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  • NATIONAL TECHNICAL UNIVERSITY OF ATHENS LABORATORY OF EARTHQUAKE ENGINEERING

    Design of Earthquake -Resistant

    Structures

    Basic principles

    Ioannis N. Psycharis

  • Basic considerations

    Design earthquake: small probability of occurrence during the

    life of the structure.

    ground motion without any damage at all.

    Flexural yielding: the stiffness is temporarily reduced but the

    structure regains its strength and stiffness when unloading

    starts.

    Economical approach:

    Allow the structure to exceed its elastic limit during the

    design earthquake.

    Control the extend of the damage.

    Exclude unwanted types of damage (e.g. brittle failure).

    Repair any damage after the earthquake.

  • Seismic response of SDOF systems

    Seismic forces ( d Alembert ):

    Restoring force:

    Damping force:

    Equation of motion:

    x (t)g

    gx (t) u(t) u(t)

    m p(t)=-m x (t)

    =K, C

    m

    K, C

    g

    x (t)g

    x(t)

    )()( txmtp g

    uKVf iis

    )()( tuCtfd

    umffp ds

    gxmKuuCum

  • Seismic response of SDOF systems

    Equation of motion:

    Eigenfrequency :

    Eigenperiod :

    Damping coefficient:

    gxuuu22

    m

    K

    mT 2

    mK

    C

    2

    dtextu

    t

    dt

    g

    d 0

    )( )(sin)(1

    )(

  • Response spectrum

    0 2 4 6 8 10

    , t (sec)

    -1.0

    -0.5

    0.0

    0.5

    1.0

    , u

    (m

    m)

    =0.1 sec, =5%

    1.03

    0 2 4 6 8 10

    , t (sec)

    -6.0

    -3.0

    0.0

    3.0

    6.0

    , u

    (m

    m)

    =0.2 sec, =5%

    -5.88

    0 2 4 6 8 10

    , t (sec)

    -16.0

    -8.0

    0.0

    8.0

    16.0

    , u

    (m

    m)

    T=0.3 sec, =5%

    -15.38

    0 2 4 6 8 10

    , t (sec)

    -2.5

    0.0

    2.5

    . .

    (m/s

    ec

    2)

    , 1986 (Long)

    0.0 0.1 0.2 0.3 0.4 0.5 0.6

    , (sec)

    0

    10

    20

    30

    40

    50

    60

    , S

    D (

    mm

    )

    1.03

    5.88

    15.38

  • Response spectrum

    Kalamata , 1985 earthquake

    Response spectra for = 0, 2%, 5%, 10%, 20%

    0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

    Ðåñßï äï ò Ô (sec)

    0

    2

    4

    6

    8

    10

    12

    14

    16

    18

    SD

    (cm

    )

    0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

    Ðåñßï äï ò Ô (sec)

    0.0

    0.4

    0.8

    1.2

    1.6

    2.0

    2.4

    2.8

    3.2

    3.6

    SA

    (g)

  • Pseudo -Spectra

    For small values of damping ( 20%)

    SA 2 SD = PSA

    SV SD = PSV

    Limits:

    T 0: SD 0 SV 0 SA

    T : SD SV SA 0

    0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

    Ðåñßï äï ò Ô (sec)

    0

    2

    4

    6

    8

    10

    12

    14

    16

    18

    SD

    (cm

    )

    0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

    Ðåñßï äï ò Ô (sec)

    0.0

    0.4

    0.8

    1.2

    1.6

    2.0

    2.4

    2.8

    3.2

    3.6

    SA

    (g)

  • Logarithmic representation

    0.01 0.1 1 10

    Ðåñßï äï ò Ô (sec)

    0.1

    1

    10

    100

    1000

    PS

    V (

    cm

    /se

    c)

    0.00

    1 g

    0.01

    g

    0.1 g

    PSA

    SD

    1 cm

    10 cm

    100 cm

  • ADRS - representation

    0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0

    SD (cm)

    0.0

    1.0

    2.0

    3.0

    4.0

    5.0

    6.0

    7.0

    8.0

    PS

    A (

    m/s

    ec

    2)

    T=

    0.5

    sec

    T=1.

    0 se

    c

    T=1.5 s

    ec

    PSA

    SD2T

  • Characteristic regions

    0.01 0.10 1.00 10.00

    , T (sec)

    0.10

    1.00

    10.00

    100.00

    , P

    SV

    (cm

    /se

    c)

    PSA=1

    00g

    PSA=1

    0g

    PSA=

    1g

    PSA=

    0.1g

    PSA=0

    .01g

    PSA=0

    .001

    g

    PSA=

    0.00

    01g

    SD=100cm

    SD=10cm

    SD=1cm

    SD=0.1cm

    SD=0.01cm

    SD=0.001cm

    A

    B

    C D

    E

  • Design spectrum

    Effect of soil conditions

  • Design spectrum

    Ground types

    according to EC 8

  • EC 8 Elastic response spectrum

    Se (T) = spectral

    acceleration for

    period T

    ag = IagR = design

    ground acceleration

    = importance

    factor

    agR = reference

    peak ground

    acceleration on type

    A ground

    S = soil factor

  • EC 8 Elastic response spectrum

    for 0 T TB

    for TB T TC

    for TC T TD

    for TD T 4.0 sec

    , T (sec)

    Se / ag

    2.5 S

    S

    0 C TD

    2.5 S TC/T

    2.5 S TC TD/T 2

    15.2T

    T1Sa)T(S

    Bge

    5.2Sa)T(S ge

    T

    T5.2Sa)T(S Cge

    2DC

    geT

    TT5.2Sa)T(S

  • EC 8 Elastic response spectrum

    , T (sec)

    Se / ag

    2.5 S

    S

    0 C TD

    2.5 S TC/T

    2.5 S TC TD/T 2

    Ground type (sec) C (sec) D (sec) S

    0.15 0.40 2.50 1.00

    0.15 0.50 2.50 1.20

    C 0.20 0.60 2.50 1.15

    D 0.20 0.80 2.50 1.35

    E 0.15 0.50 2.50 1.40

  • unacceptable

    Performance levels

    Define earthquake loadings with various probabilities of

    occurrence

    Define various acceptable level of damage

    Combine each earthquake loading with an acceptable level of

    damage Performance level

    Very small

    damage Damage

    limitation level

    Significant damage

    Collapse prevention

    Close to collapse

    Fre

    qu

    en

    cy o

    f o

    ccu

    rren

    ce o

    f the

    seis

    mic

    excita

    tion

    Large

    Frequent earthquakes

    Small

    Rare earthquakes

    Very small

    Very rare earthquakes

  • Performance requirements of seismic codes

    Most codes are based on two performance levels:

    Damage limitation level

    The structure is expected to experience limited structural

    and non -structural damage during frequent earthquakes.

    In this limit state:

    The structural members retain their strength and

    stiffness.

    No permanent deformations and drifts occur.

    No repair is needed.

    The seismic action is usually termed as the serviceability

    earthquake. Reasonable probability of exceedance = 10%

    in 10 years (mean return period = 95 years).

    Compliance criteria are usually expressed in terms of

    deformation limits .

  • Performance requirements of seismic codes

    Collapse prevention level

    Ensure prevention of collapse and retention of structural

    integrity for an earthquake with a small possibility of

    occurrence during the life of the structure:

    Significant damage might happen.

    The structure should be able to bear the vertical loads

    and retain sufficient lateral strength and stiffness to

    protect life during aftershocks.

    The seismic action is referred as the design earthquake.

    For structures of ordinary importance: 10% probability of

    exceedance in 50 years (mean return period of 475 years).

    Compliance criteria are expressed in terms of forces

    (force -based seismic design).

  • Period, T

    0.0

    0.5

    1.0

    1.5

    2.0

    2.5

    Sa /

    (S

    ag

    R)

    TB TC TD0

    Design concept

    The structure is designed to behave

    elastically up to a level of seismic forces

    lower than the one required for fully elastic

    response.

    The loads corresponding to the

    design seismic action are derived by

    dividing the elastic ones by a

    reduction factor denoted by

    R (reduction factor) or

    q (behaviour factor).

    1:q

    1:q

    How is q defined?

  • Ductility capacity

    The collapse mechanism of the structural members is related

    to their deformation and not to the forces induced to them

    during the seismic action.

    In order to comply with the non -collapse criterion, an overall

    ductile behaviour should be ensured.

    In other words: the structure should have an adequate

    capacity to deform beyond its elastic limit without substantial

    reduction in the overall resistance against horizontal and

    vertical loads.

    This is achieved through proper dimensioning and detailing of

    the structural elements.

    In addition, capacity design concepts are applied, in order to

    ensure that ductile modes of failure (e.g. flexure) should

    precede brittle modes of failure (e.g. shear) with sufficient

    reliability.

  • Nonlinear response

    Force -deformation relation

    Elastoplastic idealization

    Same area under the two curves