Suspension Bridge Cable Stayed Bridge Suspension Bridge Wizard

§ Suspension Bridge § Cable Stayed Bridge

Suspension Bridge Wizard § Suspension Bridge ü Suspension Bridge Wizard ü Suspension Bridge Analysis Control ü Analysis Example ü Construction § Analysis Cable Stayed Bridge Suspension Bridge Wizard generates a 3 -dimensional suspension bridge including self-anchored. Initial geometry is found, and unstrained lengths and initial cable forces are calculated.

Suspension Bridge Wizard § Suspension Bridge B ü Suspension Bridge Wizard ü Suspension Bridge Analysis Control ü Analysis Example ü Construction § Analysis Cable Stayed Bridge A. Geometry B. Section & Material C. Deck System A D. Preview C Input node coordinates & hanger distances D

Suspension Bridge Wizard § Suspension Bridge B ü Suspension Bridge Wizard ü Suspension Bridge Analysis Control ü Analysis Example ü Construction § Analysis Cable Stayed Bridge A. Geometry B. Section & Material C. Deck System A D. Preview C Define sections and materials of each part of the bridge. D

Suspension Bridge Wizard § Suspension Bridge Deck Cross Section defined by SPC (Sectional Property Calculator) ü Suspension Bridge Wizard ü Suspension Bridge Analysis Control ü Analysis Example ü Construction § Analysis Cable Stayed Bridge Sectional Property Calculator(SPC)

Suspension Bridge Wizard § Suspension Bridge B ü Suspension Bridge Wizard ü Suspension Bridge Analysis Control ü Analysis Example ü Construction § Analysis Cable Stayed Bridge A. Geometry B. Section & Material C. Deck System A D. Preview C Input width, height and weight of deck. D

Suspension Bridge Wizard § Suspension Bridge B ü Suspension Bridge Wizard ü Suspension Bridge Analysis Control ü Analysis Example ü Construction § Analysis Cable Stayed Bridge A. Geometry B. Section & Material C. Deck System A D. Preview C Model preview is updated in real time as the geometry data is input. D

Suspension Bridge Wizard § Suspension Bridge ü Suspension Bridge Wizard ü Suspension Bridge Analysis Control Equilibrium in X-Z Plane ü Analysis Example ü Construction § Analysis Cable Stayed Bridge Generate the model with simplified deck and pylons. Equilibrium in Y-Z Plane Find cable coordinates and forces using the equilibrium condition and nonlinear analysis of cable

Suspension Bridge Analysis Control § Suspension Bridge ü Suspension Bridge Wizard ü Suspension Bridge Analysis Control ü Analysis Example ü Construction The model from the Wizard has been simplified based on the assumptions in the wizard. Therefore, the model has to be modified according to the actual design. After updating, the 2 nd analysis has to be performed to reflect the change of the system. § Analysis Cable Stayed Bridge The actual design model The simplified model from the wizard

Suspension Bridge Analysis Control § Suspension Bridge ü Suspension Bridge Wizard ü Suspension Bridge Analysis Control ü Analysis Example Select the node group, which is to be updated, and the sag points. ü Construction § Analysis Cable Stayed Bridge Suspension Bridge Analysis Control Dialog

Suspension Bridge Analysis Control § Suspension Bridge ü Suspension Bridge Wizard ü Suspension Bridge Analysis Control ü Analysis Example ü Construction § Analysis Cable Stayed Bridge Select the node group which is to be updated and in the sag point. Select the load case for which the cable forces will satisfy the equilibrium condition. Suspension Bridge Analysis Control Dialog

Suspension Bridge Analysis Control § Suspension Bridge ü Suspension Bridge Structural Data and Convergence Criteria Wizard ü Suspension Bridge Analysis Control Perform Geometric Nonlinear Analysis Calculate inequilibrium forces Calculate node coordinates and element forces ü Analysis Example ü Construction § Analysis Cable Stayed Bridge Check Convergence with displacement difference Update node coordinates Re-calculation of the unstrained lengths Calculate the element equilibrium forces Determine the node coordinates Determine the unstrained lengths Determine the element equilibrium forces Suspension Bridge Analysis Control Dialog In case of a self-anchored suspension bridge, deformations occur at the tops of the pylons and the ends of the deck due to the axial forces in the deck. The longitudinal deformation means the change in the boundary condition, and this change is reflected by introducing the initial element forces.

Analysis Examples § Suspension Bridge ü Suspension Bridge Example of Suspension Bridges Wizard ü Suspension Bridge Analysis Control ü Analysis Example ü Construction § Analysis Cable Stayed Bridge Youngjong Bridge 3 -Dimensional Self-Anchored

Analysis Examples § Suspension Bridge ü Suspension Bridge Example of Suspension Bridges Wizard ü Suspension Bridge Analysis Control ü Analysis Example ü Construction § Analysis Cable Stayed Bridge Kwangan Bridge

Analysis Examples § Suspension Bridge Example of Suspension Bridges ü Suspension Bridge Wizard ü Suspension Bridge Analysis Control ü Analysis Example ü Construction § Analysis Cable Stayed Bridge No Hangers in the Side Spans

Analysis Examples § Suspension Bridge Example of Suspension Bridges ü Suspension Bridge Wizard ü Suspension Bridge Analysis Control ü Analysis Example ü Construction § Analysis Cable Stayed Bridge Inclined Hangers

Backward Geometric Nonlinear Analysis § Suspension Bridge ü Suspension Bridge Wizard ü Suspension Bridge Analysis Control ü Analysis Example ü Construction § Analysis Cable Stayed Bridge Perform backward nonlinear analysis considering the element forces at the initial state as the element equilibrium forces.

§ Suspension Bridge § Cable Stayed Bridge

Initial Equilibrium State Analysis § Suspension Bridge § Cable Stayed Bridge ü Initial Equilibrium State Analysis ü Cable Pretensions Find the initial cable pretensions using ‘Unknown Load Factor’ in Construction Stages ü Forward Analysis using Initial State Pretensions Obtain optimized cable pretensions satisfying the constraints. ü The Calculation of the Closing Forces ü Analysis Example Unknown Load Factor In case the numbers of constraints and unknowns are the same, pretensions can be found by simultaneous equations, which are quick and simple.

Cable Pretensions in Construction Stages § Suspension Bridge Iteration § Cable Stayed Bridge ü Initial Equilibrium State Analysis ü Cable Pretensions in Construction Stages Set up constraints and unknowns Load Factors Found ü Forward Analysis using Initial State Pretensions ü The Calculation of the Closing Forces ü Analysis Example Cable pretensions in construction stages can be also obtained by Unknown Load Factor. Iterative analysis method enables us to find cable forces of the bridges in which time dependent effects are considered. Iteration Control

Forward Analysis using Initial State Pretensions Using pretensions from the initial state analysis, cable pretensions in § Suspension Bridge the construction stages (CS) can be found without the backward analysis. § Cable Stayed Bridge ü Initial Equilibrium State Analysis ü Cable Pretensions in Construction Stages ü Forward Analysis using Initial State Pretensions ü The Calculation of the Closing Forces ü Analysis Example Pretensions in the Initial State

Forward Analysis using Initial State Pretensions § Suspension Bridge § Cable Stayed Bridge ü Initial Equilibrium The additional pretensions are required in CS because of the difference in cable lengths between the initial state and the construction stages. Such additional force is called the ‘Lack of Fit Force’. State Analysis ü Cable Pretensions Construction Analysis Control in Construction Stages ü Forward Analysis using Initial State Pretensions Cable Length in initial State ü The Calculation of the Closing Forces ü Analysis Example Cable Pretension in Initial State Cable Length in Construction Stages Cable Pretension in CS State Lack of Fit Force

The Calculation of the Closing Forces § Suspension Bridge § Cable Stayed Bridge ü Initial Equilibrium The closing force calculation is required in order to keep the key-segment become continuous with decks at the joints. The closing force is calculated by applying the lack of fit force to the beam element (key segment). State Analysis ü Cable Pretensions in Construction Without closing force Stages ü Forward Analysis using Initial State Pretensions ü The Calculation of the Closing Forces ü Analysis Example The specified displacement is calculated so that the key segment can be continuous with the neighboring elements. The displacement is transformed into element forces and applied to the key segment With closing force

Forward Analysis Using the Lack of Fit Force § Suspension Bridge Using the ‘Lack of Fit Force’, the final result of the forward analysis can be obtained as the same as the result of the initial state. § Cable Stayed Bridge Initial State ü Initial Equilibrium State Analysis ü Cable Pretensions in Construction Stages The pretension forces from the initial state are applied to the construction stage model as well. ü Forward Analysis using Initial State Pretensions ü The Calculation of the Closing Forces ü Analysis Example Construction Stage

Analysis Example of a § Suspension Bridge Cable Stayed Bridge § Cable Stayed Bridge ü Initial Equilibrium State Analysis ü Cable Pretensions in Construction Stages ü Forward Analysis using Initial State Pretensions ü The Calculation of the Closing Forces ü Analysis Example Stonecutters Bridge