Download bi̇nalarin depreme karşi si̇smi̇k perfomaslarinin ayarlanmiş

Altıncı Ulusal Deprem Mühendisliği Konferansı, 16-20 Ekim 2007, İstanbul
Sixth National Conference on Earthquake Engineering, 16-20 October 2007, Istanbul, Turkey
BİNALARIN DEPREME KARŞI SİSMİK PERFOMASLARININ
AYARLANMIŞ KÜTLE SİSTEMLERİ İLE GELİŞTİRİLMESİ
TUNED-MASS SYSTEMS TO IMPROVE THE
SEISMIC PERFORMANCE OF BUILDINGS
Peter NAWROTZKI1
ÖZET
Pasif sismik kontrol stratejileri, bir deprem anında yapıyı etkileyebilecek enerjinin azaltılması
temeline dayanır. Bazı iyi bilinen yaklaşımlar, özel elemanların sürtünme, plastik şekillendirme
veya başka tür enerji yok edici özelliklerinden faydalanırlar. Bu sunum, binaların sismik
performansını geliştirmek için, sönümün nasıl arttırılabileceğine dair özel fikirler verecektir.
Bu amaç için ilave kütle sistemleri tavsiye edilmekte ve bunların performansı sarsıntı
tablalarında da teorik olarak test edilmektedir. Genel bir kanı olarak bu tarz sistemler deprem
uygulamaları için uygun görülmemekte iken, belirli tasarım şartları dikkate alındığı takdirde
artık bu genel kanı geçerliliğini yitirmiştir. ‘Tuned Mass Control Systems’ (TMCS) –
(Dengelenmiş kütleli kontrol sistemleri) yapının deprem sırasındaki deplasmanlarını,
ivmelerini ve sistem içindeki gerilimlerini kontrol etmek için kullanılabilmektedir. Yapının
çökmeye karşı emniyeti sağlanabilmektedir. Özellikle bina içinde bir müdahale ve değişikliğin
mümkün olmadığı durumlarda, bu sistem aynı zamanda mevcut binaların depreme karşı
güçlendirilmesi için de uygulanabilmektedir. Bu sayede yapının depreme karşı güçlendirilmesi
çalışmaları sırasında, binanın içindeki normal operasyonlar da kesintiye uğramaz.
Anahtar kelimeler: Deprem güvenliği, pasif kontrol, Tuned-Mass Systems, sismik güçlendirme
ABSTRACT
Passive seismic control strategies are based on the reduction of energy, which affects a
structure in case of earthquake events. Some well known approaches make use of frictional,
plastic or other energy dissipating behaviour of special devices. The following presentation
reflects some special ideas for the increase damping in order to improve the seismic
performance of buildings. For this purpose additional-mass systems are proposed and their
performance is investigated theoretically as well as on the shaking table. Usually these systems
are considered as not suitable for seismic applications, but this thesis is no more valid as a
general rule, if certain design approaches are kept. Tuned-Mass Control Systems (TMCS) can
be used to control the displacements, accelerations and internal stress variables of a structure
in case of earthquakes. The safety against collapse and defined states of serviceability of the
structures can be achieved. This system can also be used for the seismic retrofit of existing
buildings as the inside of the structure is usually not objective to modification. Hence, the
usual operation inside the building may go on during the upgrade activities.
Keywords: Earthquake Protection, Passive Control, Tuned-Mass Systems, Seismic Retrofit.
1
Dr. P. Nawrotzki, GERB Vibration Control Systems, Berlin/Essen, Germany, [email protected]
327
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Tuned-Mass Systems to Improve the Seismic Performance of Buildings
INTRODUCTION
A well accepted strategy in utilizing seismic control systems is based on the increase of structural
damping. As a first idea damping devices can be installed solely. Then, they have the task to damp
the relative motion between two structures, two parts of the same structure, or the structure and the
‘rigid’ vicinity. The damping effects may be obtained by friction, plastic deformation or viscose
behaviour inside the device. The entire improvement of the seismic performance becomes obvious
by different national and international standards. Some well known curves are compared, and Fig.
1 provides an idea of possible control effects. Usually 5 % of critical damping can be assumed for
buildings, and an increase of the damping ratio causes a reduction of the stress or acceleration
response as indicated by the correction factor ξ. As an example the increase from 5 to 20 % of
critical damping would cause a reduction of the induced seismic responses by about 50 %
according to the Japanese provisions (see Fig. 1).
1,4
Eurocode 8
1,3
Uniform Building Code 97
Correction Factor ξ
1,2
Taiwan Building Code
1,1
Architectural Institute Japan
1,0
IEEE Std 693-1997
0,9
0,8
0,7
0,6
0,5
0,4
0
5
10
15
20
25
30
Damping in %
Figure 1. Seismic control effects depending on structural damping
Tuned-Mass Damper Systems (TMD) are widely used for the reduction of vibration caused by
wind and traffic like pedestrians or railway trains. Typical structures like slender bridges, stacks,
high and slender buildings possess low levels of damping and may therefore undergo unacceptable
vibration. TMDs cause control effects which are similar to the increase of damping. Depending on
the mass ratio, the tuning frequency and the damping capability the amplitude reduction can be
very significant and achieve values of about 10 to 20 % of the figures without TMD. The reduction
effects in these applications are higher that in case of seismic events because the governing
vibration is similar to stationary motions and the TMD gets better adjusted to the motion.
Nevertheless significant reduction effects can also be observed for seismic excitation. The ideas of
the improvement of seismic performance according to Fig. 1 can be confirmed by theoretical and
practical investigations. In order to distinguish between ordinary Tuned-Mass Systems and those
for seismic applications the expression Tuned-Mass Control Systems (TMCS) is used. The layout
of such systems is slightly different from that for a usual TMD system. Here, the mass and tuning
ratio as well as the damping are chosen according to different criteria.
A typical situation for structures is shown in Fig. 2. Here, a multi-storey building is equipped
with a tuned-mass system on the rooftop. The additional mass consists of reinforced concrete and
rests on helical steel spring devices with integrated dampers.
P. Nawrotzki
329
Figure 2. Typical tuned-mass system at the top of a building
NUMERICAL INVESTIGATIONS
Numerical simulations of buildings under earthquake with tuned-mass systems have frequently
been performed. In many cases a special building model is taken and the additional mass is
connected with the building elastically; sometimes the mass ratio is varied. Then, different
recorded earthquakes are run and the responses of the structure with and without tuned mass are
compared. The obtained results are usually not showing a unique picture. It can be concluded from
this procedure that the tuned mass improves the response behaviour for most of the investigated
cases, but there are also models under seismic excitation without significant improvement. In all of
the latter cases without significant difference the structural response without TMCS turned out not
to be dangerous for the building. The reasons are the induced internal forces and acceleration
responses which are at a low level without any need for further reduction. In these cases the
governing natural frequencies are not excited. The described steps for the layout of a tuned-mass
system do not reflect the required procedure for real projects!
For real projects there is a building with columns, beams, frames, walls, floors, and other
important members. The structure consists of certain materials, possesses certain dimensions and
there is a certain mass or mass distribution, stiffness, ductility and many other mechanical
parameters. On the other hand there is the seismic risk which can be described with statistical
parameters. The most suitable representation for engineering purposes can be seen in a site specific
response spectrum. Here, for instance, we can directly see whether the building is in the dangerous
frequency range and furthermore we can derive artificial base-excitation functions which
correspond to the project site. Also recorded seismic events can be taken for the layout of the
tuned-mass of a real structure, but in these cases the acceleration-time histories have to be scaled
according to the site specific response spectrum.
In Fig. 3 two examples for the numerical modeling of buildings with TMCS are given. On
the left hand side the first mode of an RC structure is shown with a combined lateral force resisting
system. The tuned-mass is modeled as a single mass which is elastically connected to the center of
the rooftop. A braced steel frame structure is shown on the right hand side of Fig. 3. There are four
RC blocks arranged in a manner that the dead load for a single center column is increased by about
6 % of the TMCS dead load only.
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Tuned-Mass Systems to Improve the Seismic Performance of Buildings
Figure 3. FE structures with TMCS on the roof - RC and steel frame building
0,20
Without TMCS
With TMCS
Hor. Top Displacement [m]
0,15
0,10
0,05
0,00
-0,05
-0,10
-0,15
-0,20
0
5
10
15
20
Tim e [s]
Figure 4. Typical time-history of displacement responses with / without TMCS
Fig. 4 shows the performance of the structural response improved by a TMCS. The original
response is given as a red curve and the induced peak responses are reduced by about 40 % by only
activating the tuned mass (blue curve). It becomes obvious that the mass has a significant influence
already at an early phase of the ground motion. The TMCS causes an increase of damping for the
structure and this can also be seen in the displacement-time history starting at about 10 s. The
residual motion after the strong motion phase is significantly damped out as the amplitude becomes
nearly zero after about 15 s. The unprotected structure has still amplitudes of about ±100 mm in
this time domain. Having a look at Fig. 1 we can conclude an increase of the damping ratio from 5
to 15 % when the AIJ regulation is taken as a basis. Assuming the UBC 97 we can even derive a
damping ratio of about 25 % in case of the activated TMCS.
The TMCS significantly reduces the top storey displacements, inter-storey drifts, response
accelerations and consequently induced internal stress responses due to earthquakes. The
corresponding effects of the performance with TMCS can also be shown in modified phase
diagrams (Fig. 5). On the left hand side the original response of an RC structure is given assuming
a damping ratio of 5 %. By activating a mass of less than 2 % of the total mass of the building, the
response curves change significantly. On the right hand side of Fig. 5 the improvement can be
described in terms of displacement and acceleration values. Of course, the tuning frequency plays a
role in the improvement of the seismic performance as well as the choice of the critical damping.
Optimum values can usually be found in the range of 5 to 20 % also depending on the target
motion values. The damping broadens the working frequency band of the TMCS.
Acceleration [m/s²]
Acceleration [m/s²]
P. Nawrotzki
12
8
4
0
-4
-8
-12
-100 -75
-50
-25
0
25
50
75
100
331
12
8
4
0
-4
-8
-12
-100 -75 -50 -25
0
25
50
75 100
Displacement [mm]
Displacement [mm]
Figure 5. Structural behaviour without (left) and with TMCS (right) in the phase plane
EXPERIMENTAL INVESTIGATIONS
In parallel to numerical investigations it is always important to compare the results with
experimental data. For this purpose shaking table tests have been performed at IZIIS, Skopje,
Macedonia. The geometry of the tested steel frame model is given in Fig. 6. The columns as well as
the beams are made of steel hollow profile appropriately welded at the joints. The structure in the
central span has a special bracing substructure, which is used for modeling the stiffness and
damping needed for the test. In the orthogonal direction the frame model has only one span of 1.5
m, but by adding a bracing the structural stiffness in that direction is increased several times. The
height of each floor is 0.75 m, while all three spans in the longitudinal direction amounts to 1.5m
each. The total mass of the tested structure is 19.0 t, and the mass of the TMCS is 260 kg which
corresponds to about 1.3 % of the entire mass. The total mass of 19.0 t has been obtained by adding
steel blocks on each floor without any influence on the stiffness.
SPRINGS
& DASHPOTS
TMCS
LEVEL 05
LEVEL 03
LEVEL 02
DEAD LOAD
SG
SG
SG
REFERENT BEAM
LEVEL 04
LEVEL 01
SG
SG
LEVEL 00
BIAXIAL SHAKING TABLE
Figure 6. Tested model on the shaking table with position of the TMCS
The performance of the frame with and without TMCS has been studied by simulating ten
different earthquakes records. Eight of them are recorded during the real earthquake motion, and
two are representing artificial earthquake time histories. Among them are Northridge, Kobe,
Mexico City, Vrancea (Romania), Izmit (Turkey). The effectiveness of the TMCS has been
estimated based on the difference of time responses of the tested model in terms of accelerations,
displacements and strain measurements for identification of axial loads and bending moments. At
first, the model was tested with unlocked TMCS, and all selected earthquakes were simulated for
minimum three different intensities. The same testing has been repeated with locked TMCS and
response-time histories were recorded for the same measuring points as for the case with the
unlocked TMCS.
From the large number of recorded time histories responses of relative displacements at fifth
level (top of the model) and bending strains recorded at the bottom of the middle column of the
first floor are presented. In Fig. 7 a comparison of time responses of the mentioned quantities for
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Tuned-Mass Systems to Improve the Seismic Performance of Buildings
unlocked (black curve) and locked TMCS (red curve) are presented for the Turkish earthquake
(under reduced intensity). For the locked case the peak relative top displacement is recorded to be
about 14 mm (Fig. 7, left), while the activated tuned-mass system causes an improvement of
performance by nearly 40 %.
15
600
Level 5
Middle
400
Bending strain 1E-6
Relative Displacement (mm)
10
5
0
-5
-10
200
0
-200
-400
-15
-600
0
2.5
5
7.5
Time (s)
10
12.5
15
0
2.5
5
7.5
10
12.5
15
Time (s)
Figure 7. Recorded responses with activated (black) and locked TMCS (red)
Qualitatively these results correspond very well to the numerical investigation; the
corresponding records are shown in Fig. 4. Here, the same base-excitation function has been used
for a another building and under different seismic intensity. Having a closer look at the bending
strain response of the middle column (Fig. 7, right hand side) the reduction of peak amplitudes with
activated TMCS is even higher than 40 %. It becomes obvious from Fig. 7 that the efficiency of the
TMCS becomes significantly larger after 10 seconds of ground motion in this case. The dynamics
of the tuned mass becomes better adjusted to the motion of the structure, and thus, the damping
effect becomes even more evident.
More insight into the mechanical behaviour of the structure with activated TMCS can be
derived from Fig. 8. Here the axial force response of the bottom of the middle column is shown
with locked (red) and activated tuned mass (black curve) under IEEE excitation. It is well known
that this artificial earthquake causes the high amplification of responses for structural frequencies
between 1.1 and 8 Hz. As the steel frame possesses first frequencies at about 1.9 Hz resonance
effects can be expected. The axial force response can well be controlled by the tuned mass as
shown in figure 8, left hand side. The peak values are reduced from more than 10 kN to less than 6
kN. The response is also expressed in terms of the corresponding FFT spectrum on the right hand
side of Fig. 8. A structural frequency of 1.9 - 2 Hz becomes visible for both cases, and hence, the
additional mass does not cause a significant change of the frequency. The enormous reduction of
the spectral amplitude can be understood by an effect which corresponds to the increase of the
critical damping ratio.
Figure 8. Recorded response of axial force of column and corresponding FFT spectrum
P. Nawrotzki
333
CONCLUSION
Theoretical and experimental investigations have shown that tuned-mass systems can well be
applied for the control of seismically induced responses. The quantity of the additional mass has to
be chosen according to the target control efficiency; usual values for these purposes can be found in
the range of 1.5 - 4 % of the total building mass. With an increase of the tuned mass the control
effect becomes higher.
Tuned-mass systems are especially suitable for the reduction of seismic drift ratios.
Furthermore the damage of important structural members is reduced and thus, the loss of stiffness
by cracks, plastic zones, etc., becomes significantly less. Fig. 9, left hand side, shows the typical
nonlinear structural behaviour without TMCS in case of an earthquake. The linear load deflection
curve exceeds the limit force for the concerned structural member which is given with a value of 2
units in this typical example. The seismic energy which is represented by the remaining triangle
(marked in Fig. 9, left) cannot be taken by the member and hence, it causes plastic deformation.
The nonlinear deformation (energy) is increased by the corresponding portion in the rectangular
section which is also marked in Fig. 9, left side. The resulting total deflection amounts to a value of
7.25 units where only 2 units are related to linear elastic behaviour.
On the right hand side of Fig. 9 the same energetic considerations are made for the structure
with activated TMCS. The peak forces are reduced by 40 % and hence, the damage causing energy
becomes considerably smaller. The corresponding triangle is also marked in the sketch. The
resulting overall deflection is this case corresponds to 3.25 units where again 2 units are related to
the linear elastic behaviour of this member. The damage causing energy can be reduced from 10.5
to 2.5 units only by activating the TMCS. Consequently, a remarkable decrease of the structural
frequencies by seismic effects can be avoided with a proper layout of the tuned-mass system.
Fig.
9. Nonlinear seismic effects in structures without (left) and with TMCS (right)
A slight drop of the frequencies in case of seismically induced damage would not yet cause
the malfunction of the TMCS because
a) the tuning of the additional-mass system is usually sub-critical and hence, the structural
frequencies would even approach the optimal frequencies of the TMCS,
b) usually a high percentage of critical damping is used for the relative motion between structure
and additional mass which spreads the working frequency range of the TMCS.
For the seismic upgrade of existing buildings it is also possible to take measurements in
regard to the most important structural frequencies. In this case damage sustained during the past
periods as well as soil-structure interaction effects are already included in the basic layout
parameters for the TMCS. Furthermore non-sufficient rigidity or significant loss of stiffness of the
fundamental structure would also become evident by measurement.
Properly designed tuned-mass control systems can be characterized as follows:
a) They reduce seismically induced responses in terms of displacements, accelerations, internal
stresses and strains as well as subsoil demands.
b) They increase the structural safety. The collapse of a building becomes less probable and hence,
human life is protected.
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Tuned-Mass Systems to Improve the Seismic Performance of Buildings
c) They improve the serviceability of structures. Damage and corresponding repair cost in case of
seismic events are reduced significantly.
d) In comparison to conventional strengthening methods, the building can usually be under
operation during the installation of the TMCS (if no additional measures are required).
e) Regarding the overall procedure and required material for the installation of a tuned-mass system
this strategy can be classified as 'cost effective‘.
REFERENCES
Nawrotzki P (2002) “Artificial Increase of Elasticity and Damping for Seismically Excited Structures”,
Proc. 12th European Conference on Earthquake Engineering, London, Paper No. 58.
Nawrotzki P, Jurukovski D and Rakicevic Z (2005) “Shaking Table Testing of a Steel Frame Structure with
and without Tuned-Mass Control System”, Proceedings Eurodyn 2005, Paris.
Villaverde R (2002) “Roof Isolation System Implemented with Steel Oval Elements: Exploratory Study”,
Proc. 3rd World Conference on Structural Control, Como, Italy.
Nawrotzki P and Chouw N (2004) “Effectiveness of Tuned-Mass Dampers in Reducing the Response of
Soil-Structure Systems to Near-Source Earthquakes”, Proc. The 11th International Conference on
Soil Dynamics & Earthquake Engineering, Berkeley, USA.