockwork or brickwork Since in LimitState RING the constituent blocks are assumed to be rectangular the software provides a less realistic m
89. analyzed without difficulty Original version validated by academia and industry e g see Gilbert amp Melbourne 1994 Melbourne amp Gilbert 1995 and Melbourne et al 1997 new features informed by ongoing active research 16 CHAPTER 1 INTRODUCTION 1 2 Glossary Masonry arch bridges are very different to the steel and concrete bridges which are instead constructed in their place today As the terminology used to describe different parts of masonry arch bridges can appear obscure to the non specialist common terms are given in Figure 1 1 Backfill Parapet Backing Crown Arch rings Springing Arch barrel Abutment Wing wall Skewback Figure 1 1 Masonry arch bridge terminology 1 3 LimitState RING terminology LimitState RING idealizes a bridge as a series of blocks separated by contacts where sliding crushing hinging can occur with the effects of fill modelled by live load dispersal and re straint from backfill elements The annotated image displayed in Figure 1 2 highlights the most important objects the user will encounter when using LimitState RING Upon solving LimitState RING determines the critical failure mode with hinges often forming as sections of the arch push against backfill elements designed to replicate the effect of the passive restraint offered by the fill Finally the thrust zone at collapse is also shown This gives a visual indication of both the position of the line of co
90. and Recommended system specifications are as follows ideal values given in parenthesis LimitState Ltd 18 CHAPTER 1 INTRODUCTION e 500MHz 1 5 GHz Intel or compatible processor e 120Mb 250 Mb free hard disk space e 512Mb 1 Gb RAM 1 7 Program limits The program uses a Single Document Interface which means that only one bridge project file can be open in LimitState RING at a given time However several instances of LimitState RING can be opened simultaneously if required and each of these may contain a separate bridge project file Previous versions of the software e g RING 1 5 imposed limits on the number of rings blocks etc which could be modelled In LimitState RING 3 2 a problem size is limited only by available computer power 1 8 Contact details 1 8 1 Sales To request information on pricing a formal quotation or to purchase the software please contact LimitState Ltd at sales limitstate com 1 8 2 Software support Software support for LimitState RING is available to all users with valid maintenance contracts All queries should be directed to support limitstate com 1 8 3 Website For the most up to date news about LimitState RING please visit the LimitState RING website www limitstate com ring LimitState Ltd Chapter 2 What s new in LimitState RING 2 1 More flexible arch profile definition A number of new arch profile types have been added potentially allowing u
91. axle is by default assumed to be dispersed using LimitState RING showing different distribution angles through the ballast and backfill Arch Figure 8 2 Longitudinal dispersal of a railway axle load through sleepers ballast and fill also showing default dispersion angles LimitState Ltd CHAPTER 8 LOADING MODELS 67 8 1 4 Transverse distribution and effective bridge width LimitState RING is a 2D analysis program Thus appropriate assumptions are required in order to determine the effective width of bridge which may be assumed to support an axle loading Unfortunately this is an area for which there is little real evidence on which to base rational rules By default a fixed effective bridge width of 2500mm is used This can be changed by the user or alternatively an automatically computed effective bridge width can be used which is computed as follows effective width specified sleeper width amount of load spread at the loaded sleeper with minimum fill depth extra distance to account for distribution within the arch The effective width computed using the default railway bridge parameters is shown in Figure 8 3a However it should be remembered that the automatically computed effective bridge width may not be reasonable and the user should check whether for example longitudinal cracks in the arch barrel the proximity of adjacent track or the edge of the bridge will limit the effective width illustrated in Figure 8 3b
92. ballast below the un derside of the sleepers above the 1217 5mm crown First approximation in the absence Intrados shape Segmental of a comprehensive dimensional survey Number of units per ring 80 Large number to increase precision Number of rings 10or6 6 rings in practice Table E 8 Bridge geometry span 1 Parameter Value Notes Height 6170mm Width top 2035mm Survey values Width bottom 2850mm Number of units in pier 20 Table E 9 Bridge geometry pier between span 1 and 2 LimitState Ltd 212 APPENDIX E WORKED EXAMPLES GENERAL Parameter Value Notes Span 13610mm Rise 6780mm Thickness 682 5mm Measured values Depth of fill amp ballast below the un derside of the sleepers above the 1217 5mm crown First approximation in the absence Intrados shape Segmental of a comprehensive dimensional survey Number of units per ring 80 Large number to increase precision Number of rings 10or6 6 rings in practice Table E 10 Bridge geometry span 2 Parameter Value Notes Depth of ballast below sleeper 300mm Estimated value Sleeper breadth 250mm Standard width Sleeper length 2400mm Table E 11 Track geometry Parameter Value Notes Estimated value engineering 3 Unit weight masonry 20 kN m bricks Coefficient of friction radial 0 6 Typical value Coeffic
93. ce ck oe Bree ee a oS ee GES oe See EY 139 20 1 1 Language specific variations 139 20 12 ON ae Ge AA wae ee RA 139 20 1 3 Current mouse position 139 20 1 4 Scrolling wheels ess su bien eS Ae eS ee eR 139 20 2 Viewer ES 2 nn eS OR SAE Be A A AA 140 20 2 1 Rotating the model 0h seso ps is maa a nie 140 20 9 Men s 5 0950 e a ra DAS A lo doe wwe De a oh a 142 al US MENU e ar e are e dc patos E 142 203 2 EON lt 2 Loin EE AOS AI 143 200 SES de es ok eS Re E en AE Be 143 20 3 4 VIENA Seb Bes 144 20 30 TOOS MODU o 54 42 pa EA a A 145 20 30 Analysis MENU sso Lis 4 a ca A a A woes 145 pt Help MONU as oc os id A a A SE ars 146 UA TIA ic A A A A BE E BSS 146 20 4 1 Default toolbars vo soca oia ae i e A AI TEE 146 2042 Optional tobas s o Linie pe E its AAA A Es 147 20 5 Context MENUS lt o sa so aropa a A er 147 20 5 1 Viewer pane context menu 147 20 5 2 Toolbar property editor context menu 148 20 5 3 Explorer context M 4 4 La cansa aa it 4 149 21 Analysis 151 a DID OO aa mo a a aa a A da a ee 151 21 2 ypes of analysis e A we OSS a we ee eS 151 21 2 1 Normal analysis i226 288 eee a a RES dite 4 151 21 2 2 MOTIVO anaes oi ane de Ne A 151 21 3 he OMS 1 uns a LES LR EN Se LAURE RER a EN ESS 152 21 4 Analysis results cie era AE Ce od we EOS REE Ga 153 21 4 1 Adequacy factor found oe e Behe Sa
94. cing Double Axle 11 5 Tonne 88 29 1 3 88 29 93 2 1 3 93 2 Driving 1 3m Axle 112 82 1 3 73 56 Spacing Double Axle 10 5 Tonne Driving 1 3m Axle 103 01 1 3 83 39 Spacing 2x 10 Tonne Double Axle 1 8m Axle Spacing 3x 7 Tonne Double Axle 1m Axle Spacing 3x 8 Tonne Double Axle 1m Axle Spacing 98 10 1 8 98 10 68 67 1 3 68 67 1 3 68 67 78 48 1 4 78 48 1 4 78 48 Table D 9 BD21 Annex A AW Schedule 3 load vehicles Key W1 W2 etc axle weights KN A1 A2 etc axle spacings m axle weights reversed LimitState Ltd 198 APPENDIX D STANDARD LOADING MODELS D 2 5 BD21 Annex D AXLE WEIGHTS AND SPACING VEHICLE O1 W1 A1 W2 42 W3 A3 W4 A4 W5 A5 W6 O2 m KN m KN m KN m KN m KN m KN m 32 tonne 4 Axle Rigid 1 00 63 77 1 20 63 77 3 90 112 82 1 30 73 58 1 00 38 tonne 4 Axle 2 2 Artic 1 00 63 77 3 00 112 82 5 10 98 10 1 80 98 10 1 00 40 tonne 5 Axle 2 3 Arctic 1 00 58 86 3 00 112 82 4 20 73 58 1 35 73 58 1 35 73 58 1 00 40 tonne 5 Axle 3 2 Artic 1 00 58 86 2 80 112 82 1 30 63 77 5 28 78 48 1 02 78 48 1 00 40 tonne 5 Axle 3 2 Artic 1 00 58 86 2 80 63 77 1 30 112 82 5 28 78 48 1 02 78 48 1 00 40 tonne 5 Axle 3 2 Artic 10 5 tonne drive axle 1 00 49 05
95. ck 12 20 false false 0 10 Block 13 20 false false SR o o g Block 14 20 false false Fil force H user defined o lo Block 15 20 false false Fil force V user defined 10 lo Block 16 20 false false FA force M o lo Oo Block 17 20 false false ee llo o a Block 18 20 false false SRE o lo o Block 19 20 false false Fil force H actual lo o Block 20 20 false false Fil stress actual o lo Block 21 20 false false Fil stress M o o Block 22 20 false false o 10 C aa fase fase false Jo o o b aina na lan faia falca falee a a ps Ta Figure 20 11 Explorer context menu From here you can copy and paste sections of data or by selecting View determine which properties are displayed as columns in the explorer LimitState Ltd 150 CHAPTER 20 DISPLAY OPTIONS LimitState Ltd Chapter 21 Analysis To perform an analysis on the Analysis menu click Solve Alternatively this command can be accessed via the solve button on the toolbar Y and the keyboard shortcut for the command is F5 21 1 Auto solve If the user finds that they use the Drag and solve see Section 4 1 7 method for the majority of their problems the Auto solve feature should be enabled This will cause LimitState RING to automatically solve each time the vehicle is moved To enable check the Solve automati cally box in the Preferences dialog located in the Tools menu 21 2 Types of analysis 21 2 1 Normal analysis When a
96. ct mm Output Load Case Name Vehicle s Position s mm Effective Width mm Solution 1 Load Case 1 Default 1kN Single Axle 1250 2500 455 146 Minimum adequacy factor 455 146 Note the adequacy factor is the multiplier on factored vehicle loads required to cause collapse factors Figure 7 3 Mortar loss in a LimitState RING model 7 8 2 Ring separation in multi ring brickwork arches Various bonding styles are used in the arch barrels of masonry arch bridges Figure 7 4 IEEE a stone voussoir b brick header c brick stretcher d brick hybrid 1 ring 1 ring 3 rings ES ale rings Figure 7 4 Typical masonry arch bonding patterns A powerful feature of LimitState RING is the ability to model an arch barrel which comprises a number of separate rings Figure 7 5 LimitState Ltd 60 CHAPTER 7 DETAILED BRIDGE ASSESSMENTS USING LIMITSTATE RING Bridge5 ring LimitState RING File Edit Select View Tools Analysis Help ooa 06000 OI e a 88 8 Property Editor Project Property Assessor Auto width calculation Effective bridge width Indudes reinforcement Location P Edit Bridge _LeftAbutment Spani Piera 2 Abutment Fil Profile MEA gt Segmental shape Y Midspan rise h mm 1750 Span I mm 5000 Q a a a a a a No of units Ring thick t mm LA 1 115 2 115 3 40 115 4 9
97. dge stable under own self weight but unable ii 0 lt AF lt 1 0 to carry the specified applied live loads able to carry AFx applied load Bridge able to carry specified applied live loads ciii Loa AF able to carry AF x applied load iv AF could not be Structure geometrically locked e g for a very determined locked thick arch with infinite crushing strength v AF could not be Structure unstable under action of dead loads determined unstable e g for a very thin or distorted arch Table 10 1 Computed adequacy factor AF possible scenarios In some circumstances an apparently adequate structure will be found to either be unstable under its own self weight or to have a very low computed adequacy factor i e Outcomes i ii or v In such a case the input parameters used for the analysis should be carefully reviewed and revised if necessary It will be found that changes to some input parameters can have a major influence on the computed adequacy factor Alternatively it is possible that features not included in the model are in reality significantly altering the load carrying capacity of the structure In this case recourse to an alternative analysis procedure may be necessary If outcome iv is obtained then it is generally worthwhile 77 78 CHAPTER 10 INTERPRETING OUTPUT FROM LIMITSTATE RING to re run the analysis with finite masonry crushing strength so that a sol
98. dicted carrying capacity of a given bridge if the real structure contains more than 40 blocks 7 1 1 Partial factors of safety In order to facilitate limit state analysis of bridges values for the partial factors of safety shown in Table 7 1 can be specified Partial Factor Description Symbol Permanent load masonry Yf m Permanent load fill Vf Permanent load surface fill ballast Yf sf Permanent load track yfl Axle load Ffl Dynamic load Vf dyn Material masonry strength ams Material masonry friction rat Table 7 1 Partial factors of safety used in LimitState RING 53 54 CHAPTER 7 DETAILED BRIDGE ASSESSMENTS USING LIMITSTATE RING Some assessment codes use a global condition factor A global condition factor should not normally be applied to LimitState RING analysis output since the effects of defects such as ring separation low strength masonry and the influence longitudinal cracks have on the ability of a given bridge to distribute the load transversely can all be accounted for directly 7 2 Modelling the shape of the arch In LimitState RING the arch shape can be modelled using one of the following profiles Segmental The arch profile is formed from a single segment of a circle constructed using the crown rise and span measurements User defined multi segment The arch profile is formed from multiple segments of circles which fit a series of user defined data points Use
99. done automatically 13 4 Piers To edit the geometry of a pier simply click on the relevant tab to display the dialog in Figure 13 4 LimitState Ltd 98 CHAPTER 13 BRIDGE GEOMETRY M Edit Bridge Left Abutment Span 1 Pier 1 Span2 Right Abutment Fill Profile Height h mm Thickness at top t mm Thickness at base t mm Number of blocks n Backing height over pier h mm 0 0 Figure 13 4 Geometry Pier Properties 13 4 1 Default pier model By default LimitState RING presumes that all piers are constructed similarly in that they are each 1000mm high by 1000mm wide at both the top and the base and that they are all constructed from ten blocks with no backing above them 13 4 2 Modelling piers explicitly To override the default pier model simply enter new values in the relevant boxes of each pier Aspects that can be modified include e Height e Thickness at top e Thickness at base Number of blocks Backing height see Section 5 8 4 for more details 13 5 Fill profile To edit the upper and lower profiles of the surface layer simply click on the relevant tab to display the dialog in Figure 13 5 LimitState Ltd CHAPTER 13 BRIDGE GEOMETRY 99 Taking the left springing position of the first arch as the origin enter the x and y co ordinates at a point on the lower edge of the surface fill highway or ballast railway and give the depth at that point x th
100. e bridge You can do this by dragging the vehicle in the Viewer window to the left and right sides of the model and noting the distances at which the loading is just touching the spans 2 Open the Loading dialog Ensure that the vehicle you wish to move across the bridge is selected in the dropdown menu In the Position field for the vehicle enter the far left distance as noted in Step 1 Click the Add Load Case button Select Copy an existing load case Select the target load case 0 N O Oo A Specify the number of loads that will be needed to adequately cover the whole bridge with a reasonable spacing For example for a bridge with loading from 1000mm to 6000mm 40 additional load cases would require a spacing of 175mm The exact number and spacing of the cases is left to the judgement of the user LimitState Ltd CHAPTER 15 LOADING 121 9 Click OK the new load cases will be generated Now when the problem is solved all loading cases will be considered Note that If you need to model different vehicles you should setup different models since the necessary load case spacing will differ between vehicles 15 5 2 Method 2 Drag and solve An alternative method of finding the critical load position is to enable automatic recalculation whenever the load vehicle is moved in the Viewer pane To enable this feature go to the Tools gt Preferences dialog Select the option to Solve auto matically a
101. e horizontal distance from the left springing point of the first arch mm y the vertical distance from the level of the left springing to the base of the surface fill mm Surface fill ballast depth the depth of surface fill or ballast from the top surface to point x y mm Edit Bridge Left Abutment Spani Pier 1 Span2 RightAbutment Fil Profile all co ordinates relative to intrados springer of span 1 Figure 13 5 Geometry Surface Fill Note 1 The x and y distances are always relative to the left intrados springing of Span 1 2 User defined fill profiles are formed from a series of straight lines that intersect the points specified LimitState Ltd 100 CHAPTER 13 BRIDGE GEOMETRY LimitState Ltd Chapter 14 Material properties With the exception of backing see Section X the material properties can be found and mod ified within the Materials dialog click Tools gt Materials Alternatively the command may be accessed via the toolbar and the keyboard shortcut for the command is Ctrl 4 or by clicking the Materials Dialog icon 5 on the Properties toolbar This will open the dialog shown in Figure 14 1 Edit Bridge Masonry Backfill Surface Fill Specify properties for All masonry All masonry Properties Crushing properties v Model crushing f All masonry Unit weight kN m 20 Compressive strength N mm 5 Sliding properties
102. e of Fire Engine Tonnes kN Spacing Front Rear Group m Dennis DF 16 26 159 51 3 60 59 84 99 67 1 Dennis RS amp SS 11 70 114 78 3 60 47 09 70 63 1 Dennis Rapier 11 00 107 91 3 60 43 95 63 95 1 Dennis Sabre 13 00 127 53 3 80 53 96 73 58 1 Dennis Sabre 14 50 142 25 4 20 53 96 88 29 1 Leyland MS 1600 16 26 159 51 3 68 64 84 99 77 1 Leyland MS 1600 16 26 159 51 4 62 64 84 99 77 1 Leyland MS 1600 16 26 159 51 5 26 64 84 99 77 1 Dodge 12 20 119 68 3 50 44 93 84 76 1 Dodge 13 21 129 59 3 80 47 38 89 76 1 Dodge 13 21 129 59 4 04 47 38 89 76 1 Dodge 16 26 159 51 4 50 64 84 99 77 1 Dodge 16 26 159 51 5 20 64 84 99 77 1 Dodge 16 26 159 51 5 80 64 84 99 77 1 Ford 13 00 127 53 3 73 47 38 89 76 1 Ford 13 00 127 53 4 04 47 38 89 76 1 Bedford SLR1 12 55 123 12 3 84 42 87 87 21 1 Bedford SLRA 12 55 123 12 3 51 42 87 87 21 1 rea 13 50 132 44 3 86 46 11 91 23 1 DAF FF55 230 16 26 159 51 3 90 44 15 93 20 Dodge 7 50 73 58 3 50 31 98 49 83 Dodge 6 60 64 75 3 60 22 56 48 07 Note It is apparent that for some vehicles the summation of front and rear axle loads does not equal the stated gross weight Values in the LimitState RING vehicle database have been calculated directly from the values as given in the code and are therefore compliant with this document lt should also be noted that in each case the summation is always greater than the gross value and thus leads to the calculation of a conservative solution Table D 11 BD21 Annex E Fire Engi
103. e to import details of a vehicle previously saved in a tab separated variable text txt file This type of file can easily be exported from a spreadsheet or can be created using a text editor such as Windows Notepad The Notepad text file shown in Figure 15 3 would generate the same library entry as was entered manually in the dialog above B 3x7t_Triple_Axle txt Notepad File Edit Format View Help Vehicle 3x 7 Tonne Triple Axle 1 3m Axle Spacing Axles Position i loadedLength dynamicFactor 0 1800 FALSE 1300 1800 FALSE 2600 1800 FALSE Figure 15 3 Defining a new vehicle from file The first row of the file specifies whether the vehicle is editable or not enter 0 for an editable vehicle or 1 for a non editable vehicle The second and third rows of the file define the name of the vehicle The fourth and fifth rows of the file define the number of axles The sixth row specifies the labels for the vehicle data this should be copied exactly The remaining rows in the file are the specific data relating to each axle Force The force or load imparted by the axle in KN Position The position mm of the axle Width The width of the axle Loaded length The longitudinal length mm of wheel in contact with the surface rail or road Dynamic factor Specifies whether the axle is subject to dynamic partial factors as outlined in Section 16 Using a spreadsheet the same data could have been entered as shown in Figure 15
104. e will be displayed it must be borne in mind that remote from the zone of failure this is simply one of many possible distributions LimitState Ltd 80 CHAPTER 10 INTERPRETING OUTPUT FROM LIMITSTATE RING LimitState Ltd Part IV User Guide 81 Chapter 11 The Graphical Interface 11 1 Introduction The LimitState RING graphical interface is designed to give the user maximum flexibility over defining the problem and setting problem parameters The default LimitState RING screen is divided into a number of areas as shown in Figure 11 1 Bridges ring LimitState RING Auto width calculation Bridge type Comments Effective bridge width Indudes reinforcement false amp Viewer Pane Property Editor e a a El E E Y El fe a E a is run at 18 33 53 on Thu Jan 27 20 pad Case Name Vehicle s Position s mm Effective Width mm Caen tes w Output Pane tm am re nn Note the adequacy factor is the multiplier on factored vehicle loads required to cause collapse factors Axle load 1 0 Dynamic 1 Minimum adequacy factor 455 146 x 8506 Figure 11 1 Areas utilized in LimitState RING The areas shown by default are as follows e Title bar 83 84 CHAPTER 11 THE GRAPHICAL INTERFACE Menu bar area Top toolbar area Left hand toolbar area Viewer pane Property Editor e Output pane e Status bar A brief overvie
105. ean Union vehicles 2 45 226344564840 58 50948 196 D 2 4 BD21 Annex A AW Schedule 3 197 D25 BD21 ANNER D s coa chee nee a amp HS Se we SS 198 LimitState Ltd CONTENTS 11 D26 BD21 Amnex E 24662456 45646 e625 a SEE 199 D27 BD21 ANNER re oe ee Ge eee RSS ne ra mie 200 ERE BD37 HB Loading 2426 4 2 sas aoe See oe a ee eee a 201 0 2 9 BD86 Special Vehicles e 0 wed bed Bee Ree ee Se get 202 Cee BU oe ees ue De Se Be bo ee eA eee al 204 E Worked examples general 205 E 1 Example 1 single span stone voussoir underline railway bridge 205 E 1 1 MEM ce de dates an co air gi ap he eo Ree Sh GA as mG ee a ee 205 EL Assessment data nd od Die ee Oe EA Oe owe wee ee 207 lak ANA UN ek ak Se A we we he ee ee BSR 208 Sa Stee nee eee SS SES SSS Oe Ee anses 209 E 2 Example 2 multi span multi ring brickwork underline railway bridge 210 Ba AI oir a ea is ES EEA HE BOS EES 210 E 2 2 ASESESMENTOAA 2 4 8 4 eee Rhee EOS wR memes ee eS 211 EX A alysis OSOS s ios na Me ae Ee ER ER OEE RUES me OS 213 E24 Ses ed oe REE ES See o EEE 214 F Worked examples reinforcement 217 F1 Case 1 All reinforcement in full tension 217 F2 Case 2 Bottom reinforcement in full tension top reinforcement in partial tension 219 F3 Case 3 Bottom reinforcement in full tension top reinforcement in full compression221 G Validation against bridge test
106. ed load could be either applied to the surface of the fill or optionally directly onto the arch barrel Also to allow fill to optionally be placed only on one side a keystone of extended height was used Finally the fill on the passive side could optionally be contained either side of the three quarter point hinge so as to act as a vertical dead load only Further details of the tests are provided elsewhere Gilbert et al 2007 Experimental and LimitState RING results are summarised in Table G 2 In the LimitState RING analyses measured geometrical and unit weight properties were used The measured angle of soil friction was also used Passive restraint vertical dead weight over a half span and distribution of the load were switched off in line with the circumstances of the particular test arch being modelled It is evident from Table G 2 that the LimitState RING predictions are remarkably good all within 10 of the experimental results This verifies that the simplified LimitState RING soil model is capable of capturing the key effects of backfill LimitState Ltd APPENDIX G VALIDATION AGAINST BRIDGE TEST RESULTS 227 Test Photographs of model bridges with Experimental peak load RING 3 0 As superimposed displacement vectors at capacity N results without analysis dc peak load extended keystone N mean expt result T1 107 108 107 E 104 104 106 33 99 E 141 142 140 133 94 P T3
107. ed that the bridge contains solid piers However intru sive investigations have not yet been undertaken to identify the extent nature of any backing above the piers although photographs show staining of the brickwork below what seems likely to be the top level of backing Load model LM71 is used in this assessment Photographs Figure E 3 Photographs of Example 2 bridge Commentary e This bridge will initially be analysed assuming that the rings forming the arch barrel are This is a fictitious bridge with details taken from several real bridges LimitState Ltd APPENDIX E WORKED EXAMPLES GENERAL 211 well bonded together the influence of potential ring separation will then be considered to obtain a more conservative estimate of bridge strength e When all arches in a viaduct have nominally identical geometry modelling only the two spans either side of the tallest pier is generally sufficient for the purposes of a preliminary assessment e Inthe preliminary assessment backing will conservatively be ignored although parametric studies have indicated that this could enhance carrying capacity by around 30 40 E 2 2 Assessment data Parameter Value Notes Effective width 3930mm Governed by the presence of longi tudinal cracks in arch barrel Table E 7 General Parameter Value Notes Span 13610mm Rise 6780mm Thickness 682 5mm Survey values Depth of fill amp
108. eee eS 153 21 4 2 No solution found cra A AA A 153 214 3 Aborting an analysis ke e A a RS 153 22 Post analysis functions 155 22 1 VISA DU s i Li LL SSSR di 4 SEER a SS 155 22 141 Force diagrams ike eke ee eee OS Eo Se A BRS eS 156 22 2 Quantitative output 2 ee ns en css ROE Ree eS A SS 156 LimitState Ltd 10 CONTENTS 23 Report output 159 23 1 Viewing report output coord mme ad pa sas 159 23 2 Adding a template header or footer 160 V Appendices 163 A Mathematical formulation 165 A 1 Joint equilibrium formulation adequacy factor analysis 165 A2 Joint equilibrium formulation support movement analysis 166 A 3 Including finite masonry material strength 166 Musel Algorithm ci iaa a St Us 167 AA Including reinforcement 2 4 4434 lt lt da dus 168 A 5 Worked example 0 io one dre bh we ni ER dogs A lus 170 A 5 1 Equilibrium constraints s e e isse ne tada ELA Set a 170 AE Yield constraints 2 4 Ho ds 4e d 68 Se deh CA ODS us LA 172 A 5 3 Objective function 172 A5 4 Problem matrix o 0 0 172 B Additional notes on the backfill model 175 B 1 Boussinesq distribution MOJO 2 2 ee SR RES Rues has NE ete 175 B 2 Limiting horizontal Till stresses lt lt o lt iovocerinas ear don eis 176 B 3 Passive and active fill pres
109. ent The number of blocks in the abutment and their dimensions can then be amended Note in LimitState RING no fill pressures are assumed to act behind abutment blocks so the explicit abutment modelling option should only be used when such fill is not present otherwise it may reasonably assumed that the abutments are fixed LimitState Ltd CHAPTER 13 BRIDGE GEOMETRY 95 13 3 Spans To edit the geometry of a span click on the relevant tab to display the dialog in Figure 13 8 P Edit Bridge gt Left Abutment Span 1 Right Abutment Fil Profile Type EA Stone voussoir Na MBUser defined shape multi segment A Details x mm y mm u 6 3 Z No of units Ring thickness t mm 1 40 300 Bed joints normal to intrados Assume uniform ring thickness Figure 13 3 Geometry Span properties For all span types there are options to specify the number of blocks units used for the span and the thickness of the ring 13 3 1 Number of rings The Type drop down menu offers a choice from three types of voussoir Stone voussoir the span is or acts as if it were a single ring of stonework masonry Bonded brick the span consists of multiple rings of masonry that act as if they were one e g if the barrel contains header bonded brickwork where certain bricks are laid end on to provide a mechanical connection between rings Multi ring debonded the rings of a span are model
110. er 300 18 300 21 0 300 18 300 Axle Spacing mp Lond 30 au cominner 300 18 300 26 0 300 18 300 Axle Spacing HB Load 37 5 Unit 6m Inner 375 18 375 6 0 10 18 375 Axle Spacing HB Load 87 5 0nit 6m Inner 375 1 8 375 11 0 10 1 8 375 Axle Spacing HE Los 37 5 Unit miinner 375 18 375 16 0 10 18 375 Axle Spacing US 375 18 375 21 0 10 18 375 Axle Spacing HB Load 37 5 Unit 6m Inner 375 18 375 26 0 10 18 375 Axle Spacing mB Pad 4 Dal onminner 450 18 450 6 0 450 18 450 Axle Spacing HB Load 45 Unit 6m Inner 450 18 450 11 0 450 18 450 Axle Spacing RE Laos Unit emmnet 450 18 450 16 0 450 18 450 Axle Spacing HB Load 45 Unit 6m Inner 450 1 8 450 21 0 450 18 450 Axle Spacing He Load 45 Unit Gm nnes 450 18 450 26 0 450 18 450 Axle Spacing Overnang W3 wa W5 Overhang Table D 13 BD37 HB loading models Key W1 W2 etc axle weights KN A1 A2 etc axle spacings m LimitState Ltd 202 APPENDIX D STANDARD LOADING MODELS D 2 9 BD86 Special Vehicles SV80 130 130 130 130 130 130 kN kN kN kN kN kN 1 2m 1 2m 1 2m 1 2m sal f 0 35m LO si Overall Vehicle Width je 3 0m Critical of 1 2m or 5 0m or 9 0m Note Overall vehicle width overall track width Figure D 1 BD86 SV80 loading vehicle all permutations included in LimitState RING vehicle database SV100 165 165 165 165 165 165 kN kN kN kN kN kN 1 2m 1 2m 1 2m 1 2m
111. er effects 2 csc eka cis ee mt 6 Rue Ra G 69 LimitState Ltd CONTENTS 7 8 2 Loading from highway vehicles 69 8 2 1 Highway loading models gt su Rte diet sue bed er me 69 8 2 2 Transverse distribution and effective bridge width 70 82 0 Dynamic effecis 22 he ead dou eR a OOS OES ES Oe air EYE 71 8 2 4 Other effects a a 71 9 Using other LimitState RING features to investigate bridge behaviour 73 9 1 Identifying the causes of observed cracks using the Support Movement feature 73 9 2 Exploring load paths under service loads 73 9 3 Modelling bridge spans with intermediate supports 76 10 Interpreting output from LimitState RING 77 10 1 Adequacy factor lt heeded is 8 4 dde hs SSS HR dm 77 10 2 Mode of response lt lt lt re eee UE Rob RR 78 10 3 Zone of thrust internal forces 79 IV User Guide 81 11 The Graphical Interface 83 TET sl AE 83 DS TUS Bar ei aa A A A MR SA MEN ae WP ro 84 113 Menu Bars oc cocinada ar a a ad a m eh 84 TLA TODAS o 200000 la a a ds A Ra e A AA em a e i 84 TL Viewer PaE lt cord ha ECAR ERE A ed ca dl a de a A 85 116 Property EMO dr AAA E ds A A 86 NET PANE A IT di eh ees D AU dre Oo 87 118 DOS Ba o aa Li he A dual ia tetes dada 87 11 9 Rearranging the toolbars kee ee ee ERS EE bu Hu ee 87 VTS amenu en 2000 Dic ER A san kes see 88
112. erged solutions are obtained more rapidly and reliably than was the case with RING ver sion 1 x LimitState Ltd 44 CHAPTER 5 THEORETICAL BASIS OF LIMITSTATE RING 5 7 Sliding failures Unlike many other masonry arch bridge analysis programs LimitState RING does not rule out the possibility that sliding failures might occur A saw tooth model for friction is used also referred to as associative friction This means that separation is assumed to accompany sliding The main advantage of using a saw tooth model is that the linear character of the problem is preserved Whilst it can be shown that use of a saw tooth model for friction can lead to non conservative adequacy factors being obtained if sliding is involved in the critical failure mode Drucker 1954 when previously applied to multi ring brickwork arch bridges reasonably good agreement be tween experimental and numerical results were obtained in fact it was found that the numerical multi ring model always under estimated the experimentally observed carrying capacity LimitState Ltd CHAPTER 5 THEORETICAL BASIS OF LIMITSTATE RING 45 5 8 Backfill 5 8 1 General The vertical dead weight of backfill material effectively pre stresses the masonry in an arch thereby increasing its load carrying capacity provided the constituent masonry has sufficient compressive strength The backfill also has two other beneficial effects as shown in Fig
113. es are as follows Unit weight Equal to the unit weight of the backfill this is likely to be a conservative estimate of the true unit weight Compressive strength 5MPa default although this can be overridden if desired see below Tensile strength OMPa i e tensile forces active pressures are not permitted The compressive resistance offered by the backing can be modified in the following way e Select the Block s that correspond to the backing elements that are to be modified e In the Property Editor set Fill force H Max to the desired force Note that the value should be Force op backing X Vertical projected block area where 0 backing S the allowable horizontal stress for the backing and the vertical projected block area assumes a 1m block depth into the page Where backing exists over a pier there exists the possibility for two backing elements to be associated with a block one from each of the two associated spans In such cases if there is a discrepancy in the allowable force that the backing is permitted to assume the lower more conservative value will be chosen Should the limiting force of a backing element be reached for any particular analysis the ele ment will turn green in the viewer in contrast to active backfill elements which turn blue 14 5 Surface fill The last tab in the materials dialog concerns the properties of the surface fill material or ballast material in the case of ra
114. etting it can be done in the Preferences dialog Tools gt Preferences Note that solving complex multi ring problems using CLP may result in a long computation time 21 4 Analysis results 21 4 1 Adequacy factor found Following a successful analysis the minimum Adequacy factor will be displayed at the bottom right of the LimitState RING application window and also in the Output Pane If multiple load cases are specified then this load factor will be the lowest found for all the load cases tried The Adequacy factor is the multiplier on factored vehicle loads required to cause collapse in the structure being modelled 21 4 2 No solution found When crushing of the masonry is not enabled it is possible that the applied load can be in creased without limit In this case the structure can be described as being geometrically locked This result will typically occur if the specified arch thickness is large and rigid abut ments are specified Alternatively if no part of an applied load falls on the bridge then this outcome will result Alternatively it might be that no solution could be found because no viable equilibrium state could be identified This result will typically occur if the arch is the wrong shape in relation to the specified dead loading i e the dead loads alone are sufficient to cause the structure to collapse In this case an unstable message will be reported 21 43 Aborting an analysis After an analysis
115. f sight is lost From LimitState RING 2 0 it is assumed that load dispersed beyond a free standing abutment is lost In LimitState RING 1 x no load is assumed to be lost Table H 2 Benchmark problems comparison of results using different versions of Limit State RING LimitState Ltd 236 APPENDIX H COMPARISON WITH PREVIOUS VERSIONS LimitState Ltd Bibliography Burroughs P Hughes T Hee S amp Davies M 2002 Passive pressure development in ma sonry arch bridges Proc Inst Civ Eng Structures and Buildings 152 4 331 339 Chen Y 2004 Strengthening of masonry arch bridges with near surface reinforcement PhD thesis University of Bradford Department of Civil Engineering Chen Y Ashour A amp Garrity S 2007 Modified four hinge mechanism analysis for masonry arches strengthened with near surface reinforcement Engineering Structures 29 8 1864 1871 Choo B Coutie M amp Gong N 1991 Finite element analysis of masonry arch bridges using tapered elements Proc Inst Civ Eng Part 2 91 755 770 Department of Transport 2001 DMRB Volume 3 Section 4 Part 3 BD 21 01 The Assessment of Highway Bridges and Structures Department of Transport Drucker D C 1954 Coulomb friction plasticity and limit loads Journ Appl Mec Trans ASME 21 4 71 74 Gilbert M 1997 Gross displacement mechanism analysis of masonry bridges and tunnels Proceedings of the 11th International B
116. ff angle deg in Lim itState RING 3 2 a is directly equivalent to Limiting angle rads in RING 1 5 except that the units are now degrees not radians B 6 4 Horizontal pressure type None To replicate this option in LimitState RING 3 2 a set 6 and c to zero in the section Soil Prop erties Note the LimitState RING 3 2 a import facility will also set the Factor m and Factor Mpc to zero and uncheck the box Keep m K gt 1 0 in the Advanced section Passive zone parameters Uniform To replicate this option in LimitState RING 3 2 a in the section Soil Properties set equal to 6 the selected value of the Limiting fill barrel angle of friction and c to the specified RING 1 5 uniform pressure Magnitude Click on Advanced and in the section Passive zone parameters set the Factor m to zero and Factor mpc to 1 2 tan 45 6 2 Finally uncheck the box Keep m K gt 1 0 The value given in the box m Ky c should be the required value of the uniform pressure To correctly set the required limiting backfill arch barrel angle of friction set the Friction multiplier on value to 1 0 Also set the Adhesion multiplier on c value to zero Classical To replicate this option in LimitState RING 3 2 a First click on Advanced and in the section Passive zone parameters set the Factor m to a preferred value This may be chosen as any value 0 lt mp lt 1 0 The LimitState RING 3 2 a import facility use the default value of 0 33 Then
117. fined transverse distribution rules can alternatively be used readers are referred to Section 8 1 4 and Section 8 2 2 for further guidance on choosing an effective bridge width Consider for example the stresses at the base of two geometrically similar solid masonry piers If the second pier is n times as large in all dimensions as the first then its volume and hence self weight will be n larger However the area at the base of the pier will only be n times larger so it follows that the gravity stresses at the base and elsewhere in the second pier will be n n n times larger LimitState Ltd CHAPTER 5 THEORETICAL BASIS OF LIMITSTATE RING 41 5 4 6 Range of collapse modes identifiable The general problem formulation and rigorous mathematical solvers employed mean that Lim itState RING can identify numerous potential failure mechanisms Figure 5 4 shows a selection ofthose mechanisms that have been observed whilst using the program to assess real bridges The ability of LimitState RING to identify hitherto unknown failure modes has led to some in teresting findings For example it has previously been suggested that a multi span bridge can safely be analysed as a series of separate single spans if the piers are stocky i e thick in comparison to their height However this is not in general the case For example the ade quacy factor associated with the mechanism shown on Figure 5 4 f is actually much lower than
118. fter dragging a vehicle and close the dialog Ensuring that there is only a single load case in the problem click and hold the left mouse button over the loading vehicle in the Viewer pane Drag the vehicle to a new position using the mouse and release the button The problem will solve automatically with the load at the position you have specified Using a process of trial and error the critical location can be established 15 6 Moving a load in a multiple load case problem Load case positions can be altered by specifying a new value in the Position field of the Load ing Dialog If a position is changed when multiple load cases are present the user will be asked whether to move all cases by the same increment or just to move the current case 15 7 Viewing load cases To view a particular load case and if an analysis has just been performed also the associated collapse load factor select this using the Up Down arrows in the Load case spinbox see Section 20 4 1 LimitState Ltd 122 CHAPTER 15 LOADING LimitState Ltd Chapter 16 Partial factors LimitState RING has been designed to be code agnostic That is the assignment of partial factors on load material strengths etc is left entirely up to the user The available partial factors are detailed in Table 16 1 all are set to 1 0 by default but can be overridden Partial factor name Symbol Notes Load factor applied to
119. gt span 2 results from the program should be treated as being very approximate In such cases it may often be found that the predicted load carrying capacity is in excess of the bearing capacity of the arch fill material i e is unattainable in practice 5 4 5 3D effects In general spandrel walls at the edges of a bridge can stiffen the arch prior to failure and de pending on their end restraint conditions may also enhance the ultimate limit strength Studies of the influence of spandrel walls on the carrying capacity of full scale single and multi span laboratory bridges are detailed elsewhere Melbourne amp Gilbert 1995 and Melbourne et al 1997 However if a bridge is wide in comparison to its span then the effects of the spandrel walls on the central section of the bridge may be quite minimal Furthermore a common defect observed in masonry bridges is detachment of the spandrel walls this is evident by the presence of longitudinal cracks running close to the edges of the bridge For these reasons spandrel walls are not modelled in LimitState RING Since the software idealises the arch in two dimensions it is most suited for assessing masonry arch bridges which span squarely between abutments readers are referred to Section 7 3 for further advice on modelling skew bridges By default LimitState RING utilises a user specified fixed bridge width in the analysis However an effective width which varies according to simple user de
120. h falls on or beyond a fixed support is lost Note that this differs from RING 1 x behaviour 7 6 The influence of infill material Except in the case of relatively shallow arches the passive restraint offered by infill material soil and or backing behind an arch can lead to very significant increases in carrying capacity The problem for the assessment engineer lies in determining for the purposes of analysis what level of restraint is likely to be available In the case of a bridge with apparently insufficient load carrying capacity it may be necessary to perform appropriate intrusive investigations e g dig trial pits perform penetrometer testing etc These investigations can furnish soil strength parameters for use in LimitState RING Such investigations can also be useful in identifying unexpected beneficial construction details e g the presence of generous concrete backing LimitState Ltd CHAPTER 7 DETAILED BRIDGE ASSESSMENTS USING LIMITSTATE RING 57 If internal hollow spandrel walls are encountered then these may be approximately modelled in LimitState RING by 1 specifying backing above the piers and abutments and 2 using an averaged unit weight for the fill which takes account of both the solid and voided regions of the spandrel Finally if there is evidence to suggest that the distribution of the live load is more limited than usual e g due to pulverisation of the fill material then the distr
121. he field e g see Section G 4 was that the internal constructional details and material properties were known LimitState RING was originally developed to assist with the interpretation of the results from these laboratory tests Since the original publication of the work in The Structural Engineer Melbourne amp Gilbert 1995 Melbourne et al 1997 Gilbert amp Melbourne 1994 the program has been significantly enhanced and for example now accounts for material crushing around hinges and includes more realistic models of the dispersion of the applied load through the backfill Figure G 1 Bolton bridge 5 2 containing debonded rings approaching collapse note the dif fused hinges under the load 223 224 APPENDIX G VALIDATION AGAINST BRIDGE TEST RESULTS Figure G 2 Bolton bridge Multi 2 built with detached spandrel walls awaiting testing Figure G 3 Bolton bridge Multi 2 approaching collapse note that the left and centre spans are involved in the failure mechanism gt Val Figure G 4 Bolton bridge Multi 2 immediately following collapse note that the right span has remained fully intact LimitState Ltd APPENDIX G VALIDATION AGAINST BRIDGE TEST RESULTS 225 LimitState RING analysis kN S amp A D 8 a soil B EOD As A but using RING B Bridge Description 8 amp properties except o g measured angle of experiment Sars Using Measured soil
122. he passive earth pressures m corrects for several effects including active earth pressures as listed above This is unlikely to occur for single span arches where an external load is applied above the active side such that the effect of the dis tributed load itself normally dominates the active side soil pressures It may however be relevant for a deforming arch that is part of a multispan arch bridge but not subject to an external load Burroughs et al 2002 suggested using an alternative pressure coefficient for arches Ke Ko e K Ko B 10 Where Ko is the at rest earth pressure coefficient typically taken as 1 sin though if the fill has been compacted then Ko can take on significantly higher values and e is an empirical factor When q is high and if e is taken as equal to e g the default value of m 0 33 then the pressure coefficient Ke m K since Ko is very small compared with Kp There is thus very little difference between this approach and that used by LimitState RING For low values of q the main potential advantage of the approach proposed by Burroughs et al is that it limits the minimum value of Ke to Ko However since m is designed to correct for a number of factors not just the simple passive pressure coefficient it was considered inappropriate to use this as the default approach in LimitState RING However since the user is free to select mp then this approach can be applied if desired by setting
123. he steel Revised assumed concrete force LimitState Ltd 220 APPENDIX F WORKED EXAMPLES REINFORCEMENT Concrete force 50 x 1000 x 5 x 1073 250kN Top steel reinforcement force Top steel force 250 200 50kN Hence both reinforcement bars are in tension but the top bar is not fully yielding Moment capacity 250mm 1000mm Figure F 4 Reinforced beam stress block Case 2 Taking moments about centre of compression block depth 25mm Moment capacity 25 x 50 175 x 200 36250kNmm Adequacy factor AF Moment capacity Applied moment 36250 1225 29 5918 LimitState RING calculated adequacy factor AF 29 6 to 3 significant figures LimitState Ltd APPENDIX F WORKED EXAMPLES REINFORCEMENT 221 F3 Case 3 Bottom reinforcement in full tension top reinforce ment in full compression In this example the concrete crushes to a depth below the top reinforcement with both bars fully stressed the top bar being in full compression and the bottom bar in full tension The beam properties are given in Table F3 Property Value Block size 250mm x 1000mm bridge width Beam span 5000mm 100mm block width 4900mm Applied force 1kN span 2 Top reinforcement 100kN 50mm from top surface Bottom reinforcement 400kN 50mm from bottom surface Concrete crushing strength 5 x 10 2kN mm2 Table F 3 Reinforced beam worked example Case 2 pro
124. he user to apply the dynamic factor to axles in turn to determine which loading pattern is most onerous Note that to have any effect the dynamic partial factor must also be set to an appropriate value by default it is set at unity LimitState Ltd 68 CHAPTER 8 LOADING MODELS fr ta Ballast ed le Effective width a Automatically computed effective width using default parameters based on sleeper width amp mini mum loaded sleeper ballast fill depth ssn ashi cracks Effective width b Possible reduced user specified effective width due to longitudinal cracks Spandrel Effective width c Possible reduced user specified effective width due to proximity of adjacent track and edge of bridge Figure 8 3 Transverse dispersal and effective bridge widths railway LimitState Ltd CHAPTER 8 LOADING MODELS 69 8 1 6 Other effects Nosing and centrifugal forces On curved track the vertical effects of nosing and centrifugal actions can lead to one rail being more heavily loaded than the other Both actions are speed dependent Nosing forces are caused by side contact of the wheel flange on the rail Since the forces are generally assumed to act perpendicular to the rail on canted track there will be a small vertical component to consider applied to one rail only When one rail is more heavily loaded than the other due to either effect it is usually considered prudent to con
125. heck on the limiting horizontal backfill pressures that can be applied is overridden when user defined horizontal forces pressures are specified 14 3 3 Passive zone parameters In the LimitState RING standard backfill model soil pressures in the passive zone are deter mined using modified lateral earth pressure theory This idealization is discussed further in Section 5 8 3 The horizontal stress c is given by Oh MpKpy2 MpcKpcC 14 1 where 7 is the unit weight of the backfill and z is the depth of fill at the point where the pressure is being calculated mp and mp are user defined pressure modification factors Factor m Specify the factor m for determining the resultant lateral earth pressure arising from backfill self weight as defined in equation 14 1 The resultant value of m K is given in the adjacent LimitState Ltd 108 CHAPTER 14 MATERIAL PROPERTIES box Factor m Specify the factor mpe for determining the resultant lateral earth pressure arising from the back fill cohesive strength as defined in equation 14 1 The resultant value of m K c is given in the adjacent box Note 1 Small changes to the specified passive zone parameters can lead to large changes in the computed collapse load Hence care must be exercised when selecting these values 2 The horizontal backfill stresses defined above may be reduced by the program if these are sufficiently high to cause relative sliding between
126. hich correspond to these in a work sense also become available sliding displacement opening displacement rotation This allows the collapse mechanism to be identified which in this case is a four hinge failure mechanism LimitState Ltd 174 APPENDIX A MATHEMATICAL FORMULATION LimitState Ltd Appendix B Additional notes on the backfill model B 1 Boussinesq distribution model According to Boussinesq theory the vertical stress at point X due to a uniform pressure q on a strip area of width B and infinite length is given in terms of the angles and as defined in Figure B 1 O T a sin amp cos a 26 TT Figure B 1 Vertical stresses calculated according to Boussinesq theory Although the distribution has been used for many years in masonry arch analysis programs e g Choo et al 1991 from a theoretical perspective the use of a Boussinesq type distribution is not entirely satisfactory since 1 there does not exist a semi infinite elastic half space below the load 2 the elastic distribution indicated is not really compatible with an ultimate load analysis However notwithstanding the above comments the above equation does provide a useful means of generating a suitable bell shaped curve Furthermore to avoid excessive distribution at the ultimate limit state when concentration of the load is likely the Boussinesq distribution is truncated in LimitState RING with the computed
127. hicle Explorer Load Case Explorer Edit Properties Cursor View Analysis Magnification Load Cases Zoom SEE View 3D Cursor 3D Help File lt Figure 20 10 Toolbar Property Editor context menu From here it is possible to toggle the displaying of the Property editor see Section 19 1 Output Pane see Section 11 7 Explorers see Section 19 2 and Toolbars see Section 20 4 LimitState Ltd CHAPTER 20 DISPLAY OPTIONS 149 20 5 3 Explorer context menu Right clicking within any explorer will bring a menu of the type shown in Figure 20 11 P Eridges ring Limitstate RING File Edit Select View Tools Analysis Help dd 08200 0a Block Explorer Q D Unit weigh Support Mz Support m Support m Support m Disp Project a E Skewback 0 El Span 1 Copy Ctri C E J Ring Paste Ctrl V x i Ring 2 View gt Area t Blodk1 20 o lo Block2 20 Sellect All Ctri A w Unit weight o lo Blok3 20 Deselect Al Ctrl D V Support x 0 o Block4 20 false false DR Support y o lo Block5 20 false false E o o a Boks 20 false fase Tank z o lo Bok 7 20 false false a lo o Block8 20 false false v Support movement y 0 lo Y Blok9 20 false false V Support movement rotation o o Block 10_ 20 false false y Displacement x o 10 ES Block 11 20 false false lo o v Displacement y ol Blo
128. his strongly indicates that backing or very strong fill material is present in the real structure and potentially also in similarly constructed structures in the area This can then be included in subsequent load factor analyses e Vehicles can be run across a settled bridge to investigate load paths and to see whether the hinge positions move if they are predicted to move significantly in the model under traffic and if secondary stiffening elements such as securely attached spandrel walls are not present in reality then this might be a cause for concern as continual opening and closing of joints may lead to incremental damage to the structure e Once the centering is removed many bridges appear to bed down to a statically deter minate or near statically indeterminate state This state can be approximately replicated by moving the supports appropriately Vehicles can then be introduced and load paths established If necessary an adequate margin of safety can be ensured by applying a suitable partial factor to the axle loads ensuring that the structure remains stable 129 130 CHAPTER 18 SUPPORT MOVEMENT ANALYSIS 18 2 Support movement wizard The easiest way of imposing support movements is to use the Support Movement Wizard which can be accessed via Support movements in the Tools menu Figure 18 1 Support Movement Wizard Current analysis mode Support movement applied to 1 of 3 supports Project imposed support
129. horizontal stress that can be applied is al ho cos 0 tan sind a cos a cos o tan sin 0 B 7 v cos 0 sin 0 tan sin 0 cos6 sin 0 tan B 3 Passive and active fill pressures At collapse portions of the arch will move into the backfill thereby mobilizing passive earth pressures Other portions of the arch may move away from the soil thereby mobilizing active earth pressures The passive pressures in particular can have a significant effect on the arch collapse load The semi empirical soil model employed in LimitState RING models passive earth pressures by applying empirical correction factors m and mpe to the lateral earth pres sure coefficients K and Kpc that are normally computed for vertical smooth retaining wall as follows _ 1 sing _ 2 Kyo 2 Kp 89 The LimitState RING soil model does not by default model active pressures It is important to appreciate that quantitative values of m and mpc are at present empirical and have limited theoretical basis They correct for a number of effects including e the curved shape of the arch e the magnitude of the soil arch interface friction and or adhesion e gross displacement and strength mobilization effects see also Appendix B 4 LimitState Ltd 178 APPENDIX B ADDITIONAL NOTES ON THE BACKFILL MODEL e in situ lateral earth pressures arising for example from compaction of the fill and e active pressure effects on other portion
130. ht click and select Copy from the context menu Right clicking anywhere on the window brings up the context menu 11 8 Status Bar The Status Bar is used to provide e Short term progress messages to the user e display of the x y coordinates of the current mouse position when the mouse pointer is within the Viewer pane The Status Bar is used to provide e Short term progress messages to the user e display of the x y coordinates of the current mouse position when the mouse pointer is within the Viewer pane 11 9 Rearranging the toolbars It is possible for the user to rearrange the position of the toolbars within the user interface To do this 1 Hover the mouse cursor over the left hand side of the toolbar you wish to move a four pointed arrow will be displayed 2 Click and hold the left hand mouse button 3 Drag the toolbar to a new position in the interface Available locations will be highlighted and the view will shift to accommodate the toolbar LimitState Ltd 88 CHAPTER 11 THE GRAPHICAL INTERFACE 4 Once you have located the position that you wish to place the toolbar release the left mouse button and the bar will be dropped into place Many toolbars can also be shrunk to show a reduced selection of the buttons available this is useful if you are using the software on a PC with a small screen e g a laptop These are indicated by the presence of a double arrow gt gt at the
131. ht of the extrados face of an arch block LimitState Ltd CHAPTER 14 MATERIAL PROPERTIES 109 e For an element positioned above a rigid abutment the end of the element remote from an arch block is assumed to be fixed in position e For an element positioned above an abutment block the end of the element remote from an arch block is assumed to be fixed to a vertical line drawn from up from the centroid of the top block in the abutment This means that the element will only compress if there is a relative closing movement between the backfill above the abutment block and the arch block to which the element is attached in other words no horizontal backfill pressures need be mobilised if blocks in an arch move say to the left provided the skewback on top of the abutment also slides to the left This approach effectively assumes that there is no additional backfill say to the left of the abutment block this is true for the case of an arch span adjacent to a beam span Note 1 In this release uniaxial fill elements cannot be fixed to the sides of pier abutment blocks Unchecking the Auto identify passive zones box causes the fill elements to act both in the passive and active senses e applying pressure to the arch whether this moves towards or away from the fill The user can then manually define in which areas of the bridge the pressures will be applied This is achieved by editing values in the passive res
132. i dei e Based on measured in Bolton laboratory aaa Sine Hon nao 0 5 bridges mean measured value was 0 53 Melbourne amp Gilbert 1995 Masonry crushing strength 5N mm Unit weight surface fill bal 18kN m3 last Unit weight backfill 18kN m Longitudinal angle of disper di ad sion of live loads ballast a 15 b Highway bridges equivalent to 2 1 surface fil b 26 6 as recommended in UK Highways Agency Standard BD21 01 be cogi 3 a Railway bridges b Highway bridges PA P e sd LimitState RING standard value calibrated against load tests Angle of friction 30 Cohesion c 0 kN m Model dispersion of live load true Model horizontal passive true pressures Soil arch interface friction ae 0 66 multiplier on y Soil arch interface adhesion 05 multiplier on c l Fill dispersion model ballast f Normal surface fill Fill dispersion model backfill Boussinesq With 30 cutoff Passive zone factor mp 0 33 Passive zone factor Mpc 0 05 Keep mpKp gt 1 0 true Auto identify passive zones true Table C 4 Default material properties LimitState Ltd 188 APPENDIX C DEFAULT PARAMETERS C 5 Partial factors Partial factor on Symbol Default Permanent load masonry Yfm 1 0 Permanent load fill YFF 1 0 Permanent load surface fill ballast Vfsf 1 0 Permanent load track Vet 1 0 Axle load VE 1 0 Dynamic load Y f dyn 1 0 Material masonry strength dns 1 0
133. i e visible separation of the blocks Figure 10 1b This is perfectly normal a hinging b sliding Figure 10 1 Scaled deformation leading to distortion In some cases it will be observed that the critical failure mechanism identified cannot occur in practice e g there might in reality be some obstructing element which prevents a pier from LimitState Ltd CHAPTER 10 INTERPRETING OUTPUT FROM LIMITSTATE RING 79 rotating in the manner indicated in the failure mechanism In this case the model should be modified as appropriate and the analysis re run 10 3 Zone of thrust internal forces At the point of failure the internal forces are just in static equilibrium with the applied dead and live loads The most useful visual indicator of how the compressive force is transmitted through the masonry is the line of thrust This will always stay within the masonry in order to satisfy one of the stipulated yield conditions Additionally forces are also transmitted through contacts between inter ring boundaries if present It is often useful to examine forces at specific locations in the bridge for example to facilitate subsequent checks that the abutments can withstand the thrust from the arch Note that the distribution of internal forces is only uniquely determined in parts of the structure which are at the point of collapse Thus although details of a distribution of internal forces for the entire structur
134. ibution cutoff angle should be reduced below the default value of 30 7 7 Modelling the mechanical properties of masonry In many cases the mechanical properties of the masonry are of secondary importance when ascertaining the load carrying capacity of a masonry arch bridge Indeed in some cases reasonable accuracy can be obtained even when it is assumed that the masonry possesses infinite compressive strength This is most likely to be the case when the span is relatively short and when the constituent masonry is relatively strong However in other cases it is prudent to specify a finite masonry crushing strength in LimitState RING Masonry is a composite material comprising masonry units stone brick concrete etc and mortar joints The mechanical properties of the units and the joints together give rise to com posite material properties which are generally quite different to those of either the masonry unit or masonry joint parent materials An important point to realise is that the crushing strength specified in ring should be that of the composite masonry material This will typically be lower than that of the masonry units but higher than that of the mortar in the joints Note also that in LimitState RING different strengths can be allocated to the spans and piers or even to localized areas of a span or pier Masonry typically fails in compression due to tensile splitting of the masonry units Since ten sile splitting is a quasi br
135. ient of friction tangential 0 5 Typical OF degraded mortar Boton laboratory tests measured value Estimated value engineering 2 Crushing strength masonry 15 N mm bricks with thin joints lt 8mm E Estimated value most of fill actually 3 Unit weight backfill 21 KN m brickwork backing Angle of friction backfill 30 Default value Cohesion backfill 0 kN m Default value Unit weight ballast 18 kN m Estimated value Track weight incl sleepers rails GRO JOO Ta om eis UR RES 1 90 kN m NR GN CIV 025 assuming BH rail and ballast between sleepers and timber sleepers Table E 12 Material properties characteristic values LimitState Ltd APPENDIX E WORKED EXAMPLES GENERAL 213 Parameter Value Notes Distributed part of this load model ignored initially but depending on observed failure mechanisms it may be necessary to include this later LM71 no Load model name udi Table E 13 Live load models to be considered Parameter Value Notes Spread through ballast longitudinal 15 4 1 from UIC 774 2R EN 1991 2 Spread through ballast transverse 15 P VOR CITE ENAS not used Spread through fill transverse 30 not used Boussinesq Fill dispersion model longitudinal with 30 cutoff Table E 14 Live load dispersion parameters Parameter Value Notes Masonry strength 25 Maso
136. ies of load cases In this way the user can quickly identify the critical load position Click the Add Load Case button e Check the option to Copy an existing load case e Specify the target load case usually load case 1 e Choose the number of times to copy the load case and the offset for each e g to model a vehicle at 10 positions over a 3000mm bridge copy load case 1 9 times with a 300mm offset e Click OK to return to the Loading dialog e Complete the Wizard by clicking Finish e Click the Solve button a Note For more detailed information on editing the bridge loading see Section 15 4 2 Following an analysis The collapse mechanism and associated adequacy factor multiplier on factored vehicle loads will be displayed after a short time see Figure 4 6 The processing time depends on the complexity of the problem specified and on the speed of the PC being used The output window will display details of the analysis and it is also possible to view moment shear and normal force diagrams see Section 22 1 1 diagrams for the structure LimitState Ltd CHAPTER 4 QUICK START TUTORIAL 29 Bridge4 ring LimitState RING Edt Select View A dy 08600 Qi 808 Property Editor 205998 Saa 888 86 6 Figure 4 6 Collapse mechanism and adequacy factor following a LimitState RING analysis Note For more detailed
137. igure 4 1 Alternatively click the New icon in the File toolbar E New Bridge Wizard Bridge type Highway Effective bridge width 5 Specified mm 2500 Railway underline Auto computed Bridge includes reinforcement Other details optional Geometry Bridge name New Bridge Reference N Location a Map reference Partial Factors Figure 4 1 Wizard Project Details 4 1 Using the New bridge wizard The New bridge wizard guides the user through the process of defining the bridge Geometry see Section 4 1 3 Materials see Section 4 1 5 and Applied loading see Section 4 1 6 Further explanation of all parameters that can be modified is given elsewhere all dialog pages displayed as part of the wizard are also accessible from the Tools menu Section 20 3 5 4 1 1 Introduction to the wizard The New bridge wizard function in LimitState RING is designed to help the user quickly gen erate a model of their structure 23 24 CHAPTER 4 QUICK START TUTORIAL It should be noted that at any point during the Wizard process it is possible to click Finish LimitState RING will automatically fill in any information that has not been explicitly supplied by assuming default values and using information already given up to that point In most cases the Wizard process involves entering information in a sequential manner clicking Next gt after each step However it is possible t
138. il in compres sion due to tensile splitting of the masonry units and hence widespread micro cracking may indicate that the compressive capacity of the masonry has been almost exhausted note that rough calculations of the stresses within a masonry pier can be misleading because the pier may be hollow or rubble filled The cracks may continue to propagate due to long term creep effects or due to the effects of repeated fatigue live loading Masonry compression failures although rare will generally have catastrophic consequences and thus the assessment of a bridge with such symptoms should be carried out with extreme care a simple LimitState RING analysis alone is highly unlikely to be appropriate in such a case LimitState Ltd CHAPTER 7 DETAILED BRIDGE ASSESSMENTS USING LIMITSTATE RING 63 7 9 Modelling flooded masonry arch bridges Masonry arch bridges typically derive the majority of their load carrying capacity from self weight effects In flood situations buoyancy reduces these effects and hence also potentially the load carrying capacity According to Archimedes principle the ratio of normal to flooded bridge load carrying capacities may be postulated to lie between the buoyancy ratios ratio of dry to submerged weight of the backfill and masonry typically 1 6 to 1 8 This has recently been confirmed by a recent series of tests on small scale model arch bridges Hulet et al 2006 When using LimitState RING to assess an un
139. ilways This is assumed to be uniform throughout the model and therefore is given a uniform dispersion model 14 5 1 Unit weight Enter a unit weight in kN m for the surface fill ballast material LimitState Ltd CHAPTER 14 MATERIAL PROPERTIES 111 14 5 2 Angle of dispersion Enter an angle of load dispersion for the surface fill ballast material This will be used to calculate the loading pressures on the underlying structure using a uniform model LimitState Ltd 112 CHAPTER 14 MATERIAL PROPERTIES LimitState Ltd Chapter 15 Loading In LimitState RING a database of loading vehicles can be set up and then used in load cases Multiple load cases can rapidly be set up by copying and repositioning an existing load case at regular intervals across a bridge On the Tools menu click Loading to obtain the Loading dialog shown in Figure 15 1 Alterna tively click the Loading icon B Edit Bridge Load Cases Name Load Case 1 M Gof Vehide 1 Default 1kN Single Axle elete All Cases Except Current Add Load Case s Vehide Database EJ Figure 15 1 Loading dialog 15 1 Mirrored vehicles Many loading vehicles possess an irregular spacing of axles and it can therefore be necessary to consider the path across the bridge in both directions from left to right and from right to left To facilitate this LimitState RING allows the user to
140. information on performing an analysis refer to Section 21 4 3 Output from analysis On the Analysis menu see Section 20 3 6 click Report This command opens a window displaying full details of the model and analysis results It is then possible to edit this file if necessary and then to output to a printer or paf file for later retrieval Note For more detailed information on outputting results see Section 23 4 4 Modifying properties with the property editor The Property editor allows viewing and in many cases permits modification of the properties of any object within the problem To become familiar with this powerful feature try the following Unlock the project by clicking on the padlock icon E Click on a block press and hold the CTRL key to select several blocks Selected items will change colour to bright pink Navigate to the Property editor and using the drop down menu The properties of the selected blocks will now be shown try changing the unit weight The bridge will reset so that a new analysis can take place that will account for any changes that have been made LimitState Ltd 30 CHAPTER 4 QUICK START TUTORIAL e Click the Solve button a and see the change in adequacy factor Before using LimitState RING on real life projects it is suggested that users spend time famil iarizing themselves with the property editor and its functions Note For more detailed information on the Property Edi
141. ing G 3x 8 Tonne Triple Axle 1 4m Axle Spacing E BD21 Annex D H 32 Tonne 4 Axle Rigid 38 Tonne 4 Axle 2 2 Artic 40 Tonne 5 Axle 2 3 Artic Es 40 Tonne 5 Axle 342 Artic 40 Tonne 5 Axle 3 2 Artic S 40 Tonne 5 Axle 3 2 Artic 10 5 Tonne Drive 40 Tonne 5 Axle 3 2 Artic 10 5 Tonne Driv E 41 Tonne 6 Axle 3 3 Artic EH 41 Tonne 6 Axle 3 3 Artic Es 44 Tonne 6 Axle Artic 44 Tonne 6 Axle Ar tic E 44Tonne 5 Axle 3 2 Artic 40ft ISO Container we Project vehides Standard vehides must be renamed before properties can be edited Default 1kN Single Axle 3x 7 Tonne Triple Axle 1 3m Axle Spacing Rename Vehicle Delete Vehicle Add Vehicle Force KN Local Position mm Width mm Loaded length mm 1 68 67 0 1800 300 2 68 67 1300 1800 300 3 68 67 2600 Figure 15 5 Defining a new vehicle within LimitState RING 15 2 4 Editing vehicle properties The name position and force exerted by the axles of a vehicle can all be changed by modifying the properties in the right hand window of the Vehicle Database If several vehicles are being used in the project be sure to use the drop down box to select the correct one LimitState Ltd CHAPTER 15 LOADING 117 15 2 5 Renaming a vehicle To rename a vehicle click on the Rename Vehicle button and enter the new text 15 2 6 Deleting a vehicle To delete a vehicle click on the Delete Vehicle button Note that
142. ints Si lt put la Mor each contact i 1 c A 4 where A is the load factor which is the same as the adequacy factor AF when the vehicle loads are not pre factored B is a suitable 3b x 3c equilibrium matrix containing the direction cosines and q and f are respectively vectors of contact forces and block loads Thus q n1 1 771 N2 82 M2 Ne Sc Mc f fp Af where fp and fr are respectively vectors of dead and live loads Contact and block forces dimensions and frictional properties are shown 165 166 APPENDIX A MATHEMATICAL FORMULATION in Figure A 1 Using this formulation the LP problem variables are the contact forces n1 s1 m where n gt 0 si m are unrestricted free variables and the unknown load factor A contact thickness f friction 4 3 v Figure A 1 Block and contact forces A 2 Joint equilibrium formulation support movement analysis The problem may be stated as follows Min E A 5 subject to the equilibrium constraints Bq fsup fp A 6 and a constraint specifying support movement dsupfsup E 0 A 7 where E is the support movement energy du and f are respectively vectors of pre defined block support movements and unknown block support reactions see Figure A 1 for block de grees of freedom Other terms are as defined in Appendix A 1 The yield conditions equation A 3 and equation A 4 are also be imposed in unchanged form Using
143. is started LimitState RING then waits for a solution to be found To abort this process the user should click on the red stop button on the toolbar or press the Esc key to abort the analysis and return control to the user LimitState Ltd 154 CHAPTER 21 ANALYSIS LimitState Ltd Chapter 22 Post analysis functions 22 1 Visual output Once a problem has successfully solved visual output is displayed on the viewing pane The thrust line shown is that calculated without accounting for the presence of reinforcement i e Eccentricity Axial Force Moment Depth of crushing Axial Force Masonry crushing strength x Bridge Width It follows that when the reinforcement is active the thrust line will lie outside the barrel thick ness as indicated in Figure 22 1 Figure 22 1 Thrust line lying outside the arch barrel in areas where reinforcement is active Note in the vicinity of backing the thrust line may exhibit spikes as large forces are transmitted from the arch into the backing material Also if reinforcement is specified in the problem the line of thrust may be displayed as being outside of the arch but without an associated hinge forming Both of these situations are perfectly normal 155 156 CHAPTER 22 POST ANALYSIS FUNCTIONS 22 1 1 Force diagrams To allow alternative interpretation of the behaviour of the structure when reinforcement is present in LimitState RING the capability to view norm
144. ittle phenomenon the compressive stress strain characteristics of masonry do not exhibit the long flat plateau assumed in rigid plastic theory and also in Lim itState RING As an example of this the experimental compressive stress strain loading re sponses of the masonry used in the Bolton test bridges discussed in Appendix G 1 are shown in Figure 7 2 To account for the potential lack of ductility it is possible to factor down exper imentally recorded values for the ultimate strength of the masonry However this refinement may not be deemed necessary in practice because 1 the bridge load carrying capacity is often relatively insensitive to the precise value of the specified crushing strength 2 the eccentric loading regime found in masonry arch bridges in the vicinity of hinges appears to permit realisation of higher stresses at the edge of a cross section compared with those in a specimen which has been uniformly loaded LimitState Ltd 58 CHAPTER 7 DETAILED BRIDGE ASSESSMENTS USING LIMITSTATE RING 25 00 20 00 15 00 10 00 Stress N mm 5 00 0 00 0 1000 2000 3000 4000 5000 Strain x1E 3 Figure 7 2 Bolton masonry compressive stress strain loading responses masonry solid engi neering bricks and 1 2 9 cement sand lime mortar 7 8 Modelling bridge defects The majority of masonry arch bridge stock was constructed more than a century ago and in most cases the passage of time will have led to a
145. ix F Finally it should be noted that the contact normal forces and moments reported in Limit State RING in the Property Editor Explorers and Report are total values i e as given by nto and Miot respectively LimitState Ltd 170 APPENDIX A MATHEMATICAL FORMULATION A 5 Worked example This worked example is designed to help illustrate how the mathematical formulation described in Appendix A 1 may be applied in practice To ensure that the number of problem variables and constraints are kept down to an absolute minimum a simple 3 block arch is considered as shown in Figure A 4 This geometry can be generated in LimitState RING by specifying a span of 20m a rise of 10m a ring thickness of 1 5m and 3 blocks in the span Each block labelled A B and C is for simplicity assumed to weigh 1 unit Block A is also subject to a unit live load applied at the centroid The blocks are separated by four contact surfaces labelled 1 2 3 and 4 The blocks are taken to be infinitely strong and the contacts are taken to have a coefficient of friction of 0 6 The objective is to find the load factor or multiplier which can be applied to the live load in order to cause collapse N B The load factor A is equivalent to the Adequacy Factor AF when the live load is not pre factored 20 15 Figure A 4 Details of simple 3 block arch example problem As described in Appendix A 1 the problem formulation involves equilibrium
146. ject ridges ring Limitstate RING G80 ee 000000 2909588 2 DA 6 6 OO Figure 19 1 The LimitState RING Property Editor The Property Editor opens by default when LimitState RING is started but can be toggled on and off using the View menu see Section 20 3 4 Some of the functions in LimitState RING are only accessible via the Property Editor These are described in detail in this section Other functions and attributes can be accessed and modified elsewhere but are shown for convenience in the Property Editor 131 132 CHAPTER 19 VIEWING AND MODIFYING ATTRIBUTES To begin using the Property Editor first select an area of the bridge using the methods de scribed in Chapter 20 The drop down menu in the Property Editor gives the option of viewing and or editing the attributes belonging to the different types of object that have been selected Table 19 1 lists the objects within the LimitState RING environment that may be selected along with sample related functions that can be accessed via the Property Editor Property Editor option Description Unique function s All Modify all selected objects N A Fill element s Modify only selected fill elements Limiting force Block s Modify only selected blocks Fill force H actual Fill force H max Fill force H user defined Fill force V Fill force V user defined Support move
147. l coefficient of friction 0 6 in equation A 4 and re arranging to ensure problem variables are on the left hand side 81 lt 0 6n1 A 19 z 81 0 61 lt 0 A 20 s gt 0 6n A 21 z 81 0 6n1 lt 0 A 22 These yield constraints can also be used for contacts 2 3 and 4 by simply changing the subscript according to the contact number A 5 3 Objective function In this case the objective is simply to maximise the load factor A A 5 4 Problem matrix The problem matrix also termed the linear programming tableau may now be formed as shown in Table A 1 LimitState Ltd APPENDIX A MATHEMATICAL FORMULATION 173 Main Problem variables forces Contact 1 Contact 2 Contact 3 Contact 4 Shear Normal Moment Shear MN Moment Shear Normal est zea a fase z CE sus TE Moment Equilibrium constraints 0 866 4 662 2 674 EA EA Contact 1 Yield constraints Contact 2 Contact 3 No tension a prs a N N a gt nr Sliding Sliding Contact 4 0 75 0 75 Objective Table A 1 Problem matrix Linear Programming tableau This problem can now be solved using any suitable linear programming solver For this problem the critical load factor may be found to be 2 742 Once solved values for the contact stress resultant variables shear force normal force mo ment also become available Additionally quantities w
148. lation amp licensing Further details on installation and licensing are provided in the separate Installation manual distributed with the software 3 2 Starting LimitState RING To start LimitState RING on the Start menu point to Programs and click LimitState RING A few seconds after starting LimitState RING the welcome screen shown in Figure 3 1 should appear LimitState RING Startup What do you want to do Create a new bridge project Open an existing bridge project Open a recently accessed bridge project C Documents and Settings Desktop Bridge4 ring C Documents and Settings Desktop Bridge3 ring C Documents and Settings Desktop Bridge2 ring C Documents and Settings Desktop Bridge 1 ring Show this dialog next time Figure 3 1 LimitState RING welcome screen You then have three options 21 22 CHAPTER 3 GETTING STARTED Create a new bridge project select this option and click OK to bring up the Chapter 4 Open an existing bridge project select this option and click OK to open a previously saved project or example Open a recently accessed bridge project select this option choose a file from the list and click OK to return to a recent project LimitState Ltd Chapter 4 Quick Start Tutorial The easiest way to get started using LimitState RING is to select Create a new bridge project and click OK the New bridge wizard will then start on the Project Details tab F
149. led as separate entities separated by fric tional contacts this should be used e g if ring separation also known as delamination has occurred Note a multi ring analysis is often more computationally expensive than a single ring analysis 13 3 2 Arch type As well as the type of voussoir LimitState RING gives the option to select from several types of arch shape for each span LimitState Ltd 96 CHAPTER 13 BRIDGE GEOMETRY Segmental shape A segmental arch shape assumes that the curvature of the span follows the shape of a single segment cut from a circle defined using the span and rise measure ments entered by the user By clicking on the Advanced button the user is given the option to specify the abutment angles By default the auto calculate feature is selected By unchecking this box measured angles can be entered Multi Segment User defined A multi segmental arch shape assumes that the curvature of the span follows the shape multiple segments formed from different circles based on a series of user defined points Interpolated User defined An interpolated arch profile uses an interpolated best fit b spline based on a series of user defined points Three centered Pseudo elliptic A three centered pseudo elliptic arch profile assumes that the arch profile is formed from segments of three circles using the crown rise and span measurements Pointed A pointed or Gothic arch profile is for
150. limitstate 224 LimitState RING Manual VERSION 3 2 b LimitState Ltd November 10 2016 LimitState Ltd The Innovation Centre 217 Portobello Sheffield S1 4DP United Kingdom T 44 0 114 224 2240 E info limitstate com W http www limitstate com LimitState Ltd LimitState RING LimitState Ltd All rights reserved No parts of this work may be reproduced in any form without the written permission of LimitState Ltd While every precaution has been taken in the preparation of this document LimitState Ltd assumes no responsibility for errors or omissions LimitState Ltd will not be liable for any loss or damage of any kind including without limitation indirect or consequential loss including loss of profits arising out of the use of or inability to use this document and or accompanying software for any reason This document is provided as a guide to the use of the software It is not a substitute for standard references or engineering knowledge The user is assumed to be conversant with standard engineering terminology and codes of practice lt is the responsibility of the user to validate the software for the applications for which it is to be used LimitState Ltd LimitState Ltd Contents Introduction and Quickstart 1 Introduction 11 About Gmistate RING LL ea a a eee eS eee et dha SGA BES LE See ee oes oe Be ek ee e Qo ee era a S 1 3 LimitState RING terminology cn ee eee
151. llows access to more specialized soil properties New Bridge Wizard Masonry Backfill Surface Fill Specify properties for All masonry E All masonry Properties 2 Crushing properties z Unit weight kN m 20 Y Model crushing Geometry Compressive strength Nim 5 Sliding properties 4 Model sliding excluding inter ring sliding Partial Factors i n Standard friction coeff y 0 6 1 AA Model inter ring sliding a GS f Inter ring friction coeff p 0 5 Da hy ads L_siadk _next gt _ Finish Figure 4 4 Wizard Material Properties Note 1 For more detailed information on editing the backfill properties see Section 14 2 2 For more detailed information on editing the bridge materials see Section 14 4 1 6 Step 5 Add vehicles Using the Vehicle database see Section 15 2 specify the vehicles to be used in the current project as shown in Figure 4 5 LimitState Ltd CHAPTER 4 QUICK START TUTORIAL 27 New Bridge Wizard Load Cases Name Load Case 1 e 10f 1 Vehicle Position Mirror Dynamic Factor 1 Default 1kN Single Axle 1250 false Not applied 2 v Geometry Partial Factors Delete All Cases Except Current Add Load Case s Cancel lt Back Next Figure 4 5 Wizard Adding loads 1 Click on the Vehicle Database button A dialog will appear that includes all of the pre defined vehicle types in
152. m Ke Kp However for the same reasons discussed earlier with respect to the option Keep m K gt 1 0 at the present time it is recommended that Burroughs coefficient Ke is used with caution in LimitState RING LimitState Ltd APPENDIX B ADDITIONAL NOTES ON THE BACKFILL MODEL 179 B 4 Gradual build up of passive pressures Experimental evidence has shown that peak passive pressures are only mobilised when struc tural deformations of sections of an arch into surrounding fill material are relatively large It can therefore be argued that a gross displacement analysis Gilbert 1997 is required to iden tify the peak load and that a normal LimitState RING analysis which assumes infinitesimal deformations is inappropriate However in reality the fill in most short span bridges will be very well compacted due to traf ficking and hence relatively large pressures can be expected to be mobilised even when dis placements are relatively small For example Figure B 3 shows the mean horizontal pressures mobilised above the springings or piers of three of the most well instrumented bridges tested at Bolton in the 1990s refer also to Appendix G These bridges were backfilled with a well compacted graded crushed limestone fill material O o Multi span no 2 O1 oO Bridge no 3 3 ND 5 8 gt Bridge no 3 4 gt 0 ED D O gt N O O Total horizontal pressure kN m oo 0 0 25 0 5 0 75
153. med using a segment of a circle determined using the quarterspan rise crown rise and span measurements then mirrored along a vertical line at midspan User defined profiles By opting for a user defined arch profile non uniform shapes can be accounted for When selected in the drop down menu a user defined option will display a table in which to enter x and y coordinates of points around the intrados of the arch Note the positions of all points on each arch should be measured relative to point 1 which will have co ordinates 0 0 Subsequent points should be entered in order of increasing x distance 13 3 3 Number of units Enter the number of masonry units you wish to model in the ring Note sufficiently accurate results can normally be achieved by modelling only a proportion of the actual physical units in a given ring e g 40 units per ring is often acceptable for a medium span arch this often reduces run times considerably with only moderate loss in accuracy However it should be noted that collapse load predictions obtained using this strategy may be slightly non conservative 13 3 4 Ring thickness Enter the ring thickness in mm User defined rings also have the option to have a non uniform thicknesses By unchecking the Assume uniform ring thickness box a further tab is added to the coordinates panel in which LimitState Ltd CHAPTER 13 BRIDGE GEOMETRY 97 extrados ring points can also be added usi
154. ment rotation Support movement x Support movement y Contact s Modify only selected contact surfaces Enabled Mortar loss A and B Permit hinges Permit sliding The following are only accessible when reinforcement is specified Reinforcement depth A Reinforcement depth B Reinforcement max force C A Reinforcement max force C B Reinforcement max force T A Reinforcement max force T B Reinforcement shear capacity Vehicle s Modify only selected vehicles N A Axle s Modify only selected axles N A Table 19 1 Property Editor functions 19 1 1 Fill element s Limiting force The limiting force is that force KN per metre width at which the fill i e bar element yields This is a function of the specified soil properties i e the product of the limiting fill pressure and the vertical block height To modify the limiting fill force you must alter the Fill force H max see Section 19 1 2 value of the corresponding block entity LimitState Ltd CHAPTER 19 VIEWING AND MODIFYING ATTRIBUTES 133 19 1 2 Block s Fill force H actual This is the actual horizontal passive fill force applied to the block kN per metre width This will be zero 1 before solving and 2 in zones where the structure is moving away from the fill Fill force H max This is the maximum horizontal passive fill force that can be applied to the block kN per metre width It sh
155. ments Figure 22 3 Sample arch bridge normal force shear force and moment diagrams LimitState Ltd 158 CHAPTER 22 POST ANALYSIS FUNCTIONS LimitState Ltd Chapter 23 Report output 23 1 Viewing report output Following an analysis it is often useful to summarize details of the bridge and of the analyses performed and to then print this out LimitState RING comes with an inbuilt word processor so report output can be generated on any computer exported to an Adobe pdf file and or printed To view the report as shown in Figure 23 1 on the Analysis menu click Report 159 160 CHAPTER 23 REPORT OUTPUT Report View File Edit View Format Help B eixona BeiBryu EE E Ms Shel Dig 2 Close Report View li mitstate GX This report was generated by LimitState RING 3 0 3 11112 Summary Details Bridge name ie Reference No Map reference New Bridge Bridge type Assessing organization Date of assessment Highway Mon Jan 31 2011 Comments Results acy factor 719 6 at load case 1 this is the critical load case Mode of Response for Current Load Case Units Unless specified otherwise the following units are used throughout this report Distance Force Unit weight Material strength at eme me Ready Figure 23 1 LimitState RING report From here details can be changed as required or the layout altered using commands familiar to most users who have previously used word pr
156. movement feature in LimitState RING various limiting scenar 73 CHAPTER 9 USING OTHER LIMITSTATE RING FEATURES TO INVESTIGATE BRIDGE 74 BEHAVIOUR ios can be investigated Vehicles can be run across a bridge with imposed support movements to investigate load paths and to see whether the hinge positions move if they are predicted to move significantly in the model under traffic and if secondary stiffening elements such as se curely attached spandrel walls are not present in reality then this might be a cause for concern as continual opening and closing of joints may lead to incremental damage to the structure One limiting scenario which is likely to be of interest is that which follows removal of the cen tering following initial construction It is at this point that many bridges appear to bed down to a statically determinate or near statically indeterminate state This state can be approximately replicated by moving the supports appropriately in LimitState RING e g moving the supports of a single span bridge outwards Again vehicles can then be introduced and load paths es tablished If necessary an adequate margin of safety can be ensured by applying a suitable partial factor to the axle loads with the software indicating whether or not the structure remains stable LimitState Ltd CHAPTER 9 USING OTHER LIMITSTATE RING FEATURES TO INVESTIGATE BRIDGE BEHAVIOUR 75
157. movements Block Parent s x mm y mm rotation rads 1 Block 11 Pier 1 Pick Support Block Clear Table Revert to Standard Analysis Figure 18 1 Support movement wizard 1 With the Support Movement Wizard open click on Pick support block to move 2 Using the mouse click on a support green block in the modeller window 3 The wizard will re appear now containing details of the chosen support Enter details of the movement of that block in the table Note e distances are measured in mm with positive vertical movement being upwards e rotations are measured in radians anticlockwise about the centroid of the block 4 Repeat the first two steps until all the required movements have been entered If at any time you wish to return to the wizard without selecting a block click the Escape button 5 Click OK to return to the main window An analysis may then be carried out as normal with the prescribed support movement s being visible following an analysis The result of a support movement analysis is expressed in terms of energy in Joules As small displacement theory is used computed energy dissipation will vary linearly with the mag nitude of the prescribed movement LimitState Ltd Chapter 19 Viewing and modifying attributes 19 1 Using the property editor The Property Editor feature Figure 19 1 allows the user to quickly read and or modify the attributes of one or more objects within the current pro
158. mpressive force and the minimum amount of material needed to support it LimitState Ltd CHAPTER 1 INTRODUCTION 17 Edt Select Ven Tools Analysis Hep 0800000 axle distributed backfill elements NY SV I contacts selected backfil elements off objects AO 9 60 US skewback Figure 1 2 The main objects encountered in LimitState RING 1 4 About LimitState LimitState is a University of Sheffield spin out company specializing in the development of powerful yet easy to use software applications which use unique technology to rapidly identify critical collapse mechanisms and associated margins of safety This allows engineers to move beyond simple automated hand calculations and predefined mechanisms but without the need to resort to significantly more complex and potentially cumbersome techniques e g non linear finite element analysis LimitState co founder Dr Matthew Gilbert is a Chartered Civil Engineer who has been involved in masonry arch bridge assessment and research since 1990 developing the first version of RING in 1992 1 5 Using Help The software includes an online help facility which is largely based on this Program Reference Manual Pressing F1 at any time will activate the help system 1 6 System requirements LimitState RING runs on Windows XP Vista 7 8 and 10 Operating Systems support for OSX and Linux is available on request subject to dem
159. n alternative cursor option in the Cursor toolbar Rotate cursors In addition to the Rotate tool the model can be rotated by accessing any of the rotate cursors rotate x rotate y etc individually To do this right click in the Viewer pane to bring up the context menu then select Rotate and choose from one of the four options beneath the horizontal line as described above The cursor will then change to match the chosen option Clicking and holding the left mouse button then moving the cursor anywhere within the viewer pane will rotate the model in the preferred manner To exit the Rotate tool select an alternative cursor option in the Cursor toolbar Predefined viewpoints For quick inspection it is possible to view the model in the viewer pane from one of a number of predefined 3D viewpoints To change the current view to one of these right click the mouse in the Viewer pane to bring up the context menu then select View and choose from one of the following options Top View the model from above in the negative y direction Bottom View the model from below in the positive y direction Right View the model from the right in the negative x direction Left View the model from below in the positive x direction Front View the model from the front in the positive z direction This is the default view Back View the model from the back in the negative z direction Alternately these functions can be accessed by navigating
160. n in the analysis e Consideration should be given to including backing or stronger fill material in the analy sis this may help to compensate for the damaging effects of ring separation The pres ence or otherwise of this backing material should preferably be later verified by carrying out appropriate intrusive investigations e Additionally Dynamic factors can be applied to the computed adequacy factor as deemed appro priate LimitState Ltd APPENDIX E WORKED EXAMPLES GENERAL 215 Checks can be undertaken to ensure that different partial factors increasing dead load effects are not more onerous LM71 should be applied with the addition of a user specified length of distributed load For simplicity the adequacy factor has been calculated using the loading position found to be critical in the previous single ring analysis Additional analyses should be performed to ensure the critical loading position has not changed LimitState Ltd 216 APPENDIX E WORKED EXAMPLES GENERAL LimitState Ltd Appendix F Worked examples reinforcement Note that in these examples the hand calculated values are very slightly different to those obtained using the software due to the requirement in the software to include a very small 1mm camber F 1 Case 1 All reinforcement in full tension In this example the depth of concrete crushing remains entirely in the area above the top rein
161. n item in the Property Editor indicates that there are additional sub parameters relating to that item that may be viewed Click on the ul symbol to access these Left clicking on a value in the Property Editor allows you to modify it by typing or selecting your choice unless it is read only For specific parameters a clickable button may also appear which gives access to a further dialog to provide additional functionality The calculator see Section 11 11 may be used in any numeric data entry cell Right clicking on items that have been selected brings up a context menu relevant to that item Further information about properties that can be edit are given in Section 19 1 Bridges ring Limitstate RING Help dam 088200 OW pl UT gt il LK LS 2 e w e a I e a a a a Figure 11 4 Project properties displayed in the Property Editor LimitState Ltd CHAPTER 11 THE GRAPHICAL INTERFACE 87 11 7 Output Pane The Output Pane is used to display messages and information about the analysis to the user Any portion of text may be copied and pasted to another window text box or other application To select text perform the following steps e left click on the text and drag with the mouse to select a specific block of text e double click on a word to select it e triple click on a line to select it To copy press CTRL C or rig
162. name Figure 17 2 Specifying that a project includes reinforcement Once a model has been defined as containing reinforcement there is flexibility in the way that the user can add reinforcement to the model either 1 Select one or more Contacts using the mouse and enter the reinforcement details in the Property Editor 2 Use the Contact Select Tool which can be accessed via the Select menu This tool helps the user to add circumferential reinforcement to the entirety of one or more rings or spans by automatically selecting all the radial contacts of the chosen part To use the tool click the name of the bridge part that you wish to select If more than one bridge part is required hold down the CTRL key whilst clicking see Figure 17 3 Contact Select 5 Select radial contacts in specific spans rings hold lt CTRL gt for multiple items Span 1 Ring 1 Span 2 Ring 1 Indude edge contacts Figure 17 3 Contact Select Tool the radial contacts in the top ring of both spans of a twin span bridge will be selected to allow circumferential reinforcement to be added If the end radial contacts in a ring i e those that join the ring to the abutments also contain reinforcement ensure the Include edge contacts box is ticked this is selected by default Once the relevant contacts have been selected click OK The selected contacts will be highlighted see Figure 17 4 LimitState Ltd 128 CHAPTER 17 REINF
163. nes LimitState Ltd 200 APPENDIX D STANDARD LOADING MODELS D 2 7 BD21 Annex F AXLE WEIGHTS AND SPACING VEHICLE w1 A1 w2 A2 w3 kN m kN m kN 11 5 Tonne Single Axle 112 82 9 Tonne Single Axle 88 29 7 Tonne Single Axle 68 67 5 5 Tonne Single Axle 53 96 3 Tonne Single Axle 29 43 2x 9 5 Tonne Double Axle 93 20 1 3 93 20 FE EA ca 98 10 AE Overnang w1 W2 W3 W5 Table D 12 BD21 Annex F load vehicles Key W1 W2 etc axle weights kN A1 A2 etc axle spacings m axle weights reversed LimitState Ltd APPENDIX D STANDARD LOADING MODELS 201 D 2 8 BD37 HB Loading VEHICLE W1 KN A1 m W2 kN A2 m W3 kN A3 m WA kN HB Load 1 Unit 6m Inner Axle 10 1 8 10 6 0 10 1 8 10 Spacing HB Load 1 Unit 11m Inner 10 1 8 10 11 0 10 1 8 10 Axle Spacing HB Toad T Unie Smilanes 10 1 8 10 16 0 10 1 8 10 Axle Spacing pb Lead 1 Umt 2Im inngi 10 18 10 21 0 10 18 10 Axle Spacing HB Load 1 Unit 26m Inner 10 18 10 26 0 10 18 10 Axle Spacing HB Load 30 Units 6m Inner 300 18 300 6 0 300 18 300 Axle Spacing HB Load 30 Unit 1 Unilnner 300 18 300 11 0 300 18 300 Axle Spacing HB Load 30 Unit 16m Inner 300 18 300 16 0 300 18 300 Axle Spacing HB Koad g0 Unit 21m Inn
164. nforcement bars which span across the contact Rigid Blocks B Reinforcement Depth da th A A SA Crushing De Contact i Reinforcement Bars Reinforcement Depth da A Calculated by the software when crushing enabled Figure A 3 Contact surfaces with top and bottom reinforcement bars However the presence of reinforcement has the effect of modifying the total normal force and moment at the contact as follows Total normal force carried ns Neon Ca CB Ta TB Total moment carried Miot Meont da Ca Ta t dg CB Tp Where Ca TA and Cp Tp are respectively the compressive and tensile reinforcement forces near contact edges A and B and is the contact thickness The reinforcement forces are free to take on any positive value up to a user specified limit the software will find the values corresponding to the critical load factor The increased normal force and moment which can be carried means that the predicted load carrying capacity of a bridge containing reinforcement will always be greater than or equal to that corresponding to an otherwise identical bridge without reinforcement Modelling bars separately from the line contact as described above obviates the need to use a LimitState Ltd APPENDIX A MATHEMATICAL FORMULATION 169 more complex reinforced concrete type yield surface However the equivalence of the results obtained can easily be verified See Append
165. ng causes of the cracking e g to see whether these are consistent with vertical horizontal or perhaps angular settlement of one or more of the piers or abutments Figure 9 1 The observed response of a settled bridge can also be used to verify the model idealization A settled bridge can be considered to be of almost the same value as load test to collapse because when a bridge undergoes settlements many of the same modes of resistance are mobilized as when a bridge is subjected to excessive live loading Therefore it is very useful to try to correlate actual and modelled behaviour e g if it is necessary to include backing in the numerical model in order to replicate the observed mode of response then this strongly indicates that backing or very strong fill material is present in the real structure and potentially also in similarly constructed structures in the area This can then be included in subsequent load factor analyses 9 2 Exploring load paths under service loads Masonry arch bridges are multiply statically indeterminate structures and true load paths are therefore typically difficult to ascertain It is tempting for the engineer to undertake an elastic analysis to investigate service load behavior however the solutions gained will only be accu rate if the initial stress conditions and elastic properties are established Otherwise misleading indications of the bridge response can be obtained Alternatively using the support
166. ng the same method as for the intrados The ability to turn off the Bed joints normal to intrados option also becomes available 13 3 5 Inserting a span LimitState RING allows the user to insert new spans into the project without having to build the whole bridge again from scratch Simply select the tab of a span adjacent to the place where a new one is to be inserted and click the Insert span button LimitState RING will ask the user to decide whether the new span is to be inserted to the left or right of this position and after a choice has been made a new span and new pier will be added LimitState RING will also automatically renumber all objects to accommodate these changes The inserted span will assume the geometry of the original selection However the material properties will retain the default values Note 1 After inserting a new span the dialog remains on the original tab not that corresponding to the span that has just been inserted 2 It is prudent to check the properties of the inserted span 13 3 6 Deleting a span LimitState RING also allows the deletion of spans After selecting the span to be deleted in the geometry dialog by clicking the appropriate tab and clicking the Delete span button LimitState RING will either choose the associated pier to delete if the span is connected to an abutment or ask the user to decide where the span is not connected to an abutment Re numbering of the remaining objects will be
167. nly be uniquely determined at the point of ultimate failure In addition to basic equilibrium considerations in the context of masonry gravity structures the following conditions may be used to test for ultimate collapse assuming both hinging and sliding failures at masonry joints are considered possible 1 The yield condition which may be deemed to be satisfied providing the line of thrust both lies entirely within the masonry and does not cross any joint at a subtended angle 8 of less than tan _ u where y is the coefficient of friction 2 The mechanism condition which may be deemed to be satisfied providing the line of thrust either touches exterior faces of the masonry blocks and or crosses sufficient joints Initially assuming that the masonry possesses infinite compressive strength so the line of thrust can be trans mitted through a hinge point lying on an exterior face of the arch Initially assuming that sliding failures follow a sawtooth friction model i e obey an associative flow rule where sliding is accompanied by dilatancy LimitState Ltd 36 CHAPTER 5 THEORETICAL BASIS OF LIMITSTATE RING at an angle 0 of tan yu to create the releases required to transform the structure into a mechanism Thus if a line of thrust satisfies the equilibrium and yield conditions then the true plastic col lapse load cannot be less than the applied load i e it is a lower bound Similarly
168. nry friction 1 0 Masonry unit weight 1 35 A Also check with 0 95 B Fill unit weight 1 2 A Also check with 0 95 B Ballast unit weight 1 2 A Also check with 0 95 B Track load 1 2 A Also check with 0 95 B Axle load 1 0 Dynamic load 1 0 Table E 15 Partial factors E 2 3 Analysis results Analysis 1 Partial factors A reducing dead load effects Computed adequacy factor 3 84 axles spaced between 21200 and 26000mm from the far left springing The associated failure mechanism involves both spans but not the intermediate pier LimitState Ltd 214 APPENDIX E WORKED EXAMPLES GENERAL Figure E 4 Example 2 2 span failure mechanism Analysis 2 Partial factors B reducing dead load effects and including separated rings Computed adequacy factor 1 11 axles spaced between 3364 and 8164mm from the far left springing The associated failure mechanism involves both spans note the smooth deformed shapes of the two arches The intermediate pier is not involved in the mechanism Figure E 5 Example 2 2 span failure mechanism multi ring E 2 4 Next steps e Clearly there is a very large gap between the computed failure loads arising from Analysis 1 and Analysis 2 Whilst the real failure load is likely to lie somewhere in between this is in practice difficult to accurately determine the assessment engineer may wish also to try including different amounts of ring separatio
169. number of blocks However it is advised that abutments are only modelled explicitly in special circumstances see Section 7 5 Move through the tabs filling in the relevant data and clicking Next gt to advance On the Span tab there is the option to insert additional spans into the model If you wish to do this during the Wizard process simply check the Insert span after this box and after clicking Next gt a new span and pier will be added to the right of the current position If a span has been accidentally omitted but the Wizard process is not yet complete additional spans can still be included To do this simply navigate back to a span adjacent to the position where the new span is required and click the Insert Span button A dialog will appear to ask whether the new span should be positioned to the right or left of the current one Should a span require deleting navigate to the correct tab of the Wizard and click the Delete Span button A dialog will appear the asks which of the two supporting piers should also be removed LimitState Ltd CHAPTER 4 QUICK START TUTORIAL 25 P New Bridge Wizard Left Abutment Span 1 JL R ight Abutrr nent Fill Profile Type Stone voussoir se Segmental shape Details Span mm 5000 Midspan rise h mm 1750 f 1 4 Partial Factors sd No of units Ring thickness t mm 40 300 Materials It Bed joints normal to intrados Insert
170. o move backwards through the various steps by using the lt Back button The left hand pane of the Wizard dialog serves as a reference point with the current section being highlighted in blue 4 1 2 Step 1 General project settings Many of the fields in the Project tab are optional However those at the top of the tab determine the fundamental type of model you will build and specify several other important parameters Firstly specify the type of bridge to be analysed this can be either Highway or Railway un derline Next if you wish to model a bridge that includes reinforcement tick the Bridge includes rein forcement box Upon completing the wizard you will be alerted to the fact that reinforcement properties can be specified using the Contact Select Tool and the Property Editor Lastly enter an Effective bridge width This is the transverse width of masonry arch that resists the applied loading Enter a constant value using the Specified field or if you wish to use an automatically calculated effective width select the Bridge Width Auto computed option see the Loading Chapter Section 8 4 1 3 Step 2 Geometry The next stage in the Wizard process is to model the Geometry see Section 13 of the bridge Figure 4 2 This includes data about the abutments spans piers and fill In the case of the abutments there is an Advanced see Section 13 2 2 button that will allow explicit modelling of the height thickness and
171. ocessing packages 23 2 Adding a template header or footer A style template or custom headers and footers can also be appended to the report by selecting the Tools menu clicking Preferences and selecting the Report tab as shown in Figure 23 2 LimitState Ltd CHAPTER 23 REPORT OUTPUT 161 Preferences General Report Import template template css Import header header html Import footer footer html Figure 23 2 LimitState RING report preferences LimitState Ltd 162 CHAPTER 23 REPORT OUTPUT LimitState Ltd Part V Appendices 163 Appendix A Mathematical formulation A 1 Joint equilibrium formulation adequacy factor analysis This section contains details of the mathematical formulation used in LimitState RING A joint equilibrium formulation similar to that proposed initially by Livesley 1978 is used Whilst this formulation produces a large number of constraints and variables the total number of non zero elements will generally be relatively small which means that it can be solved very efficiently using modern interior point Linear Programming LP algorithms Thus assuming there are b blocks and c contact surfaces the problem may be stated as follows Max A A 1 subject to the equilibrium constraints Bq Af fp A 2 and no tension rocking yield constraints Mi lt 0 5n t o O lor each contact i 1 c A 3 and sliding yield constra
172. odel of random rubble stone masonry arches Nevertheless given that it is unfeasible to model the actual layout of stones in a random rubble arch the software may be applied to such arches provided suitably conservative smeared properties for the masonry are adopted 5 4 3 Stress related failures In common with other limit analysis or mechanism programs LimitState RING may not ac curately predict the ultimate strength of a bridge if either of the following apply 1 The bridge comprises a long e g gt 20 30m and or flat arch e g span rise gt 6 or the arch contains very flat sections for example in the case of an elliptical arch and it can be expected that elastic deformations prior to collapse will significantly change the arch geometry 2 A brittle response of some part of the structure may be expected to prevent the formation of a ductile collapse mechanism e g abrupt failure of the bond between rings brittle hinge formation However even in these cases LimitState RING can provide an invaluable upper bound estimate of the likely strength of the bridge which can be used as a benchmark for alternative analysis methods Such alternative methods may comprise in the case of i a geometrically non linear elastic analysis in the case of ii a non linear elastic analysis incorporating a masonry material model respecting fracture mechanics principles e g using Hillerborg s cohesive crack theory Hillerbourg 1976
173. of the masonry Clearly this con sideration would add extra complexity to an already tedious hand calculation However if a finite masonry crushing strength is specified by the user then this thickness is automatically computed by LimitState RING It is assumed that the thrust is carried by an area of material under a uniform level of stress i e assuming a rectangular stress block in accordance with a rigid plastic idealisation of the masonry crushing response LimitState Ltd CHAPTER 5 THEORETICAL BASIS OF LIMITSTATE RING 37 5 3 Output from a LimitState RING analysis 5 3 1 Identification of the adequacy factor Although for simplicity the previous section considered a case where a collapse load e g Fp was to be computed it is generally more useful to compute the factor which would when applied to some specified pattern of live loads lead to collapse This factor or multiplier is commonly termed the adequacy factor and its determination for a given bridge is the principal goal of a normal LimitState RING analysis When appropriate partial factors are included in the model this adequacy factor must be greater than 1 0 for a safe structure For example if a 1kN single axle load is specified and LimitState RING indicates a computed adequacy factor of for example 154 this means that the load which would cause collapse is 154kN Alternatively if a 100kN single axle load was specified the adequacy factor computed
174. om each of the two associated spans The allowable force that the backing is per mitted to assume in these cases is the average of the two values Note that when two adjacent spans have identical heights and numbers of blocks the two backing elements between corre sponding blocks may lie on top of each other in the viewer Click selecting will pick the topmost of the two and display the limiting force as appropriate LimitState Ltd Part Ill Modelling 49 Chapter 6 Preliminary bridge assessments using LimitState RING Increasingly assessment codes and other guidance documents advocate a multi level approach to bridge assessment A preliminary or Level 1 assessment might traditionally be performed using a semi empirical assessment procedure e g the MEXE method If this assessment procedure indicates that the bridge is safe then in the past the assessment engineer has typi cally not been required to study the bridge further i e does not need to undertake a Level 2 or Level 3 analysis However there are increasing concerns over the reliability of existing semi empirical assess ment procedures and consequently their range of recommended application is being succes sively reduced by the relevant regulatory bodies The large numbers of bridges which need to be assessed therefore means that a rapid means of conservatively assessing bridge load carrying capacity is required Reflecting this LimitState RIN
175. omponents are not included in the LimitState RING database NN N wo 19 wo vt 4 Tt AAA cos E TRAIN LOAD Of 80 9 kN m J 8 25 Um 1950 2050 _2970_ Table D 5 Standard Indian Railways loading in LimitState RING LimitState Ltd 194 APPENDIX D STANDARD LOADING MODELS D 2 Highway loading models D 2 1 Construction and use AXLE WEIGHTS AND SPACING VEHICLE Wi A1 w2 A2 W3 A3 Wa A4 W5 KN m KN m kN m kN m kN Single Axle 10 5 Tan 103 01 CU Double Axle 1 02m 79 76 1 02 79 76 CU Double Axle 1 85m 99 77 1 30 99 77 CU Triple Axle 53 86 0 70 58 86 0 70 58 86 1 40m CU Triple Axle 2 70m 73 58 1 35 73 58 1 35 73 58 CU Triple Air Suspended Axle 78 48 1 30 78 48 1 30 78 48 2 60m CU B1 30 Tonne 4 Axle Rigid 59 74 1 02 59 74 4 08 89 76 1 20 89 76 CU C1 30 Tonne 5474 1 20 54 74 380 94 76 1 50 94 76 4 Axle Rigid CU D1 32 Tonne 4 Axle Articulated 39 83 2 00 99 67 4 20 89 76 1 20 89 76 CU E1 32 Tonne 5 Axle Articulated 59 74 3 10 89 76 1 20 89 76 4 00 39 83 1 02 39 83 CU F1 38 Tonne 5 Axle Articulated 56 94 2 40 95 16 4 20 73 58 1 35 73 58 1 35 73 58 CU G1 38 Tonne 5 Axle Articulated 58 86 2 80 73 58 1 50 103 01 5 28 68 67 1 02 68 67 CU G1 38 Tonne 5 Axle Articulated 58 86 2 80 103 01 1 50 73 58 5 28 68 67 1 02
176. operties Lux de den pe wR ERE dre ER Ow ER 103 14 2 Backfill Standard properties 1 1124134428 baie vbidemres ie 104 14 2 1 Soil Properties nk scs casio a na reh a a ea na SOE 104 14 2 2 Soil Effects lt lt a bed r p e 105 14 3 Backfill Advanced properties lt lt due 0 eee pue bee pute me 105 14 3 1 Live load dispersion details gt 2 24 dass eee paies dope aa Et 105 14 3 2 Soil arch interface properties 107 14 3 3 Passive zone parameters 107 14 4 Backing properties L 4 du dogs cu ha es done rie t eo 110 145 SO Mes gt 53 ole Es idees so ste a A esse 110 18 31 LME 42 ee tk tbe beige e644 ar NOIRE SI Ets 110 14 5 2 Angle of dispersion cc eed ee 4 mt bo eee 8 111 15 Loading 113 15 1 Mirrored vehicles amp ek amp d s 48 dd ou dut 8 ie ERS 113 15 2 Adding a vehicle to the project 114 15 2 1 Importing existing vehicles 4 es does Se eh a OR ee SES 114 15 2 2 Defining a new vehicle using properties saved in a file 115 15 2 3 Defining a new vehicle within LimitState RING 116 15 2 4 Editing vehicle properties 116 15 2 5 Renaming a vehicle Lis su a done brie mieu 117 15 2 6 Deleting a vehicle edi ban eed E RA 117 15 2 7 Exporting a vehicle to a file 5 4 Le 4 LA ma aria baba 117 15 3 Adding a vehicle to
177. ould be noted that the actual force applied may be lower For blocks that are associated with backing elements the maximum fill force will be calculated assuming the default backing material properties Fill force H user defined This specifies whether the user is overriding the automatically calculated horizontal force ap plied to the block If this is set to true then subsequent changes to the fill depth unit weight etc will not affect the fill horizontal force magnitude Fill force V This is the fill vertical force applied to the block kN per metre width This force results from overlying fill surface fill ballast and track self weight loads Fill force V user defined This specifies whether the user is overriding the automatically calculated vertical force applied to the block Note that if set to true then subsequent changes to the fill depth unit weight etc will not affect the fill vertical force magnitude Support movement rotation Rotational movement of support blocks can be modelled by entering a value in radians in this box Rotations are measured in an anti clockwise direction about the centroid of the block and become apparent once an analysis has taken place LimitState Ltd 134 CHAPTER 19 VIEWING AND MODIFYING ATTRIBUTES Support movement x To model a horizontal x direction movement of a block enter a value here Settlement is measured in mm and shown following an analysis Suppo
178. ovided by Page 1993 With the benefit of hindsight significantly more pre and post test investigation work should have been performed to better characterise the internal construction details and material prop erties This would have been useful in providing a more comprehensive data set for use by analysts who have since attempted to model the behaviour of the bridges under load In 2001 TRL were commissioned to independently validate ring the predecessor to Limit State RING and other available masonry arch bridge analysis software Despite the uncertain ties outlined above as part of the validation process it was decided that the programs would be used to predict the carrying capacities of 5 of the field bridges load tested more than a decade previously Details taken from the TRL report Macfarlane amp Ricketts 2001 relating to ring are provided in Table G 4 Bridge Theoretical experimental collapse load Torksey 81 Bridgemill 100 Barlae 92 Preston 90 a Strathmashie bridge was also modelled but was in poor condition and because none of the defects were modelled during the anal ysis all the programs returned non conservative results Table G 4 Correlation between TRL field bridge test and ring collapse loads independently produced by TRL It is evident that agreement between the ring predictions and the full scale test results was found to be reasonably good The TRL re
179. paration in the experimental load test This is a quasi brittle and unpre dictable phenomenon which cannot be modelled directly using ring although the program can be used to try to bound the load carrying capacity from above by modelling the barrel as a voussoir arch and from below by modelling the barrel as a series of separate arch rings The LimitState RING data files corresponding to the aforementioned analyses are distributed with LimitState RING these are located in the Examples subdirectory e g C Program Files LimitState RING3 0l1 examples Note that the predictions in column B differ from those given in the ring1 5 Theory and Modelling Guide princi pally because in the latter case a 45 cutoff angle for the Boussinesq load distribution model was specified whereas the default value of 30 was used here In fact a nominally identical bridge bridge 5 3 tested subsequently failed at an even lower load of 1000kN with failure again initiated by the onset of ring separation LimitState Ltd 226 APPENDIX G VALIDATION AGAINST BRIDGE TEST RESULTS G 2 Sheffield laboratory tests small scale A series of small scale tests were performed at the University of Sheffield to confirm the relative importance of passive restraint effects i e as parts of the arch barrel remote from the load sway into the fill and live load dispersion effects i e as the live load spreads through the fill In these tests the appli
180. permanent Masonry unit weight Vfm losa rom pi p f Load factor applied to permanent Pon IW load from backfill Surface fill ballast unit Load factor applied to permanent weight Vif load from surface fill ballast Load factor applied to permanent Tapk oag VF load from track Load factor applied to variable AKIE I9AR VF load from vehicle axles Load impact factor applied to Dynamic axles where Dynamic Factor y dun true see Section 15 3 1 has been set Material factor applied to masonr Masonry SrEngI Fons crushing er ae Material factor applied to masonry Mason CIN im mf friction coefficients Table 16 1 Default partial factors 123 124 CHAPTER 16 PARTIAL FACTORS LimitState Ltd Chapter 17 Reinforcement 17 1 Properties LimitState RING allows the user to include reinforcement in the model meaning that the the software can also be used to assess a range of reinforced arch bridges refer to Section 5 5 for advice on the assumptions made with respect to the reinforcement model Up to two layers of reinforcement can be added at at 90 across any Contact by specifying the distance measured from an end A or B and the limiting tensile and compressive forces i e select radial contacts to assign circumferential reinforcement and vice versa For example see Figure 17 1 where circumferential reinforcement has been added to the bridge model Figure 17 1 Reinforcement added
181. perties 2450mm Reinforcement bars 50mm from top and bottom faces 4900mm Figure F 5 Reinforced beam dimensions Case 3 Applied moment l Applied force x S 1 x 4900 Applied Moment PPT OREX SPa 12900 1 225kNmm Initial assumed concrete force Concrete force 400 100 300kN Concrete crushing depth Concrete crushing depth Concrete force Bridge width Concrete crushing strength Concrete crushing depth 300 1000 5 x 10 3 60mm Hence the crushing depth is greater than the depth to the top reinforcement bar i e bottom bar in full tension and top bar in full compression Moment capacity LimitState Ltd 222 APPENDIX F WORKED EXAMPLES REINFORCEMENT 100 50mm 1000mm Figure F 6 Reinforced beam stress block Case 3 Taking moments about centre of compression block depth 60mm Moment capacity 170 x 400 20 x 100 66000kNmm Adequacy factor AF Moment capacity Applied moment 66000 1225 53 8776 LimitState RING calculated adequacy factor AF 53 9 to 3 significant figures LimitState Ltd Appendix G Validation against bridge test results G 1 Bolton laboratory tests full scale At Bolton Institute UK in the early 1990 s a number of 3m and 5m span bridges were tested in the laboratory Two of the bridges tested are shown on Figure G 1 Figure G 2 Figure G 3 and Figure G 4 A key advantage of these tests over those carried out in t
182. port concluded that RING gives good results and with some investment in an improved solver ring would be a very effective tool for most assessment engineers The concern about the speed of the solver was addressed following the release of newer ver sions of RING which were up to 200x faster than RING 1 1 which was used in the 2001 TRL report LimitState Ltd 230 APPENDIX G VALIDATION AGAINST BRIDGE TEST RESULTS G 5 Validation of the reinforcement model A variety of checks have been undertaken to verify output from LimitState RING in respect to the reinforcement model e To demonstrate that the software provides the same solutions as would be calculated by hand a number of simple reinforced beam worked examples are included in Appendix F e The software has also been applied to a number of reinforced arch problems Unfortu nately much of the data available in the literature appears to be incomplete or coloured by indeterminate factors making accurate correlation difficult Nevertheless details of the validation work which has been undertaken are provided below G 5 1 Bradford arches Chen 2004 and Chen et al 2007 describe details of four tests performed on 2m span arch ribs two reinforced and two unreinforced Full details of the arches and reinforcement were available and these were used in LimitState RING to predict load carrying capacities for sim plicity in all cases the masonry crushing
183. ppear containing all the available choices 2 Copy and paste within an explorer It is also possible to cut and paste data between several cells whilst within an explorer To do this 1 Use the mouse or keyboard to highlight the cells that you wish to copy 2 Right click to bring up the 20 5 3 3 Select Copy the copied cells will now have a dashed border LimitState Ltd CHAPTER 19 VIEWING AND MODIFYING ATTRIBUTES 137 4 5 6 An ev allow gt a OO N al Note 3 Co Select the cells that you wish to paste into the dimensions of the selected area should be the same as the copied area Right click to bring up the explorer context menu Select Paste the cells will now be filled with the new data en quicker way of copying and pasting is to use the Copy Paste details functions These entire rows of data to be copied and pasted by selecting only the ID cell To do this highlight the ID cell s of the object s to be copied Right click to bring up the explorer context menu Select Copy details the copied rows will now have a dashed border Select the ID cells that you wish to paste into the dimensions of the selected area should be the same as the copied area Right click to bring up the explorer context menu Select Paste details the rows will now be filled with the new data The standard keyboard shortcuts for Copy CTRL C and Paste CTRL V can also be used
184. project Save As Ctrl Shift S Save the current bridge project under a specified name Open recent file Open one of the 5 most recently accessed files Exit Ctrl Q Exit LimitState RING Table 20 1 File menu functions LimitState Ltd CHAPTER 20 DISPLAY OPTIONS 143 20 3 2 Edit menu Bridge5 ring LimitState RING File Edit Select View Tools Analysis Es Undo Ctri Z y S O Figure 20 3 The LimitState RING Edit menu Function Shortcut Description Undo Ctrl Z Step back to the point immediately before the last action was taken Redo Ctrl Y Redo a previously undone action Table 20 2 Edit menu functions 20 3 3 Select menu e Bridges ring LimitState RING File Edit Select View Tools Analysis Help YY s ean o x Contact Select Tool a a Select Contacts Only Figure 20 4 The LimitState RING Select menu Function Description Click Select a single object or multiple objects using CTRL Rectangle Select multiple objects within a rectangular zone Contact Select Tool Opens a dialog allowing you to select multiple contacts Select Contacts Only Select only contact elements Table 20 3 Select menu functions LimitState Ltd 144 CHAPTER 20 DISPLAY OPTIONS 20 3 4 View menu Bridge5 ring LimitState RING File Edit Select View Tools Analysis Help Py a La Zoom All yu savecamera Load Camera
185. r defined interpolated The arch profile is formed from a spline interpolation of user defined data points This is the most powerful and flexible profile type suitable for use when many user defined data points are specified Three centered pseudo elliptic The arch profile is near elliptical in shape being formed from segments of three circles using the crown rise and span measurements Pointed The arch profile is pointed and is formed from segments of two circles using the quar terspan rise crown rise and span measurements This can therefore represent a gothic arch It is the shape of the arch in relation to the pattern of loadings applied to it which governs sta bility Hence it is of paramount importance that due care is taken when recording and entering the shape into LimitState RING All too often this is ignored with the default Segmental arch shape often being used without careful forethought When transverse cracks are present it follows that the arch profile must differ from that originally constructed and this makes it even more important to perform an accurate survey of the bridge prior to analysis to ensure that the true shape of the arch is modelled To obtain an indication of the influence of arch shape on carrying capacity refer to Figure 7 1 which shows the effect on the computed adequacy factor of simultaneously modifying the quarter and three quarter point rises of Bolton Bridge 3 1 see Appendix G 1
186. r modified Boussinesq distribution refer to Section 5 8 2 Figure 8 4 shows a graphical view of how the loading from a single axle is assumed to be dispersed using LimitState RING showing different distribution angles through the surface fill and backfill LimitState Ltd 70 CHAPTER 8 LOADING MODELS Fill Figure 8 4 Longitudinal dispersal of a highway axle load through surface fill and underlying backfill also showing default dispersion angles 8 2 2 Transverse distribution and effective bridge width LimitState RING is a 2D analysis program Thus appropriate assumptions are required in order to determine the effective width of bridge which may be assumed to support an axle loading Unfortunately this is an area for which there is little real evidence on which to base rational rules By default a fixed effective bridge width of 2500mm is used This can be changed by the user or alternatively an automatically computed effective bridge width can be used which is computed as follows specified axle width amount of load spread at axle with minimum fill depth extra distance to account for distribution within the arch The effective width computed using the default parameters for a highway bridge is shown in Figure 8 5a However it should be remembered that the automatically computed effective bridge width may not be reasonable and the user should check whether for example longitudinal cracks in the arch barrel the proximi
187. rch bridges Find out more about adding reinforcement in LimitState RING in Chapter 17 2 5 Expanded vehicle database The built in database of road and rail vehicles has been expanded for LimitState RING and now includes the following Railway vehicles UIC LM71 and Load trains D4 C3 E4 and E5 BD37 RU and RL railway loading Network Rail RA1 and RA10 standard and short length load trains Indian Railways Modified broad gauge A and B trains Highway vehicles Construction and Use Single double and triple axle load vehicles Restricted Construction and Use RA to RG load vehicles European Union Single double and triple axle vehicles plus EC1 to EC4 load vehicles BD21 Load vehicles from Annexes A D E and F BD37 1 30 37 5 and 45 Unit HB loading BD86 SV80 SV100 SV150 SVTrain SV196 and SVTT load vehicles BD91 32 to 44 tonne load vehicles Find out more about the standard vehicles included with LimitState RING in Appendix D 2 6 Enhanced user interface The look and feel of the user interface has been enhanced for LimitState RING Toolbar buttons are now colour coded and rendering of bridges displayed in the viewer has been improved Other improvements to the user experience such as the ability to cut and paste span profile and surface fill level data to and from external applications e g Microsoft Excel have also been implemented LimitState Ltd Chapter 3 Getting started 3 1 Instal
188. reinforced using the MARS proprietary system which in volves inserting bars in slots formed in the intrados The reinforcement comprised 622mm steel positioned 19mm from the surface and with a yield strength of 480N mm Yi 2004 The bridge was then re tested and to failure reaching an estimated failure load of 320KN a fail ure load of 276KN is also quoted by Sumon 2005 this apparently being the load at which displacement gauges were removed The bridge was analysed both before and after retrofitting The values of all parameters used in the two analyses were identical except that a steel rebar force of 149 3kN per metre width was entered for the retrofitted analysis 149 3 622 x 480 2000 It is evident from Table G 7 that the enhancement to the arch strength provided by the steel appears to be predicted well by LimitState RING The predicted failure mechanism of the reinforced arch is shown in Figure G 6 A number of other reinforced arch bridges were tested by TRL but these contained radial pins which is beyond the scope of this study Test load kN LimitState RING prediction kN Arch 1 Unreinforced benchmark 200 198 Arch 1 Post retro reinforcement 320 325 Table G 7 Validation of LimitState RING results against TRL arch tests after Chen 2004 Sumon 2005 LimitState Ltd 232 APPENDIX G VALIDATION AGAINST BRIDGE TEST RESULTS Figure G 6
189. rengths refer to Melbourne amp Gilbert 1995 However it should be borne in mind that strictly speaking the computed factor is an upper bound on the exact load factor LimitState Ltd 104 CHAPTER 14 MATERIAL PROPERTIES 14 2 Backfill Standard properties To edit the backfill properties click on the Backfill tab of the Materials dialog as shown in Figure 14 2 Edit Bridge Masonry Backfill Surface Fill Soil Properties Soil Effects Unit weight D km mein PNR 18 Model dispersion of live load Angle of friction degrees 30 Model horizontal passive pressures v Cohesion c KN m2 0 p M Standard Live load dispersion details Soil arch interface properties Boussinesq Uniform Friction multiplier on 0 66 Cutoff angle degrees 30 Adhesion multiplier onc 0 5 Passive zone parameters mK 1 Position MpcKoC 0 Left Abutm Yes Factor mp 0 05 Pier 1 Yes AS Right Abut Yes Factor m 0 33 Keep mK gt 1 0 g Auto identify passive zones Figure 14 2 Backfill properties tab 14 2 1 Soil Properties Unit weight Specify the unit weight in KN m of the backfill material Note If you wish to model an arch without fill specify a zero value for the backfill unit weight also uncheck Model dispersion of live load Angle of friction Specify the angle of friction in degrees of the backfill material Cohesion c Specify the
190. results G 1 Bolton laboratory tests full scale G 2 Sheffield laboratory tests small scale G 3 Salford laboratory tests full scale G 4 Field bridge tests G 5 Validation of the reinforcement model Bradford arches G 5 2 TRL laboratory bridge tests G 5 1 H Comparison with previous versions H 1 Version history H 2 Comparison of results between versions Bibliography LimitState Ltd 12 CONTENTS LimitState Ltd Part Introduction and Quickstart Chapter 1 Introduction 1 1 About LimitState RING LimitState RING is a rapid analysis tool for masonry arch bridges The software is primarily designed to analyze the ultimate load carrying capacity of masonry arch bridges building on the mechanism method of analysis originally pioneered by Heyman 1982 and has numerous features many of which are unique including Multi span and multi ring arch capabilities Multiple load case facility Facility to model support movements Facility for modelling the presence of arch backing material Fully user definable geometry Local material properties can be specified Effective width computations Automatic identification of the critical failure mode in multi span bridges even if this in volves only a single span Failure modes involving sliding are identified if critical Automatic detection of passive pressures allowing deep arch and multi span arch prob lems involving passive pressures to be
191. rick Block masonry conference Shanghai pp 473 482 Gilbert M amp Melbourne C 1994 Rigid block analysis of masonry structures The Structural Engineer 72 356 360 Gilbert M Smith C Wang J Callaway P amp Melbourne C 2007 Small and large scale experimental studies of soil arch interaction in masonry bridges Proc 5th International Arch Bridges Conference Madeira pp 381 388 Heyman J 1982 The masonry arch Ellis Horwood Chichester United Kingdom Hillerbourg 1976 Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements Cement and concrete research 6 773 782 Hulet K Smith C amp Gilbert M 2006 Load carrying capacity of flooded masonry arch bridges Proc Inst Civ Eng Bridge Engineering 159 3 97 103 International Union of Railways 1994 Leaflet 774 2R Distribution of axle loads on ballasted railway bridges UIC Livesley R K A 1978 Limit analysis of structures formed from rigid blocks International Jour nal for Numerical Methods in Engineering 12 1853 1871 237 238 BIBLIOGRAPHY Macfarlane A amp Ricketts N 2001 Evaluation of existing software for the assessment of ma sonry arch bridges Technical report TRL report to Railtrack Melbourne A Gilbert M amp Wagstaff M 1997 The collapse behaviour of multi span brickwork arch bridges The Structural Engineer 75 17 297 805 Melbourne C amp Gilbert M
192. roject details To edit the project details on the Tools menu click Project Details Alternatively the command may be accessed via the keyboard shortcut by pressing Ctrl 1 or by clicking the clipboard icon a on the Properties toolbar The Project Details dialog will be shown Figure 12 1 M Edit Bridge General Bridge type Highway O Railway underline Effective bridge width Specified mm 2500 O Auto computed More Bridge includes reinforcement Other details optional Bridge name Example Bridge Reference N 123 456 Location Somewhere Map reference Assessor name Anne Engineer Assessor organization LimitState Ltd Comments An example bridge 3 span underline railway bridge Span 1 west cracking over crown at 1m in from north elevation Span 2 central OK Span 3 east cracking at west springing to approx 1m Figure 12 1 The Project Details dialog 12 1 Required details Many of the details that can be specified in the Project Details section are optional However there are three choices that require attention 89 90 CHAPTER 12 PROJECT DETAILS 12 1 1 Bridge type Here the user must specify whether the bridge under consideration is subject to loading from a highway or a railway The choice made will determine what information is required displayed during modelling and analysis By default the Highway option is highlighted 12 1 2 Effective bridge width
193. rt movement y To model a vertical y direction settlement of a block enter a value here For a downwards movement the value entered should be negative Settlement is measured in mm and is shown following an analysis Note support movements cannot be specified without the selected block s first having restraint in the appropriate direction For blocks without the required restraint should a value be entered in a Support movement box LimitState RING will give a warning that a restraint will also be added to the current selection as well as the option to cancel this action 19 1 3 Contact s Enabled Specifies whether the selected contact s are active Note if this attribute is set to false the contact will be assumed to be not present in the analysis and interpenetration can freely occur Mortar loss Mortar loss can affect the results of an analysis and should therefore be modelled as carefully as possible In LimitState RING in an arch Mortar loss A refers to material removed from the contact on the intrados side of the arch whilst Mortar loss B refers to material taken from the extrados side Values for mortar loss are entered in mm Permit hinges Specifies whether hinging failures are permitted at the selected contact s Permit sliding Specifies whether sliding failures are permitted at the selected contact s LimitState Ltd CHAPTER 19 VIEWING AND MODIFYING ATTRIBUTES 135 Reinforcement
194. rt span bridge Table E 4 Live load models to be considered Parameter Value Notes Spread oo ballast 150 4 1 from UIC 774 2R EN 1991 2 longitudinal Spread through ballast transverse 15 4 1 from UIC 774 2R EN 1991 2 Spread through fill transverse 300 Boussinesq Fill dispersion model longitudinal with 30 cutoff Table E 5 Live load dispersion parameters Parameter Value Notes Masonry strength 2 5 Masonry friction 1 0 Masonry unit weight 0 95 A Also check with 1 35 B Fill unit weight 0 95 A Also check with 1 2 B Ballast unit weight 0 95 A Also check with 1 2 B Track load 0 95 A Also check with 1 2 B Axle load 1 0 Dynamic 1 0 Table E 6 Partial factors E 1 3 Analysis results Analysis 1 Partial factors A reducing dead load effects Computed adequacy factor 2 44 axles spaced between 3200 and 8000mm from the left springing The associated failure mechanism involves 4 hinges LimitState Ltd APPENDIX E WORKED EXAMPLES GENERAL 209 Figure E 2 Example 1 4 hinge failure mechanism Analysis 2 Mortar loss and partial factors A reducing dead load effects Computed adequacy factor 2 44 axles spaced between 3200 and 8000mm from the left springing i e 30mm mortar loss near the springings bottom two mortar joints does not affect the computed load carrying capacity Analysis 3
195. s the individual rings in the arch barrels of these bridges be assumed to be adequately adhered together or not From the Bolton work referred to in Appendix G 1 the following was observed e Two 5m span arch bridges containing 440mm thick arch barrels in which individual rings had been properly mortared together suffered ring separation whilst being load tested to collapse This separation prevented the bridges from reaching the collapse load they otherwise would have achieved the sudden onset of ring separation was estimated to have reduced carrying capacity by up to approximately 55 e A similarly constructed 3m span arch bridge containing a mortar bonded 215mm thick arch barrel did not suffer ring separation when loaded to collapse In addition to the in situ mechanical properties of a given joint the above bridges were con structed using a 1 2 9 sand cement lime mortar scaling effects will also be important in gov erning the likelihood of ring separation Essentially by almost doubling the span rise etc the internal stresses will also be almost doubled and for this reason very short span bridges are likely to be less susceptible to ring separation than bridges with longer spans This can be taken account of in the analysis e g a 2m span multi ring brickwork arch in good condition may justifiably be analysed with fully bonded rings but this is unlikely to be an appropriate ide alisation for a geometrically similar 20m span bridge
196. s of the arch Note that while values of the soil arch interface properties can be specified in LimitState RING these are used in a limited way as discussed in Appendix B 2 In LimitState RING the default value of m is taken as 0 33 This has been shown to give a reasonable prediction of collapse load in physical model tests on single span arches There is very limited data currently available for the effects of cohesion on arch collapse load The default factor mpe is therefore currently set conservatively at 0 05 This has been increased from the default value of 0 01 utilised in LimitState RING 2 0 in the light of additional experimental and numerical data When 6 is small m K can fall significantly below 1 0 for a value of m equal for example to the default 0 33 It may be argued that a value less than 1 0 indicates that the soil is not positively mobilising any friction to resist arch movement and is over conservative There is therefore an option in LimitState RING to ensure that the resultant value of m K never falls below 1 0 This is on by default Specific situations where this may be invalid include e situations involving small arch movements where the at rest starting lateral earth pres sure coefficient Ko was initially very much less than 1 0 This might occur in the unlikely event of poorly compacted backfill e situations involving low strength backfills where the active earth pressures are relatively high compared to t
197. sers to more closely model the shape of a given arch bridge User defined interpolated The arch profile is formed from a spline interpolation of user defined data points This is particularly suitable for use when many user defined data points are specified Three centered pseudo elliptic The arch profile is near elliptical in shape being formed from segments of three circles using the crown rise and span measurements Pointed The arch profile is pointed and is formed from segments Find out more about arch profile definition in Section 13 3 2 2 Moment normal and shear force diagrams Users can now gain an improved understanding of the way in which applied loads are resisted through the display of moment normal and shear force diagrams These are particularly useful when reinforcement is involved when plotting the zone of thrust is not particularly useful Find out more about moment and force diagrams in LimitState RING in Chapter 22 2 3 Upgraded solver engine Designed to solve large scale mathematical optimization problems in a highly efficient man ner the use of Mosek 6 linear optimizer in LimitState RING means that larger more complex problems can be solved much more quickly than before 19 20 CHAPTER 2 WHAT S NEW IN LIMITSTATE RING 2 4 Reinforced masonry LimitState RING allows the user to include reinforcement in the model meaning that the the software can also be used to assess a range of reinforced a
198. sider the single rail load case separately to determine whether or not it is critical In LimitState RING this requires the use of a suitably reduced effective width see Section 8 1 4 However since the pattern of loading is unaffected then this special load case can normally be considered retrospectively i e after an analysis has been performed by modifying the adequacy factor to account for the use of a different effective width and live load intensity Traction braking forces LimitState RING does not currently apply horizontal forces at rail level e g to model trac tion braking forces However it is possible to apply user specified horizontal forces as pres sures directly to blocks within arches and or piers See Section 19 1 2 8 2 Loading from highway vehicles 8 2 1 Highway loading models For convenience a library containing common highway load models is distributed with Limit State RING see also Appendix D Alternative loading models may also be defined by the user Of the loads listed in Appendix D the most onerous loading pattern for the majority of small to medium span masonry arch highway bridges will be that comprising a single point load LimitState RING assumes that the load from an axle is spread through the surface fill default spread 26 6 corresponding to 2 1 vertical horizontal as per Department of Transport 2001 Live load is then spread through the fill according to a user specified model uniform o
199. since the higher stresses would mean it would be likely to suffer ring separation were the bridge to be loaded to collapse 7 8 3 Cracking in the arch barrel Macro cracks There are several distinct types of macro cracks observed in masonry arch bridges e g longi tudinal transverse and diagonal The potential influence of longitudinal cracks on the effective bridge width and hence on ultimate carrying capacity will be briefly discussed in Section 8 1 4 and Section 8 2 2 Transverse cracks may be caused by small movements of the supports e g perhaps due to slight outward spreading following removal of the centering Identification in an arch of transverse cracks indicative of formation of three hinges is not necessarily of concern provided the abutments are sound This is simply the statically determinate form of an arch However if the location of the crown region crack hinge is observed to change under the action of normal traffic loading then this can be problematic with subsequent fatigue failure of the structure a possibility Less frequently transverse cracks may be identified which are indicative of the partial formation of hinges due to excessive live loading at some point in the past In general when sufficient releases hinges and or sliding planes to form a mechanism are identified this should be con sidered to be potentially very serious Whilst it is theoretically possible that there might exist LimitState Ltd 62 CH
200. solutions for a number of benchmark problems have been compared with those from LimitState RING 2 0 and RING 1 5 Sample results are shown on Table H 2 233 234 APPENDIX H COMPARISON WITH PREVIOUS VERSIONS The results from LimitState RING versions 2 0 and 3 0 are ostensibly identical and also mostly very similar to results from RING 1 5 Where the difference in results exceeds 0 5 the reason for this is indicated The input files which are used as validation tests can be obtained from the LimitState website www limitstate com files ringInputFiles zip LimitState Ltd APPENDIX H COMPARISON WITH PREVIOUS VERSIONS 235 diff a a a Ey mama ess 000 fs pressures_2 rng mg naaa Jas 43 555 a a a a 2 span_2 ring_3 rng 2 span_2ring_crushing_backing rng 0 02 a ergoen roabuimentsmng 22047 0 00 220001 000 25401 Pasan sngionde_nosbumens 1mg 13157 000 fraise 000 191008 Lasa angeaxe nostumens 2mo 6975 000 037521 000 037521 san mreneo 306 000 aasraa 000 948700 panama 88 0 versus 000 1 07509 nana J 085 000 vos 000 0 404 mama oss ooo asrese 000 esras en A rear 000 19271 meta arias 000 arsaar 000 sn mp9 J 20579 0007 05706 0 00 03735 smog ses ooo soszae 000 96 0202 Pimple ame 7208 oo fours 000 72 001 D simpesm9 seas oo sesso 000 6 4650 Cm rss oo 7
201. strength was taken as 4 2N mm the value measured in the case of two of the four tests Test load kN LimitState RING prediction kN Unreinforced arches x2 1 4 4 0 1 83 Reinforced arches x2 15 4 18 4 21 14 13 57 Table G 5 Validation of LimitState RING results against Bradford 2m arch tests after Chen 2004 Itis evident from Table G 5 that the results of the arch tests were quite variable despite the two unreinforced and reinforced arches supposedly being identical It is also clear that when full continuity of reinforcement at the supports is assumed in the analysis the LimitState RING pre dictions are non conservative However it appears that the structure supporting these arches may have been overly flexible potentially colouring the test results e g no hinge crack was ever identified at the springing remote from the load in the case of one of the two reinforced arches For this reason a further analysis was performed assuming no continuity of reinforce ment at the supports this successfully bounded from below the two reinforced arch test loads Details of other Bradford arch bridges are available but these used mortar bonded multi ring brickwork arch barrels which typically failed abruptly due to the onset of partial ring separation a brittle and highly unpredictable phenomenon This makes them unsuitable for the present verification study LimitState Ltd APPENDIX G VALIDATION AGA
202. sures 177 B 4 Gradual build up of passive pressures 179 B S Unusual failure mechanisms lt lt 2 lt lt lt ee es 180 B 6 Backfill Backwards compatibility with RING 1 5 181 AAN s ve Lui 6424S ee SEES SEAS BUS SEs 181 B 6 2 Limiting fill barrel angle of friction 181 B 6 3 Load dispersion type eee dee me dee ek bus mm ES 182 B 6 4 Horizontal pressure type css be ee Se ee e 182 B 6 5 Automatic identification of passive zones 183 C Default parameters 185 ee RUS one es a eek eo ee eGR ae Se A Geese ae e A 185 Ce SONY lt ks sua se SSR RENNES Am SS PERE ERS oe Men 185 C 3 Transverse properties only used with auto computed bridge width 186 C 4 Material properties 187 Go Paras 5 122 22 E a e Lie Res PER delle de 188 CG6 Tackpaamet s occore Lie SERBS eA AR ad BER BE 188 D Standard loading models 189 D 1 Railway loading models lt lt lt sas ae ea 190 LS PS AA 556 644 3 190 D12 BDZ oras a AA Ge ee es 191 D 1 3 Network Rail NR GN CIV 025 222 dos ee ee aa 8 ES 191 D 14 Indian RAM lt lt La sauts is eue Eu e a m8 EE es 193 D2 Highway loading models 4 44 3 4 gs Paw PR ee ra e re 194 D 2 1 Construction and use 2 ence a ha Le gui bec paie see 194 D 2 2 Restricted construction and use 195 D 2 3 Europ
203. t for the surface layer if present where a uniform distribution is adopted A default cutoff angle of 30 is used to prevent excessive distribution Further details of the Boussinesq model are provided in Appendix B 1 5 8 3 Passive restraint One dimensional bar elements for convenience hereafter termed backfill elements Figure 5 7 a are used to model the passive restraint experienced by sections of the arch moving into the fill material Backfill elements compress at constant force e g o x vertical projected area where oz is the horizontal stress but have no tensile capacity Figure 5 7 b Use of these elements ensures that pressures are mobilised in the correct sense For example in Figure 5 7 c the backfill elements only apply a force to the non loaded side of the bridge Note that in LimitState RING active pressures on the loaded side of the bridge which are usually relatively small are for simplicity ignored Backfill elements Force compressive Displacement be Y tensile a b Backfill elements off Backfill elements on Figure 5 7 a Arch restrained with uniaxial backfill elements b backfill element response c LimitState RING representation of backfill elements Classical lateral earth pressure theory developed originally for vertical retaining walls is often used in masonry arch analysis to estimate the amount of horizontal passive restraint which can
204. t shear failure is not initially governing The shear force transmitted across the contact surface KN per metre bridge width Reinforcement max force C A Reinforcement max force T A Reinforcement max force C B Reinforcement max force T B Reinforcement shear capacity Shear force read only Table 17 1 Reinforcement fields as displayed in the Property Editor Note that the Reinforcement force is the limiting force per metre width which can be carried i e Reinforcement force area of reinforcement per metre width x yield stress x any applied factors 17 2 Adding reinforcement to the project By default it is assumed that a model does not include reinforcement this is to prevent the Property Editor being populated with superfluous fields The user must therefore specify that reinforcement is to be included This can be done in one of two ways see Figure 17 2 1 Whilst setting up a model using the New Bridge Wizard tick the Bridge includes rein forcement checkbox in the Project tab 2 Whilst editing an existing bridge geometry by ticking the Bridge includes reinforce ment checkbox in the Project details dialog LimitState Ltd CHAPTER 17 REINFORCEMENT 127 Effective bridge width Specified mm 2500 Auto computed Bridge includes reinforcement Y Bridge name New Bridge Reference N Location Map reference Assessor
205. techniques were originally developed for steel components and structures but it has since been shown that these can be applied to masonry gravity structures such as piers and arches Heyman 1982 To help understand why limit analysis theory is applicable compare and contrast the response of a steel column with uniform plastic cross section and a weakly mortared masonry pier both subject to a horizontal load F as shown in Figure 5 1 steel tower rigid plastic masonry pier Rotation a b c Figure 5 1 Laterally loaded a steel column b masonry pier and c idealised response curves lt can be deduced that e whilst the tensile and compressive strength of the steel column endow it with a finite plastic moment of resistance Mp the absence of tensile strength means that the masonry pier does not possess a comparable moment capacity derived from material strength e however the thickness and self weight of the pier mean that there is some resistance against overturning and the masonry pier could conceptually be considered as possess ing a moment capacity albeit one that varies with height moment capacity equal in mag nitude to the normal force at a given cross section multiplied by half the pier thickness e furthermore provided pier displacements do not become large the resistance of the ma sonry pier against overturning at a given cross section will remain broadly constant LimitState Ltd CHAPTER 5 TH
206. tem Open the license information dialog Display LimitState RING version details 20 4 Toolbars Table 20 7 Help menu functions Default toolbars By default the toolbars listed in Table 20 8 are displayed when you open LimitState RING Toolbar Functions Analysis Solve Unlock Cursor Click Rectangle Select Zoom Pan Edit Undo Redo Delete File New Open Save Load Cases Load case spin box Magnification Displacement magnification slider View Toggle Perspective Show Contacts Show Bar Elements Show Thrust Line Show Blocks Zoom Zoom All Zoom In Zoom Out Properties Project Details Geometry Partial factors Materials Loads Table 20 8 Default toolbars LimitState Ltd CHAPTER 20 DISPLAY OPTIONS 147 20 4 2 Optional toolbars To access some of the less commonly utilized features of LimitState RING it may be necessary to open a separate toolbar To do this click View and select Toolbars You will now have the option to open one of the toolbars listed in Table 20 9 Toolbar Functions Cursor 3D Rotate the model in 3D Rotate about x Rotate about y Rotate about z View 3D View the model in 3D Top Bottom Left Right Front Back Help Help About Table 20 9 Optional toolbars 20 5 Context menus Depending upon the position of the cursor right clicking the mouse within the LimitState RING environment
207. the backfill and the arch barrel See Section 14 3 2 3 The values of the backfill pressures calculated here can subsequently be modified if re quired See the Viewing and modifying attributes section 4 To specify that horizontal backfill pressures of constant magnitude H will be mobilised when the arch sways into the backfill set the Factor m to zero and the Factor mp to a suitable value to generate a resultant m K c equal to H 5 These equations are given assuming dry conditions To model conditions where the arch is flooded to above fill level enter buoyant unit weights for both masonry and backfill Keep m K gt 1 0 Checking this box ensures m K is always greater than or equal to 1 0 The resultant value of my can fall below 1 0 for low values of and mp which can be unrealistic See Appendix B for further discussion of this point Auto identify passive zones Checking this box causes uniaxial fill elements to be included in the analysis These elements are positioned horizontally in the spandrel void area s Elements are initially placed in contact with every block in the arch extrados The elements exhibit the following characteristics e The elements are constrained to either stay the same length or to compress e The elements exhibit a rigid plastic response in compression i e they compress at a constant force This force is equal in magnitude to the specified fill pressure multiplied by the vertical heig
208. to a bridge model In a project that includes reinforcement see Section 17 2 the properties of the reinforcement In a pre release version of the software only a single limiting force value could be specified When files saved with the earlier version are loaded in LimitState RING both the tensile and compressive limiting forces will be set to this single limiting force value though can be changed subsequently 125 126 CHAPTER 17 REINFORCEMENT across each Contact are displayed in the Property Editor Property Details The depth mm to the reinforcement from contact Reinforcement depth A endpoint A intrados if radial Note that this must be a positive value equal to less than half the contact length The depth mm to reinforcement from contact endpoint Reinforcement depth B B extrados if radial This must be a positive value equal to less than half the contact length The limiting compressive force kN per metre bridge width in the reinforcement nearest endpoint A The limiting tensile force kN per metre bridge width in the reinforcement nearest endpoint A The limiting compressive force kN per metre bridge width in the reinforcement nearest endpoint B The limiting tensile force kN per metre bridge width in the reinforcement nearest endpoint B The limiting shear force kN per metre bridge width of the reinforced section Warning by default this is set at a high value so as to ensure tha
209. tor see Chapter19 LimitState Ltd Part Il Theory 31 Chapter 5 Theoretical basis of LimitState RING 5 1 Background Masonry arch bridges are statically indeterminate compression structures which resist external applied loads primarily as a result of the thickness of the masonry and their inherent self weight They tend to be resilient to small support movements with these typically transforming a struc ture into a statically determinate form Cracks which might accompany support movements are therefore not normally of great concern making the notion of crack widths or other conventional serviceability criteria not applicable Consequently engineers are generally primarily interested in guarding against the ultimate limit state i e structural collapse condition This typically oc curs when a sufficient number of hinges or sliding planes are present between blocks to create a collapse mechanism 33 34 CHAPTER 5 THEORETICAL BASIS OF LIMITSTATE RING 5 2 Analysis methods used by LimitState RING LimitState RING idealises a masonry arch bridge structure as an assemblage of rigid blocks and uses computational limit analysis methods also known as plastic or mechanism meth ods to 1 analyse the ultimate limit state determining the amount of live load that can be applied before structural collapse 2 permit investigation of the mode of response when supports undergo small movements Limit analysis
210. traint table see Figure 14 5 Select yes to include horizontal pressures and no to not include horizontal pressures vertical pressures will still be modelled Passive zone parameters m K 1 ye Factor m 0 33 Che Position Passive McKee 0 T t t Factor Mo 0 01 O m K 0 Mpe Kac C Keep mK gt 1 0 V Auto identify passive zones gt Figure 14 5 Backfill Passive restraint table For example for a single span arch which is to be loaded to the left of the crown fill pressures should be specified only to act on the right hand side RHS of the arch However this approach is likely to be problematic in many cases e g for multi spans multiple load case analyses deep arches etc Fortunately for the user if pressures are not mobilised in the correct i e passive sense the computed load factor will be a lower bound on the exact load factor Note Some additional computational effort is required when fill elements are included in the analysis Thus in certain situations e g when it is obvious in advance that fill pressures will be mobilized in a given zone there may be justification for switching off the automatic detection of fill pressures LimitState Ltd 110 CHAPTER 14 MATERIAL PROPERTIES 14 4 Backing properties Bridge backing is modelled in LimitState RING as a special implementation of the backfill model see Section 5 8 The assumed default properti
211. ty of adjacent lane or the edge of the bridge will limit the effective width illustrated in Figure 8 5b and Figure 8 5c To facilitate this a maximum cutoff value can be specified When this is set the effective width will be the lesser ofthe automatically calculated value and the specified cutoff value Refer to Section 12 1 2 for details on how to set the bridge width In addition centrifugal effects may mean that one wheel in an axle is more heavily loaded than the other This may mean that a concentrated wheel loading becomes the critical case and hence that a reduced effective width should be selected Users are referred to Section 8 2 4 for further guidance LimitState Ltd CHAPTER 8 LOADING MODELS 71 8 2 3 Dynamic effects To account for the anticipated effects of the dynamic nature of loads applied to highway bridges some assessment codes suggest the use of a dynamic factor to be applied to one or more of the axle loads When a dynamic factor is applied to all loads simultaneously the pattern of loading remains unchanged and hence dynamic effects can if necessary be considered after a LimitState RING analysis has been completed Some assessment codes refer to an impact factor rather than a dynamic factor largely de signed to take into account the effect of a vehicle travelling on an uneven road This can be considered as a dynamic factor though one which is generally only applied to only one of the axles
212. ure 5 6 i it disperses live loads ii it can restrain movement of the arch when the latter sways into the fill This is often termed passive restraint ii passive restraint t Figure 5 6 Masonry bridge soil structure interaction Each of the above effects has the potential to significantly enhance the carrying capacity of a masonry arch bridge However whereas the constituent masonry blocks of a bridge are modelled explicitly in LimitState RING the backfill is presently modelled indirectly according to the simplified model described in the following sections 5 8 2 Dispersion of live loads The vertical live load pressures on the back of an arch are assumed by LimitState RING to be either 1 uniformly distributed the intensity being governed by the depth of fill under the centre of a given axle and the specified limiting dispersal angle or 2 dispersed according to a Boussinesq type distribution with a limiting distribution angle specified by the user LimitState Ltd 46 CHAPTER 5 THEORETICAL BASIS OF LIMITSTATE RING The Boussinesq distribution model generates a suitable bell shaped distribution of load which laboratory tests have indicated better approximates reality than uniform pressure distributions and which also models the effects of overlapping dispersed loads more appropriately This is therefore the default distribution model in LimitState RING excep
213. urrounding fill It has been found that taking m 1 3 gives rise to a restraint force which is approximately equal to that measured in laboratory tests at least for backfills with relatively high angles of friction Hence this value is used as the default in LimitState RING i e when the user inputs the angle of friction for a granular backfill this is used to compute a K value which in turn is multiplied by the vertical stress c and the m modification factor default 0 33 to compute the horizontal restraining stress on Determination of m The cohesive strength of clayey backfill materials may enhance the load carrying capacity of short span bridges However limited experimental evidence is available at present and a conservative default modification factor on Kpc of mpe 0 05 is therefore currently used in LimitState RING This has been increased from the default value of 0 01 utilised in LimitState RING 2 0 in the light of additional experimental and numerical data It should be noted that this value may be inappropriate for very soft low stiffness clay backfills However these are unlikely to be encountered in practice Once equation 5 2 has been used to determine a value of the horizontal restraining stress o applied to a given block this is checked to see whether it exceeds the magnitude of horizontal LimitState Ltd 48 CHAPTER 5 THEORETICAL BASIS OF LIMITSTATE RING stress that can be applied without causing the
214. ut by pressing Ctrl 2 or by clicking the Geometry dialog icon B on the Properties toolbar 13 1 Geometry dialog The Geometry dialog is depicted in Figure 13 1 Edit Bridge CI Left Abutment Spani Right Abutment Fill Profile Type RE stone voussoir lu Segmental shape Details Span mm 5000 Se TR NT LR SEP Midspan rise h mm 1750 a ee Abutment angles No of units Ring thickness t mm v Auto calculate LHS degrees 20 02 lla RHS degrees 20 02 Figure 13 1 Geometry dialog box 93 94 CHAPTER 13 BRIDGE GEOMETRY 13 2 Abutments To edit the geometry of an abutment simply click on the relevant tab within the Geometry dialog to display the dialog in Figure 13 2 Edit Bridge Left Abutment Span 1 Right Abutment Fill Profile Backing height over abutment h mm 0 0 Explicitly model this abutment Figure 13 2 Geometry Abutment properties 13 2 1 Default abutment model By default LimitState RING presumes that all abutments are constructed similarly in that they are constructed from a single fixed block with no backing above them To specify that an abutment is overlain by backing material simply enter a suitable value in the Backing height box see Section 5 8 4 13 2 2 Modelling abutments explicitly To override the default abutment model click the Advanced button and check the box labelled Explicitly model this abutm
215. ution can be found 10 2 Mode of response LimitState RING provides the user with a valuable visual representation of the predicted mode of response of the structure either at failure or when support movements are imposed A mechanism is mobilized when sufficient releases in the structure are made In the case of a single span single ring masonry arch the structure has 3 degrees of redundancy This means that 3 1 4 releases are required for a complete collapse mechanism e g 4 hinges 3 hinges and 1 sliding plane etc Multi span and multi ring arches are have greater degrees of redundancy and so generally require more releases However it is also possible for either fewer releases to be required giving rise to an incomplete collapse mechanism or for a greater number of releases to be present giving rise to an overcomplete collapse mechanism In any event the user should satisfy him or her self that the postulated mechanism is achievable in practice Features of failure mechanisms e For a given adequacy factor the mechanism of failure is not necessarily unique i e there may be two or more failure mechanisms which correspond to the same adequacy factor e Since the analysis is based on small displacement theory scaling the displacements too much will lead to distortion Figure 10 1a e When the mechanism includes sliding the sawtooth friction model will ensure that sliding is accompanied by dilatancy
216. variety of material and or structural defects These defects can often have a bearing on the load carrying capacity of the bridge and it is therefore important that they are modelled as accurately possible 7 8 1 Missing mortar and or localised spalling of masonry units Localized areas of missing mortar or occasional spalled masonry units are inevitable in old masonry structures and need not be considered a cause for concern However in cases when mortar loss and or spalled units are more widespread and it is considered that the effective thickness of the arch barrel is being tangibly reduced then this should be accounted for in the analysis In LimitState RING localized regions of arches and or piers may be readily selected and the effective thickness reduced as required Figure 7 3 It should be noted that the influence of missing mortar spalled units on carrying capacity depends not only on the depth of missing material but also on location within an arch barrel or pier In certain locations a considerable reduction in effective thickness may be found to have little or no influence on overall carrying capacity LimitState Ltd CHAPTER 7 DETAILED BRIDGE ASSESSMENTS USING LIMITSTATE RING 59 Bridges ring Limitstate RING Fie Edt Select View Tools Analysis Help ew DIO Q gu 9 Load case 1of1 use a Q e a a a a g E El Mortar Loss Y Length of mortar loss from endpoint A intrados lo of conta
217. w of each area is given in the following sections A fuller description is given in later Chapters A full list of toolbar and menu items may be found in Chapter 19 Additional items not shown by default are the Calculator Block Explorer Contact Explorer Vehicle Explorer Load Case Explorer 11 2 Title Bar The buttons Minimize Restore Down and Close may be accessed by left clicking the relevant icons at the right end of this bar or the program icon at the right These functions may also be accessed via the context menu by right clicking anywhere on the bar 11 3 Menu Bars Menu bars may be selected by left clicking on the relevant icon There is no right click function ality on this bar 11 4 Toolbars Toolbar buttons may be activated by left clicking on the relevant button Right clicking on any part of a toolbar brings up the explorer and toolbar selection context menu as depicted in Figure 11 2 Tooltips are available by hovering the mouse over any button for a short period Further description of the toolbars may be found in Section 20 4 LimitState Ltd CHAPTER 11 THE GRAPHICAL INTERFACE 85 iv Property Editor Calculator iv Output Block Explorer Contact Explorer Vehicle Explorer Load Case Explorer Edit Properties Cursor View Analysis Magnification Load Cases RITES Zoom View 3D Cursor 3D Help File ql Figure 11 2 Explorer and toolbar selector 11 5 Viewer
218. y Mp Kyo m Ko C Keep mK gt 1 0 Auto identify passive zones Sai arch interface properties Soil Effects Model dispersion of live load Model horizontal passive pressures Friction multiplier on 0 66 Adhesion multiplier onc 0 5 Positi Figure 6 1 Backfill dialog of New Bridge Wizard Note that before LimitState RING is used to perform a series of preliminary analyses it is ad visable to review the default parameters and to check that these are reasonable for the type of bridges being assessed As an example although the default values are normally conservative in an area where bridges are constructed using very soft red bricks and lime mortar the default masonry crushing strength of 5MPa may be non conservative LimitState Ltd Chapter 7 Detailed bridge assessments using LimitState RING 7 1 Analysis parameters The first step in an analysis is typically to identify sensible values for the analysis parameters Default parameters are shown in Appendix C However it should be borne in mind that some of the default values proposed may be quite conservative and more accurate values should be used where possible Additionally in order to save computational effort a default value of 40 is often given for the number of blocks per arch ring rather than the actual number of units This may lead to a very small overestimate up to 2 or 3 of the pre

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