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1. 33 Fig 15 Examples of vertically curved bridges vertical alignment a single slope b begin and end slopes c multiple slopes d mixing slope and zero slope 33 Fig 16 Material properties of the bridge deck ee eet eterni 34 Fig 17 Box girder shape employed for the bridge deck sss 35 Fig 18 Material properties of the bent cap cccccccccccccnnnncnnnnnnnonnnnnnnnnnnonononnnnnonononononananons 36 Fig 19 Rectangular shape employed for the bent Cap oooooonnnnnncccccncnononononnnnnnnnnnnnnanonos 37 19 20 C ODIT adi 38 19 2T Coburn ST ON Stop se neas di is 38 Fig 22 Column boundary Conditions a i 39 Xl Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig Fig 23 Column properties and available beam column element types 4 24 Defhmitios OF imear colma 42 25 Column Elasaeanaterial properes aaa 42 20 Column Section DIODE TUE S suceda voee Got tcn t NN To dunt Dicta t edet 42 27 Nonlinear Fiber Section WIDOOW uisi Pe oder ee eee none id ea uds 43 28 Column nonlinear material properties a Steel02 material b ReinforcingSteel material c Concrete02 material for the core concrete d Concrete02 material for the cover material 29 Column fiber section based on PEER best modeling practices report Berry an
2. 27 3 1 PA 28 Sal ae DPOOG iio 28 342 SGA VC BIKISE ad dad 29 34 2 Horizontal Curved Bda id in 29 3 L2 2 Vertical Curved Bridge iuo i b UR B be db i idet 30 34 A A ROTER NHIEU RON 34 3 3 I3etitodseuestisteesteu quesiti ieu iue O A ue m Dn RN e Us 35 3 4 CO NEN E Nm T STEEP PEN PD 37 Sr MEE Costi metet 38 vil 3 4 2 Column Connection 20 00 cece cee eccecacccceccecccceccecccccceceececceccecescecceceecescsceecsceceecascecescs 38 549 COMM Properties arias 39 3 5 A msc a cinch censuit fud celum died deus nieto ue ced Neu unite 22 A A btt atu dit teat nae at mcs totes 52 L2 SOMIS PANES at dat 52 3 5 3 Foundation Matrix aia cies 59 3 6 AVANCE d ODON he ias 60 IOE Deck ines 6l 5435 2 Jsoldtron BENE E E e deis 64 o SEICE A e O 66 e TE EE eae 67 Jed Mesh Parame tad iia 69 P Woiiurdd ilvigce c PO 70 4 Elastic A butiment Mode Ll ti ee veg er deque 70 4 2 Roller Abutmeht MOL iiscivnedotudro a eO EIER pe de uo ted op doo o o THE IE dns 75 4 3 SDC 2004 Abutment Mode beresi a EDU ter NEED 76 43 1 Longitudinal RESPONSE aiii 76 Adios Transverse RESPONS 655 oia 80 A Ln a nT a nd eT a er 82 4 3 4 Definition of the SDC 2004 Abutment Model ooooooonononnncccccnccnnnnononnnnnnnnnnnnnnnononos 84 4 4 SDC 2010 Sand Abutment Model cocccccccnnnnnonononononnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnos 87 4 5 SDC 2910 Clay oxbutmett WOE liada a eee eee 88 4 6 PlasticPP Gap Modbios 89 4 7 AA
3. c Fig 107 Abutment response force displacement relationships a longitudinal response b transverse response and c vertical response 8 1 6 Soil Spring Responses Time Histories The soil spring responses can be accessed by clicking menu Display and then Soil Spring Response Time Histories The soil spring responses window includes the following options Fig 108 i Force Displacement Curve ii Displacement Time History iii Force Time History 134 Two directions longitudinal and transverse directions of the above responses for each soil spring are all displayed Fig 108 oil Spring Response Histories Motion RRS Abutment Bent Response Time History Bent 2 Column Bent only Column 1 Depth 4 Direction Longitudinal Response Type Force Displacement Animation Play 0 Current Step Playing Speed View Data Add Figure to Report Fig 108 Soil spring response time histories 8 1 7 Deck Hinge Responses Time Histories The deck hinge responses can be accessed by clicking menu Display and then Deck Hinge Response Time Histories The deck hinge responses window includes the following options Fig 109 i Force Displacement Curve ii Displacement Time History iii Force Time History 155 Response time histories are shown for the cable and edge hinge elements for each hinge Fig 109 Deck Hinge Response Histories Motion RRS Deck Hinge Response Time
4. DWN for vertical component AT2 data or info However the following format is also allowed Input motion name E or W for horizontal components or V for vertical component Note that the filenames with the smaller angle will be used for the longitudinal direction and the other one with the larger angle will be used for the transverse direction also the filenames containing E will be used for the longitudinal direction and the other one containing W will be used for the transverse direction The first 2 lines of each INFO file must follow the style of the example below Data points NPTS 996 Sampling period DT sec 0 020000 Where 996 and 0 02 are the number of data points and the time step respectively of an input motion component 2 Steps to Create an Input Motion Based on the above description for the directory structure of a motion set one can easily create an input motion Fig 124 158 Step 1 create a folder and rename to your motion set name e g MotionSetl see Fig 124 Step 2 create a folder under the motion set folder and rename to your bin name e g bin1 Step 3 create a folder under the bin folder and rename to your earthquake name e g Quakel Step 4 create a folder under the earthquake name and rename to your input motion name e g MOTION Step 5 create the 6 files 3 INFO files and 3 DATA files for this input motion Fig 124 Note If you
5. a Bridge Resonance Bridge Natural Periods and Frequencies Mode Natural Period sec Natural Frequency hz 0 258632 3 8665 0 243837 4 1011 0 213986 46 32 0 111429 89 434 0 106455 9 338363 0 106339 9 40387 0 0851629 11 7422 0 0835981 11 962 0 0534411 18 7122 0 0530226 18 8599 I c Fig 73 Natural periods and frequencies of bridge ND Bridge Gravity Response Bridge Column Forces and Bending Moments Under Deadload Column Location Axis Force kip Longitudinal Shear kip Transverse Shear kip Longitudinal Moment kip Transverse Moment kip Column 1 of Bent 1 Column Top 385 009 713743 46 6324 105 993 684 25 Column of Bent 1 Column Bottom 417 093 713743 4663248 509154 pao O Column 2 of Bent 1 Column Top 385009 71373 46 6324 105903 684 25 Column 2 of Bent 1 Column Bottom 417 093 713243 46 6324 509154 jeno Column 1 of Bent 2 Column 1 of Bent 2 Column 2 of Bent 2 Column 2 of Bent 2 Column 1 of Bent 3 Column 1 of Bent 3 Column Bottom 417 093 713 43 4663248 50 9154 pao Column 2 of Bent 3 Column2ofBent3 ColumnBottom 117093 743743 466320 509154 aao Fig 74 Column internal forces and bending moments after application of own weight 94 a Column and Abutment Longitudinal Responses Response Type Longitudinal Response Moment Curvature Force Drift Ratio C Force Displacement C Left Abutment Force Displac
6. Area of Cross Section 12 5663 n2 X 1 12 5663 Moment of Inertia amp Longitudinal Axis 12 5663 1 12 5663 Moment of Inertia Transverse Axis 12 5663 Fr 1 12 5663 Torsion Constant 251327 ft 251327 ok Cancel Fig 26 Column Section properties 42 By default the Steel02 material in OpenSees McKenna et al 2010 is employed to simulate the steel bars and Concrete02 material 1s used for the concrete core and cover Steel02 1s a uniaxial Giuffr Menegotto Pinto material that allows for isotropic strain hardening Concrete02 1s a uniaxial material with linear tension softening The Concrete02 material parameters were obtained from the Mander 1988 constitutive relationships for confined and unconfined concrete More details on the derivation of the default values and the OpenSees uniaxialMaterial definitions used for each material are shown in Appendix A Fig 31 Fig 32 and Fig 33 show the stress strain curves for the steel core and cover concrete materials respectively The stress strain curve is only calculated up to 6 of strain These plots can be obtained for updated material properties directly from the interface by clicking on the corresponding View Stress Strain buttons in the Column Material Properties window Fig 27 The moment curvature response for the column is shown in Fig 34 generated with consideration of the overall deck weight 2680 kip applied at the column top For comparis
7. Controlling parameter cR2 Value 66717 5 29 000 000 0 01 15 0 925 0 15 Typical range 50 000 68 000 0 005 0 025 10 20 The strain hardening ratio 1s the ratio between the T yield stiffness and the initial elastic stiffness The constants RO cR1 and cR2 are parameters to control the transition from elastic to plastic branches Table 3 Default values for Concrete02 material properties Parameter Elastic modulus ps1 Compressive strength psi Strain at maximum strength Crushing strength psi Strain at crushing strength Ratio between unloading slope Tensile strength psi Tensile softening stiffness ps1 Core 3 644 147 6 739 0 0037 6 538 0 036 0 1 943 49 255 090 Stress Strain Curve for Steel 47 Cover 3 644 147 4000 0 002 0 0 006 0 1 560 280 000 Compression Tension Y Stress Strain Curve for Steel Compression Tension Y Stress Strain Curve for Steel Compression Tension c Fig 31 Stress strain curve for a steel material default values employed a Steel01 with a strain limit b Steel02 with a strain limit and c ReinforcingSteel with a strain limit 48 q Stress Strain Curve for Core Concrete Compression Tension Compression Tension b 49 q Stress Strain Curve for Core Concrete Compression Tension c Fig 32 Stress strain curve of the core concrete ma
8. Report No SSRP 14 04 May 2014 STRUCTURAL SYSTEMS RESEARCH PROJECT MSBRIDGE OPENSEES PUSHOVER AND EARTHQUAKE ANALYSIS OF MULTI SPAN BRIDGES USER MANUAL by AHMED ELGAMAL JINCHI LU KEVIN MACKIE Final Report Submitted to the California Department of Transportation Caltrans under Contract No 65A0445 Department of Structural Engineering University of California San Diego La Jolla California 92093 0085 University of California San Diego Department of Structural Engineering Structural Systems Research Project Report No SSRP 14 03 MSBridge OpenSees Pushover and Earthquake Analysis of Multi span Bridges User Manual by Ahmed Elgamal Professor of Geotechnical Engineering Jinchi Lu Assistant Project Scientist Kevin Mackie Associate Professor of Structural Engineering at University of Central Florida Final Report Submitted to the California Department of Transportation under Contract No 65A0445 Department of Structural Engineering University of California San Diego La Jolla California 92093 0085 May 2014 Technical Report Documentation Page 4 Title and Subtitle 5 Report Date MSBridge OpenSees Pushover and Earthquake Analysis May 2014 of Multi span Bridges User Manual 7 Author s 8 Performing Organization Report No Ahmed Elgamal and Jinchi Lu UCSD SSRP 14 04 9 Performing Organization Name and Address 10 Work Unit No TRAIS Department of Structural Eng
9. a Step 1 Define Model and Che View Column and Bent Labels f Fig 3 Menu and submenu bars a menu bar b menu File c menu Execute d menu Display e menu Report and f menu Help 23 The main features in MSBridge are organized into the following menus e File Controls reading writing and printing of model definition parameters exporting the mesh to other software such as SAP2000 for Versions 7 and 15 and Matlab and exiting MSBridge Please note that exporting to SAP2000 s2k file will work only if all of the following conditions are met for now 1 The column is linearly elastic 2 The abutment model is Elastic or Roller 3 The foundation must be Rigid Base or Foundation Matrix 4 There is no Deck Hinge no Isolation Bearing or no Steel Jacket and 5 Analysis option is Pushover monotonic or Mode Shape Analysis e Execute Controls running analyses and OpenSees analysis parameters e Display Controls displaying of the analysis results e Report Controls creating the analysis report in Microsoft Word format e Help Visit the MSBridge website and display the copyright acknowledgment message Fig 4 Note that Fig 3a shows a Lock Model button which is a toggle button that prevents from overwriting analysis results after the analysis 1s done If the model 1s in Locked Mode all OK buttons and Apply buttons are disabled and users cannot make changes to the current model To unlock the model
10. D 2c d 15 Where c is the clear cover c 1 5 11 SepscO 2f epscO 1 psc0 16 C 155 Where Ec 0 043w 4 f Where w is the concrete unit weight unit kg m 111 Sepsu epscu epscu 0 004 e 2 p C Where is the ultimate steel strain 0 12 iv fpcu fou f Cepscu epscr fa A A Epse epscr 14 e SCU ep SP epsc Where epsc epscO l sle 1 C E EF 3 epsc epscr Notes 1 The information above is specific to the Steel02 and Concrete02 models of the Fiber section Other options include Fig 27 Steel01 and Concrete01 for more information 17 18 19 20 21 please see the OpenSees documentation and Elastic properties for the fibers These options can be activated by clicking on the default Steel02 or Concrete02 sections Fig 27 and changing these options 2 A different property may be specified for the Column below grade for instance to roughly represent a large pile group as a large single column If this option 1s selected 156 Fig 6 the column below grade will have linear properties as specified by 1ts diameter and Young s Modulus 3 All the equations presented in this Appendix are based on the Mander model for spiral reinforced circular concrete columns The user may want to use their own constitutive model or parameters In this case the values of these parameter can be defined d
11. 53 To define individual skew angles check the checkbox Use Individual Skew Angles 67 To define individual skew angles click Bents and Abutments in Fig 53a A window for defining skew angle properties will appear Fig 53b Adwanced Options Deck Hinges Define Deck Hinges Isolation Bearings Define Isolation Bearings Steel Jackets Define Steel Jackets Skew Angles Global Skew Angle Use Individual Skew Angles Skew Angles Bents and Abutments Abutment 5 b Fig 53 Definition of skew angles 68 3 7 Mesh Parameters To change the number of beam column elements for the bridge model click Mesh in Fig 6 Fig 54 displays the Mesh Parameters window showing the default values The number of beam column elements for a deck segment a span must be least 2 And for the bent cap segment between columns the number of elements must be even Mesh Parameters Number of Beam Column Elements For a Column For a Deck Segment For a Bentcap Segment between Columns Must be an Even Mumber Cancel Fig 54 Mesh parameters 69 4 Abutment Models Abutment behavior soil structure interaction and embankment flexibility have been found by post earthquake reconnaissance reports to significantly influence the response of the entire bridge system under moderate to strong intensity ground motions Specifically for Ordinary Standard bridge structures in California with short spans and relatively high s
12. 85 Response relationships for column 103 6 4 4 Abutment Force Displacement and Response Time Histories lt lt Response Type Abutment Response Force Displacement CJ Force History O Displacement History Direction Longitudinal P Co Transverse E Vertical Abutment Left Abutment Right Abutment Animation Play Current Step Playing Speed View Data Add Figure to Report Fig 86 Abutment response time histories 104 6 4 5 Deformed Mesh al Deformed Mesh Due to Pushover A Displacement Plot Scale Factor 32 Show Legend Show Undeformed Mesh Display Motion Animation Play Repeat Current Step Step 40 Playing Speed Fig 87 Deformed mesh and contour fill 105 al Deformed Mesh Analysis Stage Due to Pushover Plastic Hinges Plot Scale Factor 32 Show Legend Show Undeformed Mesh Display Motion a A a XY XZ YZ i Animation Play Repeat Current Step ab Step 40 a Playing Speed Fig 88 Visualization of Plastic hinges red dots represent plastic hinges developed 6 5 Eigenvalue Analysis To conduct an Eigenvalue analysis please follow the steps shown in Fig 89 and then click Save Model amp Run Analysis Fig 90 shows the output window for an Eigenvalue analysis which can be accessed by clicking menu Display Fig 3 and then choosing Deformed Mesh To switch between modes move the
13. is employed by specifying Number of Motions Running Simultaneously Fig 92 You can select as many as 8 records to be run at the same time in order to reduce the overall run time for dual core machines or better Click View Motion to view the intensity measures and response spectra of the input motion being highlighted Fig 94 SRSS stands for Square Root of the Sum of the Squares of the 2 horizontal components Click Display Intensity Measures to view the intensity measures of the input motion being highlighted Fig 95 The user can copy and paste the intensity measures to their favorite text editor such as MS Excel in Fig 95 right click and then click Select All ctrl a to highlight and then right click and then click Copy ctrl c to copy to the clipboard Click View Histograms amp Cumulative Distribution to view the histogram and cumulative distribution plots for whole input motion set Fig 96 The intensity measures include e PGA Peak Ground Acceleration e PGV Peak Ground Velocity 113 PGD Peak Ground Displacement Ds o5 Strong Motion Duration CAV Cumulative Absolute Velocity Arias Intensity SA Spectral Acceleration assuming 1 second period SV Spectral Velocity assuming 1 second period SD Spectral Displacement assuming second period PSA Pseudo spectral Acceleration PSV Pseudo spectral Velocity The strong motion duration Ds o5 is defined according to the time domain bounded by the 5
14. 0 123152 in Stiffness 4119 82 kipin Effective Period Period 0 251 sec View Data e 70 X TO TO TO B TO X TO A TO e To AX TU T Tl B X Tl Ti e T1 X Ti e T1 T ES p 69 C UJ Fo I3 6 B 6B d 68 EA EE UU FO A Add Figure to Report Intensity Measure Comparison with THA PGA hd Compare b Fig 117 Sample output of ESA for the bridge longitudinal direction a pushover load b elastic displacement demand 149 Y Comparison of ESA and THA Comparison of ESA and THA Displacements Motion FPGA q ESA Disp In THA Max Disp in Difference 75 sign means ESA less 1 167 JE LO 611 wo ca a en E un x H Ls 0 7361 44 15 16 51 58 49 14 61 58 52 6 415 27 23 0 49 39 78 307 9 4 482 142 5 33 81 Fig 118 Comparison of displacements from ESA and THA 150 Tu ESA Pushover Load Bridge Transverse Direction Pushover Load As Ratio of Tributary Weight Bent Number Bent 2 Use User Defined Acceleration Response Spectrum User Defined Acceleration Response Spectrum Please enter Period sec and Acceleration Response Spectrum g in pairs 00 6 0 1 5 022 041 5 061 15 0 8 0 9 10 7 1 40 5 1 60 4 2 0 28 240 2 40 1 5 0 08 151 Tu Equivalent Static Analysis Bridge Transverse Direction Output ca 6 e Elastic Displacement Demand Effective Mass Weight 117847 kip Mass
15. 1 85778 kip sec2 in Effective Stiffness PushoverLoad 143 569 kip Displacement 0 116362 in Stiffness 1233 82 kip in Effective Period Period 0 244 sec View Data E x A Add Figure to Report Intensity Measure PGA b Fig 119 Output of ESA for the bridge transverse direction a pushover load and bent number b elastic displacement demand 152 Appendix A Calculation of Steel and Concrete Material Properties Steel Bars By default the Steel02 material is used to simulate steel bars The format of the Steel02 command is as follows McKenna et al 2010 uniaxialMaterial Steel02 matTag fy EO b RO ScR1 cR2 Where fy is the steel yield strength EO is Young s modulus of steel and b is the strain hardening ratio ratio between post yield tangent and initial elastic tangent RO cR1 and cR2 are parameters to control the transition from elastic to plastic branches The number of longitudinal bars 1s calculated as follows A bars 5 b Where p is the longitudinal steel percentage A the column cross section area A is the cross section area of the steel bar If the number of longitudinal bars 1s known the longitudinal steel percentage reinforcement ratio can be calculated A pue 6 C Where A 1s the area of longitudinal steel which 1s equal to the area of each bar times the number of bars For example the diameter of a 18 bar is 2 257 i
16. 6 2 Isolation Bearings To define isolation bearings click Define Isolation Bearings in Fig 44 and a window for defining isolation bearing properties will appear Fig 48 A sample bridge model including 2 isolation bearings on each bent cap is displayed in Fig 49 To activate define isolation bearings on a bent cap check the checkbox immediately prior to the Bent e g Bent 2 Bearings The total number of isolation bearings implemented at the bent cap Spacing The spacing between isolation bearings A symmetric layout of bearings is assumed The default values of material properties for the isolation bearings are also shown in Fig 48 As shown in Fig 50 zeroLength elements are used for the isolation bearings Li and Conte 2013 For each zeroLength element the 2 nodes are interacted in both horizontal directions denoted as directions 1 not shown and 2 in Fig 50 but tied in the vertical direction 3 Fig 50 Note that the local coordinate system 1 2 3 may or may not coincide with the global coordinate system X Y Z Fig 1 64 Isolation Bearings e amp sz Isolation Bearing Parameters Bent Activated Bearings Spacing ft Bent 2 Bent 3 Bent 4 Bearing Material Properties Yield Strength kip Initial Elastic Stiffness kip in Post yield Stiffness Ratio OK ST Fig 48 Definition of isolation bearings Fig 49 FE mesh of a 4 span bridge model with 2 isolation bea
17. 720 June 169 Shamsabadi A Khalili Tehrani P Stewart J P and Taciroglu E 2010 Validated Simulation Models for Lateral Response of Bridge Abutments with Typical Backfills J Bridge Eng 15 3 302 311 May Werner S D 1994 Study of Caltrans Seismic Evaluation Procedures for Short Bridges Proceedings of the 3rd Annual Seismic Research Workshop Sacramento California Yang Z Elgamal A and Parra E 2003 A computational model for cyclic mobility and associated shear deformation Journal of Geotechnical and Geoenvironmental Engineering 129 12 1119 1127 Zhang J and Makris N 2002 Kinematic Response Functions and Dynamic Stiffnesses of Bridge Embankments Earthquake Engineering amp Structural Dynamics 31 11 pp 1933 1966 170
18. California Berkeley California Kotsoglu A and Pantazopoulou S 2006 Modeling of Embankment Flexibility and Soil structure Interaction in Integral Bridges Proceedings of First European Conference on Earthquake Engineering and Seismology September 3 8 Geneva Switzerland Caltrans SDC 2004 Caltrans Seismic Design Criteria Version 1 3 California Department of Transportation Sacramento California Caltrans SDC 2006 Caltrans Seismic Design Criteria Version 1 4 California Department of Transportation Sacramento California Caltrans SDC 2010 Caltrans Seismic Design Criteria Version 1 6 California Department of Transportation Sacramento California Elgamal A Yang Z Parra E and Ragheb A 2003 Modeling of cyclic mobility in saturated cohesionless soils International Journal of Plasticity 19 6 883 905 Elgamal A and Lu J 2009 A Framework for 3D finite element analysis of lateral pile system response Proceedings of the 2009 International Foundation Congress and Equipment Expo Contemporary Topics in In Situ Testing Analysis and Reliability of Foundations ASCE GSP 186 M Iskander D F Laefer and M H Hussein Editors Orlando Florida March 15 19 pp 616 623 Elgamal A Jinchi Lu J and Forcellini D 2009a Mitigation of liquefaction induced lateral deformation in a sloping stratum 3D numerical simulation Journal of geotechnical and geoenvironmental engineering ASCE Vol 135 No 11
19. Gap Model Initial Stiffness 50 kip in ft Maximum Passive Pressure 5 ksf Transverse Direction Wingwall Width 13 Transverse Backfill Pressure Factor 0 9 Fig 70 Backfill horizontal properties of the EPP Gap Abutment Model 89 4 HFD Model As suggested by Shamsabadi et al 2007 2010 a Hyperbolic Force Displacement HFD relationship is employed to represent abutment resistance to bridge displacement in the longitudinal direction Fig 71 Fut 2Ksoymax ex ult y F y a FuttYmax 2 KsoYmax m ult y Where F is the resisting force y is the longitudinal displacement F 1s the ultimate passive resistance and Kso is the secant stiffness at Fy 2 2K50 Sut y 5 Tea DO Fut Ymax In this HFD model resistance appears after a user specified gap 1s traversed and the bridge thereafter gradually mobilizes the abutment s passive earth pressure strength Herein this strength 1s specified according to Shamsabadi et al 2007 2010 at 5 5 ksf for a nominal 5 5 ft bridge deck height with full resistance occurring at a passive lateral displacement of 3 6 in the sand structural backfill scenario Similarly abutment resistance to the transverse bridge displacement is derived from the longitudinal hyperbolic force displacement relationship according to the procedure outlined in Aviram et al 2008 To define a HFD abutment model select HFD Model for the abutment model type in Fig 67 Click Advanced in Embank
20. November 1672 1682 Elgamal A Lu J Yang Z and Shantz T 2009b Scenario focused three dimensional computational modeling in geomechanics Alexandria Egypt October 3 5 4 1Y GEC 09 4th International Young Geotechnical Engineers Conference 2 6 October ISSMGE Elgamal A 2010 Calibrated 3D computational modeling of soil structure systems and liquefaction scenarios Proc Fifth Intl Conf on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics May 24 29 San Diego CA 168 Lu J 2006 Parallel finite element modeling of earthquake site response and liquefaction PhD Thesis Department of Structural Engineering University of California San Diego La Jolla CA Mackie K R and Stojadinovic B 2005 Fragility basis for California highway overpass bridge seismic decision making PEER Report No 2005 02 Pacific Earthquake Engineering Research Center University of California Berkeley Mackie K and Stojadinovic B 2006 Seismic Vulnerability of Typical Multi span California Highway Bridges Proceedings of the Fifth National Seismic Conference on Bridges and highways September 18 20 San Francisco Mackie K R Wong J M and Stojadinovic B 2008 Integrated probabilistic performance based evaluation of benchmark reinforced concrete bridges PEER Report No 2007 09 Pacific Earthquake Engineering Research Center University of California Berkeley Mackie K R Wong J M a
21. Soil spring definition window after using the soil spring data calculated based on p y COU ALONG ar 58 41 Sample FE mesh of a bridge model with soil springs included 58 42 Local coordination system for the foundation matrix ooooooonnnnncccnnnnnnnnnnnnnnnnnnnnnnos 59 xli Fig 45 Foundation matrix for each Dri ii ica 60 P19 pees Advanced Opus 61 Pi2 43 Delito ot deck Mines ul loud acura e unto due nudos 63 Fig 46 FE mesh of a 4 span model with 2 deck hinges included 63 Fig 47 OpenSees zeroLength elements for deck hinges plan view 64 Fig 48 Definition of isolation bearings eese 65 Fig 49 FE mesh of a 4 span bridge model with 2 1solation bearings included on each bent cap SO M mL du M EE LM Uum 65 Fig 50 OpenSees zeroLength elements for 1solation bearings side view of bent cap cut plan M A 66 Fic 5 ls Detimition Of steel Jacket 67 BIS DZ Okete OL steel He KU deant emat ene RR dni 67 Fig 53 Definition ol Skew angles intei t sen A V dedu ted 68 Fa S4 Mesh parameters sn DAA AA 69 1e 55 Definition OF an abument model ninio dc 71 Fig 56 General scheme of the Elastic Abutment Model a longitudinal component b transverse component c vertical COMPONEN oooooonnnnnnnnnnnnnnnnnoccnnnnnnnnnnnnnonoccnnnnnnnnnnnos 72 Fig 57 Definition of the Elastic Abutment Mode
22. Step 1 Define Model and Check Responses Model Builder Spans Deck Bentcap Columns Foundation Abutments Advanced Mesh r 9 Quick Check of Model Responses View Natural Periods View Gravity Response Longitudinal Response Transverse Response A Step 2 Select Analysis Option Analysis Options AN ZO C Pushover Mode Shape Number of Modes 10 9 Ground Shaking Select Input Motions Change Damping Equivalent Static Analysis ESA Longitudinal Direction Transverse Direction Step 3 Run FE Analysis Run Analysis Save Model and Run Analysis Ready Fig 7 MSBridge main window bridge model with soil springs and deck hinges included Zi 3 1 Spans To change the number of spans click Spans in the main window Fig 6 and Fig 8 Number of Spans The total number of spans for a multi span bridge The minimum is 2 and the default value is 4 The maximum allowable number of spans is 100 MSBridge supports models for both Straight Bridge and Curved Bridge options 3 1 1 Straight Bridge If the bridge has equal span lengths click Equal Span Length and specify the span length Fig 8 The default is 60 feet If the bridge has varied span lengths click Varied Span Length and then Modify Span Lengths to specify span lengths Fig 9 Fig 10 shows a sample straight bridge model with varied span l
23. XV Fig 114 Bridge peak accelerations for all motions a maximum bridge accelerations b maximum budec displacement na 145 Fig 115 Maximum column amp abutment forces for all motions oooonnnnnnnnnnnnnnnnnnnnnnnnns 146 Fig 116 Equivalent Static Analysis for the bridge longitudinal amp transverse directions148 Fig 117 Sample output of ESA for the bridge longitudinal direction a pushover load b elastic displacement de Mad id 149 Fig 118 Comparison of displacements from ESA and THA c00oooocccnnnncnnnnnnnnnnnnnnnnnnnnnnnos 150 Fig 119 Output of ESA for the bridge transverse direction a pushover load and bent number b clastic displacement de Maldad 152 Fig 120C DoOSIHE d moton Sarai di 160 Fig 121 Directory structure Of d Motonet es 161 Fro 122 Sample MIO Mle taa da 161 Fig 123 Sample data lea iio 162 Fig 124 Example of user defined motion ccceesseeeeeseeseeeeeeseeseeeeeeseseeseseeeseseeeeeas 162 Fig 125 Bridge Type 1 model a MSBridge b SAP2000 ssss 164 Fig 126 Bridge Type 2 model a MSBridge b SAP2000 ssese 165 Fig 127 Bridge Type 9 model a MSBridge b SAP2000 sess 166 Fig 128 Bridge Type 10 model a MSBridge b SAP2000 cccceeeeeeeeeees 167 XVI LIST OF TABLES Table 1 Default values for column reinforced concrete RC section properties 46 Ta
24. analysis EDP1 Maximum drift ratio SRSS column EDP2 Residual drift ratio SRSS column The Square Root of Sum of Squares SRSS values of the 2 horizontal components are used The drift ratios are combined separately at each time step to obtain SRSS EDP 1 Max drift ratio SRSS is the maximum of the SRSS values of all time steps EDP2 Residual drift ratio SRSS 1s the SRSS value at the last time step The drift ratio is in percentage EDP3 Maximum longitudinal relative deck end abutment displacement left EDP4 Maximum longitudinal relative deck end abutment displacement right These two EDPs are intended to address the issue of abutment impact into the backwall so they are defined as only the motion of the deck into the abutment Maximum absolute values in the longitudinal direction are used EDP5 Maximum absolute bearing displacement left abutment EDP6 Maximum absolute bearing displacement right abutment 141 These two EDPs are intended to address bearing damage whether or not an explicit representation of the bearings 1s included in the user selected abutment model Therefore the EDP for the EDP is based on the relative displacements of the deck end node to the abutment top node The SRSS values of the resulting two relative horizontal displacements is used and both motion into the backwall and away from the backwall are considered EDP7 Residual vertical displacement left abutment EDPS Residual vertical displ
25. and 95 cumulative Arias intensity of the record All of the spectral intensity measures are defined at an effective viscous damping of 5 unless otherwise noted J Step 2 Select Analysis Option Analysis Options Pushover Mode Shape Number of Modes 10 9 Ground Shaking Select Input Motio ns Fig 91 Group shaking analysis 114 Input Motions Input Motion Folder C Users jinlu Documents _MSB DOTNET Untitled_brfiles Untitled EQ Input Motions 18 Records in Total 1 Records Selected Selected Record Bin Earthquake Motion 1 TOL NORTHRIDGEXRRS 2 T02 NORTHRIDGE SCS 3 T03 CHIC HATCUOGS mw curcuwrcues s om m S mer ao jex EMO EA 02 0 02 2407 B fo 10 I B 19 014 View Motion Display Intensity Measures Scale Factor Analysis Duration Longitudinal 9 Compute Response to Entire Record Length A Free Vibration Duration 0 seconds Vertical C Compute Response from s S Analysis Parameter Simultaneous Execution Computation Time Step 0 02 conc Number of Motions Running Simultaneously 2 OK Cancel Fig 92 Input motions window 115 q Import a Motion Motion Files Longitudinal Direction C Users jinlu Documents _MSB DOTNET Untitled brfilessUntitledl E Browser Transverse Direction G Users jinlu Documents _MSB DOTNET Untitled brfileskUntitledl E Browser Vertical Direction CA Users yinlu Documents _MSB DOTNET Untitled brfilessUn
26. at Crushing Strength Ratio between Unloading Slope Concrete Crushing Strength 943 49 psi Concrete Crushing Strength 255090 32 Concrete MMaterial Properties Cover Concrete Properties Concrete Compressive Strength Concrete Strain at Maximum Strength Concrete Crushing Strength Concrete Strain at Crushing Strength Ratio between Unloading Slope Concrete Crushing Strength Concrete Crushing Strength d Fig 28 Column nonlinear material properties a Steel02 material b ReinforcingSteel material c Concrete02 material for the core concrete d Concrete02 material for the cover material 45 Fig 29 Column fiber section based on PEER best modeling practices report Berry and Eberhard 2007 a Circle b Octagon c Hexagon a b Fig 30 OpenSees quadrilateral patch employed for calculating the cover concrete fibers for a Octagon and b Hexagon cross section Table 1 Default values for column reinforced concrete RC section properties Parameter Value Longitudinal bar size US 10 Longitudinal steel 2 Transverse bar size US 7 Transverse steel 1 6 Steel unit weight pcf 490 Steel yield strength psi 66717 5 Concrete unit weight pcf 145 Concrete unconfined strength psi 4000 46 Table 2 Default values for Steel02 material properties Parameter Steel yield strength psi Young s modulus psi Strain hardening ratio Controlling parameter RO Controlling parameter cR1
27. ced lib dias Aaah S e go ect tet be a ued dlui bem Ratha clas 90 Column Responses amp Bridge Resonance sssccssccccsssssssssssccccccccccssssssssccsoees 93 Xl Bidee Natutal PSSS a 93 59 Colima Grav iy RESPONSE roto 93 5 3 Column amp Abutment Longitudinal Responses ccccccccccnncnnnnnnononononnnonncnnnnnnnnnnnnnnnnnnos 93 5 4 Column amp Abutment Transverse Responses ccccccocooooncccnnnnnnnnononocccnnnnnnnnnononccnnnnnnnnnnons 93 Pushover amp Eigenvalue Analyses sssseeeecccsssssceecococssssceecocosssssceccocosssssseceososssssseee 97 6 1 Monotonic PUSHOVED 1d 97 vill 6 2 6 3 6 4 6 4 1 6 4 2 6 4 3 6 4 4 6 4 5 6 5 7 1 7 1 1 Z2 AES Ted 8 1 8 1 1 8 1 2 8 1 3 8 1 4 8 1 5 8 1 6 8 1 7 8 1 8 8 2 8 3 8 3 1 8 3 2 8 3 3 AN toere esterase AE E EE se rece 98 DUsersDehned Pushover U Puse add 99 Output tor Pushy T Atay SIS in 100 Columna Response Profiles esc otio ete Dieta mine a 100 Column Response Time Histories ec ivi Ere xit E e i ad 101 Column Response RelatiONS HIPS cooooooooonccnonononononononoccnonnnononononococonnnnnnnonaninocoss 103 Abutment Force Displacement and Response Time Histories 104 Detormed Mesina lilas 105 UNS AA nii desi E be Soto aeketu adir ced 106 Ground SHAKING ooo po eiecti Hi PORE ea den ID HI PR MUI IM E IE 112 Definition specification of input motion ensemble Suite seeeeeussse 112
28. download the input motion files from the PEER NGA Database there 1s no need to re format the data into one column as shown in Fig 123 Just copy the data points into the corresponding DATA files And then make the INFO files containing the number of data points and the sampling period DT 2 lines according to the header information 159 q Input Motions Input Motion Folder C Program Files x66 MSBridge NET Motions gt d TE Pg To e 1 To del T04 P yb TO5 gt j Tos Scale Factor i d Ti 7 b je Tos P Tos p ES a mo 5 ro 6 me 7 m a3 To i moo d Select All De select All isplay Intensity Measures Longitudinal Transverse 1 A Vertical 1 ss Bin name Analysis Parameter Simultaneous Execution Computation Time Step 0 02 seconds Number of Motions Running Simultaneously a Cancel Fig 120 Choosing a motion set 160 Motion Set Name gane ipen New folder Jz i P Mations m Name Bin M TH RRS UP ATZ inf L UF Into IVA Sy NORTHRIDGE ET L RRS UP AT2 data W A RRS oe Earthquake Name JL 2 A RRS318 AT2 data Bu RRS228 AT2 info Motion Name j RRS228 AT2 data di TOS QC SA AO Vertical Component Lo TOR 4 Hm Horizontal components RRS UP AT2 data Date modified 9 17 26 DATA File Size 17 5 KB Fig 121 Directory structure of a motion set lad C Program Files 86 MSBridge NET Motions TOL
29. per Unit Length 3 6 kip ft Cancel Fig 19 Rectangular shape employed for the bent cap 3 4 Columns To modify column properties click Columns in Fig 6 Fig 20 shows the window to define columns The current version assumes that all bents have the same number of columns and the same Column Spacing If Number of Column for Each Bent is 1 Column Spacing will be ignored Fig 20 37 Bridge Columns Fale Mumber of Colurnns OK Number of Columns per Bent Cancel Apply Column Spacing 18 ft Column Heights Modify Column Heights Column Properties Column Properties Column Connection Fig 20 Columns 3 4 1 Column Heights To define column heights click Modify Column Heights in Fig 20 A window for defining column heights will appear Fig 21 Varied Column Heights Column Heights Bent Column Height ft Fig 21 Column heights 3 4 2 Column Connection 38 In a multi column case the number of columns per bent is equal to 2 or more the user can specify the boundary connection conditions of the columns Click Column Connection in Fig 20 to select the boundary condition for the columns and bent cap connection Three options are available Fig 22 1 fixed at top pinned at base 11 pinned at top fixed base and 111 fixed at both top and base Note In a single column case the number of columns per bent is equal to 1 both column top and base are assumed f
30. the abutment model includes the vertical stiffness of the bearing pads in series with the vertical stiffness of the trapezoidal The detailed scheme of the vertical response 1s shown in Fig 66a The typical vertical response of a bearing pad is shown in Fig 66b And the typical overall behavior of the vertical response is illustrated in Fig 66c A vertical gap 2 inch by default which can be modified by the user is employed for the vertical property of the bearing pads The embankment stiffness per unit length of embankment was obtained from Zhang and Makris 2000 and modified using the critical length to obtain a lumped stiffness In the vertical direction an elastic spring 1s defined at each end of the rigid link with a stiffness corresponding to the vertical stiffness of the embankment soil mass The embankment is assumed to have a trapezoidal shape and based on the effective length formulas from Zhang and Makris 2002 the vertical stiffness K unit 1 m can be calculated from Zhang and Makris 2002 82 E ad Ka u i vV H C z nf 3 Lo Where H is the embankment height d is the deck width z 0 5d S S is the embankment slope parameter in window see Fig 20 E 2 8G G pV p and V are the mass density and the shear wave velocity of the embankment soil respectively Deck Bearing Pad Vertical NC zeroLength L _ Vertical Gap Rigid Link Embankment Vertical Resp
31. the initial stiffness matrix Am and Ax are two user specified constants The damping ratio curve f 1s calculated based on the following equation ET Ayr f where f is frequency 120 1 Specification of Am and Ax By Defining Damping Ratios Click Change Damping in the MSBridge main window to modify the Rayleigh damping coefficients Fig 97 The user can define damping coefficients Fig 97 by specifying two frequencies f and f must be between 0 1 and 50 Hz and two damping ratios c and suggested values are between 0 2 and 20 The Rayleigh damping parameters Am and Ax are obtained by solving the follow equations simultaneously A A TT 51 4 f k fi A A m a Ar f k f 2 Direct Specification of Am and Ay The user can also directly define Rayleigh damping coefficients Am and Ax Fig 97 7 3 Save Model and Run Analysis After defining the finite element model click Save Model and Run Analysis The finite element computations will start for several earthquakes at a time Fig 98 as specified in the Input Motions window Fig 92 The user can modify the time integration scheme for the OpenSees analysis by clicking Menu Execute and then Advanced Option OpenSees Parameters Fig 99 Fig 99 shows the default parameters which are used in the analysis 121 a Rayleigh Damping Coefficients Damping Parameters By Defining Damping Ratios By Defining Dampin
32. the longitudinal load displacement curve at the column top The load refers to the shear force of the beam column element at the specified elevation Fig 106 shows the moment curvature curve at the column top The vertical axis 1s the bending moment and the horizontal axis 1s the curvature To view the data for the plot click View Data 129 Tui Column Response Relationships Motion RRS Response Type Response Relationship Mament Curvature Load Displacement Direction Longitudinal J Transverse Column Column lofBent Elevation o Animation Play Current Step Playing Speed View Data Add Figure to Report Fig 105 Load displacement curve at column top 130 Column Response Relationships Motion RRS A lel Response Type Response Relationship Q Moment Curvature Load Displacement Direction amp Longitudinal Transverse Column Elevation PR Animation Play Current Step Playing Speed View Data Add Figure to Report Fig 106 Moment curvature curve at column top 8 1 5 Abutment Responses Time Histories The abutment responses can be accessed by clicking menu Display and then Abutment Response Time Histories The abutment responses window includes the following options i Force Displacement Relationships ii Relative Deck end Abutment Displacement Time Histories iii Resisting Force T
33. 00 Table 10 Displacement unit inch of Bridge Type 9 under pushover load of 1000 kips applied at deck center along both the longitudinal and transverse directions ME sueno TE in Bent Displacement Displacement Displacement 0 1208 0 0410 1 3601 0 0423 3 0768 13913 0 0422 4 0093 0212 0 0415 1 0488 0 1240 0 0410 das 2 07571 13630 0 0423 3 0766 13950 0 0422 4 0096 02149 0 0415 0 3 0 bieen 2 Y 0 0 0 3 0 0 2 0 Whole B gt the IAIO 166 a b Fig 128 Bridge Type 10 model a MSBridge b SAP2000 Table 11 Displacement unit inch of Bridge Type 10 under pushover load of 2000 kips applied at deck center along both the longitudinal and transverse directions MD Longitudinal Transverse Vertical in Bent Displacement Displacement Displacement 1 03910 03054 0 0456 sapanq9 2 Losses cese oo 0 4210 0 0476 0 1755 0 0474 0 2917 0 0457 0 4991 0 0472 0 4309 0 0477 0 1853 0 0475 5 0 Difference a we 2 0 5 0 167 References Aviram A Mackie K R and Stojadinovic B 2008 Effect of Abutment Modeling on the Seismic Response of Bridge Structures Earthquake Engineering and Engineering Vibration 7 4 395 402 Berry M P and Eberhard M O 2007 Performance Modeling Strategies for Modern Reinforced Concrete Bridge Columns Report No 2007 07 Pacific Earthquake Engineering Research Center University of
34. 1 No of Pages 22 Price Unclassified Unclassified Form DOT F 1700 7 8 72 Reproduction of completed page authorized iii DISCLAIMER This document is disseminated in the interest of information exchange The contents of this report reflect the views of the authors who are responsible for the facts and accuracy of the data presented herein The contents do not necessarily reflect the official views or policies of the State of California or the Federal Highway Administration This publication does not constitute a standard specification or regulation This report does not constitute an endorsement by the California Department of Transportation of any product described herein For individuals with sensory disabilities this document is available in Braille large print audiocassette or compact disk To obtain a copy of this document in one of these alternate formats please contact the Division of Research and Innovation MS 83 California Department of Transportation P O Box 942873 Sacramento CA 94273 0001 ACKNOWLEDGMENTS The research described in this report was supported by the California Department of Transportation Caltrans under Contract No 6540445 This support is most appreciated ABSTRACT MSBridge is a PC based graphical pre and post processor user interface for conducting nonlinear Finite Element FE studies for multi span multi column bridge systems Finite element computations are conducted using OpenSees htt
35. 1 Deck Response Time Histories The deck response time histories can be accessed by clicking menu Display Fig 3 and then Deck Response Time Histories Fig 101 shows the window for displaying the deck longitudinal displacement time histories 8 1 2 Column Response Profiles The column response profiles can be accessed by clicking menu Display Fig 3 and then Column Response Profiles The column response window is shown in Fig 102 The columns are labeled as 1 Column 1 of Bent 2 see Fig 1 the first bent starting after left abutment 1s denoted as Bent 2 the second as Bent 3 and so on ii Column 2 of Bent 2 iii more if any Fig 103 shows the bending moment in the longitudinal plane The horizontal axis of the plot 1s the response name e g displacement bending moment etc and the vertical axis is the elevation of the column Zero elevation means the column base 8 1 3 Column Response Time Histories The column response time histories can be accessed by clicking menu Display Fig 3 and then Column Response Time Histories Fig 104 shows the window for displaying the column longitudinal displacement time histories 126 Tu Deck Response Time Histories Motion RRS Response Type Response Time History Displacement C 3 Acceleration Direction Longitudinal C Transverse Ci Vertical Location Bent 3 ViewData Add Figure to Report Fig 101 Deck longitudinal displa
36. 6 of the initial stiffness The transverse stiffness and strength of the backfill wing wall and pile system is calculated using a modification of the SDC procedure for the longitudinal direction 80 Wingwall effectiveness CL and participation coefficients CW of 2 3 and 4 3 are used according to Maroney and Chai 1994 The abutment stiffness Kabt and back wall strength Pbw obtained for the longitudinal direction from Section 7 8 of SDC 2004 are modified using the above coefficients The wing wall length can be assumed 1 2 1 3 of the back wall length The bearing pads and shear keys are assumed to act in parallel Combined bearing pad shear key system acts in series with the transverse abutment stiffness and strength Bearing Pads Deck Transverse Response zeroLength Elements Shear Keys Rigid Link Embankment Transverse Response Side View Fixity 800 mo i X 0 02953 Nox 0 6004 Y 7142 600 E Y 4772 m 400 200 F kips S 200 400 600 800 dci ci cod 20 15 10 5 0 5 10 15 20 81 Total tiansverse response 200 Pero re Stress or force kips c 50 10 0 10 20 Strain or deformation in c Fig 65 Transverse response of the SDC 2004 Abutment Model a general scheme b response of a bearing pad and shear keys curve with a higher peak value 1s the shear key response c total transverse response 4 3 3 Vertical Response The vertical response of
37. Abutment Forces for All Motions The window to display the maximum column amp abutment forces for all motions is shown in Fig 115 The responses are available in the longitudinal and transverse directions as well as for the SRSS of the 2 horizontal directions Fig 115 The figures in this window include 1 Maximum column shear forces 11 Maximum column bending moments 111 Maximum abutment forces left abutment iv Maximum abutment forces right abutment 145 Bridge Maxirnum Forces Response Type Response Forces Max Column Shear Forces C2 Max Column Bending Moments C Max Moments at Column Base O Max Left Abutment Forces O Max Right Abutment Forces Direction Longitudinal C Transverse C Horizontal SRSS Intensive Measure PGA View Data Add Figure to Report Fig 115 Maximum column amp abutment forces for all motions 146 9 Equivalent Static Analysis Equivalent Static Analysis ESA option 1s available in MSBridge for the bridge longitudinal amp transverse directions The whole bridge system 1s employed in the bridge longitudinal ESA And one single bent is employed in the bridge transverse ESA 9 1 Bridge Longitudinal Direction To conduct an Equivalent Static Analysis ESA for the bridge longitudinal direction click Longitudinal Direction in the main window Fig 116 The elastic displacement demand output 1s shown in Fig 117 The displacement demand output 1s availa
38. Available Ground Motions ccccccccsseseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeees 112 Specitications ob Input MOI 113 Rayi Dampi xoi decet veq is 120 save Model aiid Ruina Siu oed i 121 Time History and Engineering Demanding Parameter Output 125 Time History Output Quantities iiio eterne sterio hv usage su tae tein ruta o eue 125 Deck Response Time Histories d o Aia 126 Colmi Response roles iia 126 Columna Response Time Histories ienesa eio entum tube eua esses edad utu ciues 126 Column Response RelatiONS HIPS occooooooonnncncnnnnnonnnononocnnnnnnnnnnnnonocccnnnnnnnnnnanononoss 129 Abutment Responses Time ASTON SS ia A Dabei ead M qs 131 Soil Spring Responses Time H istortes isisi EA eese eene 134 Deck Hinge Responses Time Histories iss sse es bas Ua a OR RR Rasa 135 Isolation Bearing Responses Time Histories occccccncncnnnncnnnnnonnnonncnnnnnnnnnnnnnnnnnnnnnos 137 Detormicd Mesh dnd ATIS HOD ai dde t ete uu tort Nou eue ua fone Reeve deed 138 Maximum Output r OVa Ie Sos at 141 FOFO ERNEUT 141 Bridge Peak Accelerations amp Displacements for All Motions sss 143 Maximum Column amp Abutment Forces for All Motions oooooooononnncccncncnoncnnnnnnnos 145 Equivalent Static A nalyslSio nia ia 147 9 1 Bridee Donermuditial DIFE CUM 147 9 2 bridee Transverse Dit ce OM ada 147 Appendix A Calculation of Steel and Concrete Material Propert
39. Bearings Steel lackets Define Steel Jackets Skew Angles Global Skew Angle 7 Use Individual Skew Angles Skew Angles OK Cancel Fig 44 Advanced options 3 6 1 Deck Hinges To define deck hinges click Define Deck Hinges in Fig 44 and a window for defining deck hinge properties will appear Fig 45 A sample bridge model including 2 deck hinges is shown in Fig 46 61 Compression Connector Node 1 Rigid Links lt N N Deck peck 1 cables and Beari Owes ables and Bearings zeroLength Elements Compression CALU D AMANE d Connector Fig 47 shows the general scheme of a Deck Hinge which consists of 2 compression connectors located at both deck edges and cables To activate define a deck hinge check the checkbox immediately prior to the Hinge e g Hinge 2 Distance to Bent The distance to the nearest left bent Foot and meter are used for English and SI units respectively Spacing The space between transverse left and right deck connectors This space should usually approximately equal to the Deck Width Skew Angle The skew angle of the deck hinge A zero skew angle means the deck hinge is perpendicular to the bridge deck direction of Cables The total number of cables of the deck hinge Cable Spacing The spacing between cables Symmetric layout of cables is assumed Foot and meter are used for English and SI units respectively As shown in Fig 47 zeroLength el
40. History Hinge 1 Hinge Element Cable Elementi Response Type Force Displacement Animation Play Current Step Playing Speed View Data Add Figure to Report 136 Tui Deck Hinge Response Histories Motion RAS Deck Hinge Response Time History Hinge 1 v Hinge Element Response Type Force Displacement Animation Play Current Step Playing Speed al View Data Add Figureto Report b Fig 109 Deck hinge response time histories a cable element b edge element 8 1 8 Isolation Bearing Responses Time Histories The isolation bearing responses can be accessed by clicking menu Display and then Isolation Bearing Response Time Histories The isolation bearing responses window includes the following options Fig 110 i Force Displacement Curve ii Displacement Time History iii Force Time History Three translational directions and three rotational directions of the above responses for each bearing are displayed Fig 110 137 Isolation Bearing Response Histories Motion RRS Bent Response Time History Bent 4 Bearing Bearing 1 Direction Longitudinal Response Type Ferce Dis lacement Force Displacement v Animation Play Current Step Playing Speed View Data Add Figure to Report Fig 110 Isolation bearing response time histories 8 2 Deformed Mesh and Animation The deform
41. Motion T OTVMORTHRIDGEXRRS Intensive Measure IM Longitudinal Transverse Horizontal SRSS Vertical PGA g 0 82101 0 48468 0 85697 0 8004 PGV in sec PGD in 11 653 10 614 D 5 95 sec CAV in sec Arias Intensity in sec 280 51 157 48 SA g E 0 77363 92104 SV in sec SD in PSA g 1827 PSV in sec 1124 24 145 54 SV 5D PSA and PSV are calculated at Period 1 sec Fig 95 Intensity measures of individual motion 118 Intensive Measure PGA Co PGV PGD DG 95 CAV Arias Intensity C3 SA Period 1 sec C3 SV Period 1 sec C3 SD Period 1 sec 5 PSA Period 1 sec PSV Period 1 sec Direction Longitudinal O Transverse Vertical Horizontal SR55 Plot Histogram 5 Cumulative Distribution 119 A Histograms and Cumulative Distribution Intensive Measure Cumulative Distribution PGA o PGV OQ PGD O D 5 95 J CAV Arias Intensity SA Period 1 sec SV Period 1 sec J SD Period 1 sec PSA Period 1 sec PSV Period 1 sec Direction Longitudinal J Transverse Vertical Horizontal SRSS Plot J Histogram Cumulative Distribution b Fig 96 Histogram and cumulative distribution for the whole input motion set a histogram b cumulative distribution 7 1 3 Rayleigh Damping MSBridge employs Rayleigh damping which takes the form C A nM A K where M is the mass matrix C is the viscous damping matrix K is
42. Passive Pressure 5 ksf Transverse Direction Wingwall Width 13 Transverse Backfill Pressure Factor 0 9 d 86 Sl Embankment Vertical Stifness ca 2 EX Embankment Vertical Direction Soil Mass Density 109 87 pcf Soil Shear Wave Velocity 492 13 ft s Embankment Slope Vertical Horizontal 0 5 Embankment Top Width 39 Embankment Height 32 Recalculate Stiffness Embankment Stiffness Embankment Vertical Stiffness 9470479 kip in e Fig 67 Definition of the SDC 2004 Abutment Model a main parameters b bearing pad properties c shear key properties d SDC abutment properties e embankment properties 4 4 SDC 2010 Sand Abutment Model This model is similar to the SDC 2004 abutment model but employs the parameters of the most recent SDC 2010 for a sand backfill Embankment Fig 68 To define a SDC 2010 Sand Abutment Model select SDC 2010 Sand for the abutment model type in Fig 55 Table 5 shows the initial stiffness and the maximum passive pressure employed for the SDC 2010 Sand Abutment Model compared to other similar abutment models including SDC 2004 SDC 2010 Clay EPP Gap and HFD Models 87 A Embankment Lateral stiffness ca s es Longitudinal Direction SDC 2010 Sand Model Initial Stiffness 50 kip in ft Maximum Passive Pressure 5 ksf Transverse Direction Wingwall Width 13 Transverse Backfill Pressure Factor 0 9 Cancel Fig 68 Backfill horizont
43. Springs To define soil springs choose Soil Springs Fig 35 and then click Modify Soil Springs to define soil spring data or click Modify Shaft Foundation to define pile shaft data Fig 35 It is possible to include a shaft foundation at particular bents or abutments simply check the box to turn off on shaft foundation for each bent abutment Parameters defining the pile foundation include Fig 36 Pile Diameter the diameter of the pile shaft the cross section 1s assumed to be circular which is 48 in by default Young s Modulus Young s Modulus of the pile shaft The foundation piles are assumed to remain linear Pile Group Layout see Fig 36 This option allows defining the numbers of pile as well as the spacing in the bridge longitudinal and transverse directions For now this option is only available for both abutments For a bent one single pile is assumed 52 Tui shaft Foundation Bent Number Shaft Foundation of Abutment 1 Abutment 1 L No Shaft Foundation for Abutment 1 Bent 2 Bent 3 Bent 4 Stemwall Height ft Abutment 5 Shaft Foundation Parameters Pile Group Layout Bridge Longitudinal Bridge Transverse Number of Piles F A Spacing ft A 6 Pile Properties Pile Diameter in Young s Modulus ksi Use Shaft Foundation Parameters of this Bent for All Other Bents ok Cancel Fig 36 Shaft foundation for abutments and bents When implementing the soil springs for an abutment section co
44. a plastic hinge 139 marker stays once the plastic hinge is developed The plastic hinge is developed when rebar fails in tension or first concrete fiber reaches the maximum strain capacity Deformed Mesh Analysis Stage Due to Shaking Response Plastic Hinges y n Fu P Plot Scale Factor 62 Show Legend Show Undeformed Mesh Display Motion Longitudinal Component 3D XY XZ YZ Transverse Component FP Vertical Component Animation Play Repeat Current Step Step 224 Time 446882 Fig 112 Visualization of Plastic Hinges 140 8 3 Maximum Output Quantities 8 3 1 EDP Quantities At the end of the finite element analysis phase the following output EDP quantities for each earthquake record are available Table 6 Engineering Demand Parameters EDP EDP EDP names Maximum column drift ratio Residual column drift ratio Maximum relative deck end abutment displacement left Maximum relative deck end abutment displacement right Maximum bridge abutment bearing displacement left Maximum bridge abutment bearing displacement right Approach residual vertical displacement left Approach residual vertical displacement right CONN NM BW N The EDP outcomes can be shown against the input base shaking IMs The sections below detail how the response quantities are obtained for each EDP for the annotated model that is used to describe the location of sampling points during time history
45. acement right abutment This EDP is used to gage immediate repairs for rideability and is not a measure of the permanent slumping of the embankment for example Therefore the EDP 1s calculated as the vertical displacement of the abutment top node relative to the deck end node The residual value is used value at the final time step The EDP quantities for all input motions can be accessed by clicking menu Display Fig 3 and then EDP Quantities for All The window to display EDP quantities 1s shown in Fig 113 The EDP quantities are displayed against any of the 11 intensity measures The EDP quantities for each input motion are displayed by bin of the motion see legend in Fig 113 When an IM is paired with an EDP and all the individual realizations are plotted the result is typically termed a demand model or probabilistic seismic demand model PSDM 142 Y Bridge EDP Quantities e Pene Response Type 9 Max Drift Ratio SRSS Max Residual Drift Ratio SRSS Max Long Relative Deck end Abut Disp Left Max Long Relative Deck end Abut Disp Fight Max Abs Bearing Disp Left Abut Max Abs Bearing Disp Right Abut Residual Vertical Disp Left Abut Residual Vertical Disp Right Abut Intensive Measure PGA View Data Add Figure to Report Fig 113 EDP quantities for all motions 8 3 2 Bridge Peak Accelerations amp Displacements for All Motions The bridge peak accelerat
46. al Properties Pile Width Soil Spring Depth ft Submerged Unit Weight Friction Angle 30 Kpy 200000 Loading Options Static Loading 2 Cyclic Loading Shear Strength Profile Please enter depth ft and shear strength psi in pairs c Fig 39 Soil spring calculations based on p y equations a Soft Clay Matlock b Stiff Clay without Free Water Reese c Sand Reese 57 Y Soil Springs Bent Number Depth ft Soil Springs at Depth 0 ft for Abutment 1 Abutment 1 Please enter below displacement in and Bent 2 force kip in pairs Bent 3 Bent 4 Abutment 5 0 48 3 78866466005407 0 96 4 77341835619492 1 44 5 46419997800184 1 92 6 01413026692457 244 6 4785254387165 2 88 6 88446057311962 3 36 7 24745476928518 3 84 7 57732932010813 4 32 7 88074007034691 4 8 8 16243057251833 6 24 8 9084186353269 7 68 9 54683671238985 9 12 101096790253428 Delete Depth 10 56 10 6159873881356 12 11 0781226701383 Add Depth 13 44 11 5046173248552 14 88 11 9016378614929 Select from p y Curves Cancel Fig 40 Soil spring definition window after using the soil spring data calculated based on p y equations Fig 41 Sample FE mesh of a bridge model with soil springs included 58 3 5 3 Foundation Matrix The third foundation type available is Foundation Matrix Fig 35 Li and Conte 2013 In this method the foundation only for bent columns 1s represented by the coupled foundation stiffness ma
47. al properties for the SDC 2010 Sand Abutment Model Table 5 SDC Abutment Properties Initial Stiffness Maximum Passive Pressure Abutment Model kip in ft ksf SDC 2004 20 5 SDC 2010 Sand 50 5 SDC 2010 Clay 25 5 EPP Gap User defined User defined 50 sand HFD Model 25 clay 3 5 Denotes average soil stiffness K50 4 5 SDC 2010 Clay Abutment Model This model is similar to the SDC 2004 abutment model but employs the parameters of the most recent SDC 2010 for a Clay backfill Embankment Fig 69 To define a SDC 2010 Clay Abutment Model select SDC 2010 Clay for the abutment model type in Fig 67a Table 5 shows the initial stiffness and the maximum passive pressure employed for the SDC 2010 Clay Abutment Model compared to other similar abutment models 88 Tui Embankment Lateral Stiffness ca s DX Longitudinal Direction SDC 2010 Clay Model Initial Stiffness 25 kip in ft Maximum Passive Pressure 5 ksf Transverse Direction Wingwall Width 13 Transverse Backfill Pressure Factor 0 9 Cancel Fig 69 Backfill horizontal properties of the SDC 2010 Clay Abutment Model 4 6 ElasticPP Gap Model This model is similar to the SDC 2004 Abutment Model but employs user defined parameters for the stiffness and maximum resistance Fig 70 To define an EPP Gap Abutment Model select EPP Gap for the abutment model type in Fig 67 S Embankment Lateral stifness s EX Longitudinal Direction EPP
48. alysis oooooooooonoccccccnononononnnononononononanananos 99 Fig 82 Usersdetmed pushover U PUs is 100 Fig 83 ColiminTesponse protesta 101 Fig 54 Column response time Mones bid 102 Fig 85 Response relationships for column seen 103 Fig 56 Abutment response time NISIOTICS in 104 Fig 87 Deformed mesh and contour fill esses 105 Fig 88 Visualization of Plastic hinges red dots represent plastic hinges developed 106 X1V Fi E g 89 Steps to perform an Eigenvalue analySIS ooooooooooooncccccncncnnnnnnnnnnnnnonononananoos 107 Fig 90 Sample output for an Eigenvalue analysis for the default bridge model a first mode b second mode c third mode d fourth mode and e fifth mode 111 L15 91 Groupshakino anal SiS oeste dene a ia 114 Fic 92 Input mottOns WEIGOOW scra i Erde eb veu tbv bus de ere ve Eb Poen UR dv Reus 115 Fig 93 Importing a user defined motion a choosing data files b message showing new motion has Desnradaded ii is 117 Fig 94 Time histories and response spectra of individual motion 118 Fig 95 Intensity measures of individual MOTION ccceeseesesseeeeseeeeeesessesseeeseeseeeeees 118 Fig 96 Histogram and cumulative distribution for the whole input motion set a histogram b cumulativo distan 120 Fig 97 Ray le1 dato did 122 Fig 98 Simultaneous executio
49. and section properties MSBridge uses an elastic material model for the bridge bentcap elements Fig 18 shows the default values for the bentcap material properties including Youngs Modulus Shear Modulus and Unit Weight Fig 18 also shows the bentcap Section properties Section properties can be input directly in Fig 18 if available If this information is not available MSBridge will generate properties based on a rectangular section dimensions Click Recalculate Section from Rectangular in Fig 18 to define the new rectangular shape Fig 19 Weight per Unit Length is equal to the Area of Cross Section times the Unit Weight defined in Fig 18 35 Click OK in Fig 17 1f the user would like to use the defined cross section Corresponding entries in Fig 18 will be updated Bridge Bentcap Material Properties Youngs Modulus Shear Modulus Unit Weight Section Properties Area of Cross Section Moment of Inertia Horizontal Axis Moment of Inertia Vertical Axis Torsion Constant Weight Weight per Unit Length kip ft Recalculate Section from Rectangle Cancel Fig 18 Material properties of the bent cap 36 Tui Rectangular Bentcap Section Geometry Width in Horizontal Direction Height in Vertical Direction Properties Recalculated Automatically Area of Cross Section 24 ft2 Moment of Inertia Horizontal Axis 37 Ft4 Moment of Inertia Vertical Axis T2 ft4 Torsion Constant 75124 ft Weight
50. ble 2 Default values for Steel02 material properties oooooonnncnnnnnnnnnnnononcccnnnnnnnnnnnonnns 47 Table 3 Default values for Concrete02 material properties ooooncccnnnnnnnnnnnoonnccnnnnnnnnnnnnos 47 Table 4 Geometric and Material Properties of a Bearing Pad occcnccccccncnnnnnnnnnnnnnnnnnnooo TI Table 5 SDC Abutment Properties 88 Table 6 Engineering Demand Parameters EDP cccccnnnnnnnnnnnnncncncnnnnnnnnnnnnnnnnononnnanonos 141 Table 7 Typical Bridge Configurations in California After Ketchum et al 2004 163 Table 8 Displacement unit inch of Bridge Type 1 under pushover load of 2000 kips applied at deck center along both the longitudinal and transverse directions 164 Table 9 Displacement unit inch of Bridge Type 2 under pushover load of 2000 kips applied at deck center along both the longitudinal and transverse directions 165 Table 10 Displacement unit inch of Bridge Type 9 under pushover load of 1000 kips applied at deck center along both the longitudinal and transverse directions 166 Table 11 Displacement unit inch of Bridge Type 10 under pushover load of 2000 kips applied at deck center along both the longitudinal and transverse directions 167 xvii 1 Introduction 1 1 Overview MSBridge is a PC based graphical pre and post processor user interface for conducting nonlinear Finite Element FE studies
51. ble for the longitudinal components of the input motions To view the comparison of displacements from ESA and Time History Analysis THA click Compare with THA The comparison result is shown in Fig 118 However the comparison is only available for ESA for the longitudinal components of the input motions Fig 117 The procedure of the bridge longitudinal ESA is as follows l Specify a load F of the total weight see below for now to calculate the total weight do pushover and get a displacement d 2 Calculate the Stiffness K F d 3 Calculate the Period T 21 sqrt M K 4 From the spectral acceleration of the input motion get Sa 5 Calculate D M Sa K and this is the elastic displacement demand 6 Check the abutment displacement Dz compared to abutment yield displacement D If D Dy lt 2 stop Da is the demand If DD gt 4 set abutment spring to 0 1 its initial stiffness recalculate the displacement demand Dz If 2 lt DyD lt 4 linearly interpolate abutment stiffness between its full and 0 1 values and ratios of 2 and 4 then recalculate the displacement demand The whole bridge system is employed in the bridge longitudinal ESA As such the pushover load is applied at the bridge center along the bridge deck longitudinal direction The total weight is equal to the total deck weight plus Y column weight The deck weight should be distributed weight over span elements or applied to nodes by tributary lengt
52. calculate Section from Box Girder in Fig 16 to define the new box girder shape Fig 17 The default values of geometrical properties are of typical for a four cell reinforced concrete box girder deck configuration Weight per Unit Length is equal to the Area of Cross Section times the Unit Weight defined in Fig 16 Click OK in Fig 17 if the user would like to use the defined cross section Corresponding entries in Fig 16 will be updated 34 IMPORTANT NOTE If using self defined section properties the Box Width in Fig 17 will be used as the deck width of the bridge To use a different deck width the user needs to modify Box Width in Fig 17 q Box Girder Box Girder Fillet Box Width Including Owerhang 39 Top Fillet Width Box Depth 6 Top Fillet Depth Top Slab Thickness g Bottom Fillet Width Bottom Slab Thickness 6 Bottom Fillet Depth Web Number of Interior Webs Interior Web Thickness Exterior Web Thickness Properties Recalculated Automatically Exterior Web Offset i rea of Cross Section 68111 ft2 Moment of Inertia Horizontal Axis 356 043 ft4 Overhang Overhang Width Moment of Inertia Vertical Axis 8235532 ft4 Outside Thickness Torsion Constant 078 38 ft4 Inside Thickness Weight per Unit Length 10 216 kip ft Cancel Fig 17 Box girder shape employed for the bridge deck 3 3 Bentcap To change bent cap properties click Bentcap in Fig 6 Fig 18 shows the window to modify the bentcap material
53. carries one sixth of the load and each of the middle springs carries one third Fig 56a The vertical components translational and rotational are similar to the longitudinal ones 1 e each of the distributed springs carries its tributary amount in the vertical direction However the transverse component 1s different only the both end springs carry the load In other words each of the end springs carries half of the load along the transverse direction translational and rotational By default the number of distributed springs is 2 In this case these 2 springs are located at the both ends of the Rigid element the length of which is equal to deck width shown in Fig 56 However due to the coupling of the longitudinal and vertical translational springs the option of using a single node at each abutment is possible this gives the user full control over the true rotational stiffness apart from the translational stiffness 70 a Bridge Abutments Abutment Model Type SDC 2010 Sand Number of Distributed Springs Longitudinal Gap Bearing Pad Number of Bearings Bearing Height Advanced Shear Keys Number of Shear Keys Advanced Embankment Lateral Stiffness Backwall Width Backwall Height Embankment Vertical Stiffness Cancel Fig 55 Definition of an abutment model The abutment will be rotated counter clockwise if the skew angle 1s positive rotated clockwise if negative Fig 59 shows the direction of l
54. cement response time histories q Column Response Profiles Motion RRS Response Type Response Profile Displacement C Bending Moment C Shear Force C2 Acceleration 3 Rotation Direction Longitudinal 23 Transverse O Vertical Column ColumnlofBent2 View Data Add Figure to Report Fig 102 Displacement profile in the longitudinal plane 127 Column Response Profiles Motion RAS Response Type Response Profil C Displacement Bending Moment C Shear Force C Acceleration Rotation Direction Longitudinal 3 Transverse C Vertical Column Columnl of Bentz Add Figure to Report Fig 103 Bending moment profile in the longitudinal plane 128 X Column Response Time Histories Motion RRS Response Type Response Time History 9 Displacement Bending Moment Shear Force Acceleration Rotation Direction Longitudinal Transverse Vertical Column Column lofBentz Elevation TN View Data Add Figure to Report Fig 104 Response time histories and profiles for column and pile shaft displacement is shown at the nodes 8 1 4 Column Response Relationships The column response relationships can be accessed by clicking menu Display Fig 3 and then Column Response Relationships The Elevation box includes all elevations starting from column top Zero elevation refers to the column top Fig 105 shows
55. co I Ez File Edit Search View Encoding Language Settings Macro Run Plugins Window E RAS228 AT2 info 1 Data points NPTS 996 isampling period DT 3ec i0 020000 3 In 1 Col 24 Sel 0 UNIX Fig 122 Sample info file 161 lad C Program Files 86 MSBridge NET Motions T01 e l z2 File Edit Search View Encoding Language Settings Macro Run Plugins Window A IBAS C E ARS228 4T2 info E RRS229 AT2 data Ea a feos 3 5133640e 05 l 78z38lU08e Uz 1 48587853e6 Uz ln il Col 1 Sel 0 Dos Windows Fig 123 Sample data file a Search MO P Organize Burr New folder 4 MotionSetl Name 4 Bint _ MOTIONI UP AT2 data 4 Quakel _ MOTION1 UP AT2 info PE MOTIONI1000 AT2 data gt MSBridgeMotionSetl _ MOTION1000 AT2 info PerfLogs E mE E ME _ MOTION1090 AT2 data Fern E MOTION1090 AT2 info p Program Files Ls nd MOTION1000 AT2 data Date modified 9 23 2010 2 36 PM DATA File Size 18 5 KB Fig 124 Example of user defined motion 162 Appendix C Comparison with SAP2000 for Representative OB Configurations A large portion of bridges in the current California bridge inventory share similar construction characteristics especially those owned and maintained by the California Department of Transportation CalTrans Mackie and Stojadinovic 2007 Eleven bridge configurations were selected by Ketchum e
56. cution of the finite element analysis and display the analysis progress bar 2 2 3 Finite Element Mesh Region The Finite Element FE mesh region Fig 2 displays the generated mesh In this window the mesh can be manipulated by clicking buttons shown in Fig 5 The FE mesh shown in MSBridge is automatically generated The user can also click the button at the top right corner shown in Fig 5 to re draw the FE mesh based on the input data entered 25 Fig 5 Available actions in the FE Mesh window 26 E Q A a D AY KZ YZ aul 3 Bridge Model In MSBridge the bridge deck columns and bentcaps are modeled using beam column elements The foundation 1s fixed based type by default Fig 2 Other available foundation types including soil springs and foundation matrix are modeled using zeroLength elements To define a bridge model click corresponding buttons Fig 6 To include a deck hinge isolation bearing or use a non zero skew angle for any bent or abutment click Advanced To change the numbers of beam column element used for the deck bentcaps and columns click Mesh Fig 7 shows a bridge model with soil springs and deck hinges included a Step 1 Define Model and Check Responses Model Builder Spans Deck Bentcap Columns Fig 6 Model builder buttons Y MSBridge Untitled msb File Execute Display Report Help OE OOQ Unit System SI Units 9 US English Units 20 A
57. d Eberhard 2007 a Circle b Octagon c Hexagon ccccccccncccncnnnnonncnnnnnnnnnnnnnononononos 46 30 OpenSees quadrilateral patch employed for calculating the cover concrete fibers for a Octagon and b Hexagon cross section sse nnne eene eene 46 31 Stress strain curve for a steel material default values employed a Steel01 with a strain limit b Steel02 with a strain limit and c ReinforcingSteel with a strain limit 32 Stress strain curve of the core concrete material default values employed a Elastic No Tension b Concrete01 and c ConcreteOZ oocccccnooconnccnonnnnncnnnnnoncccnnnnoncnnnaninccnnnnnnnos 50 33 Stress strain curve of the cover concrete material default values employed a Concreie T and D ConcteleU esit reto ttov td b rubri oeste eive bes 51 34 Moment curvature response for the column with default steel and concrete parameters and the deck weight 2680 kip applied at the column top ccccccccnnnnncnnnnnncnncncnnnnnnno 51 35 Foundation types available in MSBridge occoooonoonoooononcccccccncnonononnnononoss 22 36 Shaft foundation for abutments and bent sssssssessssse 53 37 Pile foundation model for abutments esses 54 E LIA RR EET I ETT mat dae 55 39 Soil spring calculations based on p y equations a Soft Clay Matlock b Stiff Clay without Free Water Reese c Sand Reese 57 40
58. ded is shown in Fig 41 54 q sail Springs Bent Number Depth ft Sail Springs at Depth 0 ft for Abutment 1 Abutment 1 Please enter below displacement in and force kip in pairs me 1 20 424 25 ase 2 76 939 56 Bent 4 Abutment 5 Delete Depth Add Depth OK Fig 38 Soil springs 55 Soil Springs based on p y equations Soil Material Number of Line Seqments Soft Clay Matlock 20 Soil Material Properties Soil Spring Depth ft Pile Width Submerged Unit Weight Strain at 50 Stress Level e50 Loading Options Static Loading Shear Strength Profile Please enter depth ft and shear strength psi in pairs 034 50 5 6 mm Cancel Recalculate p y q Soil Springs based on p y equations Soil Material Number of Line Segments Stiff Clay w out Free Water Reese Soil Material Properties Pile Width Submerged Unit Weight Strain at 50 Stress Level e50 Loading Options Static Loading O Cyclic Loading Cycles 100 Shear Strength Profile Please enter depth ft and shear strength psi in pairs 034 50 5 6 b S6 p y Curves p y Curves 0 00 ft 4 00 ft 6 00 ft 12 00 ft 20 00 ft 30 00 ft 40 00 ft 50 00 ft 0 00 ft A0 ft 6 00 ft 12 00 ft 20 00 ft 30 00 ft 40 00 ft 50 00 ft q Soil Springs based on p y equations Soil Material Number of Line Segments Sand Reese 20 Soil Materi
59. del for a curved bridge with a positive skew angle 4 3 2 Transverse Response The transverse response is based on the system response of the elastomeric bearing pads exterior concrete shear keys abutment piles wing walls and backfill material The bearing pad model discussed above is used with uncoupled behavior with respect to the longitudinal direction The constitutive model of the exterior shear keys 1s derived from experimental tests Megally et al 2003 Properties yield and ultimate stresses of shear keys depend on ultimate capacity of the bridge which is defined as 30 percent of dead load at abutment The detailed scheme of the transverse response is shown in Fig 65a The typical response of a bearing pad and a shear key 1s shown in Fig 65b And the typical overall behavior of the transverse response 1s illustrated in Fig 65c The superstructure forces are transmitted through the parallel system of bearing pads and shear keys T1 to the embankment T2 in series The ultimate shear key strength is assumed to be 30 of the superstructure dead load according to equation 7 47 of SDC 2004 A hysteretic material with trilinear response backbone curve is used with two hardening and one softening stiffness values The initial stiffness 1s a series system stiffness of the shear and flexural response of a concrete cantilever with shear key dimensions 16849 ks1 The hardening and softening branches are assumed to have magnitudes of 2 59
60. dge 4 2 Roller Abutment Model The Roller Abutment Model Fig 61 consists of rollers in the transverse and longitudinal directions and a simple boundary condition module that applies single point constraints against displacement in the vertical direction 1 e bridge and abutment are rigidly connected in the vertical direction These vertical restraints also provide a boundary that prevents rotation of the deck about its axis torsion This model can be used to provide a lower bound estimate of the longitudinal and transverse resistance of the bridge that may be displayed through a pushover analysis To choose the Roller Abutment Model select Roller for the Model Type in Fig 55 and Fig 62 75 Deck Rigid Link Roller Fixity Fig 61 General scheme of the Roller Abutment Model Tui Bridge amp butments Abutment Model Type Roller Number of Distributed Springs Fig 62 Selection of the Roller Abutment Model 4 3 SDC 2004 Abutment Model SDC 2004 Abutment Model was developed based on the Spring Abutment Model by Mackie and Stojadinovic 2006 This model includes sophisticated longitudinal transverse and vertical nonlinear abutment response Detailed responses of the abutment model in the longitudinal transverse and vertical directions are described below 4 3 1 Longitudinal Response The longitudinal response 1s based on the system response of the elastomeric bearing pads gap abu
61. ed mesh can be accessed by clicking menu Display Fig 3 and then Deformed Mesh The deformed mesh window is shown in Fig 111 Analysis stages include Due to gravity and Due to pushover or Due to base shaking The response types include i Deformed mesh il Resultant Disp 111 X Displacement iv Y Displacement v Z Displacement vi Plastic Hinges 138 In the Ground Shaking Analysis the input motion is also animated at the deformed mesh window along with bridge displacement Fig 111 Deformed Mesh Analysis Stage Due to Shaking Response X Displacement Plot Scale Factor 62 4 Show Legend Show Undeformed Mesh 2 986 000 Display Motion 1 338e amp 000 iv Longitudinal Component ee ee E 1 617e 000 Transverse Component 1 457e 000 1 297e 000 1 137e 000 m 9 767e 001 Animation 2 166e 001 Play Fi b o64e 001 ar 4 963 001 Current Step 3 362e 001 m 1 760e 001 1 591e 002 224 1 442 e 001 h 3 044e 001 Time 446882 Miu jode 6 246e 001 1 848e D01 9 440e 001 1 105e 000 L Vertical Component Step Playing Speed Fig 111 Deformed mesh Visualization of plastic hinges 1s available if the nonlinear beam column element is used for the columns In the Ground Shaking Analysis the input motion is also animated at the deformed mesh window along with the development of plastic hinges Fig 112 In the current version the visualization is implemented in such a way that
62. ement CD Right Abutment Force Displacement Fig 75 Column longitudinal responses a Column and Abutment Longitudinal Responses Response Type Longitudinal Response C Moment Curvature 3 Force Drift Ratio C Force Displacement CD Left Abutment Force Displacement Right Abutment Force Displacement Fig 76 Abutment longitudinal responses 95 a Column and Abutment Transverse Responses Response Type Transverse Response Moment Curvature Force Drift Ratio C Farce Displacement CD Left Abutment Force Displacement C Right Abutment Force Displacement Fig 77 Column transverse responses a Column and Abutment Transverse Responses Response Type Transverse Response C Moment Curvature Force Drift Ratio D Force Displacement CD Left Abutment Force Displacement Right Abutment Force Displacement Fig 78 Abutment transverse responses 96 6 Pushover amp Eigenvalue Analyses To conduct a pushover analysis a load pattern must be defined As shown in Fig 79 first choose Pushover in the Analysis Options and then click Change Pattern The load pattern window 1s shown in Fig 80 Step 2 Select Analysis Option Analysis Options 9 Pushover Change Pattern Mode Shape Number of Modes 10 Ground Shaki ng Fig 79 Pushover analysis option 6 1 Monotonic Pushover The pushover options include Monotonic Pushover Cyclic Pushover and U Push pushover by a user defi
63. ements are used for cables and compression connectors The bearing pads are included in the cables For each zeroLength element both nodes are interacted in the longitudinal direction denoted as direction 1 in Fig 47 but tied in the vertical direction 3 not shown in Fig 47 as well as the transverse direction denoted as direction 2 in Fig 47 The above conditions would force both sides of deck segments to move in the same plane Note that the local coordinate system 1 2 3 may or may not coincide with the global coordinate system X Y Z Fig 1 The default values of properties for the compression connectors cables bearing pads are also shown in Fig 45 62 q Deck Hinges Pe JE tr Pez Deck Hinges Hinge Activated Distance to Bent ft Spacing ft Skew Angle deg Cables Cable Spacing ft Hinge 1 Deck Hinge Material Properties Connector Compression Properties Gap 2 Yield Force 57100000 Compression Stiffness 571000 Cable and Bearing Properties Gap 0 5 Yield Force 57100000 Tension Stiffness 258 6 Bearing Lateral Stiffness 58 Cancel Fig 45 Definition of deck hinges Fig 46 FE mesh of a 4 span model with 2 deck hinges included 63 Compression Connector gt Node 1 Rigid Links WW MAS Deck ina L Cables and Beari C E y ables and Bearings zeroLength Elements Compression ewe Connector Fig 47 OpenSees zeroLength elements for deck hinges plan view 3
64. engths ES dae Spare Y Bridge Spa Spans Number of Spans Cancel Span Lengths O Equal Span Length 60 ft Varied Span Lengths Modify Span Lengths Curved Bridge 2 Horizontal Alignment Modify Horizontal Curve Vertical Alignment Modify Vertical Curve Fig 8 Spans 28 Varied Span Lengths m CAN Ta E Span Lengths Fig 9 Varied span lengths Fig 10 Straight bridge with different span lengths 3 1 2 Curved Bridge To define a curved bridge please check Horizontal Alignment and or Vertical Alignment in Fig 8 3 1 2 1 Horizontal Curved Bridge To define a horizontally curved bridge check Horizontal Alignment in Fig 8 Fig 11 shows the window to define the horizontal curves Begin Curve Length refers to the starting location of the horizontal curve see Fig 12a Curve Radius refers to the radius of the horizontal curve Curve Length refers to the arc length of the horizontal curve And the directions Left or Right refers to the arc rotation direction relative to the 29 starting location Right clockwise rotation in XY plan view Left counter clockwise in XY plan view Click Insert Curve to add a horizontal curve and click Delete Curve to remove the chosen curve Fig 14 shows examples of horizontal alignment 3 1 2 2 Vertical Curved Bridge To define a vertically curved bridge check Vertical Alignment in Fig 8 Fig 13 shows the window to define
65. engths obtained from Zhang and Makris 2002 and Werner 1994 is included in the calculation of the participating mass due to the embankment of the abutment The user can modify the lumped mass through the soil mass For design purposes this lumped mass can be ignored and set to be zero Table 4 Geometric and Material Properties of a Bearing Pad shear Modulus G 1034 2 kPa 0 15 ksi Young s Modulus E 34473 8 kPa 5 ks1 Yield Displacement 150 shear strain GA Lateral Stiffness h where A is the cross section area and h is the height Longitudinal gap 4 in hardening ratio 1 EA Vertical Stiffness um Vertical Tearing Stress 15513 2 kPa 2 25 ks1 Longitudinal gap 2 in uy Bearing Pad Lateral Response SDC Embankment zeroLength Elements Longitudinal Response Plan View a b 78 1000 SDC 2004 Backwall 500 IEEE eel eMe te ai E AAA o 5 3 5 3 BPs shear resistance A amp backwall gap in parallel Sti ec A ee eee No 1000 3 20 10 10 20 Strain or deformation in c Fig 63 Longitudinal response of the SDC 2004 Abutment Model a general scheme b longitudinal response of a bearing pad c total longitudinal response 79 Longitudinal Gap Deck Rigid Link eo Bearing Pad Lateral Response zeroLength Elements LN SDC Embankment Plan View Skew Angle Longitudinal Response Fig 64 Longitudinal response of the SDC 2004 Abutment Mo
66. erties c shear key properties d SDC abutment properties e embankment properties EAEE E E A 87 Fig 68 Backfill horizontal properties for the SDC 2010 Sand Abutment Model 88 Fig 69 Backfill horizontal properties of the SDC 2010 Clay Abutment Model 89 Fig 70 Backfill horizontal properties of the EPP Gap Abutment Model 89 Fig 71 Definition of the HFD Abutment Model a HFD abutment model and b HFD parameters for abutment backfills suggested by Shamsabadi et al 2007 and c backfill properties OF TNS HBD MOGOSI suni ve t p te tovs ved tetigit saree 92 Fig 72 Buttons to view column amp abutment responses and bridge resonance 93 Fig 73 Natural periods and frequencies of DIIABE o ooooooooooanaccccccccnnnononnnnnnnnnnnnnnnnonananos 94 Fig 74 Column internal forces and bending moments after application of own weight 94 Fig 75 Columim loneiudiandl TespOIlSeS olaaa 95 Fig 76 Abutment longitudinal responses occcoccccccooooonoooooonnnnononononnonononoononnnnononononnnnnnnnnns 95 Fig 75 Column transverse response Serinin dte o io sanie 96 Fig 78 Abutment transverse responses ccccesessssseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeees 96 Fie 79 Pushover analysis ODLOf ou do A a bet edes 97 Fig 80 Load pattern for monotonic pushover analysSIS ooooonnnncccnnnnnnnnnnnnnnnnnnnnnnanannnos 98 Fig 81 Load pattern for cyclic pushover an
67. es to view column lateral responses abutment responses and bridge natural periods Fig 7 and Fig 72 Quick Check of Model Responses View Matural Periods View Gravity Response Longitudinal Response Transverse Response Fig 72 Buttons to view column amp abutment responses and bridge resonance 5 1 Bridge Natural Periods Click View Natural Periods Fig 72 to view the natural periods and frequencies of the bridge Fig 73 A mode shape analysis is conducted in this case The user can copy and paste the values to their favorite text editor such as MS Excel in Fig 73 right click and then click Select All ctrl a to highlight and then right click and then click Copy ctrl c to copy to the clipboard 5 2 Column Gravity Response Click View Gravity Response Fig 72 to view the column internal forces and bending moments after application of own weight Fig 74 5 3 Column amp Abutment Longitudinal Responses Click Longitudinal Response Fig 72 to view the column longitudinal responses Fig 75 and the abutment longitudinal responses Fig 76 A pushover up to 5 of drift ratio in the longitudinal direction is conducted in this case 5 4 Column amp Abutment Transverse Responses Click Transverse Response Fig 72 to view the column transverse responses Fig 77 and the abutment transverse responses Fig 78 A pushover up to 4 of drift ratio 1n the transverse direction is conducted in this case 93
68. for multi span multi column bridge systems Main features include 1 Automatic mesh generation of multi span straight or curved bridge systems 11 Options of foundation soil springs and foundation matrix 111 Options of deck hinges isolation bearings and steel jackets Iv Management of ground motion suites v Simultaneous execution of nonlinear time history analyses for multiple motions V1 Visualization and animation of response time histories Finite element computations are conducted using OpenSees http opensees berkeley edu McKenna et al 2010 Mazzoni et al 2009 an open source framework developed by the Pacific Earthquake Engineering Research PEER Center The analysis options available in MSBridge include 1 Pushover Analysis 11 Mode Shape Analysis 111 Single 3D Base Input Acceleration Analysis iv Multiple 3D Base Input Acceleration Analysis v Equivalent Static Analysis ESA This document describes how to conduct the above analyses in MSBridge For information on how to download and install MSBridge please visit the MSBridge website http www soilquake net msbridge 1 1 Units MSBridge supports analysis in both the US English and SI unit systems the default system is US English units This option is located at the top of the main window Fig 2 and can be interchanged during model creation MSBridge will convert all input data to the new unit system For conversion between SI and English Units
69. g Coefficients Damping Ratios Damping Ratio 1 2 Frequency 1 0 1 50Hz 1 Period 1 Seconds 1 Damping Ratio 2 25 2 Frequency 2 0 1 50Hz 6 Period 2 Seconds 0 166667 Damping Coefficients Mass Proportional Damping Coefficient Am Stiffness Proportional Damping Coefficient Ak Recaculate Damping Curve Fig 97 Rayleigh damping 122 Y MSBridge Untitled msb File Execute Display Report Help DEGA Unit System O SI Units US English Units LA Sl OpenSees Analysis in Progress Base Shaking Overall Progress Reached 4 18 Motions Current Motion 1 1 TOTVWMORTHRIDGEXRRS Run 2 of 2 Base shaking Finished 4 888824 19 94 seconds 25 Current Motion 2 2 TOANORTARIDGE SCS Run 2 of 2 Base shaking Finished 6 16 40 seconds 15 Current Motion 3 3 TOS CHE CHA TCUO6S Run 2 of 2 Base shaking Finished 13 42 70 seconds Current Motion 4 4 TOP CHE CHA TCU068 Run 2 of 2 Base shaking Finished 18 56 70 seconds r 27 a Step 3 Run FE Analysis Run Analysis Save Model and Run Analysis Fig 98 Simultaneous execution of analyses for multiple motions 123 a OpenSees Parameters Algorithm Algorithm Newmark Integration Gamma Beta Convergence Tolerance Tolerance Fig 99 Parameters for OpenSees analysis 124 8 Time History and Engineering Demanding Parameter Output 8 1 Ti
70. h Column weight applied at top column node or 1f more than one element is used per column distributed to column nodes by tributary length 9 2 Bridge Transverse Direction 147 To conduct an ESA for the bridge transverse direction click Transverse Direction in the main window Fig 116 The output is shown in Fig 119 Only one single bent is employed in the bridge transverse ESA As such the pushover load 1s applied at the bent cap center along the bent cap direction bridge transverse direction The total weight is equal to the deck weight of left half span and right half span for the bent plus Y column weight Equivalent Static Analysis ESA Longitudinal Direction Transverse Direction Fig 116 Equivalent Static Analysis for the bridge longitudinal amp transverse directions ESA Pushover Load Bridge Longitudinal Direction Pushover Load As Ratio of Tributary Weight Use User Defined Acceleration Response Spectrum User Defined Acceleration Response Spectrum Please enter Period sec and Acceleration Response Spectrum q in pairs 00 6 0115 0 22 0 4 1 5 0 5 1 15 0 8 0 9 10 7 140 5 1 50 4 2 0 28 240 2 40 1 5 0 08 Conduct ESA Cancel 148 Tui Equivalent Static Analysis Bridge Longitudinal Direction Output E e Elastic Displacement Demand Effective Mass Weight 25721 kip Mass 5 65657 kip secZ in Effective Stiffness PushoverLoad 51442 kip Displacement
71. he abutment and bent numbering so Span goes from Abutment to Bent 2 and so on For multi column scenarios the columns are numbered consecutively along the transverse Y direction starting from 1 in the most negative side e g in Fig 1 the columns at the negative side of the transverse Y direction are referred to as Column while those at the positive side are called Column 2 For Bent 3 there are Column 1 of Bent 3 and Column 2 of Bent 3 which are used in MSBridge when referencing these 2 columns Local coordinate systems will also be used in this document to describe certain components e g deck hinges isolation bearings distributed spring abutment models with a skew angle etc In that case labels of 1 2 and 3 or lower case x y and z will be used Please refer to appropriate section for the corresponding description 19 1 3 System Requirements MSBridge runs on PC compatible systems using Windows NT V4 0 2000 XP Vista or 7 8 The system should have a minimum hardware configuration appropriate to the particular operating system For best results the system s video should be set to 1024 by 768 or higher 14 Acknowledgments This research project was funded by California Department of Transportation CalTrans OpenSees currently ver 2 4 0 is employed is a software framework McKenna et al 2010 for developing applications to simulate the performance of s
72. hinge length Lp is the equivalent length of column over which the plastic curvature 1s assumed constant for estimating plastic rotation SDC 2010 The material options available for the steel bar include Elastic Steel01 Steel02 and ReinforcingSteel The material options available for the concrete include Elastic ENT Elastic No Tension Concrete01 and Concrete02 40 X Column Properties Column Properties C Column is Linearly Elastic Cross Section Circle Octagon Hexagon Parameters Column Diameter Longitudinal Bar Size Mumber of Longitudinal Bars Transverse Bar Size Transverse Bar Spacing in CO Rectangle Elastic Material Properties Section Properties Nonlinear Fiber Section Beam Column Element Type Force Based Beam Column Fig 23 Column properties and available beam column element types 41 Tui Column Properties Column Properties Column ts Linearly Elastic Cross Section Circle Octagon Hexagon Parameters Column Diameter D Rectangle Elastic Material Properties Section Properties Fig 24 Definition of linear column W Column Elastic Material Properties ca 2 PX Material Properties Youngs Modulus ksi Shear Modulus ksi Unit Weight 150 pct OK Cancel Fig 25 Column Elastic material properties Y Column section Properties m ed Section Properties Grass Properties Cracked Section Factors Cracked Properties
73. ic Pushover in Fig 80 and then define Number of Steps for the First Cycle and Step Increment per Cycle Fig 81 98 q Pushover Type Method Monotonic Pushover Farced Based Method i Cyclic Pushover Define Cyclic Displacement Based Method U Push Force Incremer bongitidinah q Cycle Pushover Cyclic Pushover Transverse Y Number of Steps for the First Cycle A Step Increment per Cycle Moment of X Moment of Y TFC CUN Cancel Moment of Z j kip ft Rotation around Z Location Time Loading Location Bridge Deck Center Total Number of Steps OK Cancel Fig 81 Load pattern for cyclic pushover analysis 6 3 User Defined Pushover U Push Click U Push and then click Define U Push to enter your own load pattern U Push In this case the displacement or force parameters entered in Fig 82 are used as the maximum values The U Push data entered are used as the factors of the maximum displacement or the maximum force entered 99 q Pushover Type Method Monotonic Pushover 9 Forced Based Method C Cyclic Pushover Displacement Based Method U Push Define U Push Force Y U Push U Push Factor Data Please enter factors below one number at a line Longitudinal X Force Transverse Y Force Vertical Z Force Moment of X Moment of Y Moment of 7 Location Loading Location Fig 82 User defined pushover U Push 6 4 Output for Pushover Analysis O
74. ies 153 Appendix B How to Incorporate User defined Motions 158 Appendix C Comparison with SAP2000 for Representative OB Configurations 163 References 168 LIST OF FIGURES Fig 1 Global coordinate system employed in MSBridge 19 He 2 MS Bride ma W ndo Weenen a 21 Fig 3 MSBridge s menu and submenu bars a menu bar b menu File c menu Execute d menu Display e menu Report and f menu Help ooccccccncnnncnnnnnnnnnnnnncnno 23 Fig 4 MSBridge copyright and acknowledgment window eee 25 Fig 5 Available actions in the FE Mesh window seen 26 F19 6 Model puilde DUDAS iii iuo edi neste Doc besitos 21 Fig 7 MSBridge main window bridge model with soil springs and deck hinges included M N EE 27 PS PAN abia 28 E15 SV arods pan Jens 29 Fig 10 Straight bridge with different span lengths sse 29 Fe Horizontal l anene na a a a 30 Fig 12 Horizontal and vertical alignments a horizontal alignment plan view b vertical MI A e E NO tet ue etas 31 Tio o5 AA atte esatto Sioases loft to 3l Fig 14 Examples of horizontal curved bridges horizontal alignment a single radius horizontal curve b multi radius horizontal curve c horizontal curve connecting to straight parts
75. ime Histories Three directions longitudinal transverse and vertical directions of the above responses for both left and right abutments are all displayed Fig 107 shows the abutment response time histories The force refers to the resisting force acting on deck end and the displacement refers to the relative deck end abutment displacement 131 Tui Abutment Response Time Histories Motion RRS Response Type Abutment Response Force Displacement _ Force History O Displacement History Direction Longitudinal C Transverse C 3 Vertical Abutment 3 Left Abutment Right Abutment Animation Play Current Step Playing Speed Add Figure to Report 132 Tui Abutment Response Time Histories Motion RRS Response Type Abutment Response Force Displacement J Force History C Displacement History Direction CD Longitudinal Transverse C Vertical Abutment 3 Left Abutment Right Abutment Animation Play Current Step Playing Speed View Data Add Figure to Report b 133 Tui Abutment Response Time Histories Motion RRS Response Type Abutment Response 9 Force Displacement Force History Displacement History Direction Longitudinal Transverse a Vertical Abutment Left Abutment 9 Right Abutment Animation Play Current Step Playing Speed View Data Add Figure to Report
76. ineering School of Engineering University of California San Diego Be IO La Jolla California 92093 0085 65A0445 12 Sponsoring Agency Name and Address 13 Type of Report and Period Covered Final Report California Department of Transportation Division of Engineering Services Isi SpOneoHng Adoney poda 1801 30 St MS 9 2 5i Sacramento California 95816 15 Supplementary Notes Prepared in cooperation with the State of California Department of Transportation 16 Abstract MSBridge is a PC based graphical pre and post processor user interface for conducting nonlinear Finite Element FE studies for multi span multi column bridge systems Finite element computations are conducted using OpenSees http opensees berkeley edu an open source framework developed by the Pacific Earthquake Engineering Research PEER Center The analysis options available in MSBridge include 1 Pushover Analysis 11 Mode Shape Analysis ni Single 3D Base Input Acceleration Analysis iv Multiple 3D Base Input Acceleration Analysis and v Equivalent Static Analysis ESA This document describes how to conduct the above analyses in MSBridge For information about how to download and install MSBridge please visit the MSBridge website http www soilquake net msbridge 17 Key Words 18 Distribution Statement Finite Element Time History Analysis Unlimited 19 Security Classification of this report 20 Security Classification of this page 2
77. ions and displacements for all input motions can be accessed by clicking menu Display Fig 3 and then Bridge Peak Accelerations amp Displacements for All Motions The window to display the bridge peak accelerations for all motions is shown in Fig 114 The responses are available in the longitudinal and transverse directions as well as for the SRSS of the 2 horizontal directions Fig 114 The figures in this window include 1 Maximum bridge acceleration 11 Maximum bridge displacement iil Bridge peak acceleration input peak acceleration 143 Bridge Peak Accelerations Bridge Peak Response Peak Response Peak Accelerations Peak Displacements D Peak Acceleration Peak Input Direction Longitudinal C Transverse c 2 Horizontal SRS5 Intensive Measure PGA View Data Add Figure to Report 144 Bridge Peak Accelerations Bridge Peak Response Peak Response Peak Accelerations Peak Displacements Peak Acceleration Peak Input Direction Longitudinal Transverse Horizontal 5R55 Intensive Measure View Data Add Figure to Report b Fig 114 Bridge peak accelerations for all motions a maximum bridge accelerations b maximum bridge displacements 3 3 Maximum Column amp Abutment Forces for All Motions The maximum column amp abutment forces for all input motions can be accessed by clicking menu Display Fig 3 and then Maximum Column amp
78. irectly in Fig 27 157 Appendix B How to Incorporate User defined Motions 1 Directory Structure of a Motion Set To conduct a base input acceleration analysis input motions must be defined Fig 91 The window to define the input motions is shown in Fig 92 Click Browse to select a motion set Fig 120 Click on the motion set name e g Motions and then click on OK to choose this motion set Fig 120 In MSBridge the input motions are organized in a format that the program can read Specially the input ground motions are sorted into bins Fig 121 shows the directory structure of a motion set named Motions The second level directories are bins e g TO1 see Fig 120 and Fig 121 The third level directories are earthquake names e g there 1s earthquake NORTHRIDGE see Fig 121 And the fourth level directories are the input motion names e g there is 1 input motion under earthquake NORTHRIDGE RRS see Fig 121 Each motion is composed of 3 perpendicular acceleration time history components 2 laterals and one vertical As shown in Fig 121 each motion folder contains 6 files categorized into 2 file types the DATA files contain the time history acceleration unit in g of a component and the INFO files contain the characteristics of the corresponding component Fig 122 and Fig 123 displays sample INFO amp DATA files Naming of these files usually has to follow the format below Input motion name angle or UP or
79. ixed Tui Column Connection Column Connection Fixed at Top Pinned at Base Pinned at Top Fixed at Base 9 Fixed at both Top and Base mr Cancel Fig 22 Column boundary conditions 3 4 3 Column Properties To define the material and geometrical properties of column click Column Properties in Fig 20 For now all columns will assume to have the same material and geometrical properties Uses can choose to use the linearly elastic column or nonlinear Fiber column By default the nonlinear Fiber section is used Fig 23 3 4 3 1 Cross Section Types The cross sections currently available in MSBridge include Circle Octagon Hexagon and Rectangle Fig 23 For the Circular Octagonal and Hexagonal sections the user needs to define the Column Diameter For Rectangular section the user needs to define the widths in bridge longitudinal and transverse directions Fig 23 3 4 3 2 Linearly Elastic Column To activate the linear column check the checkbox Column is Linearly Elastic Fig 24 Elastic beam column element elasticBeamColumn McKenna et al 2010 is used for the column in this case 39 Click Elastic Material Properties to define Youngs Modulus Shear Modulus and Unit Weight of the column Fig 25 Click Section Properties to change the column section properties by changing the cracked section factors as shown in Fig 26 3 4 3 3 Nonlinear Fiber Section To use nonlinear Fibe
80. l eene 73 Fig 58 Parameters of the Elastic Abutment Model 22 eene 73 Fig 59 Longitudinal components of the Elastic Abutment Model in a curved bridge a left abutment D right AUNAR bete ERR usen rete mit uu 74 Fig 60 Bridge model with multiple distributed springs and a positive skew angle a straight padoe D GUEVed DIIGO ao p ro ind tUm rha ton ab i tumet os bred toda 75 Fig 61 General scheme of the Roller Abutment Model sues 76 Fig 62 Selection of the Roller Abutment Model eee 76 Fig 63 Longitudinal response of the SDC 2004 Abutment Model a general scheme b longitudinal response of a bearing pad c total longitudinal response 79 Fig 64 Longitudinal response of the SDC 2004 Abutment Model for a curved bridge with a POSVE SKEeW angle sss cea nie t Rant mM detenta are eae ees 80 xili Fig 65 Transverse response of the SDC 2004 Abutment Model a general scheme b response of a bearing pad and shear keys curve with a higher peak value is the shear key response c f tal transverse PCS DOSE wall 82 Fig 66 Vertical response of the SDC 2004 Abutment Model a general scheme b vertical response of a bearing pad c total vertical reSsponse ooooocooconoooocccccccncnnononononononoss 84 Fig 67 Definition of the SDC 2004 Abutment Model a main parameters b bearing pad prop
81. me History Output Quantities At the end of the FE analysis phase time histories and bridge responses will be available of the form 1 Column Response Time Profiles 11 Column Response Time Histories 111 Column Response Relationships iv Abutment Responses v Deformed Mesh In addition for multiple earthquake analysis scenarios Intensity Measures IMs and response spectra for each input motion are calculated and are available for display in Table and Figure formats Engineering Demand Parameter EDP Quantities and Bridge peak accelerations for all employed shaking motions are also available for display against any of the computed IMs The post processing capabilities can be accessed from Menu Display Fig 3 To display output for a different input motion click Menu Display and then Detailed Output Please Select Input Motion Fig 3d The name of the selected input motion will also appear on the menu items Fig 3d ub select Motion Please Select a Motion Bin Earthquake Motion Motion TOL MORTHRIDGE RRS TOLANORTHRIDGE RRS T 2 NORTHRIDGE SCS TO3 CHI CHLTCU06S TU CHICHA TEL TOIS EOBE TAZ Tig TABAS TAB TOR DUZCE BOL T S LA amp MDERS LCM T S S ANFERMNANDO PLIL TIO IMPERDSLVALLEYH E06 Til IMPERIASLVALLEY H AGR TI TMPERIALWALLEYH BCR Ti NORTHRIDGE ORR TI LANDERS OS TIVLANDERS MH TIS KOBE KAEK T1S9 KOBE NIS TO COYOTELAKE ENE Fig 100 Selection of an input motion 125 8 1
82. ment Lateral Stiffness box Fig 67 to define the backfill horizontal properties Fig 71c Parameters of the backfill soil are defined based on soil types sand clay or User defined and the overall abutment stiffness or maximum passive pressure resist are calculated using the SDC equations 90 HFD MODEL Fut g EN SANDY SOIL E 1 Dy Ymax 0 05H 0 5Ea iid C OK I Tul Jmax COHESIVE SOIL f p Ls l l Ymax 0 10H Fut Y max O 50 y in i n a Table 4 Suggested HFD Parameters for Abutment Backfills Maximum Pressure Average soil stiffness displacement Abutment backfill type kPa ksf kN cm m K in ft Ymar H Granular 265 5 5 290 50 0 05 Cohesive 265 5 5 145 25 0 10 Note Abutment backwall height 1 67 m 5 5 ft Compacted to at least 95 relative compaction per ASTM D 1557 b 91 al HFD Abutment Model Soil Type HFD Model Parameters Sand Max Displacement ymax C Clay K50 kip in ft C User Defined Max Passive Pressure ksf Recalculate Curve Constants Calculated Curve Constants Constant C 1090 View HFD Model e Constant D 711 515 View Parameters of HFD Model c Fig 71 Definition of the HFD Abutment Model a HFD abutment model and b HFD parameters for abutment backfills suggested by Shamsabadi et al 2007 and c backfill properties of the HFD Model 902 5 Column Responses amp Bridge Resonance MSBridge provides featur
83. n of analyses for multiple motions 123 Fig 99 Parameters for OpenSees analySIS occcccccccncncnnnnnononnnnonnnnncnnnnnnnnnnnnnnnnnonnnnnnnnnos 124 Fig TOO Selection or an mpult MOM ii 125 Fig 101 Deck longitudinal displacement response time histories 127 Fig 102 Displacement profile in the longitudinal plane occccccnnnnnnnnnnnnnnnnnnnmm gt 127 Fig 103 Bending moment profile in the longitudinal plane 128 Fig 104 Response time histories and profiles for column and pile shaft displacement 1s shown AU UNS MOG eR CE 129 Fig 105 Load displacement curve at column top senes 130 Fig 106 Moment curvature curve at column top c0ooooococcccocaoonononononononononononononononnnonnononos 131 Fig 107 Abutment response force displacement relationships a longitudinal response b transverse response and c vertical reSponSe oooonnncnnnnnnnnnnnnooncnnnnnnnnnnnnnnnanoccnnnnnnos 134 Fig 108 Soil spring response time histories nn 135 Fig 109 Deck hinge response time histories a cable element b edge element 137 Fig 110 Isolation bearing response time HIStOTIES ccccccnnnnnoooooooooonnnnnnnonocnncnnnnnnnnnnnos 138 Me 111 De TOMS messi idiota 139 Pig 112 Vasualization t Plastic Himes dia 140 Fig 113 EDP quantities for all motions essen 143
84. nches so area is 4 in If there are 10 bars 1n a 36 inch diameter circular column then 10 4 0 039 S Z 36 4 or 3 9 The transverse steel percentage reinforcement ratio for a spirally confined circular column currently the only type of column supported in the interface 1s 153 day P sd Where dpr is the diameter of the transverse spiral always smaller than the diameter of the longitudinal bars The spacing between transverse bars 1s s The diameter of the confined core is dc which is the gross diameter minus twice the cover and minus the diameter of the transverse bars see Eq 10 So for a 5 spiral spaced at 3 inches on center in the same column mentioned above p 0913 8 336 2Q or 1 3 Currently the transverse reinforcement does affect the shear response through changes in the uniaxial constitutive model for the concrete core However the columns are modeled considering only flexurally dominated response 1 e there is no accounting for shear flexibility or shear degradation directly Additional relevant details on the parameters used in both the Cover and Core Concrete are included below Cover concrete The Concrete02 material 1s used to simulate the concrete for both cover and core The format of the Concrete02 command is as follows uniaxialMaterial Concrete02 matTag fpc epscO fpcu Sepsu lambda ft Ets Where fpc is the concrete compressive strength ep
85. nd Set3 as well as the additional Bin NEAR of Setl Once an input motion data set 1s specified the user interface will extract calculate Intensity Measures IMs for each of these motions In total 11 different Intensity Measures are defined for each motion and presented to the user in table and graphical forms including quantities such as Peak Ground Acceleration PGA Peak Ground Velocity PGV Arias Intensity AI and so forth 7 1 2 Specifications of Input Motions To conduct a ground shaking analysis input motions must be defined Fig 91 The window to define input motions 1s shown in Fig 92 To select all motions click Select All To un select all motions click De select All To remove one motion select the motion by clicking on it and then click Delete To remove all motions click Remove All To add a user defined motion click Import and then follow the simple steps to import a new motion Fig 93 The resulting motion will be added to the current suites of input motion To obtain a complete new set of input motions use Delete All to remove all existing input motions and then use Import to add new motions To import a ground motion file first save the ground acceleration time history easy in a notepad txt file with each new line being the next acceleration time step This data in this file should have the acceleration units of g The finite element computations can be conducted for several earthquakes at a time This
86. nd Stojadinovic B 2010 Post earthquake bridge repair cost and repair time estimation methodology Earthquake Engineering and Structural Dynamics 39 3 281 301 Mackie K R Wong J M and Stojadinovic B 2011 Bridge damage and loss scenarios calibrated by schematic design and cost estimation of repairs Earthquake Spectra 27 1127 1145 Maroney B H and Chai Y H 1994 Seismic Design and Retrofitting of Reinforced Concrete Bridges Proceedings of 2nd International Workshop Earthquake Commission of New Zealand Queenstown New Zealand Mander J B Priestley M J N and Park R 1988 Theoretical Stress Strain Model for Confined Concrete Journal of the Structural Division ASCE 114 pp 1804 1826 Mazzoni S McKenna F Scott M H Fenves G L et al 2009 Open System for Earthquake Engineering Simulation User Command Language Manual Pacific Earthquake Engineering Research Center University of California Berkeley OpenSees version 2 0 May Megally S H Seible F Bozorgzadeh A Restrepo J and Silva P F 2003 Response of Sacrificial Shear Keys in Bridge Abutments to Seismic Loading Proceedings of the FIB Symposium on Concrete Structures in Seismic Regions May 6 9 Athens Greece Shamsabadi A Rollins K M and Kapuskar M 2007 Nonlinear Soil Abutment Bridge Structure Interaction for Seismic Performance Based Design Journal of Geotechnical and Geoenvironmental Engineering 133 6 707
87. ned loading pattern Two methods of pushover are available Fig 80 force based and displacement based If Force Based Method is chosen please enter the parameters of force increment per step Longitudinal X Force Transverse Y Force Vertical Z Force Moment X Moment Y and Moment Z If Displacement Based Method is chosen please enter the displacement increment parameters per step Longitudinal Displacement Transverse Displacement Vertical Displacement Rotation around X Rotation around Y and Rotation around Z The pushover load displacement linearly increases with step in a monotonic pushover mode The pushover load displacement is applied at the bridge deck center or the deck location at a bent 97 q Pushover Type Method Monotonic Pushover Farced Based Method CJ Cyclic Pushover Displacement Based Method U Push Force Increment per Step Displacement Increment per Step Longitudinal X Force kips Longitudinal X Displacement 0 1 Transverse Y Force kips Transverse Y Displacement 0 Vertical 2 Force kips Vertical 4 Displacement Moment of X i kip ft Rotation around X Moment of Y D kip ft Rotation around Y Moment of Z kip ft Rotation around Z Location Time Loading Location Bridge Deck Center Total Number of Steps OK Cancel Fig 80 Load pattern for monotonic pushover analysis 6 2 Cyclic Pushover To conduct a Cyclic Pushover click Cycl
88. nsider Fig 37 asa representation of the model The abutment nodes are the same nodes that will be referred to in the abutment model section These nodes are described as the fixities in each of the SDC models figures 53 Deck Width Abutment Nodes Stemwall Height f Rigid Link a for py springs e Pile Shatts Fig 37 Pile foundation model for abutments Parameters defining soil springs are shown in Fig 38 Two identical horizontal soil springs one for the bridge longitudinal direction and the other one for the transverse direction will be applied at each depth Button Insert Depth inserts a depth after the current depth being highlighted Button Delete Depth removes the current depth being highlighted as well as the associated soil spring data To calculate the soil spring data based on p y equations click Select from p y Curves Fig 38 For now three types of soil p y curves are available Soft Clay Matlock Stiff Clay with no Free Water Reese and Sand Reese Fig 39 show the calculated p y curves for the above mentioned soil materials respectively The methods to calculate these p y curves are based on the procedures described in the reference by Reese and van Impe 2001 To use the soil spring data calculated based on p y curves click OK and then click Yes The soil spring data chosen will replace the existing any soil spring data Fig 40 A sample bridge model with soil springs inclu
89. ode Mode 5 HERAS i Playing Speed e Fig 90 Sample output for an Eigenvalue analysis for the default bridge model a first mode b second mode c third mode d fourth mode and e fifth mode 111 7 Ground Shaking To conduct a single earthquake analysis or a multiple earthquake analyses the Ground Shaking option under Analysis Options Fig 2 and Fig 91 is used For that purpose the input earthquake excitation s must be specified If only one earthquake record is selected out of a specified ensemble suite of input motions then a conventional single earthquake analysis will be performed 7 1 Definition specification of input motion ensemble suite 7 1 1 Available Ground Motions A set of 20 motions provided by CalTrans are available as the default input motion package The above ground motion data sets were resampled to a sampling frequency of 50 Hz regardless of whether initial sampling frequency was 100 or 200 Hz due to the computational demands of running full ground structure analyses for an ensemble of motions Standard interpolation methods were used to resample the time domain signals so that the signal shape is preserved The resampled records were then baselined to remove any permanent velocity and displacement offsets Baselining was accomplished using a third order polynomial fitted to the displacement record In addition four sets of input motions are also available can be downloaded from
90. on XSECTION CalTrans 1999 result is also available Fig 34 Y Column Fiber Section l I te sa RC Section Properties RC Materials Longitudinal Steel 75 Steel Material Steel02 Material Properties View Stress Strain Curve Transverse Steel A PA PR SA Steel Unit Weight 490 pcf Core Concrete Material Concrete 2 Material Properti View Stress Strain Curve Steel Vield Strength 866717 5 psi oncr Material Properties View Stress Strain Curve Steel Strain Limit 0 12 Cover Concrete Material Concrete 2 Material Properties View Stress Strain Curve Concrete Unit Weight 145 pct Concrete Unconfined Strength 4000 psi View Moment Curvature Response Cancel Fig 27 Nonlinear Fiber Section window 43 Tui steel Material Properties Pe Jm 8 Steel Properties Youngs Modulus 29000000 psi Strain hardening Ratio 0 01 Controlling Parameter RO 15 Controlling Parameter cR1 Controlling Parameter cRZ Tui Reintorcingsteel Material Properties Pe Jm e Steel Properties Youngs Modulus 29000000 psi Ultimate Stress 76900 psi Youngs Modulus at Initial Stress hardening 1200000 psi Strain at Initial Strain hardening 0 005 Strain at Peak Stress 0 135 b 44 Tui Concrete MMaterial Properties Core Concrete Properties Concrete Compressive Strength Concrete Strain at Maximum Strength Concrete Crushing Strength Concrete Strain
91. ongitudinal springs in a curved bridge with a non zero skew angle Fig 60 shows a bridge model with 5 distributed abutment springs and a non zero skew angle 71 Plan View Fixity Rigid Link Longitudinal Response zeroLength Element Elastic a zeroLength Element m Deck Rigid Link Transverse Response Elastic Side View Fixity b Deck zeroLength Rigid Link Element Vertical Response Elastic Side View Fixity c Fig 56 General scheme of the Elastic Abutment Model a longitudinal component b transverse component c vertical component 12 Tui Bridge amp butments Abutment Model Type Elastic Number of Distributed Springs Fig 57 Definition of the Elastic Abutment Model E Elastic Abutment ca 2 EX Elastic Properties Longitudinal Stiffness kip in Transverse Stiffness kipin Vertical Stiffness kipin Rotation Longitudinal Axis kip in rad Rotation Transverse Axis kip in rad Rotation Vertical Axis kip in rad OK Cancel Fig 58 Parameters of the Elastic Abutment Model 73 Skew Angle Fixity a Rigid Link Deck Skew Angle zeroLength Elements b Fig 59 Longitudinal components of the Elastic Abutment Model in a curved bridge a left abutment b right abutment 74 b Fig 60 Bridge model with multiple distributed springs and a positive skew angle a straight bridge b curved bri
92. onse Side View Material Force Displacement b 83 E 9 Total Vertical response A e a a o F kips i a is A a is iii 20 d in c Fig 66 Vertical response of the SDC 2004 Abutment Model a general scheme b vertical response of a bearing pad c total vertical response 4 3 4 Definition of the SDC 2004 Abutment Model To define a SDC 2004 Abutment Model please follow the steps shown in Fig 67 To define a SDC 2004 Abutment Model select SDC 2004 for the abutment model type in Fig 55 The resulting window 1s shown in Fig 67a 84 Tui Bridge A amp butments e J ss Abutment Number of Distributed Springs 2 Longitudinal Gap in Bearing Pad Number of Bearings Bearing Height in Advanced Shear Keys Number of Shear Keys Advanced Embankment Lateral Stiffness Backwall Width fe Backwall Height ft Advanced Embankment Vertical Stiffness 85 S Bearing Pad Fere Bearing Pad Properties Pad Length 20 in Shear Modulus 0 15 ksi Young s Modulus 5 ksi Vertical Yield Strength 2 25 ksi Yield Strain 150 75 Y Shear Key e lele Shear Key Properties Initial Elastic Stiffness 1 000 kip in Ultimate Capacity as Ratio of 03 Tributary Deadload at Abutment Gap 0 in ok Cancel Tui Embankment Lateral Stifness Pe lale Longitudinal Direction SDC 2004 Model Initial Stiffness 20 kip in ft Maximum
93. p opensees berkeley edu an open source framework developed by the Pacific Earthquake Engineering Research PEER Center The analysis options available in MSBridge include 1 Pushover Analysis 11 Mode Shape Analysis 111 Single 3D Base Input Acceleration Analysis 1v Multiple 3D Base Input Acceleration Analysis and v Equivalent Static Analysis ESA This document describes how to conduct the above analyses in MSBridge For information about how to download and install MSBridge please visit the MSBridge website http www soilquake net msbridge vi TABLE OF CONTENTS JURO BP LI ULL M iv ACKNOWLEDGMDNBENTS 2 1 1 oa as aero Dei eee eoo oa red eo eun aod V ABSTRAC d pet n vi TABEF OOBRCONLDENJLS iiiteisdeseeeteeecornnildeeeos eesvento eaa o6 P2 EE ias vii ID E POR PIG BR Ld UP I xi DAS OE DA BETS wicssascosccsiesdetesasctccsuissiocevencosecsdendsnevussteccbissincctessolecedsnecnesoosSoucbussionstessesseeusvenss xvii 1 IO AU CIO iii A a A A ad 18 1 1 A e A E E oue 18 I UO RR RR RU M IUE EUR 18 1 2 COOPdIHate Sy LETS iii 19 1 3 A AAA E 20 1 4 AckhowleCOPTHebls a A 20 2 GETS SEAL LE cuo Ete Ot a 21 2 1 MUDA 21 2 2 o A anes dell haa hata sae dell a uaenk teil ah ian Ak ecdb abet atias 21 Di O Te Ale oye hashed URDU DRE E TE 22 22 NOEL I PUERCO ities EE tion ac ou neauee tied iustis muse deae Pies sumet tad 25 2 23 Dine Element Mesh ReCO stg Dese ro ii 25 3 Bridoe a Erro ec G
94. please check http www unit conversion info Some commonly used quantities can be converted as follows l kPa 0 14503789 psi l psi 6 89475 kPa Im 39 37 in 18 lin 0 0254 m 1 2 Coordinate Systems The global coordinate system employed in MSBridge is shown in Fig 1 The origin is located at the left deck end of the bridge The bridge deck direction in a straight bridge is referred to as longitudinal direction X while the horizontal direction perpendicular to the longitudinal direction is referred to as transverse direction Y y In a curved bridge the bridge deck direction at the left deck end will be used as the longitudinal direction At any time Z denotes the vertical direction Vertical axis Z Longitudinal axis X Right abutment Transverse Bent 4 axis Y Bent3 Span4 Bent 2 js Span 3 Span2 Origin Span 1 es Column 1 of Bent 3 Column 2 of Bent 3 Fig 1 Global coordinate system employed in MSBridge When referencing different members and locations the numbering and names used in MSBridge follow designations as follows The left abutment is designated Abutment 1 or Left Abutment Moving rightward and starting with Bent 2 the bents are numbered consecutively The right abutment is designated Right Abutment or Abutment N where N is the last Bent number plus one e g the right abutment can be referred to as Abutment 5 The span numbering corresponds to t
95. r section for the column click Nonlinear Fiber Section Fig 23 The window for defining the Fiber section is shown in Fig 27 Click Material Properties buttons to define the material properties for the rebar the core and the cover concrete Fig 28 Nonlinear beam column elements with fiber section for the circular cross section Fig 29 are used to simulate the column in this case The calculations of fibers for the octagonal and hexagonal cross sections are similar to that of the circular cross section except for the cover Fig 30 shows a slightly treatment of fiber calculations for the octagonal and hexagon cross sections For Rectangular section the number of bars refers to the number of reinforcing bars around the section perimeter equal spacing Two types of nonlinear Beam Column Elements are available for the column Beam With Hinges and Force Based Beam Column McKenna et al 2010 By default Forced based beam column elements nonlinearBeamColumn McKenna et al 2010 are used the number of integration points 5 The default values for the material properties of the column are shown in Tables 2 4 When the Beam With Hinges Element is used the calculation of the plastic hinge length L for the column is based on Eq 7 25 of SDC 2010 r 0 082 0 15 pdy 2 0 3f d in ksi 0 08Z 0 022f d 0 044f dy mm MPa Where L is the column height fye 1s the steel yield strength dj 1s the longitudinal bar size The plastic
96. rings included on each bent cap 65 Isolation Bearings Deck Node Column Top Bent Cap zeroLength 3 Column element 2 Fig 50 OpenSees zeroLength elements for isolation bearings side view of bent cap cut plan 3 6 3 Steel Jackets To define steel jackets click Define Steel Jackets in Fig 44 and a window for defining steel jacket properties will appear Fig 51 For now the steel jacket option is only available to the circular column To activate define steel jacket for all columns for a bent please nonzero values for the corresponding row Fig 51 In the case of partial length of steel jacket Fig 52 please specify enough number of elements for the column since the equal size of elements is used for the columns within a bent for now The steel properties used in the steel jacket implementation are the same as user defined properties for the steel reinforcement of the column shown in Fig 27 66 E Steel Jackets ca e EX Steel lacket Parameters OK Bent Length ft Thickness in Location ft Cancel Bent 2 0 Bent 3 Bent 4 Fig 51 Definition of steel jackets Column Jacket Thickness Steel Jacket Jacket Length Column Height Jacket Location Fig 52 Sketch of steel jacket 3 6 4 Skew Angles The user can choose to use a single global skew angle or individual skew angles for abutments and bents By default a zero Global Skew Angle is assumed Fig
97. scO is the concrete strain at maximum strength fpcu is the concrete crushing strength Sepsu is the concrete strain at crushing strength all of the above values are entered as negative lambda is the ratio between unloading slope at epsu and initial slope ft is the tensile strength and Ets is tension softening stiffness absolute value slope of the linear tension softening branch For cover concrete fpc is equal to the concrete unconfined strengthError Reference source not found epscO 0 002 fpcu 0 0 Sepscu 0 006 Slambda 0 1 ft 0 14 fpc and Ets ft epscO Core concrete 1 For core concrete of circular column cross sections according to the Mander model the procedure to calculate the confined concrete strength fpc f is as follows 154 f f 1 254 2 254 Larga 2 s 9 Where f is the unconfined compressive strength and f can be obtained from the following equation f KA 10 Where f isthe steel yield strength o is the transverse steel percentage and K can be t obtained from the following equation for spirally confined circular columns ay K e 11 1 P Where pol co A 12 An assumed value of the area of the confined core is used for default values This area should be modified based on the expected compressive block in the column during lateral loading 2 A EL 13 4 md S 14 PG Where dp is the transverse bar diameter do
98. slider or click the spin button to cycle through them 106 A Step 2 Select Analysis Option Analysis Options 2 Pushover Change Pattern Mode Shape Number of Modes 10 D Ground Shaking Fig 89 Steps to perform an Eigenvalue analysis a Deformed Shape Mode 1 Penod 0 2576 sec Frequency 3 8817 Hz Analysis Stage Plot Scale Factor 385 Show Legend Show Undeformed Mesh Display Motion Animation Play Repeat Current Mode Mode HN BO DLS ull Playing Speed 107 a Deformed Shape Mode 2 Period 0 2422 sec Frequency 4 1291 Hz Analysis Stage Plot Scale Factor 3 1 Show Legend Show Undeformed Mesh Display Motion Animation Repeat Q amp a T 3D XY AZ YZ b 108 a Deformed Shape Mode 3 Period 0 2134 sec Frequency 4 6856 Hz Analysis Stage Plot Scale Factor 226 Show Legend Show Undeformed Mesh Display Motion Animation Repeat Q amp a T 3D XY AZ YZ 109 a Deformed Shape Mode 4 Penod 0 1113 sec Frequency 8 9808 Hz Analysis Stage Plot Scale Factor 187 Show Legend Show Undeformed Mesh Display Motion Animation Repeat N NS BO DLS d 110 a Deformed Shape Mode 5 Penod 0 1064 sec Frequency 9 4001 Hz Analysis Stage Plot Scale Factor 209 Show Legend Show Undeformed Mesh Display Motion Animation Repeat Current M
99. t al 2004 as representative of typical statewide bridge construction in California These bridge configurations are listed in Table 7 Table 7 Typical Bridge Configurations in California After Ketchum et al 2004 Bridge ES i G i Bent Column Column Deck Type poe ee COMICI Columns Height Height Width l 120 150 150 150 120 Straight l 22 39 6 2 120 150 150 150 120 Straight 3 22 68 6 3 80 100 100 100 80 Straight l 22 39 4 4 80 100 100 100 80 Straight 3 22 68 4 D 80 100 100 100 80 Straight l 22 39 5 2 6 80 100 100 100 80 Straight 3 22 68 5 2 7 120 120 Straight l 22 39 6 2 8 120 120 Straight 3 22 68 6 2 9 120 150 150 150 120 1000 radius 1 22 2 6 10 80 100 100 100 80 30 skew 3 22 68 4 11 120 150 150 150 120 Straight l 50 39 6 The above models were built without much effort in MSBridge Linear columns Roller abutment model and Rigid base were assumed default values were used for other bridge parameters The SAP2000 models s2k files were obtained by clicking Menu File and then Export SAP2000 s2k Text File Linear analyses of monotonic pushover show both MSBridge and SAP2000 gave the identical results for all of the 11 bridge configurations shown in Table 7 For example Fig 125 shows the models built in MSBridge and SAP2000 for Bridge Type 1 Table 8 shows the displacement of the deck at each bent under the pushover load of 2000 kips applied at the deck cen
100. ter along the longitudinal and transverse directions Fig 126 and Table 9 show the comparison for Bridge Type 2 Fig 127 and Table 10 show the comparison for Bridge Type 9 Fig 128 and Table 11 show the comparison for a skewed bridge case Bridge Type 10 Both MSBridge and SAP2000 essentially gave the same result 163 a b Fig 125 Bridge Type 1 model a MSBridge b SAP2000 Table 8 Displacement unit inch of Bridge Type 1 under pushover load of 2000 kips applied at deck center along both the longitudinal and transverse directions 164 Longitudinal Transverse Vertical in Bent Displacement Displacement Displacement 0 68199 0 05127 2 38939 0 05235 SAP2000 2 15946 0 05204 0 50487 0 05278 0 68326 0 0513 2 39682 0 0524 2 15976 0 0520 0 50778 0 0528 0 0 Differens m m 0 0 1 0 a RN b Fig 126 Bridge Type 2 model a MSBridge b SAP2000 Table 9 Displacement unit inch of Bridge Type 2 under pushover load of 2000 kips applied at deck center along both the longitudinal and transverse directions BMlL E Transverse Vertical in Bent Displacement Displacement Displacement 0 117 0 0728 0 4988 0 074 SAP2000 0 4082 0 0737 4 02946 00304 0 0742 1 0303 01159 0 073102 Ed 2 0320 0 5099 0 074236 0 4097 0 074008 0 03116 0 074469 1 0 2 0 0 0 3 0 i No Difference 165 b Fig 127 Bridge Type 9 model a MSBridge b SAP20
101. terial default values employed a Elastic No Tension b Concrete01 and c Concrete02 Stress Strain Curve for Cover Concrete am Compression Tension a 50 q Stress Strain Curve for Cover Concrete Compression Tension b Fig 33 Stress strain curve of the cover concrete material default values employed a Concrete01 and b Concrete02 Moment Curvature Analysis Moment Curvature Response Parameters Axial Load 2680 kip Maximum Curvature 0 002 rad in Number of Loading Steps 500 Number of Unloading Steps 0 Compare with ASECTION ASECTION Options Core Concrete Model Mander s Confined OpenSees Cover Concrete Model Mander s Unconfined xXSECTION Steel Model Park Display ASECTION Output Recalculate Moment Curvature Fig 34 Moment curvature response for the column with default steel and concrete parameters and the deck weight 2680 kip applied at the column top SI 3 5 Foundation 3 5 1 Rigid Base There are three types of foundations available Fig 35 Rigid Base Soil Springs and Foundation Matrix If Rigid Base is chosen all column bases will be fixed in 3 translational and 3 rotational directions In that case the fixity nodes of the abutment models are also fixed Tui Bridge Foundation Foundation Type Rigid Base Soil Springs Foundation Matrix Fig 35 Foundation types available in MSBridge 3 5 2 Soil
102. the website http www soilquake net msbridge Motion Set 1 These 100 motions were obtained directly from the PEER NGA database and all files have been re sampled to a time step of 0 02 seconds This PBEE motion ensemble Medina and Krawinkler 2004 obtained from the PEER NGA database http peer berkeley edu nga consists of 100 3D input ground motions Each motion 1s composed of 3 perpendicular acceleration time history components 2 lateral and one vertical These motions were selected through earlier efforts Gupta and Krawinkler 2000 Mackie et al 2007 to be representative of seismicity in typical regions of California The moment magnitudes Mw of these motions range from 5 8 7 2 distances from 0 60 km The engineering characteristics of each motion and of the ensemble overall may be viewed directly within MSBridge The provided ground motions are based on earlier PEER research Mackie and Stojadinovic 2005 Motion Set 2 These motions 160 in total were developed by Dr Kevin Mackie from the 80 motions of Setl excluding the 20 motions of Setl in the bin NEAR to account for site classification Motion Set 3 These motions 80 in total were developed by Dr Jack Baker for PEER Additional information about these motions is available at the website http peer berkelev edu transportation projects ground motion studies for transportation systems 112 Motion Set 4 These motions 260 in total include the above Set2 a
103. the vertical curves Begin Curve Length refers to the starting location of the beginning slope of the vertical curve see Fig 12b Curve Length refers to the length of the vertical curve End Curve Slope refers to the slope of the end slope Note that the slope value can be negative zero or positive Similarly Click Insert Curve to add a horizontal curve and click Delete Curve to remove the chosen curve Fig 15 shows examples of horizontal and vertical alignment Note that the horizontal curve alignment employs the circular arc while the vertical curve alignment employs the parabolic equation Any two horizontal or vertical curves cannot be overlapped and any newly added curves must be located outside all previous curves For the detailed technical information on the horizontal amp vertical alignments please refer to the CalTrans Course Workbook for Land Surveyors 2011 Y Horizontal Alignment NNNM CS ere Horizontal Curve Parameters q Delete Curve Curve Beging Length ft Radius ft Direction Curve Length ft Curvel 0 amp m uns Cancel Fig 11 Horizontal alignment 30 Begin Length Left Abutment Radius a Curve Length mi E Beginning Slope Left Abutment End Slope b Fig 12 Horizontal and vertical alignments a horizontal alignment plan view b vertical alignment side view Vertical Curve Parameters Delete Curve 10 Insert Curve Begin Slope C
104. titledi E Browser Parameters Motion Longitudinal Direction Time Step 0 02 Number of Header Lines to Skip 0 View Motion Longitudinal Direction Redraw Motion Names Ein Name TB Earthquake Name EQ Motion Name Motion OK Cancel 116 u Input Motions Input Motion Folder CAUsersinlukDocuments MSBXDOTMETSUntitled brfilessUntitled EQ View Histograms amp Cumulative Distribution Input Motions 19 Records in Total 1 Records Selected Selected Record Bin Earthquake Motion Points Timestep sec Duration sec 1 TOL NORTHRIDGEXRRS 996 0 02 19 92 2 T02 NORTHRIDGE SCS 2000 002 J40 3 T03 CHI CHATCUOGS 4 Tos cHi cHnTcuosg 3500 002 70 X Scale Factor Longitudinal T ncs Free Vibration Duration 0 Vertical C Compute Response from n en Analysis Parameter Simultaneous Execution Computation Time Step 0 02 Number of Motions Running Simultaneously 2 OK b Fig 93 Importing a user defined motion a choosing data files b message showing new motion has been added 117 W Motion TOMNORTHRIDGE ARS Type Time History Acceleration Velocity Displacement Direction Longitudinal Transverse Vertical Horizontal SRSS amp Time History Pseudo Spectrum View Data Add Figure to Report Fig 94 Time histories and response spectra of individual motion ES Intensive Measures Intensive Measures of
105. tment back wall abutment piles and soil backfill material Prior to impact or gap closure the superstructure forces are transmitted through the elastomeric bearing pads to the stem wall and subsequently to the piles and backfill in a series system After gap closure the superstructure bears directly on the abutment back wall and mobilizes the full passive backfill pressure The detailed scheme of the longitudinal response is shown in Fig 63a The typical response of a bearing pad is shown in Fig 63b And the typical overall behavior is illustrated in Fig 63c The yield displacement of the bearings is 76 assumed to be at 150 of the shear strain The longitudinal backfill back wall and pile system response are accounted for by a series of zero length elements between rigid element 2 and the fixity Fig 63a The abutment initial stiffness Kabt and ultimate passive pressure Pabt are obtained from equations 7 43 and 7 44 of SDC 2004 Fig 64 shows the directions of zeroLength elements for a curved bridge with a skew angle Each bearing pad has a default height h of 0 0508 m 2 in which can be modified by user and a side length square of 0 508 m 20 1n The properties of a bearing pad are listed in Table 4 The abutment is assumed to have a nominal mass proportional to the superstructure dead load at the abutment including a contribution from structural concrete as well as the participating soil mass An average of the embankment l
106. trix Lam and Martin 1986 Specifically the stiffness of a single pile is represented by a 6 x 6 matrix representing stiffness associated with all six degrees of freedom at the pile head The local coordination system employed for the foundation matrix 1s parallel to the global coordination system Fig 42 To define foundation matrix select Foundation Matrix and then click Modify Foundation Matrix Fig 35 Fig 43 shows the window defining the foundation matrix for the column base of each bent To apply the matrix defined for any bent for the remaining bents select that bent in the Bent No box and then check Use this Matrix for All Other Bents e Fx Fig 42 Local coordination system for the foundation matrix 59 q Foundation Matrix Bent Number Bent 2 x Foundation Matrix for Bent 2 The entry below must be non positive FE gi kip in 10000 kip Fy 800 kip in 10000 kip 30000 kip in 20000000 kip in Symmetric 20000000 kip in 50 kip in All values must be non negative except otherwise stated Use this Matrix for All Other Bents T Cancel Fig 43 Foundation matrix for each bent 3 6 Advanced Options The advanced options in MSBridge include Deck Hinges Isolation Bearings and Skew Angles Click Advanced in Fig 6 to include any of these options as shown in Fig 44 into the bridge model 60 A Advanced Options Deck Hinges Define Deck Hinges Isolation Bearings Define Isolation
107. tructural and geotechnical systems subjected to earthquakes for more information please visit http opensees berkeley edu MSBridge is written in Microsoft NET Framework Windows Presentation Foundation or WPF OpenTK OpenGL library website http www opentk com 1s used for visualization of FE mesh And OxyPlot http oxyplot codeplex com is employed for x y plotting For questions or remarks about MSBridge please send email to Dr Ahmed Elgamal elgamal ucsd edu or Dr Jinchi Lu Qinlu ucsd edu 20 2 Getting Started 2 1 Start Up On Windows start MSBridge from the Start button or from an icon on your desktop To Start MSBridge from the Start button 1 Click Start and then select All Programs 11 Select the MSBridge folder 111 Click on MSBridge icon Y The MSBridge main window is shown in Fig 2 ee EEE 0 oc File Execute Display Report Help BFAD ILT Unit System SI Units US English Units A Step 1 Define Model and Check Responses Quick Check of Model Responses View Natural Periods View Gravity Response rel A a 9 3D XY XZ YZ Lo 1 Equivalent Static Analysis ESA Longitudinal Direction A Step 3 Run FE Analysis Fig 2 MSBridge main window 2 2 Interface There are 3 main regions in the MSBridge window menu bar the model input and the FE mesh 21 2 2 1 Menu Bar The menu bar shown in Fig 3 offers rapid access to most MSBridge main fea
108. tures Lock Unlock Model MSBridge Untitled File Execute Display Report Help 9 About MSBridge New Model 3 mi Open Model Save Model Run Analysis a re incio Execute Display Report Help New Model Open Model Save Model Save Model As Compare Models 7 Export SAP2000 V15 52k Text File SAP2000 V7 s2k Text File C inluXDaocumentsVMSBSUntitled msb AutoCAD did File GID msh Mesh File Matlab m File Aj bit i Save Model and Run Analysis Advanced Option OpenSees Parameters 22 EDP Quantities for All Motions Bridge Peak Accelerations and Displacements for All Motions g Maximum Column and Abutment Forces for All Motions 5 SI Units Step 1 De Detailed Output Select Input Motion Current RRS Model Build Deformed Mesh Motion RRS f Deck Response Time Histories Motion RRS Foundatior Column Response Profiles Motion RRS Column Response Time Histories Motion RRS Column Response Relationships Motion RRS Abutment Response Time Histories Motion RRS Quick Chec Step 2 Se Deck Hinge Response Time Histories Motion RRS Soil Spring Response Time Histories Motion RRS Isolation Bearing Response Time Histories Motion RRS Start Report Session Close Report Session Open Report File Contents and Index MsSBridge Website Unit System Q Abut A SI Units
109. uperstructure stiffness the embankment mobilization and the inelastic behavior of the soil material under high shear deformation levels dominate the response of the bridge and the intermediate column bents Kotsoglu and Pantazopoulou 2006 and Shamsabadi et al 2007 2010 Seven abutment models have been implemented in MSBridge The abutment models are defined as Elastic Roller SDC 2004 SDC 2010 Sand SDC 2010 Clay EPP Gap and HFD abutment models To define an abutment model click Abutments in Fig 6 A window for defining an abutment model is shown in Fig 55 4 1 Elastic Abutment Model The Elastic Abutment Model consists of a series of 6 elastic springs 3 translational and 3 rotational at each node at the end of the bridge Fig 56 To choose the Elastic Abutment Model select Elastic for the Model Type in Fig 55 Fig 57 The main window to define the Elastic Abutment Model is shown in Fig 58 By default no additional rotational springs are specified but can be added by the user As shown in Fig 56 and Fig 58 MSBridge allows the user to define multiple distributed springs equal spacing within deck width The values specified in Fig 58 are the overall stiffness for each direction translational or rotational For the longitudinal direction translational and rotational each of the distributed Elastic springs carries its tributary amount e g Fig 56 shows a case of 4 distributed springs Each of the both end springs
110. urve Beging Length ft Curve Length ft End Slope Fig 13 Vertical alignment 31 Fig 14 Examples of horizontal curved bridges horizontal alignment a single radius horizontal curve b multi radius horizontal curve c horizontal curve connecting to straight parts a b c d Fig 15 Examples of vertically curved bridges vertical alignment a single slope b begin and end slopes c multiple slopes d mixing slope and zero slope 33 3 2 Deck To change Deck properties click Deck in Fig 6 Fig 16 shows the window to modify the deck material and section properties MSBridge uses an elastic material model for the bridge deck elements Fig 16 shows the default values for the deck material properties including Youngs Modulus Shear Modulus and Unit Weight k Bridge Deck Material Properties Youngs Modulus Shear Modulus Unit Weight Section Properties Area of Cross Section 68 111 Moment of Inertia Horizontal Axis 356 043 Moment of Inertia Vertical Axis 8235 53 Torsion Constant 978 381 Weight Weight per Unit Length 10 216 kip ft Recalculate Section from Bax Gi rder OK Cancel Fig 16 Material properties of the bridge deck Fig 16 also shows the deck Section properties Section properties can be input directly in Fig 16 if available If this information is not available MSBridge will generate properties based on general box girder section dimensions Click Re
111. users need to click the Lock Model button If the model is in Unlocked Mode analysis results 1f any will be overwritten if analysis is launched 24 a About MSBridge MSBridge Beta 0 5 9 April 29 2014 Copyright and Acknowledgment MSBridge is developed by Drs Ahmed Elgamal UC San Diego Jinchi Lu UC San Diego and Kevin Mackie Univ of Central Florida Acknowledgment This research is funded by California Department of Transportation CalTrans OpenSees currently ver 2 4 0 is employed is a software framework for developing applications to simulate the performance of structural and geotechnical systems subjected to earthquakes For more information please visit http opensees berkeley edu For questions or remarks about MSBridge please send email to Dr Ahmed Elgamal elgamaligucsd edu or Dr Jinchi Lu jinlu ucsd edu Fig 4 MSBridge copyright and acknowledgment window 2 2 2 Model Input Region The model input region controls definitions of the model and analysis options which are organized into three regions Fig 2 Step 1 Define Model amp Check Responses Controls definitions of bridge parameters including material properties Meshing parameters are also defined in this step Step 2 Select Analysis Option Controls analysis types pushover analysis mode shape analysis or ground shaking Equivalent Static Analysis ESA option is also available Step 3 Run FE Analysis Controls exe
112. utput windows for a pushover analysis include 1 Response time histories and profiles for column and pile shaft under grade 11 Response relationships force displacement as well as moment curvature for column and pile shaft under grade 111 Abutment response time histories iv Deformed mesh contour fill plastic hinges and animations 6 4 1 Column Response Profiles 100 a Column Response Profiles Response Type Response Profile Displacement 2 Bending Moment C Shear Force C Acceleration Rotation Direction Longitudinal E Transverse C Vertical Column Column 1 of Bent2 Add Figure to Report Fig 83 Column response profiles 6 4 2 Column Response Time Histories 101 S Column Response Time Histories Response Type Response Time History Displacement C Bending Moment C Shear Force C Acceleration Rotation Direction Longitudinal Transverse C2 Vertical Column ColumniofBent2 Elevation O ft View Data Add Figure to Report Fig 84 Column response time histories 102 6 4 3 Column Response Relationships q Column Response Relationships Response Type Response Relationship i Moment Curvature Load Displacement Direction Longitudinal C Transverse Column Column 1 of Bentz Elevation loft Animation Play Current Step Playing Speed View Data Add Figure to Report Fig

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