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TYPOLOGY OF SEISMIC MOTION AND SEISMIC TYPOLOGY OF SEISMIC MOTION AND SEISMIC ENGINEERING DESIGNENGINEERING DESIGN
E. MistakidisR. Apostolska (Petrusevska), D. Dubina, W. Graf, G. Necevska-Cvetanovska, P. Nogueiro, S. Pannier, J.-U. Sickert, L. Simões da Silva, A. Stratan, U. Terzic
COST C26: Urban Habitat Constructions under Catastrophic EventsWG2: Earthquake resistance
Workshop Prague, March 30-31, 2007
Introduction
Earthquake forces on structures a characteristic case where an action can be exceptional and therefore lead to catastrophic events.It is admitted that there exists a high probability that the value of the seismic forces will at some time exceed the value prescribed in the design.
Inherent uncertaint nature of the seismic action Incomplete or inadequate knowledge of the structural
behavior.
Seismological aspects
It has been demonstrated that the characteristics of the ground motions vary between recording stations. Two main regions with different types of ground motions are considered (Gioncu et al 2000). The far-source region. The near-source region.
˘ The vertical component could be greater than the horizontal ones.
˘ The significance of higher vibration modes increases ˘ Due to the pulse characteristics of the actions, the ductility
demands could be very high.
After Kobe earthquake it has been verified that earthquake loading conditions in the near-source region subject buildings to more severe
conditions than previously assumed.
Influence of the ground conditions The following parameters influence the amplification or attenuation of the seismic action on the structures the thickness of the soft and stiff soil layers, the shear wave velocities of the rock and soil layers, the soil/rock impedance ratio, the layering properties of the soil layers etc.
Attention to landsliding, liquefaction surface fault rupture
Structure related itemsStructure related itemsMagnification of the seismic action on short period structuresConnections in steel structures have been identified as crucial for the structural response after the Kobe and Northridge earthquakes. Concrete structures suffer from micro-cracks induced by relatively moderate earthquakes that influence the structural response under design-level earthquakes. The case of old existing structures has to be identified as one where the seismic events may be catastrophic due to the fact they were designed (if so) with old codes, proved to be inadequate.
Overview of the presentationOverview of the presentationFirst part (ground motion – uncertainty)
Seismic motions with specific characteristics that lead to exceptional actions on structures. Near-fault ground motions and the local site parameters are examined and the latest developments in the field are presented. Modeling of the ground motion specifically for the needs of the seismic analysis of structures. Behaviour of structures in the short period range and the corresponding magnification of the seismic action that has been observed. Uncertainty in structural analysis (uncertainty in the seismic motion parameters and uncertainty in the model parameters).
Second part (structural behaviour)Performance based design as a tool for the analysis of the structural behaviour under extreme seismic events. Influence of the connection behaviour in steel structuresCapacity design methodology for the design and evaluation of the seismic resistance of reinforced concrete structures. Direct displacement-based design approach for the design of reinforced concrete structures.
NearNear--fault ground motionsfault ground motions
Near-field (distance to fault < 20-60 km): site position with respect to the focus is importantForward directivity - rupture propagates toward a site: large period, high-amplitude velocity pulse of short durationBackward directivity - rupture propagates away from a site: short period, low-amplitude motion, long duration
NearNear--fault ground motionsfault ground motions
Near-fault regions:large period, high-amplitude velocity pulselarge vertical component
Near-fault in design codes:scarcely representedwhen considered (by an amplification coefficient - UBC97), does not account for change in frequency content of the ground motion
Local site conditionsLocal site conditions
Basin effectsseismic wave may be "trapped" inside the basin amplification and increase of duration of the seismic motions
Surface topography: amplification of seismic motion for irregular topographies
crestcanyonslope
Important parameters affecting ground motion characteristics.
Local site conditionsLocal site conditionsFrequency content of the ground motion
Stiff soil: amplification of spectral accelerations in the short-period rangeSoft soil: amplification of spectral accelerations in the long-period range
Seed et al, 1976 (NEHRP 2000)
Influence of the frequency content on the inelastic Influence of the frequency content on the inelastic structural responsestructural responseStructures designed for seismic forces lower than the ones corresponding to an elastic responseComponents of the force reduction factors R=RμRS:
ductility-related Rμ (major contribution)overstrength RS
Frequency content strongly influences inelastic structural response:
T<TC: "equal displacements"T>TC: "equal energy"
0 5 10 15 200
2
4
6
8
μ
Rμ
VR77-INC-NS
ElasticEPP, T=0.2EPP, T=0.5EPP, T=1EPP, T=1.5EPP, T=2
( )1 1 CC
C
T for T TTR
for T Tμ
μ
μ
⎧ − + ≤⎪= ⎨⎪ >⎩
F elastic
EPP
Ground motions with control period larger than the system’s period impose large ductility demands Bucharest 1977 record (Tc=1.42sec)
Seismic motions with high Seismic motions with high TTCC valuesvalues
Soft soils
Directivity effect in case of near-field earthquakes
Check: (Stratan 2003)496 European records6.5<Mw<7.8PGA>0.9 m/s2
Values ofValues of TTCC computed and records computed and records divided into two groupsdivided into two groups::
0.3<0.3<TTCC<0.4<0.4All motions All motions were were recorded on recorded on rock or firm rock or firm soilsoil
1.1<1.1<TTCC<1.7<1.7Motions recorded on soft Motions recorded on soft soils or were nearsoils or were near--field field records records (<35 km)(<35 km)
Seismic force reduction factorsSeismic force reduction factorsIn spite of the strong relationship between Rμ and the frequency content of the ground motion, code force reduction factors are constant:
empirically based on structural performance in past earthquakeslarger overstrength of low-period structuressmaller ductility-related force reduction factor for low-period structures
This simplification may not be correct for ground motions with large values of control period TC:
soft soil conditionsdirectivity effects in near-fault ground motions
R
R
T
Rμ
RS1
TC
MODELLING OF GROUNDMODELLING OF GROUND--MOTION AND SEISMIC ANALYSIS MOTION AND SEISMIC ANALYSIS OF STRUCTURESOF STRUCTURES
Time history representation of ground motionTime history representation of ground motion
Recorded accelerograms: should be adequately qualified with regard to the seismogenetic features of the sources and to the soil conditions appropriate to the site.Simulated accelerogram: generated through physical simulation of seismic source, travel path, and local site conditions.Artificial accelerograms: generated so as to match the code elastic spectrum.Simple pulses can be used to model ground motion (especially useful in case of near-fault ground motions).
For many years the structural design was performed with elastic analysis and reduced seismic forces.The recently introduced nonlinear methods (pushover, time-history nonlinear analysis) require the accurate representation of the ground motion.
Magnification of seismic action Magnification of seismic action on short period structureson short period structures
The target displacement is given by the equationδt =C0 C1 C2 C3 Sa g (T/2π)2
C0 : relates the spectral displacement with the displacement of the upper level of the building. C1 :takes in to account the magnification of the maximum displacement due to
inelastic behaviour. C1=1/R+(1-1/R)Tg/T, με C1<2 γιά T<0.1sec , C1 = 1 για T>TCR : elastic strength ratioTg : characteristic period (dependent on the soil)
C2 : takes into account the quality of the hysteretic responseC3 : takes into account the increased displacements when the second-order
effects become significant.
Force
Displacementδ teδ
eF
Ft
Reliability of the Reliability of the Displacement Coefficient Displacement Coefficient MethodMethodThe DCM is based on the statistical analysis of the results obtained by the time history analysis of SDOF oscillators of various types.
Αρ Code Date Magnit. Station Comp PGA (g) Char.period(sec)
1 ARGO183-1 17/01/1983 ΜL=6.5 Argostoli L 0.171 0.35
2 ATHENS-2 07/09/1999 ΜL=5.9 Halandri Τ 0.159 0.333 ΑΤΗΕΝS-3 07/09/1999 ΜL=5.9 KEΔΕ T 0.302 0.54 ATHENS-4 07/09/1999 ΜL=5.9 ΓΥΣ L 0.121 0.45
5 ARGO183-7 23/03/1983 ΜL=5.7 Argostoli Τ 0.192 0.55
6 ΖΑΚ188-4 16/10/1988 ΜL=5.5 Zante Τ 0.170 0.3757 ΚΑL186-1 13/09/1986 ΜL=5.5 Kalamata Τ 0.273 0.38 EDE190-1 21/12/1990 ΜL=5.4 Edessa L 0.101 0.4
9 ΑRGO183-8 24/03/1983 ΜL=5.1 Argostoli Τ 0.305 0.4
10 PAT393-2 14/07/1993 ΜL=5.1 Patras T 0.401 0.3511 LEF194-1 25/02/1993 ΜL=5.1 Lefkas T 0.136 0.4
12 KYP187-1 10/06/1987 ΜL=5.0 Kyparissia Τ 0.127 0.25
13 ΑRGO192-1 23/01/1992 ΜL=5.0 Argostoli L 0.204 0.35
14 PYR193-8 26/03/1993 ΜL=5.0 Pyrgos L 0.165 0.515 ΚΑL286-2 15/09/1986 ΜL=4.8 Kalamata Τ 0.263 0.516 LEF188-2 24/04/1988 ΜL=4.5 Lefkas T 0.245 0.317 ΙΕR183-3 26/08/1983 ΜL=4.4 Ierissos Τ 0.178 0.5
RECORDS USED IN THE ANALYSISSelection from a database of 220 records with earthquakes between 1980 and 1994according to the following criteria:
Peak ground acceleration (PGA) >0.1gMagnitude ML >4.4 in the Richter scale
F
Δ
F
Δ Δ
F
a) b) c)
Type ΑElastoplastic model with 5% hardening. Corresponds to perfect response and is used here as a reference model.
Type ΒElastoplastic model with 5% hardening but with reduced stiffness. Characteristic for wall systems with dominant the bending response.It’s typical for new buildings designed according to newer theories.
Type CElastoplastic model with softening behaviour (-10%) and with reduced stiffness. It’s typical for masonry systems where, for increased displacements, the strength is reduced.
Models used in the analysisModels used in the analysis
Two types of dynamic analyses were performedIn the first type the displacement ductility μ was considered as constant
(μ=2,4,6,8)In the second type the strength reduction factor R was considered as
constant (R=2,3,4,5,6).The ratio dn/de is monitored, wheredn : maximum displacement of the non-linear oscillatorde : maximum displacement of the elastic oscillator having the same stiffness with the initial stiffness of the non-linear oscillator.
Πλαστιμότητα μετακινήσεων - Displacement ductility μ=2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2T (sec)
dn / de
Πλαστιμότητα μετακινήσεων - Displacement ductility μ=4
0
0.5
1
1.5
2
2.5
3
3.5
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2T (sec)
dn / de
As the ductility increases, the scattering increases as well.For T > 0.4-0.6 sec, the mean values are very close to 1. The scattering increases for lower values of the period.For Τ <0.4-0.6sec, the increase of the ductility leads to larger mean values
Type A model
Results for constant μ
F
Δ
Πλαστιμότητα μετακινήσεων - Displacement ductility μ=2
00.20.40.60.8
11.21.41.61.8
2
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2T (sec)
dn / de
Πλαστιμότητα μετακινήσεων - Displacemenτ ductility μ=4
0
0.5
1
1.5
2
2.5
3
3.5
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2T (sec)
dn / de
The mean values for periods between 0.1-0.4 sec tend to be greater than the corresponding ones for the type A model
Type B model
Results for constant μ
F
Δ
The scattering increases (values between 0.4 and 6.5)The mean values for Τ between 0.1-0.4 sec are significantly higher than those of the type Α model.
Πλαστιμότητα μετακινήσεων - Displacement ductility μ=2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2T (sec)
dn / de
Πλαστιμότητα μετακινήσεων - Displacement ductility μ=4
0
0.5
1
1.5
2
2.5
3
3.5
4
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2T (sec)
dn / de
Type C modelResults for constant μ
Δ
F
Mέσοι όροι, Μοντέλο Α Mean values, Μοdel A
0 0.5
1 1.5
2 2.5
3 3.5
0 0.5 1 1.5 2
T (sec)
d n /d e μ=2μ=4μ=6μ=8
Tυπική απόκλιση, Μοντέλο ΑStandard deviation, Μοdel A
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.5 1 1.5 2
T (sec)
d n/d
e
μ=2μ=4μ=6μ=8
Mέσοι όροι, Μοντέλο BMean values, Μοdel B
0
0.5
1
1.5
2
2.5
3
3.5
0 0.5 1 1.5 2T (sec)
d n/d
e
μ=2μ=4μ=6μ=8
Τυπική απόκλιση, Μοντέλο ΒStandard deviation, Model B
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.5 1 1.5 2T (sec)
d n/d
e
μ=2μ=4μ=6μ=8
The mean values are smaller than 1 for large periods (the linear systems overestimate the displacements of the non-linear systems).
In the short period range, the results differ according to the ductility level.
The mean values are greater than 1 even for high periods (especially for large values of the displacement ductility) in the results of Model C
The values of the standard deviation in Model C are greater than the corresponding values of the type A and B models.
Mέσοι όροι, Μοντέλο ΓMean values, Μοdel C
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 0.5 1 1.5 2
T (sec)
d n/d
e
μ=2μ=4μ=6μ=8
Τυπική απόκλιση, Μοντέλο ΓStandard deviation, Model C
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 0.5 1 1.5 2
T (sec)
d n/d
e
μ=2μ=4μ=6μ=8
Τhe results are close to 1 until a frequency of about 2.5.
After that value, a great scattering occurs.
R=2
0123456789
10
0 1 2 3 4 5 6 7 8 9 10Frequency ν
dn / de
R=4
0
2
4
6
8
10
12
14
16
18
20
0 1 2 3 4 5 6 7 8 9 10Frequency ν
dn / de
Type A model
Results for constant R
F
Δ
The mean values are increased with respect to the values that correspond to model A.
Type B model
Results for constant R
R=2
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10Frequency ν
dn / de
R=4
0
2
4
6
8
10
12
14
16
18
20
0 1 2 3 4 5 6 7 8 9 10Frequency ν
dn / de
F
Δ
These models are vulnerable to collapse
From the 1700 examined oscillators (17 ground motions x 20 frequency values x 5 levels for R), 692 oscillators failed.
Type C model
Results for constant R
R=2
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 1 2 3 4 5 6 7 8 9 10Frequency ν
dn / de
R=4
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 1 2 3 4 5 6 7 8 9 10Frequency ν
dn / de
R 2 3 4 5 6 Failed oscillators 53 113 145 176 205
Percentage % 15.5 33.2 42.7 51.8 60.0
Structures exhibiting negative hardening (softening) should remain elastic in order to avoid collapse
Δ
F
Mέσοι όροι, Μοντέλο ΑMean values, Model A
0
1
2
3
4
5
6
7
8
9
0 2 4 6 8 10
Frequency ν
d n/d
e
R=2R=3R=4R=5R=6
Τυπική απόκλιση, Μοντέλο ΑStandard deviation, Model A
0
1
2
3
4
5
6
7
8
0 2 4 6 8 10
Frequency ν
d n/d
e
R=2R=3R=4R=5R=6
Mέσοι όροι, Μοντέλο BMean values, Model B
0
1
2
3
4
5
6
7
8
9
0 2 4 6 8 10
Frequency ν
d n/d
e
R=2R=3R=4R=5R=6
Τυπική απόκλιση, Μοντέλο BStandard deviation, Model B
0
1
2
3
4
5
6
7
8
0 2 4 6 8 10
Frequency ν
d n/d
e
R=2R=3R=4R=5R=6
The mean values are close to 1 for v<2.5, for all R levels. For ν>2.5, the mean values increase, depending on R. Large values of the standard deviation appear in the high-frequency range.
For (v<2.5) the values of C1 arereliable.For high frequencies, there is a strong dependance on RC1 cannot describe effectively the response of inelastic systems with large R values in the high frequency range.
Proposal C1= 1 + (R-1)(Tg /T - 1)/2 για Τg < T <0.1sec
R=2
0
0.5
1
1.5
2
2.5
3
0 1 2 3 4 5 6 7 8 9 10Frequency ν
d n/d
e
DCM, T2=0.4
MODEL-A
PROPOSITION
R=4
0
1
2
3
4
5
6
7
0 1 2 3 4 5 6 7 8 9 10Frequency ν
d n/d
e
DCM, T2=0.4
MODEL-A
PROPOSITION
R=6
0
1
2
3
4
5
6
7
8
9
0 1 2 3 4 5 6 7 8 9 10Frequency ν
d n/d
e
DCM, T2=0.4
MODEL-A
PROPOSITION
Uncertainty in structural Uncertainty in structural earthquake assessment and earthquake assessment and simulationsimulation
earthquake loading aging processesstorm loading damageimpact loads material parameters
Classification of uncertaintyClassification of uncertainty
In general data and models are uncertain. This fact has a significant influence for the results of the analysis. Uncertainty has to be described with suitable models and considered within the analysis.
Uncertainty in engineering analysisUncertainty in engineering analysis
Stochastic uncertaintyA random result (e.g. of an experiment under identical boundary conditions) are observed almost indefinitely
Informal uncertaintyThe system overview is incomplete or if only a small number of observations are available.
Lexical uncertaintyThe uncertainty is quantified by linguistic variables, transformed onto a numerical scale.
Fuzz
ines
s
Examples of fuzzinessExamples of fuzziness•
••
•••
Modelling of uncertainty with fuzzy variablesModelling of uncertainty with fuzzy variables
fuzzy set
( )( ){ }AA x; x x X= μ ∈%
support S(A)~
membership function μA(x)μA(x)
1
0
triangular fuzzy number A and α-levels:
α-level
μA(x)
1
0x1 x2 x3 x
α
~
Expresses the „certainty“ withwhich a quantity is known
{x |k
Aα = ∈X ( ) k}μ ≥ αx
∈
From the fuzzy quantity crisp sets
may be extracted for real numbers ak (0, 1]. These crisp sets are called a-level sets.
Solution techniqueSolution technique
cartesian product1 2 ... nK A A A= × × ×% % %%
[ ][ ] ⎭
⎬⎫
⎩⎨⎧
=μ=μ∈
μ=μ==
n;...;1i;)x(min)x(;Xx )x;...;x;x()x();x;...;x;x(x
K~iAiKii
n21KKn21
μA1(x1)
μA2(x2)fuzzy input value x2 = A2
~
1.0
0.0x1
1.0
0.0x2
μK(x)
1.0
0.0
x1
x2
K = A1 x A2~~~
~
fuzzy input value x1 = A1~ ~
×
(interaction of fuzzy quantities)
Solution techniqueSolution technique
α α= i
1
α α= i
1
α α= i
1
generation of an uncertain input subspace (bunch parameters s1,1, s1,2, s1,3)
μ(s1,1)
s1,1;αl s1,1;αr s1,1 s1,2;αl s1,2;αr s1,2 s1,3;αl s1,3;αr s1,3
μ(s1,2) μ(s1,3)
s1,1;αl s1,1;αr s1,1
s1,3
s1,3;αr
s1,2;αl
s1,2;αr
s1,2
s1,3;αl
n-dimesionaluncertaininput subspace
~ ~ ~
Solution techniqueSolution technique
( ) ( )j,r 1 2v g ..., s , ... g s , s= =% % %%
mappingoperator
0.01.0 ακ 0.0 1.0ακ
μ(s1) μ(s2)k1, ls α
k1, rs α
k2, ls α
k2, rs α
kj j,v v α∈
kj,v α
α-level optimization
2s
k2,s α
1s
k1,s α
kj, rv αkj, lv α
1.0ακ
0.0
μ(vj)
fuzzy result value vj~
fuzzy input value s1 fuzzy input value s2~~
k1 1,s s α∈k2 2,s s α∈
vj
Illustrative exampleIllustrative example
3.00
3.00
3.00
3.00
3.00
3.00
3.00
6.006.00 6.00
LoadsDead load 30.0 kN/mLive load 15.0 kN/m
Seismic papametersSpectral acceleration: 0.16g, Soil type: B, Effective damping: 5%Importance factor 1.00
Foundation factor: 1.00
Beamsupper reinforcement 8.0cm2
Lower reinforcement 4.0cm2
ColumnsTotal amount of the longitudinal reinforcement 20.24cm2 (uniformly distributed along the perimeter of the column).AnalysisElastoplastic (pushover)Determination of target displacement (ATC40)
Input quantitiesInput quantitiesFuzzy numbers representing the
steel yield stress and the concrete compressive strength
1.00
0.75
0.50
0.0
0.25Cer
tain
ty
1.00
0.50
0.25
0.75
0.0
Steel yield stress (Mpa)350 400 450
Cer
tain
ty
Concrete compressive strength (Mpa)13 16 19
0.10
0
0.05
0
0.400
0.300
0.200
0.100
0.20
0
0.15
0
0.10
0
0.05
0
0.100
0.200
0.300
0.400
0.10
0
0.15
0
0.20
0
0.05
0
0.00
0
0.000
0.400
0.300
0.200
0.100
H/V
Displacement (m)
0.20
0
0.15
0
Elastic Point
"Fuzzy" capacity curve
Fuzzy capacity curve
Cer
tain
ty
0.25
0.0
1.00
0.50
0.75
12 1513 14Horizontal displacement (cm)
Fuzzy top-horizontal displacement
ResponseResponse quantitiesquantities
Capacity Design Methodology for Design and Evaluation of Seismic Resistance of RC Building Structures
MAIN PURPOSE:Define strength and deformability capacity of the structureDefine nonlinear behaviour of the structure for a given earthquake effectEvaluation of seismic resistance
Definition of the structural system of the building and determination of the quantity and quality of the built-in material.STEP 1
Determination of the Q- Δ diagram for each element and the storey Q- Δ diagrams (RESIST computer program).STEP 2
Definition of the seismic parameters and the design criteria.STEP 3Nonlinear dynamic analysis of the structural system for a given earthquake effect (INELA computer program).STEP 4
Selection of an optimal system in newly designed structures and evaluation of the seismic resistance for the existing structuresSTEP 5
RESIST-INELA Methodology[Author: Golubka Necevska-Cvetanovska, IZIIS, 1991]
Settlement Kapistec
Application of RESIST-INELA Methodology
Settlement Jane Sandanski
Application of RESIST-INELA Methodology
Settlement Novo Lisice
Application of RESIST-INELA Methodology
Settlement John Kennedy
Application of RESIST-INELA Methodology
To conceive particular aspects of EC8 for frame structural systems and compare them with the requirements and criteria prescribed with our national existing seismic regulations (SP-81), and methodology developed at Institute of Earthquake Engineering and Engineering Seismology – Skopje, several structures were analyzed.
Presented here are the results from the analysis of structure B-2, Unit 4, "Vardar" settlement – Skopje, (fYRepublic of Macedonia).
Correlation with Modern Design Codes
Characteristic plan and weights of building storeys
X-X direction
0 200 400 600 800 1000
1
2
3
4
5
6
7
8
Sto
rey
S eismic forces [kN]
IZIISEC-8SP- 81
Y-Y direction
0 500 1000 1500
1
2
3
4
5
6
7
8
Sto
rey
S eismic forces [kN]
IZIISEC-8SP- 81
Correlation with Modern Design Codes
Seismic forces obtained according to SP-81, EC8 and IZIIS Methodology
Ulcinj (Albatros) Amax=0.4g x-x direction
0
1
2
3
4
5
6
7
8
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
Required displacement (cm)
Stor
ey
EC-8SP-81IZIIS
Ucinj (Albatros) Amax= 0.4g y-y direction
0
1
2
3
4
5
6
7
8
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
Required displacement (cm)St
orey
EC-8SP-81IZIIS
Correlation with Modern Design Codes
Required displacements for Ulcinj (Albatros) Earthquake
Direct Displacement Based Design Approach for Design of RC Frame Building Structures
Displacement-Based Seismic Design, DBDDisplacementDisplacement--Based Design vs. Forced Based Design vs. Forced --Based Design Based Design
Displacement-based seismic design is defined broadly as any seismic design method in which displacement-related quantities are used directly to judge performance acceptability.
Concrete cracking and reinforcement yielding
Formation of flexural plastic hinge
The extent of damage is related to the amount of deformation (turn to displacement) in plastic hinge
Insignificant change of forces despite change of wall behaviour from elastic to deeply nonlinear
Direct Displacement-Based Seismic Design, DDBD
The most developed and the most important method in the field of direct displacement-based design of RC building structures, both with frame and with shear wall lateral bearing system is the Priestley’s method, (Priestley, 2000, 2002).
“Substitute structure approach”, (Shibata and Sozen, 1975)
Design Example – RC Frame Building
In order to determine the effort needed for direct displacement-based design of a RC frame building, an example structure is designed using the Priestley’s method (Priestley, 2000, 2002) with minor changes that do not affect the essence of the original. Later, an example structure is analyzed using a nonlinear static procedure, (Terzic, 2006).
B
B
3030
470
30
470
30
470
30
470
470
30
30 30470
30470
30470
30470
30470
60 60
440
60
440
60
440
60
440
60
440
500
500
500
500
500
500500500500500
Layout of typical storey and cross-section of the structure
Design Example –Applied Method
1921.813461.946.5019.403.7037049840.150.5552%/50 years
1123.984049.466.0112.941.8537049840.150.27810%/50 years
2890.5920828.322.653.810.9237049840.150.13920%/50 years
(kN)(kN/m)(s)(kg)(m)(m)
VBKeTeξμme∆y∆dEarthquake
Assume dimensions of elements
Determine storey yield drift θy
Select target performance levels according to FEMA 356 and for each performance level select critical drift θu, corresponding earthquakes
probability of occurrence and design Sd-T diagram
Determine design displacements at different storeys Δi
For each performance level transform MDOF system into equivalent SDOF
system and calculate base shear VB
Distribute base shear force vertically in proportion to the storey mass and
displacement profile
Determine transverse and column longitudinal reinforcement applying
capacity design approach
END OF DESIGN
Calculate required longitudinal reinforcement in structural members assuming that beams have stiffness at
maximum response, and columns cracked-section stiffness and hinges at
base with base resisting moment applied
Determine design displacement Δd for SDOF system
Determine yield displacement Δy
at the height of the resultant lateral seismic force
Determine ductility μs
Determine effective damping ξe
Determine effective mass me
Determine effective period Te
from Sd-T diagram
Calculate effective stiffness Ke
Calculate design base shear VB
425002%/50 year CP
247510%/50 year LS
122520%/50 year IO
Critical Drift θu
(%)
Return Period (yrs)
Probability of earthquake occurrence
Performance Level
Analysis Results for Target Drifts
Percentage of Members Achieving State Earthquake Drift
(%) IO LS CP
20%/50 year 0.42 39 0 0 10%/50 year 0.61 66 0 0 2%/50 year 1.43 100 0 0
Percentage of Members Achieving State Earthquake Drift
(%) IO LS CP
20%/50 year 0.39 2 0 0 10%/50 year 0.66 61 0 0 2%/50 year 1.25 100 0 0
20%/50 year EC10%/50 year EC
2%/50 year EC
IO D
eman
d
LS D
eman
d
CP D
eman
d
20%/50 year DDBD10%/50 year DDBD
2%/50 year DDBD
0500
100015002000250030003500400045005000550060006500
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10
Displacement (m)
Base
She
ar (k
N)
Target drifts-DDBD Target drifts-EC8
Capacity curve for building designed according to DDBD and EC8
Influence of connection Influence of connection behaviourbehaviour on the seismic on the seismic response of structuresresponse of structures
1. Influence of pinching
3.50
m3.
50m
7.50m 7.50m7.50m 7.50m
E9,15
E9,16E11,14E11,12
E11,11 E11,13
E11,10E11,8
E11,7 E11,9
E11,4 E11,6
E11,5E11,3
E9,2
E9,1
HE
A22
0Composite section
Hysteretic curve for external E9 connection Hysteretic curve for internal E11 connection
Base Base5.80m
HE
B32
0H
EB
320
3.0m
4.0m
sec
m/sec2
sec
m/sec2
J4
J4
Base2m/sec
sec
IPE450
IPE450
5.80m
J3 IPE400
J2 IPE360
J1 IPE300
3.0m
3.0m
3.0m
HE
B32
0H
EB
240
HE
B28
0
HE
B28
0H
EB
240
HE
B32
0H
EB
320
HE
B32
0
HE
B28
0H
EB
240
HE
B32
0H
EB
320
HE
B32
0
J1
J2
J3
J4
J4
J1
J2
J3
J4
J4
J1
J2
J3
J4
J4IPE450
IPE450
IPE400
IPE360
IPE300
Performed analysesDynamicN2 (uniform)N2 (modal)
Connections rot. (mrad)dynamic
rot. (mrad) N2 (uniform)
rot. (mrad) N2 (modal)
E 9,15 48.0 27.6 30.2 E11,7 46.3 30.4 33.3
J231E/J4 15.7 13.9 15.8 J53EF/J-X610 8.8 16.9 20.3
Analysis results
ConclusionFor study of the behaviour of the
connections, the monotonic methods have some limitations, because they give insufficient hysteretic information.
2. Comparative effect of extreme event
Influence of the connections simulated with semi-rigid behaviour and partial strengthwith rigid behaviour and full strength
9.0m 6.0m
4.335m
4.135m
4.135m
4.135m
4.135m
4.135m
4.135m
4.135m
Ground Floor
Floor 1
Floor 2
Floor 4
Floor 3
Floor 6
Floor 5
Floor 7
Floor 8 6.0m
0
100
200
300
400
500
600
700
800
900
1000
0,00 0,20 0,40 0,60 0,80 1,00Top Disp.* [m]
V* [KN]
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0,00 0,20 0,40 0,60 0,80 1,00Top Disp.* [m]
V* [KN]
0
2
4
6
8
10
12
14
16
18
0,00 0,10 0,20 0,30 0,40 0,50 0,60 0,70Sd [m]
Sa [m/s2]
Espectro EC8 0,50 gBilinear
0
2
4
6
8
10
12
14
16
18
0,00 0,10 0,20 0,30 0,40 0,50 0,60 0,70Sd [m]
Sa [m/s2]
Espectro EC8 0,50 gBilinear
