1. ISEC-02 Second International Structural Engineering and Costruction Conference September 22-26,2003, Rome “EVALUATION AND RESULTS’ COMPARISON IN DYNAMIC STRUCTURAL RESPONSE OF MESSINA CABLE-SUSPENDED BRIDGE” Marco Ciani Structural Engineer, Rome, Italy Valerio Barberi Structural Engineer, Rome, Italy Luciano Catallo PhD Student, University of Rome “La Sapienza”, Rome, Italy

2. THE SUBJECTS OF THE ARTICLE ARE: SECTION 1 THE CHECK OF MESSINA STRAIT BRIDGE MODEL ACCURANCY THROUGH TWO DIFFERENT CALCULATION CODES ANSWER. SECTION 2 THE SHELL ELEMENTS USED IN DECK’S MODELING AND DECK INSERTING IN THE GLOBAL MODEL Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo

3. Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Models Tav. 1 OBJECTIVE Sap 2000

4. CHARACTERISTICS OF MESSINA STRAIT BRIDGE MODELS Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Tav. 2 CENTRAL SPAN: 3300 m LATERAL SPAN SICILY: 960 m LATERAL SPAN CALABRY: 810 m HEIGHT TOWERS: 376 m ELEMENTS TYPE: FRAME ELEMENTS NUMBER: 1582 NODES NUMBER: 1097 DEGREE OF FREEDOM: 10000 Sap 2000

5. NON LINEAR ANALYSIS Type of non linearity MATERIAL NON LINEARITY CONTACT NON LINEARITY GEOMETRICAL NON LINEARITY Change material properties during load application Change boundary condition during load application Deformation and finite displacements‘ effects are included in equilibrium equations ANSYS solves a non linear analysis stepping or ramping total load during the time SAP 2000 uses the P-  method Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Tav. 3

6. LEVEL OF ANALYSIS First order elastic analysis 2 Second order elastic analysis First order inelastic analysis Second order inelastic analysis K g geometric stiffness matrix K m plastic reduction matrix 1 3 4 Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Tav. 4

7. ANALYSES NON LINEAR STATIC ANALYSIS TRANSIENT DYNAMIC ANALYSIS TRANSIENT DYNAMIC ANALYSIS ACC. MIN: -4.71 m/s^2 time t = 43.54 s ACC. MAX: 4.64 m/s^2 time t = 47.94 s ACC. MIN: -5.89 m/s^2 time t = 59.14 s ACC. MAX: 5.301 m/s^2 time t = 53.26 s ACC. MIN: -4.42 m/s^2 time t = 52.945 s ACC. MAX: 4.402 m/s^2 time t = 54.06 s MODAL ANALYSIS Longitudinal Direction Transverse DirectionVertical Direction Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Tav.5

8. GENERAL CHARACTERISTICS: Structure’s natural periods Modal shapes Modal excited mass ratios GENERAL CHARACTERISTICS: Structure’s natural periods Modal shapes Modal excited mass ratios EVALUETED ENTITIES Modal analysis is a way to evaluate any differences in model’s behaviour regarding modal partecipation mass ratios, natural periods and modal deformed shape Modal analysis is a way to evaluate any differences in model’s behaviour regarding modal partecipation mass ratios, natural periods and modal deformed shape MODAL ANALYSIS TRANSIENT DYNAMIC ANALYSIS SPECIFIED POINTS : Displacements External reactions Internal forces SPECIFIED POINTS : Displacements External reactions Internal forces Some significant points, describing bridge’s global behavior Some significant points, describing bridge’s global behavior Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Tav. 6

9. MODAL ANALYSIS OF MESSINA STRAIT BRIDGE Structural masses were self calculated by codes using material density and geometrical characteristics of the sections; their positioning, as lumped masses, is made according to the codes defaults, i.e. coincident to the nodes at the end of each frame element used in bridge’s modeling. SAP2000 ANSYS Masses representing live load contribution were also positioned on the deck’s node, for these masses were introduced new elements, which are masses element having the same traslational characteristics in each directions, but not rotational one. Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Tav. 7

10. SAP2000 MODAL SHAPES and NATURAL PERIODS ANSYS Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Tav. 8

11. MODAL-PARTICIPATING-MASS-RATIOS VS MODE NUMBER In a modal analysis, the accurancy of structural response was evaluated considering the exiceted mass as reference parameter, so modes number was increased till to excite at least 85% of the total mass in every direction. It’s evident that 85% of excited mass is already reached in longitudinal and transverse direction by only 100 modes, but to obtain the same value also in vertical direction about 800 modes are required. TRANSVERSE Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Tav. 9

12. TRANSIENT DYNAMIC ANALYSIS OF MESSINA STRAIT BRIDGE Transient Dynamic Analysis, is a technique used to determine the dynamic response of a structure under the action of any general time-dependent load Transient Dynamic Analysis, is a technique used to determine the dynamic response of a structure under the action of any general time-dependent load The mode superposition method sums factored mode shape (eigenvectors) from a modal analysis to calculate the structure’s response The mode superposition method sums factored mode shape (eigenvectors) from a modal analysis to calculate the structure’s response The full method uses the full system matrices to calculate the transient response The full method uses the full system matrices to calculate the transient response SAP 2000 uses a technique called: Mode superposition transient analysis SAP 2000 uses a technique called: Mode superposition transient analysis ANSYS uses a technique called: Full transient analysis ANSYS uses a technique called: Full transient analysis Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Tav. 10

13. TRANSIENT DYNAMIC ANALYSIS: RESULTS and COMPARISONS Some significant points, describing bridge’s global behaviour, were chosen; in particular were evaluated middle cables point, in every of three spans, also points situated on the top of the towers and other located at the connection between towers and lower transverse tower’s element were considered. The bridge was subjected to a load combination constituted by self weigth added to a superimposed load consisting of railings, road topping and other. SICILYCALABRY Joint 29-30 Joint 167-168 Joint 570-571 Joint 1008-1009 Joint 105-106 Joint 946-947 Joint 1064-1065 DISPLACEMENT COMPARISON Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Tav. 11

14. TRANSIENT DYNAMIC ANALYSIS: RESULTS and COMPARISONS FINAL DISPLACEMENT COMPARISON LONGITUDINAL DIRECTION Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Tav. 12

15. TRANSVERSE DIRECTION VERTICAL DIRECTION TRANSIENT DYNAMIC ANALYSIS: RESULTS and COMPARISONS FINAL DISPLACEMENT COMPARISON Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Tav. 13

16. TRANSIENT DYNAMIC ANALYSIS: RESULTS and COMPARISONS SICILYCALABRY Joint 1096- 1097-1092- 1093 Joint 940-941 Joint 1047-1048- 1051-1044-1045-1046 Joint 100-99 Joint 1-2-5-6 Joint 57-58- 59-62-63-64 REACTIONS’ COMPARISON Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Tav. 14

17. TRANSIENT DYNAMIC ANALYSIS: RESULTS and COMPARISONS FINAL REACTION COMPARISON TRASVERSE DIRECTION Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Tav. 15

18. LONGITUDINAL DIRECTION VERTICAL DIRECTION TRANSIENT DYNAMIC ANALYSIS: RESULTS and COMPARISONS FINAL REACTION COMPARISON Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Tav. 16

19. Rayleigh-Damping In the Rayleigh damping, it is assumed that the damping is proportional to the mass and the stiffness of the structure The coefficients a o and a 1 can be determined from specified damping ratios at two indipendent dominant modes (say i th and j th modes) It is important to note that the damping ratio at a mode between the i th and j th mode is less than . And, in practical problems the specified damping ratios should be chosen to ensure reasonable values in all the mode shapes that lie between the i th and j th mode shapes. TRANSIENT DYNAMIC ANALYSIS: RESULTS and COMPARISONS THE DAMPING EFFECTS ON STRUCTURAL RESPONSE Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Tav. 17

20. TRANSIENT DYNAMIC ANALYSIS: RESULTS and COMPARISONS Next figures present some results obtained by changing  a o and a 1 values in ANSYS code to compare Rayleigh damping method with constant damping ratio (2%) of SAP2000 code Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Tav. 18

21. TRANSIENT DYNAMIC ANALYSIS: RESULTS and COMPARISONS Next figures present some results obtained by changing  a o and a 1, values in ANSYS code to compare Rayleigh damping method with constant damping ratio (2%) of SAP2000 code Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Tav. 19

22. SECTION 1: CONCLUSIONS IN CONCLUSION TWO CODES HAVE BEEN USED IN ORDER TO OBTAIN A VALID MODEL AND CONSEQUENTLY RELIABLE RESULTS. THE CALCULATION CONFIRMS THE DIFFERENCES BETWEEN THE TWO CODES, BUT THE GLOBAL TREND OF THE ANSWERS IS QUITE CLOSE. THE CONCEPT ALREADY CITED OF ROBUSTNESS HAS THE PURPOSE OF TO MINIMIZE THE POSSIBLE ERRORS OF MODELING.

23. PRESENT INVESTIGATIONS: DECK Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Tav. 20 154 m 30 m

24. PRESENT INVESTIGATIONS: HIGHWAY BOX GIRDER Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Tav. 21 VIEW OF HIGHWAY BOX GIRDER BOX GIRDER RIB TRANSVERSE ELEMENT 26 m SHELL ELEMENTS OF SINGLE MODULE (26 m) ARE: 9773 12.75 m 2.345 m

25. PRESENT INVESTIGATIONS: RAILWAY BOX GIRDER Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Tav. 22 VIEW OF RAILWAY BOX GIRDER BOX GIRDER RIB TRANSVERSE ELEMENT LONGITUDINAL ELEMENT 26 m SHELL ELEMENTS OF SINGLE MODULE (26 m) ARE: 7186 8.288 m 2.320 m

26. PRESENT INVESTIGATIONS: TRANSVERSE BOX GIRDER Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Tav. 23 VIEW OF TRANSVERSE BOX GIRDER: VERTICAL MESH OF THE TRANSVERSE BOX GIRDER WAS MADE BY 9 ELEMENTS 4.5 m 4.0 m 52.0 m SHELL ELEMENTS OF SINGLE TRANSVERSE ELEMENT ARE: 8500

27. PRESENT INVESTIGATIONS: SUMMARIZE Particular view of highway box girder Frontal view of transverse box girder Particular view of transverse box girder Particular view of railway-highway and transverse box girder Particular view of railway box girder Bottom view of decks Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Tav. 24

28. SUBSTRUCTURING OF THE GLOBAL MODEL OF MESSINA STRAIT BRIDGE ON THE MIDDLE SPAN ZONE SUBSTRUCTURING OF THE GLOBAL MODEL OF MESSINA STRAIT BRIDGE ON THE MIDDLE SPAN ZONE GLOBAL VIEW OF THE MODEL PARTICULAR OF CONNECTING DEVICES BETWEEN HANGERS AND TRANSVERSE ELEMENTS PARTICULAR VIEW OF IMPLEMENTED ZONE Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Tav. 25

29. SUBSTRUCTURING OF THE GLOBAL MODEL OF MESSINA STRAIT BRIDGE CLOSE TO THE SPECIAL ZONE SUBSTRUCTURING OF THE GLOBAL MODEL OF MESSINA STRAIT BRIDGE CLOSE TO THE SPECIAL ZONE GLOBAL VIEW OF THE BRIDGE PARTICULAR VIEW OF IMPLEMENTED ZONE Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Tav. 26 184 m 30 m 35 m 50 m 30 m

30. PARTICULAR OF CONNECTING DEVICES BETWEEN HANGERS AND TRANSVERSE ELEMENTS PARTICULAR VIEW OF SUBSTRUCTURED ZONE SUBSTRUCTURING OF THE GLOBAL MODEL OF MESSINA STRAIT BRIDGE CLOSE TO THE SPECIAL ZONE SUBSTRUCTURING OF THE GLOBAL MODEL OF MESSINA STRAIT BRIDGE CLOSE TO THE SPECIAL ZONE Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Evaluation and Results’ Comparisons in Dynamic Structural Response of Messina Cable-Suspended Bridge Marco Ciani - Valerio Barberi - Luciano Catallo Tav. 27

31. SECTION 2: WORK IN PROGRESS THE RESEARCH GROUP LED BY PROFESSOR FRANCO BONTEMPI IS WORKING ABOUT THE NEW MODEL OF MESSINA STRAIT BRIDGE, CHECKING THE STRESS STATE IN DECK. SUBSTRUCTURES ARE LOCATED NEAR THE TOWERS AND IN THE MIDDLE OF THE MAIN SPAN. IN ORDER TO VERIFY THE CORRECT MEASURING OF BRIDGE ELEMENTS, THE STRESS STATE IN EACH TWO CASES WILL BE EVALUATED. THANK YOU FOR YOUR ATTENTION

32. GENERAL CHARACTERISTICS OF MESSINA STRAIT BRIDGE SICILYCALABRY 960 m3300 m810 m 118.0 m 53.5 m70.04 m 0.0 m 18.0 m 53.5 m 394.0 m 376.0 m 18.0 m 118.0 m 394.0 m 376.0 m MESSINA STRAIT BRIDGE TOWERS