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Stay Tuned! Practical Cable Stayed Bridge · PDF fileMidas Training Series 3 Cable Stayed Bridge Design in midas Civil 1. Introduction Major Characteristics of Cable Stayed Bridge

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  • 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.

  • Midas

    Training

    Series

    4

    Cable Stayed Bridge Design in midas Civil

    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

  • Midas

    Training

    Series

    5

    Cable Stayed Bridge Design in midas Civil

    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 stays size.

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

    method.

    a b

  • Midas

    Training

    Series

    6

    Cable Stayed Bridge Design in midas Civil

    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

  • Midas

    Training

    Series

    7

    Cable Stayed Bridge Design in midas Civil

    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.

  • Midas

    Training

    Series

    8

    Cable Stayed Bridge Design in midas Civil

    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

  • Midas

    Training

    Series

    9

    Cable Stayed Bridge Design in midas Civil

    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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    Training

    Series

    10

    Cable Stayed Bridge Design in midas Civil

    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

  • Midas

    Training

    Series

    11

    Cable Stayed Bridge Design in midas Civil

    2. Modeling of Cable Stayed Bridge

    Truss Element

    Uniaxial tension-compression line elementUsed to model space trusses or diagonal bracesUndergoes 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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    Training

    Series

    12

    Cable Stayed Bridge Design in midas Civil

    2. Modeling of Cable Stayed Bridge

    Elastic Catenary Cable Element

    Capable of transmitting axial tension force onlyReflects 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)

  • Midas

    Training

    Series

    13

    Cable Stayed Bridge Design in midas Civil

    2. Modeling of Cable Stayed Bridge

    (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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    Training

    Series

    14

    Cable Stayed Bridge Design in midas Civil

    element length

    h

    Lh: horizontal projection length of the cable element

    3. Nonlinear Effect

    (1) Sag Effects of Long Cables

    h

  • Midas

    Training

    Series

    15

    Cable Stayed Bridge Design in midas Civil

    3. Nonlinear Effect

    (2) P-Delta Effect

  • Midas

    Training

    Series

    16

    Cable Stayed Bridge Design in midas Civil

    3. Nonlinear Effect

    (3) Large deformations

  • Midas

    Training

    Series

    21

    Cable Stayed Bridge Design in midas Civil

    Unknown Load Factor in midas Civil

    4. Initial Cable Forces

    This function optimizes tensions of cables atthe initial equilibrium position of a cablestructure. The p

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