Bridging Your Innovations to Realities

Transcription

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2 Contents: I. Introduction II. Modeling of the cable-stayed bridge a. Bridge wizard b. Stiffening girder III. Initial Cable Forces a. The Unknown Load Factor function - Constraints - Influence matrix IV. Construction Stage Analysis a. Backward and forward analysis b. Initial cable forces at the time of installation - The Unknown Load Factor function -The Lack-of-Fit function c. Creep and shrinkage d. Temperature e. Camber control f. Tuning of cables g. Temporary support & temporary cable h. Cable tensioning in multiple steps i. Prestressed concrete j. Composite steel girder V. Nonlinear Effect a. Sag effects of long cables b. P-Delta effects c. Large deformations d. Material nonlinearity VI. Dynamic Analysis a. Modal analysis b. Seismic analysis c. Multiple support excitation VII. Post-Processing a. Max / Min stress check during erection b. Cable configuration c. Cable efficiency 2

3 1. Introduction Process of calculating initial prestressed force Modeling Apply self weight and unit load for prestressed force Find the initial prestressed force using Unknown Load Factor Tuning cable forces using Cable Force Tuning Determine initial prestressed force in cables

4 1. Introduction Process of calculating optimal cable pretension (Forward or Backward Construction Stage) Find Initial Cable Pretension Force Construction Stage Analysis Verify Member Force & Adjust Pretension Generate camber for tower and PC girder Verify final displacement and camber Construction Stage Analysis with Camber Determine Cable Pretension for all the stages Verify cable tension & Member Force at each stage Lack of Fit Force Unknown Load Factor Cable Force Tuning

5 2. Modeling of (1) Bridge Wizard Modeling symmetric or Asymmetric bridge truss & Cable element Box sloped girders Vertical station of Girder Wizard

6 2. Modeling of (2) Stiffened Girder using SPC The Import function permits the use of AutoCAD DXF Import files. CAD data Simple data entry using various modeling functions or The section property calculations are provided for Define the sections input section in SPC configuration by generating fully automated optimum meshes. The properties of hybrid sections composed of different material properties can be calculated. Define Section Shape in CAD Import SPC Section using Value Type of PSC Section Composite Section imported from SPC

7 3. Initial Cable Forces (1) Traditional "Zero Displacement" Method a. Fix the vertical & horizontal displacement of tower. b. Apply prestress force to have 0 vertical displacement at the center of the mid-span. c. Release the horizontal displacement of tower and adjust the prestress force to have 0 horizontal displacement at the tower and vertical displacement at the girder (span center).

8 3. Initial Cable Forces (2) Force Equilibrium Method a. Assume that all the cable support and tower connection as fixed supports. b. Compose cable influence matrix. c. In this case, nonlinearity due to cable sag effect is ignored and prestress of each end is assumed as identical. d. Assume that bending moments of girders are affected by cables connected to the girders only. And bending moments of tower is affected by cables connected to the tower only.

9 3. Initial Cable Forces (3) Force Method a. In order to solve the indeterminate structure, Assume the internal forces and convert it as determinate structure. b. Calculate the desired member force. Advantage Using the member forces due to live loads, member forces due to dead loads can be obtained. Member force can be determined considering the material properties.

10 3. Initial Cable Forces (4) Unknown Load Factor in midas Civil This function optimizes tensions of cables at the initial equilibrium position of a cable structure. The program can calculate the initial cable force by inputting the restrictions such as displacement, moment, etc. and satisfying the constraints.

11 3. Initial Cable Forces (4) Unknown Load Factor in midas Civil Object Function type: Select the method of forming an object function consisted of unknown load factors. Linear: The sum of the absolute values of Load factor x scale factor Square: The linear sum of the squares of Load factor x scale factor Max Abs: The maximum of the absolute values of Load factor x scale factor Sign of Unknowns: Assign the sign of the unknown load factors to be calculated. Negative: Limit the range of the calculated values to the negative (-) field. Both: Do not limit the range of the calculated values. Positive: Limit the range of the calculated values to the positive (+) field.

12 3. Initial Cable Forces (4) Unknown Load Factor in midas Civil Girder Bending Moment before Cable Force Tuning Girder Bending Moment after Cable Force Tuning

13 3. Initial Cable Forces (5) Tuning of Cables Reduce the repetitive computation process to obtain the optimum cable pretension. Calculates the effects of the cable pretension (or load factor) on the displacements/ member forces/ stresses through influence matrix and updates the results graph in real time. The process of Cable Force Tuning 1. Adjust the cable pretension (or load factor) using the table or bar graph. 2. Select the result item for which the effects of the cable pretension are to be checked. 3. Produce the results graph for the result item selected from step 2. If the pretension (or load factor) is adjusted in step 1, it is reflected in the results graph in real time. 4. Save the adjusted pretension forces in a load combination or apply the new pretension forces to the cables directly using the pre-programmed buttons.

14 4. Construction Stage Analysis (1) Backward and Forward Analysis Backward Construction Stage Analysis Forward Construction Stage Analysis

15 4. Construction Stage Analysis (2) Initial cable forces at the time of installation Lack-of-Fit Force table

16 4. Construction Stage Analysis (2) Initial cable forces at the time of installation Lack-of-Fit Force table Lack of Fit Force in Truss Lack of Fit Force in Beam

17 4. Construction Stage Analysis (3) Unknown Load Factor Update Cable Pretension

18 4. Construction Stage Analysis (4) Consideration in Construction Stage Components PC Girder Steel Girder Creep & Shrinkage V No Need Temperature Gradient V V Camber Control Temporary Support & Temporary Cable Cable Tensioning in Multiple Steps V (Construction Camber) V No Need V (Construction Camber & Manufacture Camber) V V

19 5. Nonlinear Effect (1) Sag Effects of Long Cables

20 5. Nonlinear Effect (2) P-Delta Effect

21 5. Nonlinear Effect (3) Large deformations

22 5. Nonlinear Effect (4) Material Nonlinearity Inelastic Time History Analysis of Extradosed Bridge Ground Acceleration Inelastic Hinge [Status of Yielding] [Ductility Factor] Hysteresis Curve (Rz-Mz)

23 6. Dynamic Analysis (1) Initial Stiffness in Cable Elements Initial Element Forces are used to calculate geometric stiffness in general linear analysis. This function includes geometric stiffness in linear stiffness. It is applied to linear static, linear buckling, eigenvalue, response spectrum and time history analyses.

24 6. Dynamic Analysis (1) Modal Analysis Type of Analysis Eigen Vectors Subspace Iteration Lanczos Ritz Vectors

25 6. Dynamic Analysis (2) Seismic Analysis Response Spectrum Analysis Inelastic Time History Analysis Boundary Nonlinear Analysis Pushover Analysis

26 6. Dynamic Analysis (3) Multiple Support Excitation Arrival time, : t = 2 seconds Arrival time : t = 0 sec Ground Acceleration

27 7. Post-processing (1) Max/Min Stress Check during Erection Min/Max Final Stage

28 7. Post-processing (2) Cable configuration

29 7. Post-processing (2) Cable Efficiency

30 Thank You!