Ductility assessment of structural steel and composite joints€¦ · 2/9 M Rpl M Ru S t Φ u M-S...

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Transcript of Ductility assessment of structural steel and composite joints€¦ · 2/9 M Rpl M Ru S t Φ u M-S...

  • Ductility assessment of structural

    steel and composite joints

    Jean-Pierre Jaspart

    Adrien Corman

    Jean-François Demonceau

    11-13 September 2019, Prague, Czech Republic

    The International Colloquium on Stability and Ductility of Steel Structures

  • Introduction: joint behaviour

    1/9

    M

    z

  • Introduction: joint behaviour

    1/9

    MRpl

    MRuSj,st

    Φu

    M

    Φ

    Sj,iniM

    z

  • Introduction: joint behaviour

    1/9

    MRpl

    MRuSj,st

    Φu

    M

    Φ

    Sj,iniM

    z

    4 key parameters

    • Initial stiffness 𝐒𝐣,𝐢𝐧𝐢 =𝐄𝐳𝟐

    𝐢𝟏/𝐤𝐢

    𝐌𝐑𝐩𝐥 = 𝐦𝐢𝐧 𝐌𝐑𝐩𝐥,𝐢

    𝐒𝐣,𝐬𝐭 =𝐄𝐳𝟐

    𝐢𝟏/𝐤∗

    𝐌𝐑𝐮 = 𝐦𝐢𝐧 𝐌𝐑𝐮,𝐢

  • Introduction: joint behaviour

    1/9

    MRpl

    MRuSj,st

    Φu

    M

    Φ

    Sj,iniM

    z

    4 key parameters

    • Initial stiffness 𝐒𝐣,𝐢𝐧𝐢 =𝐄𝐳𝟐

    𝐢𝟏/𝐤𝐢

    • Plastic bending resistance 𝐌𝐑𝐩𝐥 = 𝐦𝐢𝐧 𝐌𝐑𝐩𝐥,𝐢

    𝐒𝐣,𝐬𝐭 =𝐄𝐳𝟐

    𝐢𝟏/𝐤∗

    𝐌𝐑𝐮 = 𝐦𝐢𝐧 𝐌𝐑𝐮,𝐢

  • Introduction: joint behaviour

    1/9

    MRpl

    MRuSj,st

    Φu

    M

    Φ

    Sj,iniM

    z

    4 key parameters

    • Initial stiffness 𝐒𝐣,𝐢𝐧𝐢 =𝐄𝐳𝟐

    𝐢𝟏/𝐤𝐢

    • Plastic bending resistance 𝐌𝐑𝐩𝐥 = 𝐦𝐢𝐧 𝐌𝐑𝐩𝐥,𝐢

    • Post-plastic stiffness 𝐒𝐣,𝐬𝐭 =𝐄𝐳𝟐

    𝐢𝟏/𝐤∗

    𝐌𝐑𝐮 = 𝐦𝐢𝐧 𝐌𝐑𝐮,𝐢

  • Introduction: joint behaviour

    1/9

    MRpl

    MRuSj,st

    Φu

    M

    Φ

    Sj,iniM

    z

    4 key parameters

    • Initial stiffness 𝐒𝐣,𝐢𝐧𝐢 =𝐄𝐳𝟐

    𝐢𝟏/𝐤𝐢

    • Plastic bending resistance 𝐌𝐑𝐩𝐥 = 𝐦𝐢𝐧 𝐌𝐑𝐩𝐥,𝐢

    • Post-plastic stiffness 𝐒𝐣,𝐬𝐭 =𝐄𝐳𝟐

    𝐢𝟏/𝐤∗

    • Ultimate bending resistance 𝐌𝐑𝐮 = 𝐦𝐢𝐧 𝐌𝐑𝐮,𝐢

  • Introduction: the component method

    2/9

    MRpl

    MRuSj,st

    Φu

    M

    Φ

    Sj,iniM

    z

    4 key parameters

    • Initial stiffness 𝐒𝐣,𝐢𝐧𝐢 =𝐄𝐳𝟐

    𝐢𝟏/𝐤𝐢

    • Plastic bending resistance 𝐌𝐑𝐩𝐥 = 𝐦𝐢𝐧 𝐌𝐑𝐩𝐥,𝐢

    • Post-plastic stiffness 𝐒𝐣,𝐬𝐭 =𝐄𝐳𝟐

    𝐢𝟏/𝐤∗

    • Ultimate bending resistance 𝐌𝐑𝐮 = 𝐦𝐢𝐧 𝐌𝐑𝐮,𝐢

  • Introduction: the component method

    2/9

    MRpl

    MRuSj,st

    Φu

    M

    Φ

    Sj,iniM

    z

    Tension zone

    Compr. zone

    Shear zone

    1. Identification

    4 key parameters

    • Initial stiffness 𝐒𝐣,𝐢𝐧𝐢 =𝐄𝐳𝟐

    𝐢𝟏/𝐤𝐢

    • Plastic bending resistance 𝐌𝐑𝐩𝐥 = 𝐦𝐢𝐧 𝐌𝐑𝐩𝐥,𝐢

    • Post-plastic stiffness 𝐒𝐣,𝐬𝐭 =𝐄𝐳𝟐

    𝐢𝟏/𝐤∗

    • Ultimate bending resistance 𝐌𝐑𝐮 = 𝐦𝐢𝐧 𝐌𝐑𝐮,𝐢

  • Introduction: the component method

    2/9

    MRpl

    MRuSj,st

    Φu

    M

    Φ

    Sj,iniM

    z

    Tension zone: ki, FRpl,i

    Compr. zone: ki, FRpl,i

    Shear zone: ki, FRpl,i

    2. Characterization

    4 key parameters

    • Initial stiffness 𝐒𝐣,𝐢𝐧𝐢 =𝐄𝐳𝟐

    𝐢𝟏/𝐤𝐢

    • Plastic bending resistance 𝐌𝐑𝐩𝐥 = 𝐦𝐢𝐧 𝐌𝐑𝐩𝐥,𝐢

    • Post-plastic stiffness 𝐒𝐣,𝐬𝐭 =𝐄𝐳𝟐

    𝐢𝟏/𝐤∗

    • Ultimate bending resistance 𝐌𝐑𝐮 = 𝐦𝐢𝐧 𝐌𝐑𝐮,𝐢

  • Introduction: the component method

    2/9

    M

    z

    Tension zone: ki, FRpl,i

    Compr. zone: ki, FRpl,i

    Shear zone: ki, FRpl,i

    Sj,ini

    MRpl

    MRuSj,st

    ΦuΦpl

    M

    Φ

    MRelSj,ini/7

    Φel

    3. Assembly

    4 key parameters

    • Initial stiffness 𝐒𝐣,𝐢𝐧𝐢 =𝐄𝐳𝟐

    𝐢𝟏/𝐤𝐢

    • Plastic bending resistance 𝐌𝐑𝐩𝐥 = 𝐦𝐢𝐧 𝐌𝐑𝐩𝐥,𝐢

    • Post-plastic stiffness 𝐒𝐣,𝐬𝐭 =𝐄𝐳𝟐

    𝐢𝟏/𝐤∗

    • Ultimate bending resistance 𝐌𝐑𝐮 = 𝐦𝐢𝐧 𝐌𝐑𝐮,𝐢

  • Introduction: the component method

    2/9

    M

    z

    Tension zone: ki, FRpl,i

    Compr. zone: ki, FRpl,i

    Shear zone: ki, FRpl,i

    Sj,ini

    MRpl

    MRuSj,st

    ΦuΦpl

    M

    Φ

    MRelSj,ini/7

    Φel

    3. Assembly

    4 key parameters

    • Initial stiffness 𝐒𝐣,𝐢𝐧𝐢 =𝐄𝐳𝟐

    𝐢𝟏/𝐤𝐢

    • Plastic bending resistance 𝐌𝐑𝐩𝐥 = 𝐦𝐢𝐧 𝐅𝐑𝐩𝐥,𝐢 . 𝐳

    • Post-plastic stiffness 𝐒𝐣,𝐬𝐭 =𝐄𝐳𝟐

    𝐢𝟏/𝐤∗

    • Ultimate bending resistance 𝐌𝐑𝐮 = 𝐦𝐢𝐧 𝐌𝐑𝐮,𝐢

  • Introduction: the component method

    2/9

    M

    z

    Tension zone: ki, FRpl,i

    Compr. zone: ki, FRpl,i

    Shear zone: ki, FRpl,i

    Sj,ini

    MRpl

    MRuSj,st

    ΦuΦpl

    M

    Φ

    MRelSj,ini/7

    Φel

    3. Assembly

    4 key parameters

    • Initial stiffness 𝐒𝐣,𝐢𝐧𝐢 =𝐄𝐳𝟐

    𝐢𝟏/𝐤𝐢

    • Plastic bending resistance 𝐌𝐑𝐩𝐥 = 𝐦𝐢𝐧 𝐅𝐑𝐩𝐥,𝐢 . 𝐳

    • Post-plastic stiffness 𝐒𝐣,𝐬𝐭 =𝐄𝐳𝟐

    𝐢𝟏/𝐤∗

    • Ultimate bending resistance 𝐌𝐑𝐮 = 𝐦𝐢𝐧 𝐌𝐑𝐮,𝐢

  • Problem: ductility assessment

    3/9

    M

    z

    Tension zone: ki, FRpl,i

    Compr. zone: ki, FRpl,i

    Shear zone: ki, FRpl,i

    Sj,ini

    MRpl

    MRuSj,st

    ΦuΦpl

    M

    Φ

    MRelSj,ini/7

    Φel

    Ductility?

    4 key parameters

    • Initial stiffness 𝐒𝐣,𝐢𝐧𝐢 =𝐄𝐳𝟐

    𝐢𝟏/𝐤𝐢

    • Plastic bending resistance 𝐌𝐑𝐩𝐥 = 𝐦𝐢𝐧 𝐅𝐑𝐩𝐥,𝐢 . 𝐳

    • Post-plastic stiffness 𝐒𝐣,𝐬𝐭 =𝐄𝐳𝟐

    𝐢𝟏/𝐤∗

    • Ultimate bending resistance 𝐌𝐑𝐮 = 𝐦𝐢𝐧 𝐌𝐑𝐮,𝐢

  • Problem: ductility assessment

    3/9

    M

    z

    Tension zone: ki, FRpl,i

    Compr. zone: ki, FRpl,i

    Shear zone: ki, FRpl,i

    Sj,ini

    MRpl

    MRuSj,st

    ΦuΦpl

    M

    Φ

    MRelSj,ini/7

    Φel

    Ductility?

    Need for joint ductility:

    • Design of a structure based on a plastic global analysis

  • Problem: ductility assessment

    3/9

    M

    z

    Tension zone: ki, FRpl,i

    Compr. zone: ki, FRpl,i

    Shear zone: ki, FRpl,i

    Sj,ini

    MRpl

    MRuSj,st

    ΦuΦpl

    M

    Φ

    MRelSj,ini/7

    Φel

    Ductility?

    Need for joint ductility:

    • Design of a structure based on a plastic global analysis

    • Mitigation of the risk of progressive collapse under exceptional loading

  • Problem: ductility assessment

    3/9

    M

    z

    Tension zone: ki, FRpl,i

    Compr. zone: ki, FRpl,i

    Shear zone: ki, FRpl,i

    Sj,ini

    MRpl

    MRuSj,st

    ΦuΦpl

    M

    Φ

    MRelSj,ini/7

    Φel

    Ductility?

    Need for joint ductility:

    • Design of a structure based on a plastic global analysis

    • Mitigation of the risk of progressive collapse under exceptional loading

    • Energy dissipation under earthquakes

  • Problem: ductility assessment

    3/9

    M

    z

    Tension zone: ki, FRpl,i

    Compr. zone: ki, FRpl,i

    Shear zone: ki, FRpl,i

    Sj,ini

    MRpl

    MRuSj,st

    ΦuΦpl

    M

    Φ

    MRelSj,ini/7

    Φel

    Ductility?

    4 key parameters

    • Initial stiffness 𝐒𝐣,𝐢𝐧𝐢 =𝐄𝐳𝟐

    𝐢𝟏/𝐤𝐢

    • Plastic bending resistance 𝐌𝐑𝐩𝐥 = 𝐦𝐢𝐧 𝐅𝐑𝐩𝐥,𝐢 . 𝐳

    • Post-plastic stiffness 𝐒𝐣,𝐬𝐭 =𝐄𝐳𝟐

    𝐢𝟏/𝐤∗

    • Ultimate bending resistance 𝐌𝐑𝐮 = 𝐦𝐢𝐧 𝐌𝐑𝐮,𝐢

  • Problem: ductility assessment

    3/9

    M

    z

    Tension zone: ki, FRpl,i

    Compr. zone: ki, FRpl,i

    Shear zone: ki, FRpl,i

    Sj,ini

    MRpl

    MRuSj,st

    ΦuΦpl

    M

    Φ

    MRelSj,ini/7

    Φel

    Ductility?

    4 key parameters

    • Initial stiffness 𝐒𝐣,𝐢𝐧𝐢 =𝐄𝐳𝟐

    𝐢𝟏/𝐤𝐢

    • Plastic bending resistance 𝐌𝐑𝐩𝐥 = 𝐦𝐢𝐧 𝐅𝐑𝐩𝐥,𝐢 . 𝐳

    • Post-plastic stiffness 𝐒𝐣,𝐬𝐭 =𝐄𝐳𝟐

    𝐢𝟏/𝐤∗

    • Ultimate bending resistance 𝐌𝐑𝐮 = 𝐦𝐢𝐧 𝐌𝐑𝐮,𝐢

    Φu

  • Estimation of Sj,st

    4/9

    Sj,st =Ez2

    1k∗

    M

    z

    Tension zone: ki, FRpl,i

    Compr. zone: ki, FRpl,i

    Shear zone: ki, FRpl,i

    Sj,ini

    MRpl

    MRuSj,st

    ΦuΦpl

    M

    Φ

    MRelSj,ini/7

    Φel

  • Estimation of Sj,st

    4/9

    1

    k∗=

    m

    1

    ki,m MRpl,m>MRpl,lim

    + p

    1

    kst,p MRpl,p≤MRpl,lim

    M

    z

    Tension zone: ki, FRpl,i

    Compr. zone: ki, FRpl,i

    Shear zone: ki, FRpl,i

    Sj,ini

    MRpl

    MRuSj,st

    ΦuΦpl

    M

    Φ

    MRelSj,ini/7

    Φel

    Sj,st =Ez2

    1k∗

  • Estimation of Sj,st

    4/9

    M

    z

    Tension zone: ki, FRpl,i

    Compr. zone: ki, FRpl,i

    Shear zone: ki, FRpl,i

    Sj,ini

    MRpl

    MRuSj,st

    ΦuΦpl

    M

    Φ

    MRelSj,ini/7

    Φel

    Elastic components

    1

    k∗=

    m

    1

    ki,m MRpl,m>MRpl,lim

    + p

    1

    kst,p MRpl,p≤MRpl,lim

    Sj,st =Ez2

    1k∗

  • Estimation of Sj,st

    4/9

    M

    z

    Tension zone: ki, FRpl,i

    Compr. zone: ki, FRpl,i

    Shear zone: ki, FRpl,i

    Sj,ini

    MRpl

    MRuSj,st

    ΦuΦpl

    M

    Φ

    MRelSj,ini/7

    Φel

    Elastic components Yielded components

    1

    k∗=

    m

    1

    ki,m MRpl,m>MRpl,lim

    + p

    1

    kst,p MRpl,p≤MRpl,lim

    Sj,st =Ez2

    1k∗

  • Estimation of Sj,st

    4/9

    M

    z

    Tension zone: ki, FRpl,i

    Compr. zone: ki, FRpl,i

    Shear zone: ki, FRpl,i

    Sj,ini

    MRpl

    MRuSj,st

    ΦuΦpl

    M

    Φ

    MRelSj,ini/7

    Φel

    MRpl,lim = 1,65MRpl

    1

    k∗=

    m

    1

    ki,m MRpl,m>MRpl,lim

    + p

    1

    kst,p MRpl,p≤MRpl,lim

    Sj,st =Ez2

    1k∗

  • Estimation of Sj,st

    4/9

    M

    z

    Tension zone: ki, FRpl,i, kst,i

    Compr. zone: ki, FRpl,i, kst,i

    Shear zone: ki, FRpl,i, kst,i

    Sj,ini

    MRpl

    MRuSj,st

    ΦuΦpl

    M

    Φ

    MRelSj,ini/7

    Φel

    kst =

    EstEki → components in tension/compression

    2 1 + υ

    3

    EstEki → column web panel in shear

    1

    k∗=

    m

    1

    ki,m MRpl,m>MRpl,lim

    + p

    1

    kst,p MRpl,p≤MRpl,lim

    Sj,st =Ez2

    1k∗

  • Estimation of Sj,st

    4/9

    1

    k∗=

    m

    1

    ki,m MRpl,m>MRpl,lim

    + p

    1

    kst,p MRpl,p≤MRpl,lim

    Sj,st =Ez2

    1k∗

    M

    z

    Tension zone: ki, FRpl,i, kst,i

    Compr. zone: ki, FRpl,i, kst,i

    Shear zone: ki, FRpl,i, kst,i

    Sj,ini

    MRpl

    MRuSj,st

    ΦuΦpl

    M

    Φ

    MRelSj,ini/7

    Φel

  • Estimation of MRu

    5/9

    MRu = min FRu,i . z

    M

    z

    Tension zone: ki, FRpl,i, kst,i

    Compr. zone: ki, FRpl,i, kst,i

    Shear zone: ki, FRpl,i, kst,i

    Sj,ini

    MRpl

    MRuSj,st

    ΦuΦpl

    M

    Φ

    MRelSj,ini/7

    Φel

  • Estimation of MRu

    5/9

    M

    z

    Tension zone: ki, FRpl,i, kst,i, FRu,i

    Compr. zone: ki, FRpl,i, kst,i, FRu,i

    Shear zone: ki, FRpl,i, kst,i, FRu,i

    Sj,ini

    MRpl

    MRuSj,st

    ΦuΦpl

    M

    Φ

    MRelSj,ini/7

    Φel

    MRu = min FRu,i . z

    FRpl,i (fy) ↔ FRu,i (fu)

  • Estimation of MRu

    5/9

    M

    z

    Tension zone: ki, FRpl,i, kst,i, FRu,i

    Compr. zone: ki, FRpl,i, kst,i, FRu,i

    Shear zone: ki, FRpl,i, kst,i, FRu,i

    Sj,ini

    MRpl

    MRuSj,st

    ΦuΦpl

    M

    Φ

    MRelSj,ini/7

    Φel

    MRu = min FRu,i . z

  • Estimation of ductility

    6/9

    Φu =MRu −MRpl

    Sj,st

    M

    z

    Tension zone: ki, FRpl,i, kst,i, FRu,i

    Compr. zone: ki, FRpl,i, kst,i, FRu,i

    Shear zone: ki, FRpl,i, kst,i, FRu,i

    Sj,ini

    MRpl

    MRuSj,st

    ΦuΦpl

    M

    Φ

    MRelSj,ini/7

    Φel

    Ultimate rotation capacity

  • Estimation of ductility

    6/9

    Φu =MRu −MRpl

    Sj,st

    M

    z

    Tension zone: ki, FRpl,i, kst,i, FRu,i

    Compr. zone: ki, FRpl,i, kst,i, FRu,i

    Shear zone: ki, FRpl,i, kst,i, FRu,i

    Sj,ini

    MRpl

    MRuSj,st

    ΦuΦpl

    M

    Φ

    MRelSj,ini/7

    Φel

    Plastic rotation capacity

    Φu −Φpl =MRu −MRpl

    Sj,st−MRpl

    Sj,ini/3

  • 0

    20

    40

    60

    80

    100

    120

    140

    160

    180

    200

    220

    0 10 20 30 40 50 60 70 80 90 100

    Be

    nd

    ing

    mo

    men

    t [k

    Nm

    ]

    Joint rotation [mrad]

    TEST T1

    Experimental results

    Analytical prediction

    0

    10

    20

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    0 10 20 30 40 50 60 70 80 90 100

    Ben

    din

    g m

    om

    en

    t [k

    Nm

    ]

    Joint rotation [mrad]

    TEST 013

    Experimental results

    Analytical prediction

    Validation

    7/9

    0

    10

    20

    30

    40

    50

    60

    70

    80

    90

    0 10 20 30 40 50 60 70 80 90 100

    Be

    nd

    ing

    mo

    me

    nt

    [kN

    m]

    Joint rotation [mrad]

    TEST 07

    Experimental results

    Analytical prediction

    (Jaspart, 1991) (Jaspart, 1991)

    0

    20

    40

    60

    80

    100

    120

    140

    160

    0 10 20 30 40 50 60 70 80 90 100

    Be

    nd

    ing

    mo

    me

    nt

    [kN

    m]

    Joint rotation [mrad]

    TEST T9

    Experimental results

    Analytical prediction

    (Zoetemeijer, 1974) (Demonceau & Jaspart, 2004)

  • Conclusions

    8/9

    4 key parameters

    • Initial stiffness 𝐒𝐣,𝐢𝐧𝐢 =𝐄𝐳𝟐

    𝐢𝟏/𝐤𝐢

    • Plastic bending resistance 𝐌𝐑𝐩𝐥 = 𝐦𝐢𝐧 𝐌𝐑𝐩𝐥,𝐢

    • Post-plastic stiffness 𝐒𝐣,𝐬𝐭 =𝐄𝐳𝟐

    𝐢𝟏/𝐤∗

    • Ultimate bending resistance 𝐌𝐑𝐮 = 𝐦𝐢𝐧 𝐌𝐑𝐮,𝐢

    Ultimate rotation capacity: Φu =MRu−MRpl

    Sj,st

    • Eurocode 3, Part 1-8

    • Present paper

    M

    z

    Tension zone: ki, MRpl,i, kst,i, MRu,i

    Compr. zone: ki, MRpl,i, kst,i, MRu,i

    Shear zone: ki, MRpl,i, kst,i, MRu,i

    MRpl

    MRuSj,st

    Φu

    M

    Φ

    Sj,ini

  • Conclusions

    8/9

    4 key parameters

    • Initial stiffness 𝐒𝐣,𝐢𝐧𝐢 =𝐄𝐳𝟐

    𝐢𝟏/𝐤𝐢

    • Plastic bending resistance 𝐌𝐑𝐩𝐥 = 𝐦𝐢𝐧 𝐅𝐑𝐩𝐥,𝐢 . 𝐳

    • Post-plastic stiffness 𝐒𝐣,𝐬𝐭 =𝐄𝐳𝟐

    𝐢𝟏/𝐤∗

    • Ultimate bending resistance 𝐌𝐑𝐮 = 𝐦𝐢𝐧 𝐌𝐑𝐮,𝐢

    Ultimate rotation capacity: Φu =MRu−MRpl

    Sj,st

    • Eurocode 3, Part 1-8

    • Present paper

    M

    z

    Tension zone: ki, FRpl,i, kst,i, MRu,i

    Compr. zone: ki, FRpl,i, kst,i, MRu,i

    Shear zone: ki, FRpl,i, kst,i, MRu,i

    Sj,ini

    MRpl

    MRuSj,st

    ΦuΦpl

    M

    Φ

    MRelSj,ini/7

    Φel

  • Conclusions

    8/9

    M

    z

    Tension zone: ki, FRpl,i, kst,i, FRu,i

    Compr. zone: ki, FRpl,i, kst,i, FRu,i

    Shear zone: ki, FRpl,i, kst,i, FRu,i

    Sj,ini

    MRpl

    MRuSj,st

    ΦuΦpl

    M

    Φ

    MRelSj,ini/7

    Φel

    4 key parameters

    • Initial stiffness 𝐒𝐣,𝐢𝐧𝐢 =𝐄𝐳𝟐

    𝐢𝟏/𝐤𝐢

    • Plastic bending resistance 𝐌𝐑𝐩𝐥 = 𝐦𝐢𝐧 𝐅𝐑𝐩𝐥,𝐢 . 𝐳

    • Post-plastic stiffness 𝐒𝐣,𝐬𝐭 =𝐄𝐳𝟐

    𝐢𝟏/𝐤∗

    • Ultimate bending resistance 𝐌𝐑𝐮 = 𝐦𝐢𝐧 𝐅𝐑𝐮,𝐢 . 𝐳

    Ultimate rotation capacity: Φu =MRu−MRpl

    Sj,st

    • Eurocode 3, Part 1-8

    • Present paper

  • Conclusions

    8/9

    M

    z

    Tension zone: ki, FRpl,i, kst,i, FRu,i

    Compr. zone: ki, FRpl,i, kst,i, FRu,i

    Shear zone: ki, FRpl,i, kst,i, FRu,i

    Sj,ini

    MRpl

    MRuSj,st

    ΦuΦpl

    M

    Φ

    MRelSj,ini/7

    Φel

    4 key parameters

    • Initial stiffness 𝐒𝐣,𝐢𝐧𝐢 =𝐄𝐳𝟐

    𝐢𝟏/𝐤𝐢

    • Plastic bending resistance 𝐌𝐑𝐩𝐥 = 𝐦𝐢𝐧 𝐅𝐑𝐩𝐥,𝐢 . 𝐳

    • Post-plastic stiffness 𝐒𝐣,𝐬𝐭 =𝐄𝐳𝟐

    𝐢𝟏/𝐤∗

    • Ultimate bending resistance 𝐌𝐑𝐮 = 𝐦𝐢𝐧 𝐅𝐑𝐮,𝐢 . 𝐳

    Ultimate rotation capacity: Φu =MRu−MRpl

    Sj,st

    • Eurocode 3, Part 1-8

    • Present paper

    Ductility

  • Thank you!

    Questions?

    Jean-Pierre Jaspart

    Adrien Corman

    Jean-François Demonceau

    11-13 September 2019, Prague, Czech Republic

    The International Colloquium on Stability and Ductility of Steel Structures

  • References

    • Jaspart, J.-P., 1991. « Etude de la semi-rigidité des nœuds poutre-

    colonne et son influence sur la résistance et la stabilité des ossatures en

    acier », PhD dissertation , Liège University.

    • Zoetemeijer, P., 1974. « A design method for the tension side of statically

    loaded, bolted beam-to-column connections ». Heron, Vol. 20, N°1,

    1974)

    • Demonceau, J.-F. & Jaspart, J.-P., 2004. « Experimental and analytical

    investigations on single-sided composite joint configuration », 5th

    International PhD Symposium in Civil Engineering, Balkema, pp. 341-

    349.

  • Introduction: the component method

    M

    z

    Tension zone: ki, FRpl,i

    Compr. zone: ki, FRpl,i

    Shear zone: ki, FRpl,i

    Sj,ini

    MRpl

    MRuSj,st

    ΦuΦpl

    M

    Φ

    MRelSj,ini/7

    Φel

    3. Assembly

    4 key parameters

    • Initial stiffness 𝐒𝐣,𝐢𝐧𝐢 =𝐄𝐳𝟐

    𝐢𝟏/𝐤𝐢

    • Plastic bending resistance 𝐌𝐑𝐩𝐥 = 𝐦𝐢𝐧 𝐌𝐑𝐩𝐥,𝐢

    • Post-plastic stiffness 𝐒𝐣,𝐬𝐭 =𝐄𝐳𝟐

    𝐢𝟏/𝐤∗

    • Ultimate bending resistance 𝐌𝐑𝐮 = 𝐦𝐢𝐧 𝐌𝐑𝐮,𝐢