Bridging Your Innovations to Realities

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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

Contents: 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


1. Introduction

midas Civil Cable Stayed Bridge

Process of calculating initial prestressed force

Modeling Cable Stayed Bridge

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


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

Construction Stage Analysis with Camber

Verify cable tension &

Member Force at each stage

Verify final displacement and

camber

Determine Cable Pretension for all

the stages

Lack of Fit Force

Unknown Load Factor

Cable Force Tuning


2. Modeling of Cable Stayed Bridge

(1) Bridge Wizard


Modeling symmetric or Asymmetric bridge

truss & Cable element

Box sloped girders Vertical station of

Girder

Cable Stayed Bridge Wizard


2. Modeling of Cable Stayed Bridge

(2) Stiffened Girder using SPC


Import CAD data

or

Define sections in SPC

Define Section

Shape in CAD

Import SPC Section

using Value Type of PSC

Section

Composite Section imported from SPC

The Import function permits the use of AutoCAD DXF files. Simple data entry using various modeling functions The section property calculations are provided for the input section configuration by generating fully

automated optimum meshes. The properties of hybrid sections composed of different material properties can be calculated.


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).




(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.


(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.




(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.


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.





Girder Bending Moment before Cable Force Tuning

Girder Bending Moment after Cable Force Tuning







(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.


4. Construction Stage Analysis


(1) Backward and Forward Analysis

Backward Construction Stage Analysis Forward 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



(2) Initial cable forces at the time of installation

Lack-of-Fit Force table




(3) Unknown Load Factor

Update Cable Pretension




(4) Consideration in Construction Stage

Components PC Girder Steel Girder

Creep & Shrinkage V No Need

Temperature Gradient V V

Camber Control V

(Construction Camber)

V (Construction Camber & Manufacture Camber)

Temporary Support & Temporary Cable

V V

Cable Tensioning in Multiple Steps

No Need V


5. Nonlinear Effect


(1) Sag Effects of Long Cables


5. Nonlinear Effect


(2) P-Delta Effect


5. Nonlinear Effect


(3) Large deformations


5. Nonlinear Effect


(4) Material Nonlinearity

Hysteresis Curve (Rz-Mz) [Ductility Factor] [Status of Yielding]

Inelastic Hinge

Ground Acceleration

Inelastic Time History Analysis of Extradosed Bridge


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.

6. Dynamic Analysis

(1) Initial Stiffness in Cable Elements



6. Dynamic Analysis


(1) Modal Analysis

Type of Analysis

Eigen Vectors

Subspace Iteration

Lanczos

Ritz Vectors


6. Dynamic Analysis


(2) Seismic Analysis

Pushover Analysis Boundary Nonlinear Analysis

Inelastic Time History Analysis Response Spectrum Analysis


6. Dynamic Analysis


Arrival time : t = 0 sec

Arrival time, : t = 2 seconds

Ground Acceleration

(3) Multiple Support Excitation


7. Post-processing


(1) Max/Min Stress Check during Erection

Min/Max

Final Stage


7. Post-processing


(2) Cable configuration


7. Post-processing


(2) Cable Efficiency


Thank You! Thank You!

Bridging Your Innovations to Realities -...

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