midas Civil Cable Stayed Bridge Bridging Your Innovations to Realities

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2 Contents: Introduction Problem Statement Preliminary Design Determination of Cable Force Optimization of Deck Construction Stage Modeling Cable Tension Forces in Construction Stages Time Dependent Material Effect Non Linear Effect Dynamic Analysis Post Processsing Wind Load Analysis 2

3 1. Introduction Wheel Load Flexure In Deck Cable Supports Tension In cables Axial Load in Pylon

4 Project Applications Stiffness of the cable is dependent on : 1. Load Applied 2. Tension Applied P1 P1 P2 P2 midas Civil

5 Project Applications Cable Stiffness can be determined as per the following two techniques: 1. Equivalent Truss Method 2.. Elastic Catenary Cable midas Civil

6 Project Applications Cable Bridges are highly indeterminate structures: midas Civil

7 Project Applications Change of Cable Stiffness with Pretension High Indeterminacy Difficult Analysis midas Civil

8 Project Applications Cable Shape and pretension are in turn dependent on the load applied on the cable.: Geometric Non Linear Analysis midas Civil

9 2. Problem Statement Problem Statement: 100 m 200 m 100 m

10 2. Design Process Steps of Design : Preliminary Design Determination of Cable Forces for Fully Constructed Model Check for Resisting Moments of Deck and Pylon Section Change the Deck and Pylon Sections Construction Stage Analysis Non Linear Analysis Dynamic Analysis Check for Final Design

11 3. Preliminary Design Preliminary Design 1. Deck, Pylon Cross section. 2. Diameter of Cables. 3. Height of Pylons

12 4. Determination of Cable Tension Determination of Cable Forces 1. Use the unknown Load factor. What is Unknown Load Factor? Ans: It is a feature with which you can calculate the cable pretension force that would satisfy certain constraints in terms of displacements, bending moments etc.

13 4. Determination of Cable Tension

14 5. Optimization Check the Design forces for the deck, pylon and cables and modify.

15 6. Forward Construction Stage Analysis Modeling of Structure Defining Structure Groups Defining Loads under Load Group Defining Boundary under Boundary Groups Generation of Construction Stages Defining Construction Stage Data Construction Stage Analysis Control

16 6. Forward Construction Stage Analysis Implication with Forward Construction Stage Analysis Stage 10 S New Tendons Stage 11 More Pretension is required

17 6. Forward Construction Stage Analysis Lack of Fit Force: It calculates the additional pretension required for cable installation

18 7. Unknown Load Factor With Time Dependent Materials Construction Stage The material Properties changes with time and the cable pretension force depends on the creep. The unknown load factor can take that into consider and the program can perform iterations to find the pretension in the cable which will include the time dependent effect. Unit Pretension loading Unknown Load Factor Set constraints and calculate unknown load factor by step Construction Stage Using influence coefficient to reanalyze construction stage Check End [Iterative analysis procedure to calculate unknown load factor]

19 8. Eigen Value Analysis Analysis -> Eigen Value Analysis Control Ritz Vectors Unlike the natural eigenvalue modes, load dependent Ritz vectors produce more reliable results in dynamic analyses with relatively fewer modes. The Ritz Vectors are generated reflecting the spatial distribution or the characteristics of the dynamic loading.

20 9. Eigen Value Analysis To convert the final stage Cable forces to be used for determining cable stiffness for the Eigen Value Analysis

21 9. Eigen Value Analysis Step 2: Eigen Value Analysis Results A) Natural modes (or mode shapes) B) Natural periods (or frequencies) C) Modal participation factors. D) Effective modal mass. Eigenvalue analyses must precede dynamic analyses such as Modal Time History analysis or Response spectrum analysis. The response spectrum analysis uses the natural periods from the eigenvalue analysis.

22 10. Time History Analysis

23 10. Time History Analysis Linear Case Non Linear Case R(x,xa) : Viscous Damping Fs(x): Variable Stiffness

24 10. Time History Analysis Procedure of Eigenvalue Analysis: Define Properties of Non linear Links Input Non Linear Links Define Time History Load Case Time Forcing Function Ground Acceleration Perform Non Linear Time History Analysis Check the Results

25 10. Time History Analysis Step 1: Defining Properties of Non Linear Links Model -> Boundaries -> General Link Properties

26 10. Time History Analysis Base Isolators Provided in midas Civil Base Isolators: Lead Rubber Bearing Isolator Friction Pendulum System Isolator Viscoelastic Damper Gap Hook Hysteresis System Base Rubber isolator Friction Pendulum System isolator

27 10. Time History Analysis Step 2: Define Time History Load Case Load -> Time History Analysis Data -> Time History Load Case Transient: Time history analysis is carried out on the basis of loading a time load function only once. This is a common type for time history analysis of earthquake loads. Periodic: Time history analysis on the basis of repeatedly loading a time load function, which has a period identical to End Time. This type is applicable for machine vibration loads.

28 10. Time History Analysis Step 2: Define Time History Load Case Load -> Time History Analysis Data -> Time History Load Case Order in Sequential Loading: Select a time history analysis condition previously defined, which precedes the time history analysis condition currently being defined. The Analysis Type and Analysis Method for the current time history analysis condition must be consistent with those for the preceding load condition

29 10. Time History Analysis Damping Method: the damping method can be one of : 1. Modal 2. Element Mass & Stiffness Proportional 3. Strain Energy Proportional For Element Mass & Stiffness Proportional the relevant has to be provided in : Model -> Properties -> Group Damping: Element Mass and Stiffness Proportional

30 10. Time History Analysis Load -> Time History Analysis Data -> Time Forcing Function The user can select the time history function from the list of various database earthquake or can generate its own:

31 10. Time History Analysis Load -> Time History Analysis Data -> Ground Acceleration Select the Earthquake for X,Y and Z direction Rotational angle about GCS Z-axis signifying the direction of the horizontal component of the ground acceleration. Sign convention is (+) in the counter-clockwise direction and (-) in the clockwise direction, with reference to the X-axis.

32 10. Time History Analysis Load -> Time History Analysis Data -> Dynamic Nodal Loads The user can do the time history analysis with Moving loads using this feature. The user needs to define the moving loads as Dynamic Nodal Loads.

33 10. Time History Analysis Load -> Time History Analysis Data -> Multiple Support Excitation In a structure with multiple supports, different time history forcing functions in terms of ground acceleration can be applied to different supports at varying times.

34 Thanks