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Suspension Bridge Suspension Bridge
Cable Stayed Bridge Cable Stayed Bridge
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Cable Stayed Bridge Cable Stayed Bridge
Suspension Bridge Suspension Bridge
Suspension Bridge Wizard
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
Analysis
Control Analysis
Example Construction
Analysis
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Cable Stayed Bridge Cable Stayed Bridge
Suspension Bridge Suspension Bridge
Suspension Bridge Wizard
A
A. Geometry
B. Section & Material
C. Deck System
D. Preview
B
C
D
Input node coordinates & hanger distances
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Cable Stayed Bridge Cable Stayed Bridge
Suspension Bridge Suspension Bridge
Suspension Bridge Wizard
A
A. Geometry
B. Section & Material
C. Deck System
D. Preview
B
C
D
Define sections and materials of each part of the bridge.
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Cable Stayed Bridge Cable Stayed Bridge
Suspension Bridge Suspension Bridge
Suspension Bridge WizardDeck Cross Section defined by SPC (Sectional Property Calculator)
Sectional Property Calculator(SPC)
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Cable Stayed Bridge Cable Stayed Bridge
Suspension Bridge Suspension Bridge
Suspension Bridge Wizard
A
A. Geometry
B. Section & Material
C. Deck System
D. Preview
B
C
D
Input width, height and weight of deck.
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Cable Stayed Bridge Cable Stayed Bridge
Suspension Bridge Suspension Bridge
Suspension Bridge Wizard
A
A. Geometry
B. Section & Material
C. Deck System
D. Preview
B
C
D
Model preview is updated in real time as the geometry data is input.
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Cable Stayed Bridge Cable Stayed Bridge
Suspension Bridge Suspension Bridge
Suspension Bridge Wizard
Equilibrium in X-Z Plane
Equilibrium in Y-Z Plane
Find cable coordinates and forces using the equilibrium condition and nonlinear analysis of cable
Generate the model with simplified deck and pylons.
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Cable Stayed Bridge Cable Stayed Bridge
Suspension Bridge Suspension Bridge
Suspension Bridge Analysis ControlThe 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 2nd analysis has to be performed to reflect the change of the system.
The simplified model from the wizardThe actual design
model
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Cable Stayed Bridge Cable Stayed Bridge
Suspension Bridge Suspension Bridge
Suspension Bridge Analysis Control
Select the node group, which is to be updated, and the sag points.
Suspension Bridge Analysis Control Dialog
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Cable Stayed Bridge Cable Stayed Bridge
Suspension Bridge Suspension Bridge
Suspension Bridge Analysis Control
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
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Cable Stayed Bridge Cable Stayed Bridge
Suspension Bridge Suspension Bridge
Suspension Bridge Analysis Control
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.
Suspension Bridge Analysis Control Dialog
Structural Data and Convergence Criteria
Perform Geometric Nonlinear AnalysisCalculate inequilibrium forcesCalculate node coordinates
and element forces
Check Convergencewith displacement difference
Update node coordinatesRe-calculation of the unstrained lengths
Calculate the element equilibrium forces
Determine the node coordinatesDetermine the unstrained lengths
Determine the element equilibrium forces
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Cable Stayed Bridge Cable Stayed Bridge
Suspension Bridge Suspension Bridge
Analysis Examples
Example of Suspension Bridges
Youngjong Bridge
3-Dimensional Self-Anchored
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Cable Stayed Bridge Cable Stayed Bridge
Suspension Bridge Suspension Bridge
Analysis Examples
Kwangan Bridge
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Example of Suspension Bridges
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Cable Stayed Bridge Cable Stayed Bridge
Suspension Bridge Suspension Bridge
Analysis Examples
Example of Suspension Bridges
No Hangers in the Side Spans
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Cable Stayed Bridge Cable Stayed Bridge
Suspension Bridge Suspension Bridge
Analysis Examples
Example of Suspension Bridges
Inclined Hangers
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Cable Stayed Bridge Cable Stayed Bridge
Suspension Bridge Suspension Bridge
Backward Geometric Nonlinear Analysis
Perform backward nonlinear analysis considering the element forces at the initial state as the element equilibrium forces.
Suspension
Bridge
Wizard Suspension
Bridge
Analysis
Control Analysis
Example Construction
Analysis
Suspension Bridge Suspension Bridge
Cable Stayed Bridge Cable Stayed Bridge
Suspension Bridge Suspension Bridge
Initial
Equilibrium
State
Analysis Cable
Pretensions in
Construction
Stages Forward
Analysis
using Initial
State
Pretensions The Calculation
of
the Closing
Forces Analysis
Example
Cable Stayed Bridge Cable Stayed Bridge
Initial Equilibrium State Analysis
Unknown Load Factor
Obtain optimized cable pretensions satisfying the constraints.
In case the numbers of constraints and unknowns are the same, pretensions can be found by simultaneous equations, which are quick and simple.
Find the initial cable pretensions using ‘Unknown Load Factor’
Initial
Equilibrium
State
Analysis Cable
Pretensions in
Construction
Stages Forward
Analysis
using Initial
State
Pretensions The Calculation
of
the Closing
Forces Analysis
Example
Suspension Bridge Suspension Bridge
Initial
Equilibrium
State
Analysis Cable
Pretensions in
Construction
Stages Forward
Analysis
using Initial
State
Pretensions The Calculation
of
the Closing
Forces Analysis
Example
Cable Stayed Bridge Cable Stayed Bridge
Cable Pretensions in Construction Stages
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
Load Factors Found
Set up constraints and
unknowns
Iteration Control
Initial
Equilibrium
State
Analysis Cable
Pretensions in
Construction
Stages Forward
Analysis
using Initial
State
Pretensions The Calculation
of
the Closing
Forces Analysis
Example
Suspension Bridge Suspension Bridge
Initial
Equilibrium
State
Analysis Cable
Pretensions in
Construction
Stages Forward
Analysis
using Initial
State
Pretensions The Calculation
of
the Closing
Forces Analysis
Example
Cable Stayed Bridge Cable Stayed Bridge
Using pretensions from the initial state analysis, cable pretensions in the construction stages (CS) can be found without the backward analysis.
Forward Analysis using Initial State Pretensions
Pretensions in the Initial State
Initial
Equilibrium
State
Analysis Cable
Pretensions in
Construction
Stages Forward
Analysis
using Initial
State
Pretensions The Calculation
of
the Closing
Forces Analysis
Example
Suspension Bridge Suspension Bridge
Initial
Equilibrium
State
Analysis Cable
Pretensions in
Construction
Stages Forward
Analysis
using Initial
State
Pretensions The Calculation
of
the Closing
Forces Analysis
Example
Cable Stayed Bridge Cable Stayed Bridge
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’.
Forward Analysis using Initial State Pretensions
vb
ub
L
L’
ΔL
(ub = uj - ui)
(vb = vj - vi)
L' - L L = Vb UbCos Sin
EAΔT = ΔL
L f iT = T + T
L
L’
(Ui, Vi)
(Uj, Vj)
Cable Length in initial State
Cable Length in Construction Stages
Construction Analysis Control
Cable Pretension in
CS State
Cable Pretension in Initial State
Lack of Fit Force
Initial
Equilibrium
State
Analysis Cable
Pretensions in
Construction
Stages Forward
Analysis
using Initial
State
Pretensions The Calculation
of
the Closing
Forces Analysis
Example
Suspension Bridge Suspension Bridge
Initial
Equilibrium
State
Analysis Cable
Pretensions in
Construction
Stages Forward
Analysis
using Initial
State
Pretensions The Calculation
of
the Closing
Forces Analysis
Example
Cable Stayed Bridge Cable Stayed Bridge
Reference Level
Key SegmentΘ Θ
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).
The Calculation of the Closing Forces
Key Segment Without closing force
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
Initial
Equilibrium
State
Analysis Cable
Pretensions in
Construction
Stages Forward
Analysis
using Initial
State
Pretensions The Calculation
of
the Closing
Forces Analysis
Example
Suspension Bridge Suspension Bridge
Initial
Equilibrium
State
Analysis Cable
Pretensions in
Construction
Stages Forward
Analysis
using Initial
State
Pretensions The Calculation
of
the Closing
Forces Analysis
Example
Cable Stayed Bridge Cable Stayed 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.
Forward Analysis Using the Lack of Fit Force
Initial State
Construction
Stage
The pretension forces from the initial state are applied to the construction stage
model as well.
Initial
Equilibrium
State
Analysis Cable
Pretensions in
Construction
Stages Forward
Analysis
using Initial
State
Pretensions The Calculation
of
the Closing
Forces Analysis
Example
Suspension Bridge Suspension Bridge
Initial
Equilibrium
State
Analysis Cable
Pretensions in
Construction
Stages Forward
Analysis
using Initial
State
Pretensions The Calculation
of
the Closing
Forces Analysis
Example
Cable Stayed Bridge Cable Stayed Bridge
Analysis Example
Example of a
Cable Stayed Bridge
Initial
Equilibrium
State
Analysis Cable
Pretensions in
Construction
Stages Forward
Analysis
using Initial
State
Pretensions The Calculation
of
the Closing
Forces Analysis
Example
Stonecutters Bridge
