0235
STUDY OF THE DYNAMIC AND EARTHQUAKE BEHAVIOR OF ANCIENT
COLUMNS AND COLONNADES WITH AND WITHOUT THE INCLUSION OF
WIRES WITH ENERGY DISSIPATION CHARACTERISTICS
G. C MANOS1, M. DEMOSTHENOUS2, V. KOURTIDES3 And J. EVISON-MANOU4
SUMMARY
Ancient Greek and Roman structures composed of large heavy members that simply lie on top of
each other in a perfect-fit construction without the use of connecting mortar, are distinctly different
from relatively flexible contemporary structures. The colonnade (including free-standing
monolithic columns or columns with drums) is the typical structural form of ancient Greek or
Roman temples. The columns are connected at the top with the epistyle (entablature), also
composed of monolithic orthogonal blocks, spanning the distance between two columns. The
seismic response mechanisms that develop on this solid block structural system during strong
ground motions can include sliding and rocking, thus dissipating the seismic energy in a different
way from that of conventional contemporary buildings. This paper presents results and
conclusions from an experimental study that examines the dynamic response of rigid bodies,
representing simple models of ancient columns or colonnades. The rigid bodies employed in this
study were made of steel and are assumed to be models of prototype structures 20 times larger.
These models are subjected to various types of horizontal base motions (including sinusoidal as
well as earthquake base motions), reproduced by the Earthquake Simulator Facility of Aristotle
University. It also studies the influence on the response of the examined models arising from the
inclusion of wires having energy dissipation characteristics. Summary results and conclusions
from the observed dynamic performance are presented and discussed. As can be seen from the
results obtained so far the performance of the model colonnades, exhibit similar stability trends
with that observed for the individual column. The excessive rocking and sliding and subsequent
collapse of the epistyle is an additional form of unstable response in addition to the excessive
rocking, rotation and sliding of the individual columns. Moreover, the scheme of insertion of
certain SMA wires with energy dissipation characteristics seems to inhibit, up to a point, unstable
modes of response, whereas these identical model structures without the wires developed certain
types of unstable response at lower excitation amplitudes.
STUDIED STRUCTURAL CONFIGURATIONS
The rigid bodies employed in this study for forming these models were made of steel and are assumed to be
models of prototype structures 20 times larger. Certain models that were also examined were made of marble but
their response is not included in this paper. Three basic configurations are examined here, as outlined in the
following:
Model Single Steel Column.
The first studied structural configuration is that of a model single steel truncate cone assumed to be a model of a
monolithic free-standing column, as shown in figures 1 and 2. As reported elsewhere by Manos and
Demosthenous (1991, 1997), these model columns, as all steel columns which were employed in the formation
of model colonnades that are described next, were manufactured in such a way that they could represent
1
2
3
4
Professor, Dept. Civil Eng, Aristotle University, Thessaloniki, Greece, Fax 003031 995769, email [email protected]
Dr. Civil Engineer, Aristotle University of Thessaloniki and ITSAK
Dr. Civil Engineer, Aristotle University of Thessaloniki
Aristotle University
prototype columns either sliced in drums or monolithic columns. For the tests reported here for the single steel
column or for the steel column colonnades all model columns are monolithic.
103mm
14.5 mm
28.0mm
96.2
76.0
SMA WIRE
ACCELEROMETER
Load cell
522mm
522mm
LVDT
LVDT
LVDT
2
1
LVDT
47.95mm
95.0mm
98.5mm
NORTH
Load cell
SOUTH
AXIS OF EXITATION
E
S
N
97mm
W
Figure 1. Geometry of the single steel column
Figure 2. Single steel column on the shaking table
Two-Steel Column Model Colonnade.
The second studied structural configuration is formed by
two steel truncate cones, of the same geometry as the
model of the individual column described in 1.1 before,
but supporting a rectangle of solid steel at the top,
representing in this way the simplest unit of a
colonnade; this is shown in figure 2. In this second
configuration the weight of the epistyle was varied. This
variation of the weight of the epistyle results in
numerous sub-formations from which two distinct cases
are reported here; one with this weight of the epistyle
being equal to 286Nt whereas the second had the weight
of 605Nt. The centers of this two-steel column model
colonnade coincided with the axis of the horizontal base
motion. In a number of experiments with the model
single column or with the models of the two-column
colonnade a special supporting platform for these
models was constructed on top of the shaking table
platform in order to measure the forces transferred
during the excitation sequence from the excited
structures to the base. However, as this testing
arrangement was rather complex, it was used in a limited
number of tests; for most tests the moving platform of
the shaking table provided the foundation base for the
model structures.
21.6 cm
6.75 cm
52.2 cm
LOAD CELL
1
2
LOAD CELL
CH.06 / PC1
CH.14 / PC2
CH.07 / PC1
CH.15 / PC2
2
1
2
1
1.8 cm
4.8 cm
1.0 cm
1.0 cm
9.85 cm
LOAD CEL
49.6 cm
AXIS OF EXCITATION
21.6 cm
E
25.8 cm 2.88 cm
29.8 cm S
Í
0.90 cm
W
Figure 3. Two-steel column model colonnade
Four-Steel Column Model Colonnade.
The third configuration is again a model colonnade formed by four steel truncate cones with identical geometry
to the ones used before. A monolithic rectangular steel epistyle with dimensions shown in figures 4a, 4c and 4d
was placed at the top of these identical four steel columns in a perfect fit condition. This model structural
formation is depicted in figure 4a showing the four column assembly looked at from the top of the epistyle as it
is resting on the shaking table moving platform. Indicated in this figure is the relevant orientation of this model
formation with the North (N) - South (S) direction coinciding with the direction of the horizontal motion of the
shaking table. Moreover, as can be seen in figures 4a, 4c and 4d the four-steel column model colonnade is
symmetric with respect to this N-S axis of horizontal excitation. It can also be considered as a twin of the two2
0235
steel column model colonnade described in 1.2 before, because of the identical geometry and the weight of the
epistyle on the four-column formation which is approximately twice as much of the weight of the epistyle for the
two-column formation. Some details on the geometry and the instrumentation that was employed in this testing
arrangement with the four-column model is also depicted in figures 4a to 4d.
SHAKING TABLE
E
E
217mm
580mm
37.5
N
3
4
SETRA 4
LVDT1 (TOP)
SETRA 5
SETRA 6
LVDT 3
SETRA 1
S
480mm
LVDT 7
LVDT 6
LVDT 2
1
200mm
N
37.5
3
4
SETRA 3
217mm
SETRA 2
1mm SMA Wire
590mm
217mm
LVDT 4
2
LVDT 5
1
S
2
ACCELEROMETR
SETRA
W
COLUMNS AND 1mm WIRES SET UP
W
PLAN VIEW
Figure 4b Location of theSMA wires
Figure 4a. Four-column colonnade (Plan View)
LVDT 6
LVDT 7
LVDT 7 & LVDT 6
200mm
SETRA 3
LVDT 1
SETRA 4
SETRA 2
SETRA 6
217mm
SETRA 3
67mm
SETRA 5
67mm
SETRA 5
522 mm
522 mm
49mm
LOAD CELL
1
2
2
LVDT 2
LVDT 4
LVDT 3
LVDT 5
3
LVDT 4
LVDT 5
SETRA 1
20mm
200mm
275mm
N
580 mm
W
S
480mm
E
VIEW FROM SOUTH SIDE
AXIS OF EXCITATION
VIEW FROM WEST SIDE
Figure 4c
Four column colonnade. Testing
arrangement along the axis of the horizontal base
motion.
Figure 4d
Four column colonnade. Testing
arrangement transverse to the
axis of the
horizontal base motion.
Configurations of Columns and Colonnades with Wires.
The experimental investigation was supplemented by an additional study that aimed to examine influences on
the dynamic response arising from a certain intervention technique with wires having energy dissipation
characteristics. These wires were applied at critical locations and aimed to provide an increased resistance as
well as energy dissipation capacity. The wires that are used throughout were 1mm in diameter and were provided
by FIP Industriale of Padova, Italy, in the framework of a cooperative research project supported by the
European Union (Manos, 1998). Their mechanical properties were fully investigated by a special testing
campaign conducted at the Joint Research Center of the European Union at Ispra, Italy. A limited number of
basic tests were also conducted at the Laboratory of Strength of Materials of Aristotle University with the wires
that were directly employed in the present investigation.
3
0235
For this purpose a fully dynamic uniaxial tensile
testing machine was utilized whereby specimens
of the wires could be tested in a fully cyclic manner
with the desired amplitude and frequency. Figure 5
depicts the stress-strain plot from such a test with
the frequency of the cyclic loading sequence being
equal to 0.1Hz. As can be seen from this figure the
loading cyclic behavior is characterized by almost
plastic upper and lower plateaus with a recovery of
the plastic strain due to the basic material
properties that lead to the name shape memory
alloy; for this reason these wires are designated in
this paper as SMA wires. SMA wires with 1mm
diameter were used in all the studied model
structures mentioned in 1.1, 1.2 and 1.3 before.
Stress (N t/m m 2)
400
1m m D iam eter SM A W ire
(Length 240m m ,w ith Coolant) 300
200
100
0
-0,03
-0,02
-0,01
0
0,01
0,02
0,03
-100
-200
-300
Strain(m m /m m )
Frequency ofApplied
Displecem ent :0.1 H z
-400
Figure 5. Mechanical properties of the used SMA wires
In the single steel column and the two-steel column colonnade the SMA wires were positioned through the
centers of the columns and were anchored at the base and the top, as shown in figures 2 and 3, respectively. For
the colonnade with the four steel columns the position of the wires is depicted in figure 4b as well as in figures
4c and 4d. A special anchoring case was firmly attached at the epistyle and the SMA wires were anchored there
as well as at the moving platform of the shaking table. The number of wires employed here was either four or
eight. The arrangement shown in figure 4b is for the eight wires. The removal of the four wires located the
furthest from the center of this model colonnade resulted in the four wire arrangement.
EXPERIMENTAL INVESTIGATION.
During this experimental sequence the model structures described in 1.1, 1.2 and 1.3 are subjected to a variety
of base motions before and after the intervention technique with the SMA wires. During testing, acceleration and
displacement measurements were recorded in order to identify sliding and rocking modes of response. A very
stiff, light metal frame was built around the studied model structure in order to carry the displacement
transducers that measured the rocking angle; this metal frame also provided temporary support to the specimen
during excessive rocking displacements indicating overturning. The sequence of tests included a series of
sinusoidal base excitations as well as earthquake simulated tests. Moreover, through a series of relatively strong
intensity base motions, the stability of the model formations was studied together with the resulting collapse
modes at certain stages focusing on the influence that the inclusion of the SMA wires has on such collapse
modes. Finally, the dynamic and simulated earthquake base motions were supplemented with tests named ‘Pull
Out Static Tests’. During these tests a well controlled horizontal displacement was imposed at the top of the
studied model formation at a slow rate. The displacement response of the model was monitored together with the
horizontal load that resulted at the top from the imposed horizontal displacement.
OBTAINED EXPERIMENTAL MEASUREMENTS
Model single steel column without SMA wires.
Sinusoidal Tests :
During these tests the frequency of motion was varied from 1.5Hz to 4Hz. This resulted in groups of tests with
constant frequency for the horizontal sinusoidal motion for each test. In the various tests belonging to the same
group of constant frequency, the amplitude of the excitation was varied progressively from test to test. Summary
maximum response results from such tests are depicted in plots such as these of figure 6a. The following points
can be made from the observed behavior during these tests:
- For small amplitude tests the rocking behavior is not present; the motion of the specimen in this case follows
that of the base.
- As the horizontal base motion is increased in amplitude, rocking is initiated. This rocking appears to be subharmonic in the initial stages and becomes harmonic at the later stages.
4
0235
- Further increase in the base motion amplitude results in excessive rocking response, which after certain buildup
leads to the overturning of the specimen. Large rocking response is also accompanied by significant sliding at
the base and by rotation and rocking response out-of-plane of the excitation axis.
Summary results for the single steel column without any wires are depicted in the plot of figure 6a. The ordinates
in this plot represent the amplitude of the base acceleration whereas the absiscae represent the frequency of the
base horizontal dynamic excitation. The following observations summarize the main points as they can be
deduced from this plot:
- The stable-unstable limit rocking amplitude increases rapidly with the excitation frequency.
- For small values of the excitation frequency the transition stage from no-rocking to overturning, in terms of
amplitude, is very small and it occurs with minor amplitude increase.
0,7
0,7
S IN G LE S TEE L C O LU M N
FFT Amplitude at Base
FFT Amplitude at Base
S IN G LE S TEE L C O LU M N
0,6
w ithout S M A W IR ES
0,5
M ock-up w ith Load cell at Base
0,4
S ep. 1998
U nstable R ocking
0,3
0,2
0,1
N o R ocking
0,6
M ock-up w ith Load cell at Base
0,5
0,4
0,3
w ith P restressing
SM A w ires
S table R ocking
w ithout S M A W ires
0,2
0,1
U nstable R ocking
0
0
1
2
3
1
4
3
4
Frequency (H z)
Frequency (H z)
Figure 6a
SMA wires
2
Single column dynamic response with
Figure 6b Single column dynamic response with
SMA wires
Model single steel column with SMA wires.
Sinusoidal and Simulated Earthquake Tests.
Tests similar to the ones described above were performed for the single column with one SMA wire passing
through the center of the column (figure 2). Due to space limitations only summary results are presented here
from the testing sequence with the sinusoidal horizontal base motions. The response curve obtained from these
tests for the single steel column with the SMA wire is depicted in figure 6b together with the corresponding
response curve of the single steel column without the SMA wire. As already mentioned, when discussing the
response curve of the single steel column without the SMA wire of figure 6a, this curve represents in this case a
boundary between stable-unstable rocking response. When this boundary is exceeded, because of an increase of
the amplitude of the base motion of constant frequency, it leads to the overturning of the model structure
(instability). In contrast, the plotted response curve for the model structure with the SMA wire does not represent
a stable-unstable boundary. Because of certain limitations in the capacity of the shaking table and in order to
protect the SMA wires and their anchoring fixtures from repeated damage from overturning, the stable-unstable
boundary was not established in this case. Instead, the plotted curve indicates amplitudes of the base motion with
the model structure fitted with the SMA wire still exhibiting stable rocking response. Obviously, the stableunstable boundary for the model structure with the SMA wire is expected to occur at higher amplitudes of the
base excitation than those represented by the plotted curve which in this case is designated as stable rocking
response. By comparing the stable rocking response curve in figure 6b for the model single steel column with the
SMA wire with the stable-unstable boundary for the same structure without the SMA wire the favourable
influence of the insertion of the SMA wire on the stability of the dynamic sinusoidal response can be clearly
identified. Similar favourable influence of the insertion of the SMA wire on the stability of the model structure
was observed during the earthquake simulated tests.
Pull Out Static Tests
This testing arrangement was described in paragraph 2 before. The obtained response in terms of nondimensional rocking angle (ordinates) and applied horizontal load at the top of the single steel column with the
SMA wire (absiscae) is depicted in figure 7a; figure 7b shows the measured response for this model structure in
terms of non-dimensional rocking angle (ordinates) and overturning moment (absiscae). As can be seen from
5
0235
SIN G LE STEEL SO LID C O LU M N
50
W ith 1m m SM A W ire Through its C enter
45
40
35
30
ècr=11.14
25
o
20
15
SIN G LE STEEL SO LID C O LU M N
350
Overturning Moment (Nt.mm
148mm below base
Top Pull out Horizontal For
480mm from Base
figures 7a and 7b the insertion of the SMA wire leads to an almost elastoplastic force-displacement response;
moreover the unloading path is accompanied by a lower plateau and a recovery of the plastic strain similar to the
one observed during the uniaxial tests of the individual SMA wire (figure 5). This observation is also true for the
overturning moment response; in this way the overturning moment transmitted from the model structure to the
foundation is limited by the observed upper plastic plateau.
147 N t Prestressing Force
10
5
W ith 1m m SM A W ire Through its C enter
300
250
200
o
ècr=11.14
150
147 N t Prestressing Force
100
50
0
0
0
0,1
0,2
0,3
0,4
0
0,5
0,1
0,2
0,3
0,4
0,5
N one D im ensionalAngle R ocking (è/ècr)
N one D im ensionalAngle R ocking (è/ècr)
Figure 7b. Static pull-out response of single steel
column with SMA wire
Figure 7a. Static pull-out response of single steel
column with SMA wire
Model colonnade with two-steel columns without and with SMA wires.
Sinusoidal base motions.
The testing sequence, based on the sinusoidal excitation which was described in 3.1.1. before, is repeated here.
This was done once with the two columns supporting an epistyle with 286Nt weight and was repeated with an
epistyle of 605Nt weight.
0,7
TW O C O LU M N S T E E L C O LO N A D E FR E E
FFT Amplitude at Base (
FFT Amplitude at Base
0,7
w ithout S M A W IR E S
0,6
0,5
0,4
U nstable R ocking
E pistyle 286N t
M ock-up w ith
Load cell at B ase
0,3
E pistyle 605N t
M ock-up at
S haking T able
P latform
0,2
0,1
0
T W O C O LU M N S T E E L C O LO N A D E FR E E
0,6
M ock-up w ith Load cellat B ase
0,5
E pistyle 286N t
0,4
S table R ocking
w ith 2
P restressed S M A
W ires (98N t)
0,3
0,2
U nstable R ocking
w ithout S M A
W ires
0,1
0
1
2
3
4
1
Frequency (H z)
2
3
4
Frequency (H z)
Figure 8a. Two column colonnade dynamic response
without SMA wires
Figure 8b Two column colonnade dynamic response
with SMA wires
Discussion of the Observed Performance :
- The behavior of the examined model colonnade with two steel columns without the SMA wires, being
subjected to sinusoidal base excitations, exhibits similar trends to those observed for the individual steel column
without the SMA wire, with regard to the influence that the excitation frequency exerts on the rocking amplitude.
That is, for higher frequency of excitation larger excitation amplitude is required to cause the overturning of the
structure; this can be seen in both figures 8a and 6a.
- For medium rocking angles, the observed response of the model colonnade with the two steel columns tends to
remain in-plane. This observation is valid for both the sinusoidal as well as the simulated earthquake excitations.
- There are no noticeable variations on the stability of this model colonnade without the SMA wires that result
from the increase of the weight of the epistyle during the sinusoidal dynamic excitation test sequence. This can
6
0235
be seen from the plot of the measured response during this experimental sequence as expressed through the
stable-unstable boundary curves in figure 8a, whereby the boundary curves for the two epistyle weight cases
almost coincide. This confirms such an expected performance to dynamic excitations whereby the stabilizing
influence of the increase of the weight of the epistyle is offset by a corresponding increase in the inertia
horizontal forces.
- By comparing the stable rocking response curve in figure 8b for the model colonnade with the two steel
columns with the SMA wire with the stable-unstable boundary for the same structure without the SMA wire, the
favourable influence of the insertion of the SMA wire on the stability of the dynamic sinusoidal response can be
clearly identified.
Simulated Earthquake Tests
The shaking table tests were performed with the model two-steel column colonnade with the epistyle having
286Nt weight (see figure 2). The earthquake simulated tests were based on the prototype recordings of the
horizontal ground motion during the El Centro 1940 and the Kern County 1953 (Taft) Californian earthquakes.
The horizontal acceleration as recorded at the shaking table moving platform is a measure of the intensity of the
simulated earthquake motion. This is depicted in figure 9a and it is a simulated earthquake motion. This
excitation was used in two tests with the two-column model colonnade; the first without the SMA wires and the
second with the SMA wires.
1,5
B ase A cceleration
R ecorded atthe Shaking Table
M ax=1.488g
0,5
0
0
4
8
12
16
-0,5
-1
M in=1.47g
-1,5
Tim e (sec)
None Dimensional Rocking Angle (è
Figure 9a. Acceleration recorded on the shaking
Table
R ocking R esponse ofTw o SteelC olum n Colonade
0,7 w ith 1m m SM A W ires
None Dimensional Rocking Angle (è
Base Acceleration
1
The rocking response for the model colonnade with the
SMA wires is depicted in figure 9b whereas the
corresponding response without the SMA wires for the
same simulated excitation is depicted in figure 9c. The
plotted parameter is that of the ratio of the rocking
angle (θ) by the critical rocking angle (θcr); values of
this ratio larger than 1 indicates overturning, which is
evident for the case without the SMA wires but not in
the case of with the SMA wires (figures 9b and 9c ).
Thus the favourable influence of the insertion of the
SMA wire on the stability of the model structure could
also be observed during the earthquake simulated tests
with the two-steel column colonnade on the shaking
table.
M ax=0,566
0,5
0,3
0,1
-0,1 0
4
8
12
16
-0,3
-0,5
M in=-0.576
-0,7
2
R ocking R esponse ofTw o SteelC olum n C olonade
w ithoutSM A W ires
M ax=1.540
1,5
1
0,5
0
-0,5
0
4
12
16
-1
-1,5
-2
M in=-2.376
-2,5
Tim e (sec)
Tim e (sec)
Figure
9b Rocking response of the model
colonnade with the SMA wires
8
Figure 9c Rocking response of the model colonnade
without the SMA wires
Model colonnade with four steel columns with and without SMA wires.
Sinusoidal base motions and Simulated Earthquake Tests.
The testing sequence based on the sinusoidal excitation which was described in 3.1.1 is repeated again here. This
was done once with the four columns supporting an epistyle with 649Nt weight; the anchoring fixtures for the
SMA wires were present during the tests for the model with and without the SMA wires. The weight of the
7
0235
epistyle together with the weight of these anchoring fixtures was 706Nt. As already mentioned in paragraph 1.4,
two arrangements for the SMA wires were tried here; the first with 8 SMA wires and the second with 4 SMA
wires.
The observed dynamic performance of the
configuration with the 8 SMA wires is
depicted in figure 10 together with the same
configuration without any SMA wires.
0,7
FFT Amplitude at Base
FO U R C O LU M N STEEL C O LO N A D E
0,6
M ock-up at Shaking Table P latform
0,5
w ithout SM A
W IR ES
E pistyle 649N t
0,4
Stable R ocking
w ith 8
P R ES TR ESSED
SM A W IR ES
(98N t)
0,3
0,2
0,1
U nstable R ocking
- The observed performance of the model
colonnade with two columns without the SMA
wires (figures 8a) can also be observed here
with a typical stable-unstable response
boundary (figure 10).
0
1
2
3
4
Frequency (H z)
Figure 10. Dynamic response of four column colonnade
with and without SMA wires
- Due to the presence of four columns in this
model colonnade the observed rocking
response remains mainly in plane even for
large rocking angles, without exhibiting
tendencies for significant out-of-plane
response.
- By comparing the stable rocking response curve in figure 10 for the model with the SMA wires with the stableunstable boundary for the same structure without the SMA wires the favourable influence of the insertion of the
SMA wires can again be clearly identified.
CONCLUSIONS
1. The dynamic performance, in terms of stability, of the examined model structures, that is of the single column,
of the model colonnade with two columns and finally of the model colonnade with four columns, exhibited
similar trends with regard to the influence that the excitation frequency and amplitude exert on the rocking
amplitude and the subsequent overturning of these structural formations.
2. The insertion of the SMA wires, as described, had a noticeable favourable influence on the stability of the
studied model formations. The model structures with the insertion of the SMA wires developed stable response
at amplitudes higher than those at which the model structures without the SMA wires had already overturned.
This is more apparent for relatively lower frequencies.
ACKNOWLEDGMENTS
The partial support of the European Commission (DIR XII , ENV.4-CT.96-0106, project
gratefully acknowledged.
ISTECH),
is
REFERENCES
Manos, G.C., and Demosthenous, M. 1991. Comparative study of the dynamic response of solid and sliced rigid
bodies, Proc., Florence Modal Analysis Confer., pp.443-449.
Manos, G.C. and Demosthenous, M. 1997. “Models of Ancient Columns and Colonnades Subjected to
Horizontal Base Motions - Study of their Dynamic and Earthquake Behavior” STREMA V, pp 289-298.
Manos, G.C. Reports on Task 1, Task 2 and Task 8, 1998. ISTECH project, Program Environment and Climate,
European Commission, Contract No. ENV4-CT95-0106.
Spanos, P.D. and Koh A.S., 1984. Rocking of rigid blocks due to harmonic shaking. J. of Engin. Mech., ASCE
110 (11), pp. 1627-1642
8
0235