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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