en curs10 dsis

7/29/2019 En Curs10 Dsis

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Structural Dynamics and EarthquakeEngineering

Course 10

Design of buildings for seismic action (2)

Course notes are available for download athttp://www.ct.upt.ro/users/AurelStratan/

Combination of the effects of the components ofthe seismic action

Seismic action has components along three orthogonalaxes:

2 horizontal components

1 vertical components

Peak values of ag forhorizontal motion are NOTrecorded at the same time instant

Peak values of response are NOTrecorded at the same time instant

0 5 10 15 20 25 30 35 40-2

-1

0

1

2

1.62

timp, s

acceleratie,m/s2

Vrancea, 04.03.1977, INCERC (B), EW

0 5 10 15 20 25 30 35 40-2

-1

0

1

2

-1.95

timp, s

acceleratie,m/s2

Vrancea, 04.03.1977, INCERC (B), NS


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Simultaneous action of two orthogonal horizontalcomponents (lateral force or spectral analysis):

Seismic response is evaluated separately for each direction ofseismic action

Peak value of response from the simultaneous action of twohorizontal components is obtained by the SRSS combination ofdirectional response:

Alternative method for combinationof components of seismic actions

2 2

Ed Edx EdyE E E= +


When vertical componentis considered as well:

2 2 2

Ed Edx Edy EdzE E E E= + +


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Vertical component

Vertical component of seismic action shall be consideredwhen vertical peak ground acceleration agv0.25g, and thestructure has one of the following characteristics:

has horizontal elements spanning over 20 m

has cantilever elements with a length over 5 m

has prestressed horizontal elements

has columns supported on beams

is base-isolated

Conceptual design of buildings

Seismic response of structures subject to considerableuncertainties:

characteristics of future seismic motions

diff. between structural models and real structural behaviour

elastic model inelastic response

static analysis dynamic behaviour

Conceptual design of buildings located in seismic areasis necessary, in order to provide an adequate seismicresponse:

structural simplicity

uniformity, symmetry and redundancy

bi-directional strength and stiffness

torsional resistance and stiffness

diafragmatic behaviour at storey levels

adequate foundation


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Structural simplicity

Simple, compact, symmetric structures

Modelling, analysis, design, detailing and construction ofstructures subjected to smaller uncertainties

Uniformity, symmetry and redundancy

Structures should be as regular as possible, with auniform plan layout, allowing for a short and directtransmission of inertia forces to lateral resisting system

Redundancy: failure of a single member does not implyfailure of the whole structure


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Bi-directional strength and stiffness

Gravity - force resisting systems Lateral - force resisting systems

Seismic motion has components on both horizontaldirections

Structures should have similar strength and stiffnessalong two main directions

sistem de preluare

a fortelor laterale

sistem de preluare a fortelor gravitationale

Torsional resistance and stiffness

Seismic forces centre of mass (CM)

Resisting forces centre of rigidity (CR)

Torsionally flexible systems large forces anddeformations in perimetral elements

Conclusion (1): lateral force resisting systems are moreefficient away from the centre of rigidity

lateral-forceresisting system

lateral-force

resisting system

gravity-force

resisting system

gravity-force

resisting system


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Torsional resistance and stiffness

Seismic forces

centre of mass (CM) Resisting forces centre of rigidity (CR)

Eccentricity torsion increased displ. and forces

Conclusion (2): lateral force resisting systems should belocated as symmetrical as possible

CR=CM CM

CR

X

Y

DDDD1x

2x

DDDD1x

2x

Fx Fx

DDDD1y

DDDD2y

e0y

Storey diaphragms

Behaviour of floors as rigid diaphragms

Collect and transmit forces to lateral-force resisting systems

Lateral-force resisting systems work together

Especially relevant in case of complex and non-uniform layouts oflateral-force-resisting systems, or combination of such systemsof different stiffness

F F


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Foundations

Design and construction of the foundations and of theconnection to the superstructure shall ensure that thewhole building is subjected to a uniform seismicexcitation

Recommendations:

discrete number of structural walls, of different width andstiffness

box-type or cellular foundation

individual foundation elements

foundation slab or tie-beams between these elements

Criteria for structural regularity

Structural regularity:

plan

elevation

Regularity of a structure affects: structural model, 2D or 3D

analysis method, lateral force method or modal responsespectrum analysis

value of the behaviour factor q, that need to be reduced forstructures irregular in elevation


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Criteria for regularity in plan

A symmetrical distribution of stiffness and mass Compact plan configuration, close to a convex polygonal

shape (set-backs of max 15% from floor area)

Rigid diaphragms at storey levels

At each level, in each principal direction of the structure,the eccentricity shall satisfy:

eox , eoy - the distance between the centre of stiffness and

the centre of mass, measured in the direction normal tothe direction of analysis consideredrx, ry the square root of the ratio of the torsionalstiffness to the lateral stiffness in each direction

("torsional radius")

eox 0,30 rx

eoy 0,30 ry

Criteria for regularity in elevation

Lateral-force resisting systems shall run withoutinterruption from their foundations to the top of thebuilding

Mass and lateral stiffness shall be constant or reducegradually with height

In framed buildings the ratio of the actual storeyresistance to the resistance required by the analysisshould not vary disproportionately between adjacentstoreys

Stiffness: reductions are no larger than 30% with respectto adjacent storeys

Strength: reductions are no larger than 20% with respectto adjacent storeys

Mass: is not larger than 50% of the mass of adjacentstoreys


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Criteria for regularity in elevation

Restrictions on setbacks

Consequences of structural regularity on analysisand design

*Only if building height is less than 30 m and fundamentalperiod of vibration T1 < 1.50 s

Plan irregularity: large torsional eccentricities 3Dmodels

Vertical irregularities: significant contribution of higher

modes of vibration

modal response spectrum analysis

reduced values of behaviour factor

Reduced valueModalSpatialNONO

Reference valueModalSpatialYESNO

Reduced valueModalPlanarNOYES

Reference value* Lateral forcePlanarYESYES

Linear-elastic analysisModelElevationPlan

Behaviour factor (q)Allowed simplificationRegularity


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Structural model

The model of the building shall adequately represent thedistribution of stiffness and mass

Floors that cannot be modelled as infinitely rigid in-plane

translational masses (only) can be considered lumpedin nodes

Floors that can be modelled as infinitely rigid in-planestorey masses can be lumped at the centre of mass ofeach storey:

2 translational components

1 rotational components

X

Y

Mx

My

Mzz

mxi

myi

mi

CM

di

x y iM M m= =

2

zz i iM m d=

Accidental torsional effects

Uncertainties associated to distribution of storey massesand/or spatial variation of ground motion

Accidental eccentricity e1i= 0.05 Li

Spatial structural model:

CMFx e

1yLy CM

Fy

e1x

Lx

X

Y

iii FeM 11 =

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