Stay Tuned! Practical Cable Stayed Bridge Designuk.midasuser.com/web/upload/sample/Midas_training_series_Cable... · Midas Training Series 3 Cable Stayed Bridge Design in midas Civil

Stay Tuned!Practical Cable Stayed Bridge Design

midas

Civil

Francesco Incelli

Midas

Training

Series

2017

midas

Civil

2015

Midas

Training

Series

I. Introduction

II. Modeling of the cable-stayed bridgea. Bridge wizardb. Girder Cross Section

III. Nonlinear Effecta. Sag effects of long cablesb. P-Delta effectsc. Large deformationsd. Material nonlinearity

IV. Initial Cable Forcesa. The Unknown Load Factor function

- Constraints- Influence matrix

b. Tuning of cables

2017

midas

Civil

Midas

Training

Series

3

Cable Stayed Bridge Design in midas Civil

1. Introduction

Major Characteristics of Cable Stayed Bridge

• The deck acts as a continuous beam with a

number of elastic supports with varying

stiffness.

• The deck and pylon are both in compression and

therefore bending moment in these elements

will be increased, due to second order effects.

Application of these moments will be non-linear.

The use of influence lines, which rely on the

principles of linear superposition, can only be

used as an approximate method of determining

the stay loads.

• Nonlinear material properties (Creep and

shrinkage) will also influence the design.

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1. Introduction

Determine Back span to main span

ratio

Determine Cable Spacing

Determine Deck Stiffness

Determine Pylon Height

Determine Preliminary Cable

Force

Deck Form

(Concrete / Composite / Hybrid)

Deck Design

Deck Erection

(Backward / Forward Stage

Analysis)

Static Analysis Dynamic Analysis

Lack of Fit ForceUnknown Load FactorCable Force Tuning

Design Process in Cable Stayed Bridge (Forward or Backward Construction Stage)

Unknown Load Factor

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Design Step 1. Back span to main span ratio

• The ratio between back span and the main span should be less than 0.5. It influences the

uplift forces at the anchor pier and the range of load within the back stay cables supporting

the top of the pylon.

• The optimum length: between 0.4 ~ 0.45 of the main span.

1. Introduction

Design Step 2. Cable spacing

• The spacing of the stay anchors along the deck should be compatible with the capacity of the

longitudinal girders and the limiting stay’s size.

• The spacing should also be small enough so that the deck may be erected using cantilevering

method.

a b

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Design Step 3. Deck stiffness

• The deflection of the longitudinal girders is primarily determined by the stay layout.

• Depth of girders should be kept to minimum, subject to sufficient area and stiffness being

provided to carry the large compressive forces without buckling.

1. Introduction

Design Step 4. Pylon height

• The height of the pylon will determine the overall stiffness of the structure. As the stay angle

increases, the required stay size will decrease as will the height of the pylon. However, the

deflection of the deck will increase as each stay becomes longer.

• The most efficient stay is that with a stay inclination of 45°. In practice the efficiency of the

stay is not significantly impaired when the stay inclination is varied within 25 ~ 65°.

• This implies an optimum ratio of pylon height above the deck (h) to main span (l) is between

0.2 and 0.25.

h

l

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Design Step 5. Preliminary stay forces

• The main span stay forces resist the dead loads such that there is no deflection of the deck or

pylon.

• An initial approximation of the main span stay forces can be determined by considering the

structure as a simple truss ignoring bending stiffness of both the pylon and the deck. Ignoring

bending stiffness of the pylon will be a valid assumption as the bending stiffness of the pylon

is usually small when compared to the axial stiffness of the stays.

• The back stay anchoring forces can be calculated assuming the horizontal component of the

main span and back span stay forces are balanced at the pylon.

1. Introduction

Design Step 6. Deck form

• The primary factors influencing the choice of deck will be the length of the main span and

deck width.

• Concrete deck section is the most economic for the span range 200-400m and the composite

deck above 400m.

• Above 600m a hybrid combination is economic with the back span as concrete and the main

span in an all steel construction.

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Design Step 7. Deck design

• It is possible to minimize the moments in the deck under the dead load by tuning the loads

in the stays to the small local moments arising from the span between stays.

• The balance between positive and negative live load moments at any section along the girder

will not be equal.

• In most cases the properties of the deck section will be more favorable when resisting positive

moments.

1. Introduction

Design Step 8. Deck erection

• The common method of deck erection is the cantilever method.

• The stay forces that are compatible with the final distribution of dead load moment and the

defined structure geometry are known. However the initial stay forces introduced at each

stage of the erection are not.

• Backward stage analysis: the completed structure is dismantled stage by stage.

• Forward stage analysis

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Design Step 9. Static analysis

1. Introduction

Design Step 10. Dynamic analysis

• The seismic analysis of the structure

• Response of the structure to turbulent wind

• Time history transient analysis of vibrations

• For the final analysis, the most common approach is to model either a half or the entire

structure as a space frame. The pylon, deck and the stays will usually be represented within

the space frame model by truss elements.

• The stays can be represented with a small inertia and a modified modulus of elasticity that will

mimic the sag behavior of the stay.

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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

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Truss Element

•Uniaxial tension-compression line element•Used to model space trusses or diagonal braces•Undergoes axial deformation only

Equivalent truss element

• Tension-only line element• Capable of transmitting axial tension force only• This will consider decreased axial stiffness of cable due to sagging effect.• Cable element is simulated as Equivalent truss element in linear analysis.

element length

h

Lh: horizontal projection length of the cable element

h

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Elastic Catenary Cable Element

•Capable of transmitting axial tension force only•Reflects the change in stiffness varying with internal tension forces (sagging effect) •Tangent stiffness of a cable element applied to a geometric nonlinear analysis (Large displacement effect)

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(2) Stiffened Girder using SPC

Import CAD dataor

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.

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element length

h

Lh: horizontal projection length of the cable element

3. Nonlinear Effect

(1) Sag Effects of Long Cables

h

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3. Nonlinear Effect

(2) P-Delta Effect

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3. Nonlinear Effect

(3) Large deformations

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Unknown Load Factor in midas Civil

4. Initial Cable Forces

This function optimizes tensions of cables atthe initial equilibrium position of a cablestructure. The program can calculate theinitial cable force by inputting the restrictionssuch as displacement, moment, etc. andsatisfying the constraints.

Copy & Paste

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Object Function type: Select the method of forming an object function consisted of unknown loadfactors.

✓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.

Simultaneous Equations MethodUsing linear algebraic equations, the equality conditions are solved. If the numbers of the unknownloads and equations are equal, the solution can be readily obtained from the matrix or the linearalgebra method.



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Inequality condition

T2

T1

Numerous solutions satisfying the inequality conditions

Object Function type

midas Civil finds a solution to Inequalityconditions, which uses variables thatminimizes the given object functions.

✓ Linear

✓ Square

✓ Max. Abs

Linear

Square

Max. Abs

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Influence Matrix

Moment/Displacement at the corresponding element/Node ID due to a unit load applied for each load case.

Ti δi

Value = Σ(Ti * δi)

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✓ Constraint Position: Vertical Deformation of Span Center NodeHorizontal Deformation of Pylon Top Node

✓ Once it is converged, try to increase Constraint condition.✓ Once it is converged, try to decrease Constraint range.



Tip to enter Constraint

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The unknown load factors obtained by using the Unknown Load Factor feature for the final stagemodel do not include the change in stiffness of the cable due to the change in pretension.Therefore the user must use truss element in Unknown Load Factor. In order to determine thepretension in the truss element to satisfy constraints, iteration will be required. The followingprocedure can be adopted:

1. Define the constraints and obtain the Unknown Load Factors for the Pretension Forces.2. Determine the Pretension Force by multiplying those factors with the assigned Pretension Loads3. Change the Pretension Forces with the new ones ( obtained in step 2)4. Perform the Analysis.5. Check whether the constraints are satisfied with modified pretensions6. If not then determine the Unknown load factors again and keep repeating steps 2 to 5 till you get

the constraints satisfied after static analysis ( step 5)



Note when using Cable elements

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Girder Bending Moment before Cable Force Tuning

Girder Bending Moment after Cable Force Tuning



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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.

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5. FAQ in Cable Stayed Bridge

(1) When Nonlinear Analysis is required?

In the cable stayed bridge or suspension bridge, engineers will determine the initial cable force in the complete state(final shape) without construction stage. After that, construction stage analysis will be performed. If this initial cable force is correctly found, the cable force will be above 70% of its yielding force and it will behave very similar to the truss element. Therefore in the most of the general cable-stayed bridge, the engineers can assume the cable to act like truss element and there is no need to consider large deformation analysis (=nonlinear geometric analysis).

However, if the bridge span is very large (ex. Larger than 600m) and shape is complex (like stonecutter bridge or sutong bridge), engineers will perform large deformation analysis.

There is no clear criteria when exactly the engineer need to perform nonlinear analysis. However, in the general case for cable bridge, it is not very common to perform nonlinear geometric analysis if they have correct value of initial cable force.

One way to determine it clear will be performing both analysis, linear and nonlinear. By comparing the results, if the difference in these two analysis are very large, nonlinear analysis will be needed.

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Stay Tuned! Practical Cable Stayed Bridge Designuk.midasuser.com/web/upload/sample/Midas_training_series_Cable... · Midas Training Series 3 Cable Stayed Bridge Design in midas Civil