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www.argenco.ulg.ac.be Oslo, November 8th, 2007
Design
of
Earthquake Resistant Steel StructuresIn the context of
Eurocode 8
Prof.Dr.ir. Andr PLUMIER
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Earthquake Action
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Whats an earthquake?
Physical phenomenomTectonic plates: tendancy to move, but friction
=> Stresses at edges
If stresses > friction => sudden move => wave propagation= EQ
EQ also existInside plates
intraplate EQ
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Slippage at San Andreas fault(California)
Components of seismic action
Action applied to a structure by an earthquake
A move Horizontal & vertical components
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Caracterisation of earthquakes.
Magnitude: Richter scale, total liberated energy
Intensity I: Mercalli scale, effects on buildings at a given location
Acceleration ag(t) accelerogram at a given location
Displacement of ground dg(t) physical&measured data
Sub-products: usual design data in earthquake engineering agR: maximum ofag(t) , at bedrock
= Peak Ground Acceleration PGA
0,4 g 0,6g highly seismic zones Japan, Turkey0 0,1g low seismic zones
acceleration response spectrum
Duration => cumulation of damage
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Maps of PGA agR
the world
Europe
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Peculiar effects of earthquakes.
Soil settlement Dry sand Tsunami
Soil Liquefaction Fine sand saturated by waterShear resistance of soil: R= ( u ) tg : friction angle ( u): effective pressure
: applied pressure u: internal water pressureMove of soil => u => R max : R= ( u ) tg = 0= > a liquid => soil liquefaction
Effects Inclination & tilt of structures
Landslides if liquefiable soil layerclayConditions high vibration energy required => u
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Earthquake hazard in a given zone Caracterisation : PGA agR
=> maps
Design value ofagR?
Define a probability of the earthquake against which the design is madeChoice : a balance safety cost a less probable EQ => highera
gRand cost
Eurocode 8, EN1998-1 :2004 Design Earthquake
No collapse Earthquake: probability of exceedance in 50 yearsPNCR = 10%
ULS Equivalent: return period TNCR
= 475 years
Damage Limitation to non structural elements Earthquake: SLS
probabilityPDLRof exceedance in 10 years =10% return period TDLR= 95 years
Frequency of earthquakes
(cumulated number/year)
As function of magnitude Ms
For Belgium
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UncertaintiesOn seismic hazard :
- Poor data base: measurement since 1950
return period NCR = 475 years
- Major Eq not frequent
- Hypothesis : history repeat itself- Partial knowledge of geology of sites
recent earthquakes unvail new faults
Northridge (1994), Kobe (1995), Kocaeli (1999)
after earthquake : zone seismic level increasedEx:Istanbul from 0,2g to 0,4g after Kocaeli (1999)
Effective mitigation of uncertainties on seismic action ?
Design with ductilityResistance maintained independently of displacement
=> STEEL STRUCTURES
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du du
Concept a Concept b
V
d
Concept a: low-dissipativestructure
Concept b: dissipativestructure
Velastic responseStructure designed to remain
elastic under design earthquake
VreducedStructure designed to yield under
design earthquake
du
Ultimate displacement
Dissipative and non dissipative global behavior of structures.
The non dissipative structure fails in a single storey mechanism.
large sections
only elastic stresses
smaller sections
a design
for numerous plastic zones
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Steel structures are good at providing energy dissipation capability
Due to:
Ductility of steel material Many possible ductile mechanisms in steel elements
in connections
Effective duplication of plastic mechanisms at a local level
Reliable geometrical properties
Relatively low sensitivity of bending resistance M
to coincident axial force N
Guaranteed material strength, as result a of controlled production Designs and constructions made by professionals
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A tool to evaluate the effects of earthquakes:
Response Spectra
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u (t)
u0Vibrations
non amortiesc = 0
t
T = 2/ T = 2/u(t)
Figure 2.2. Types de vibrations libres (p(t))=0) ralises par cartement u0 de la position dquilibre
Vibrations
amorties
c 0
0
Amortissement critique
= 1
u t
d
M
H
Undamped
Vibrations
= 0
Undamped
Vibrations
0
Critical Damping
= 1
SDOF
Single Degree of Freedom
OscillatorFundamental vibration period
EI
MHT
32
3
1 =
: damping relative to critical damping
Elastic behaviour
Steel structures 1%
Concrete 2%Seismic behaviour
Cracks in RC
Friction in steel connections
partitions-structures=> all structures = 5%
k
MT 21 =
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dFmax=M.(T1)
d
MH
dg(t)
Consider 1 SDOF oscillator having a fundamental period T1Soil move dg(t) => CM Center of Mass is displaced d(t)
Equation of dynamics M u(t) + c u(t) + ku(t) = - M dg(t)Resolved => d(t) and dmax
=> define: a forceF equivalent [gives same dmax]
=> write Fmax as being Fmax=M(T1)=> put in a graph(T1) as function of T1=> do it for a family of oscillators of periods T1i=> a curve: the elastic response spectrum (T1)
If you know T1 of a structure=> you know Fmax=> M, V, N => design
(T1)
T1(s)T1i
ag
i
0
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Code elastic response spectrum Se(T1) A zone average
Parameters
Soil & site : S TB TC TDDamping, if 5%
Importance class of building: I
I agRS
2,5 I agRS
Se(T)
T
( ) 55,05/10 +=
Se(T)
T(s)TB0 TC
Computed spectrum 1
Elastic accelerationspectrum "average"
Computed spectrum 2
Table 1. Importance classes for buildings and recommended values ofI(EN1998-1:2004).
Importance
class
Buildings I
I Buildings of minor importance for public safety,
for example agricultural buildings.
0,8
II Ordinary buildings not belonging in the other categories. 1,0
III Buildings whose seismic resistance is of importance
in view of the consequences associated with a collapse,
for example schools, assembly halls, cultural institutions.
1,2
IV Buildings whose integrity during earthquakes
is of vital importance for civil protection,
for example hospitals, fire stations, power plants, etc.
1,4
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Spectrum Type 1
Remote Earthquake
MS 5,5
Spectrum Type
Nearby Earthquake
MS < 5,5
Table 2. Eurocode 8 values of parameters S , TB , TC and TD defining the elastic
response spectra Type 1 and Type 2.
Type 1 Earthquake Type 2 Earthquake
Soil S TB(s) TC(s) TD(s) S TB(s) TC(s) TD(s)
A Rock or rock-like formation,
including at most 5 m of weaker
material at the surface.
1,0 0,15 0,4 2,0 1,0 0,05 0,25 1,2
B Deposits of very dense sand,
gravel, or very stiff clay, several tens
of metres in thickness,
gradual increase of mechanical
properties with depth.
1,2 0,15 0,5 2,0 1,35 0,05 0,25 1,2
C Deep deposits of dense or
medium-dense sand, gravel
or stiff clay with thickness
from several tens
to many hundreds of metres.
1,15 0,20 0,6 2,0 1,5 0,10 0,25 1,2
D Deposits of loose-to-medium
cohesionless soil or of
predominantly soft-to-firm
cohesive soil.
1,35 0,20 0,8 2,0 1,8 0,10 0,30 1,2
E A surface alluvium layer
of soil similar to C or D
with thickness varying between
about 5 m and 20 m,
underlain by stiffer material
1,4 0,15 0,5 2,0 1,6 0,05 0,25 1,2
S1 Deposits consisting, or
containing a layer at least
10 m thick, of soft
clays/silts with a high
plasticity index (PI > 40)
and high water content
Special studies
S2 Deposits of liquefiable soils,
of sensitive clays, or
any other soil profile
not included in types A E orS1
Special studies
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Code Design Response SpectrumSd(T1) Fmax = M Sd(T1)
Takes into account the capacity of the structure to dissipate energy
by plastic deformations: a behaviour factor q reduces the spectrum
The structure achieves the displacement ds imposed by the
earthquake accepting plastic deformationsin intended places called dissipatives zones
CD
EMFd=M.Sd(T)
Fe=M.Se(T)
Fd=Fe/q
d
ds=q.dyde=dy
Fd = Fe/ q
!!!
ds = q. de
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Summary
The design response spectrumSd(T1) Fmax=M Sd(T1)
Is a function of:
soil & site S TB TC TD
damping
capacity to dissipateenergy in plastic
deformations q
Sd(T1) est fonctionde la priode T1
T1=0,0 sH=5 m
concretebunker
T1=0,7 sH=17 m
T1=1,5 sH=5 m
T1=2,7 sH=100 m
0 1 2 3 4 5
1
2
3
4
T(s)
Soil A - q = 1,5
Soil C - q = 1,5
Soil C - q = 4
Sd(T)(m/s)
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B
Lecture du spectre
1
er
mode 2
e
mode 3
e
mode
D
Calcul des MNV M1bcorrespondant chaque
rponse modaleExemple : EEi = M base, i
E
Calcul de EE = Mbase =2
3
2
2
2
1 bbb MMM ++ (moyenne quadratique)
Sd (T)
Sd (T3)
Sd (T2)
Sd (T1)
Multimodal ResponseSeveral vibration modes
Masses associated to the different mode
Modal Superposition SRSS
Square Root of the Sum of the Squares
E: moments, shear, deformationsmodes: independants
problem: all positive !
CQC: idem, more general
Addition
2EiE EE =
global flexure storey in shear floor vibration
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Seismic massPeriods Tare functions of the masses M=> correct evaluation of real M necessary
=> seismic mass based on weight W =
E,i to estimate a likely value of service loads, computed as: can be
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Lateral force method of analysisIf structure response 1st vibration mode
the case for structure regular in elevation Approximate method: seismic base shearFb Advantage: signs of action effects are correct
( ) = mTSF 1db
Fb
Estimation of fundamental period T1 ?
Statistical relationships function of: structural type
height H
The lateral force method is the Approximate Method for Seismic Design
i,ki,Ej,k Q""G + m=
= 0,85
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.
Caution!
Units have to be consistent MassesM KgHeightH m
Acceleration Response SpectrumSd(T) m/s2
=>Forces N
Formulae for the estimation of the fundamental period T1 of a building.
Period T1 Reference structure
EI3MH2T
3
1 =
Exact formula for Single Degree of Freedom Oscillator.
Mass Mlumped at top of a vertical cantilever of heightH.Cantilever mass MB = 0
EI3
HM24,02T
3
B1 =
Exact formula for Single Degree of Freedom Oscillator.
Vertical cantilever of heightHand of total mass MB
EI3
H)M24,0M(
2T
3
B
1
+
=
Exact formula for Single Degree of Freedom Oscillator.
Mass Mlumped at top of a vertical cantilever of heightHand of total mass MB.
4/3t1 HCT =
H building height in mmeasured from foundation
or top of rigid basement.
Approximate Relationship (Eurocode 8).
Ct = 0,085 for moment resisting steel space framesCt = 0,075 for eccentrically braced steel frames
Ct = 0,050 for all other structures
d2T =1 Approximate Relationship (Eurocode 8).
d: elastic horizontal displacement of top of buildingin m under gravity loads applied horizontally.
( ) = mTSF 1db
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jj
iibi
ms
msFF
=
jj
iibi
mzmzFF
=
j
ibi
z
zFF
=
Storey Forces
If deformes shape simplified into linear
If storey masses are all equal
s: deformed shape
W4
W3
W2
W1
F4
h2
F3
F2
F1
Fb
z2
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Caracterisation of Structures
Specific to Seismic Design
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CD
EMFd=M.Sd(T)
Fe=M.Se(T)
Fd=Fe/q
d
ds=q.dyde=dy
Energy dissipation capacity
To increase safety and reduce costs:
dissipate permanently energy in plastic deformationsm u(t)u(t) + c [u(t)]2dt + F(u) u(t)dt = - m dg(t) u(t) dt
Ekintic + Eviscous + Edeformation = Etotal input
Edeformation = EEL +EEP
Fd = Fe/ q
!!!
ds = q. de
M
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Ductilit = max / y
MEP = 1/2 MELenergy of elastic deformation (triangle) at dmax : EELenergy absorbed plastically after one cycle (+ dmax, - dmax) : EEP = 2EEL
after 4 cycles (+ dmax, - dmax ): EEP = 8EELCondition: 2
Lower cost, because: MRd MEL in the non-dissipative structure
MRd = 0,5 MEL = MEP in the dissipative structureCost reduction : max 50%
Definition ofq ? Based on ductility: q = max / y = 2
dmax
H
A
max MEP
MEL
EP
EL
MA
max+ max
y
Currently: = 6 to 8 in steel elements
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2 // Universe
The real behaviour
The elasto-plastic behaviour
The designer sees onlythe elastic part of
the real behaviour
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Values of the behaviour factor q ?Reflect the potential for energy dissipation of the structural type
the design
Code values ofq: safe side estimates
In reality q varies depending on: seismicity redundancy influence of design conditions other than EQ
F
P
F
P
F
P
4 plastic hinges 1 plastic diagonal no plastic mechanism
q=6 q=4 q=1 (1,5)
* Stability of a K bracing depends on slender diagonal in compression, which fails in a brittle way.
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With a given local plastic rotation capacity ,a global mechanisme allows greater ultimate displacements
Eurocode 8 Definition of Ductility Classes or DC for design
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Ductility classes
The designer can choose to design structures: as usual, non dissipative
dissipative
Modern seismic design codes leave the choice open
define several Ductility Classes.
Eurocode 8: 3 Ductility Classes DCL Low Ductility, non dissipative structures
DCM Medium Ductility
DCH High DuctilityDCL: highest seismic design forces, only usual static design checks (Eurocode 3)
DCH: smallest possible design earthquake actions & seismic action effects
bending moments, etc are reduced in comparison to DCL[note: not displacements]
But other requirements to fulfil:
Example: class of sections related to q for dissipative elements
DCM: less requiring
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Behaviour factors q (maximum values).
Ductility ClassSTRUCTURAL TYPE
DCL DCM DCHMoment resisting frames (MRF) 1,5 (2*) 4 5u/1
Concentric diagonal bracings
Concentric V-bracings
1,5 (2*) 4
2
4
2,5
Eccentric bracings 1,5 (2*) 4 5u/1
Inverted pendulum 1,5 (2*) 2 2u/1MRF with concentric bracing 1,5 (2*) 4 4u/1
MRF with unconnected concrete or masonry
infills in contact with the frame
MRF with infills isolated from the frame
1,5 (2*) 2
4
2
5u/1
*the National Annex can allow q = 2 in class DCL
Behaviour factors in Eurocode 8.
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Conditions required for a very dissipative behaviour
Reliable dissipative zones
Local plastic deformation capacity with constant resistance arelimited. Ex: plastic rotation of a classe A section: 50 mrad
Numerous dissipative zones
To avoid excessive local plastic deformation as a result
of a concentration of deformations in few points
Dissipative zones in a decided scheme refering to a global plastic mechanism
Because it is not thinkable to have all zones of the structure with ideal
characterisics for plastic deformations
No to partial failure mechanism Fig: concept b concept a
concept a = du/ h1 tage
concept b
= du
/ h4 tages
concept b = concept a/4
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Design aiming at a global plastic failure mechanism
1. Define the objective: a global mechanism
2. Pay a price at local zones: criteria for local ductility
3. Pay a price for the mechanism to be global:
criteria to form numerous dissipative zones
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2. Pay a price at local zones:
Capacity Design
of resistances of all elements other than the plastic zones
overstrength of all zones adjacent to the intended plastic zones
=> stronger, elastic and stable
during the plastic deformations of the fuse zone
ductile link i other links j
fuse fragile
Computed action effect Edi = P Edj = P
Required resistance R di > Edi (Rdi / Edi) Edj >> P !!!
Capacity design Examples
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Capacity design . Examples.Beam in portal frames: dimensions results from several criteria:
resistance under 1,35 G + 1,5 Q Deflection limits Earthquake Mpl,Rd MEd
Checks of beam and connection adjacent to the plastic hinge in bending
For shear resistance
VEd,G due to non seismic actions
VEd,Mdue to Mpl,Rd,A et Mpl,Rd,Bsigns at ends A et B
VEd, can be >> VEd, analysis
Design bending moments
of connections
> MEd
, , , , ,( ) /Ed M pl Rd A pl Rd BV M M L= +, ,Ed Ed G Ed M
V V V= +
Non-seismic design Seismic design: t2 >> t1 a2 > a1
+1,1 ovMpl,Rd,beam
-1,1 ovMpl,Rd,beam
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3. Pay a price for the mechanism to be global: Example
Criteria to form numerous dissipative zones
Moment resisting frames:
rule of hierarchy of formation of plastic hinges
RbRc
MM 3,1
MRb beams resisting moments = fusesMRc columns resisting moments
At each node
S h i d i i
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Synthesis on design options
VEd
dSDe (T)
DCL
DCM
DCH
a)
b)
c)
Behaviour of frames with equal period Tsubmitted to pushover up to a design displacementSDe(T) :
a) Elastic design DCL
b) Medium ductility project DCM
c) Very dissipative project DCH
[Note : the design displacement is approximately independent ofq ]
Base Shear
Seismic action effects
are smaller in DCH.
This includes Base Shear
and Base Moments.
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General rules for the design of buildings in
Eurocode 8.
EN1998-1:2004 . Chapter 4
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General rules for the design of buildings in Eurocode 8.
EN1998-1:2004 . Chapter 4
Seismic action - definition of objective
No collapse Design Earthquake ULS
No damage Service Earthquake SLS
Regularity in plan geometrical criteria
in elevation criteria on stiffness distribution
torsional stiffness
Methods of analysis and regularity
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Linear Methods of Analysis.
Modal response using a design spectrum.
Standard method applicable to all types of buildings
regular or irregular in plan and/or elevation
Lateral force method
A static analysis for regular structures
which respond essentially in one single mode of vibration.
Can be applied to planar models of the structure depending on regularity criteria.
Structural regularity and permissible simplifications in seismic analysis in Eurocode 8.
Regularity Permissible Simplification Behaviour factor
Plan Elevation Model Linear-elastic
Analysis
q
YesYes
Limited
No
No
YesNo
Yes
Yes
No
2 planar2 planar
2 planar
1 model 3D
1 model 3D
Lateral forceModal response
Lateral force
Lateral force
Modal response
Reference valueReference value /1,2
Reference value
Reference value
Reference value /1,2 &
reduced u/1
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Non Linear Methods of analysis.
Pushover analysis
Non-linear static analysis carried out under constant gravity loads G
and monotonically increasing horizontal loads
Applied to verify or revise u/1 to estimate the expected plastic mechanisms
the distribution of damage
to assess the structural performance of existing/retrofitted buildings
Non-linear time-history analysis
Dynamic analysis direct numerical integration of differential equations of motion
Earthquake action: accelerograms (min 3)
For research and code background studies
Torsion
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3 reasons: eccentricity at every storey between the storeys resultant force
passing at mass centre CM and centre of rigidity CR.
rotation aspects of ground movement for very long structures uncertainty on exact location ofCM
=> accidental eccentricity = 5% of building length ppd to earthquake direction
CR: point where an applied force generates only a translation parallel to that force
Effects of torsion are determined based on CM-CR distance + the accidental eccentricity in + or -
Irregular structures
Computation of torsional effects from non coincidence CM/ CR => a 3-D model
Effects of accidental eccentricity: found applying at every level a torquecomputed as: (storey force) x (CM-CR distance)
Structures symmetrical in plan with CM= CR
Effects of accidental eccentricity approximated by amplifyingthe translational action effects by
x distance in plan between the seismic resisting structure considered and CM
Le the distance between two extreme seismic resisting structures
Symmetrical buildings with peripheral resisting structures: 1,3
e
6,01L
x+=
Di l t i di i ti t t
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Displacements in dissipative structures.
ds = q de
Combination of the effects of the components of the seismic action
Horizontal components of the seismic action are taken as acting simultaneously
Action effects evaluated separately
Maximum of each action effect due to the two horizontal componentsestimated by: SRSS of the action effect due to each horizontal component
Alternative
a) EEdx "+" 0,30EEdyb) 0,30EEdx "+" EEdy"+" implies "to be combined with'';
EEdx: action effects due to seismic action along horizontal axis xEEdy: due to seismic action along horizontal axis y
Behaviour factorq may be different in x and y
Vertical component of the seismic action
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Vertical component of the seismic action
If avg > 0,25 g the vertical component of the seismic action is taken into account: for horizontal structural members span 20 m
for horizontal cantilever 5 m
for beams supporting columns
in base-isolated structures
Analysis for determining the effects of the vertical componentmay be based on a partial model of the structure
If the horizontal components are also relevant for these elements: SRSSOr combinations:
a) EEdx ''+" 0,30 EEdy "+" 0,30 EEdzb) 0,30 EEdx "+" EEdy "+" 0,30 EEdzc) 0,30 EEdx "+" 0,30 EEdy "+" EEdz
Ultimate limit state No collapse requirement
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Ultimate limit state. No-collapse requirement .Conditions on resistance, ductility, equilibrium, foundation stability and seismic joints
Resistance condition
Rd is the design resistance of the element
Ed is the design value of the action effect due to the seismic design situation:
Ed = Gk,j + P + 2i.Qki + 1AEdIf necessary, second order effects are taken into account in the value ofEd
Limitation of second order effects mitigation of soft storey
2nd order momentsPtot
dr 1st order moments V
toth at every storey
Ptot total G at and above the storey considering seismic mass h: storey height
dr : drift based on ds = q de Vtot : total seismic shear at considered storey
0,1 => P- effects negligible
0,1 < 0,2 => multiply action effects
by 1/(1 - )Always: 0,3
dd RE
N
V
N
V
Ptot
dr= q.dre
h
Vtot
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Global and local ductility condition
Capacity design principle
Resistance of horizontal diaphragmsDiaphragms and bracings in horizontal planes able to transmit with overstrength
the effects of seismic action to the lateral load-resisting systems
resistance verifications:seismic action effects in the diaphragm from the analysis x d = 1,1
Resistance of foundations
Rd overstrength factor EF,G due to the non-seismic actionsEF,E : action effect from the analysis of the design seismic action
: value ofRdi/Edi of the dissipative element i of the structurewith highest influence on effectEF under consideration;
Rdi design resistance of the zone or element i;Edi design value of the action effect
Check always: Rdi/Edi q
RbRc 3,1 MM
EF,RdGF,Fd EEE +=
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Seismic joint condition
SRSS of the maximum horizontal displacements of the two buildings x 0,7 if same owner
Damage limitation
Non-structural elements of brittle materials attached to the structure: Ductile non-structural elements:
Non-structural elements not to interfering with structural deformationsOr no non-structural elements:
dr design interstorey drifth storey height;
reduction factor for lower return period of the seismic actionassociated with the damage limitation requirement.
Recommended : = 0,4 for importance classes III and IV = 0,5 for importance classes I and II
hd 005,0r
hd 0075,0r
hd 010,0r
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Architecture of Earthquake Resistant Buildings
Architecture of Earthquake Resistant Buildings.
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Architecture of Earthquake Resistant Buildings.
Basic features of an earthquake resistant building.Buildings are boxes
Subjected to earthquakes they work in the way sketched
Storey forces are attracted
by the diaphragms
which distribute them
to the vertical resisting structures
which transfer the forces
down to the foundations.
P i t t S d t t
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Primary structure Secondary structure.The vertical load resisting structure may comprise:
a main or primary system designed to carry the total earthquake effects
a secondary structure designed to carry only gravity loadsThe contribution to lateral stiffness and resistance of the secondary structure
should not exceed 15% of that of the primary structure.The members of the secondary structure and their connections must be able:
to accommodate the displacements of the primary structure
responding to an earthquake
to remain capable of carrying the gravity loading
Secondarystructure
Primarystructure
Conceptual design.
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p g
A good conceptual design enables the development of a structural systemto resist earthquakes at low additional costs in comparison to a non-seismic design.
Conceptual design: apply to the primary resisting system
leave freedom in the design of the secondary structure
Principles of conceptual design of earthquake resistant structures
Structural simplicity
Clear and direct paths for the transmission of the seismic forces
Modelling, analysis, designing, detailing and construction of simple structures
less uncertainties
more reliable prediction of seismic behaviour
Uniformity in plan
Even distribution of structural elements
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Even distribution of structural elements
Short and direct transmission of inertia forces created by the masses of the building
Symmetric layout of vertical earthquake resistant structures: achieves uniformity
eliminates large eccentricities between mass and stiffness
minimises the torsional moments
Uniformity may be realised by subdividing a building
by seismic joints into dynamically independent units
Favourable in-plan shapes
action
reactiontorsion
Don't do Do
Symmetrical in-plan shapes reduce torsion.
Structural systems distributed close to the periphery are the most effective at resisting torsion.
joints
Uniformity over the height
Avoids the occurrence of sensitive zones: concentrations of stress
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Avoids the occurrence of sensitive zones: concentrations of stress
large ductility demands
possible premature collapseRequires that non structural elements do not interfere with the structural elements
to localise the plastic deformations
like in soft storey mechanism
infills
soft storey
plastic
hinges
Redundancy
Evenly distributed
structural elements
increases redundancy
facilitateredistribution of action effects
energy dissipation
spread reactions at the foundations
action
d
reactions
Small lever arm of reactions
Don't do
action
d
reactions
Great lever arm of reactions
Do
Small lever arm of reactions Great lever arm of reactions
Torsional resistance and stiffness
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Limit torsional movements.
Structural systems distributed close to the periphery are the most effective.
Diaphragms
Distribute storey seismic force in the earthquake resisting frames.
Particular care with:
very elongated in-plan shape
large floor openings, especially those located near vertical structural elements.
Foundations
Ensure that the whole building is subjected to a uniform seismic excitationDesign should reduce problems with differential settlement under seismic action.
=>Rigid, box-type foundation:
foundation slab+ cover slab
Footings should be tied togetherby a foundation slab or tie-beams
Recommended