shake table testing of stiff model statue structures considering … · 2016-09-14 · shake table...
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Shake Table Testing of Stiff Model Statue Structures
Considering Mass Eccentricity Christine E. Wittich & Tara C. Hutchinson Department of Structural Engineering, University of California-San Diego
ABSTRACT
This work was supported by the National Science Foundation under IGERT Award #DGE-0966375,
“Training, Research, and Education in Engineering for Cultural Heritage Diagnostics.” Additional
support was provided by the World Cultural Heritage Society, Friends of CISA3, and the Italian
Community Center of San Diego. The authors thank Dr. Richard Wood for his assistance during the
field work conducted as part of this study, and Professor Falko Kuester for his input to the scope of
the work. Findings from this study are those of the authors and do not necessarily reflect the
opinions of the sponsoring agencies.
Berto, L., Favaretto, T. Saetta, A., Antonelli, F., and Lazzarini, L. (2012). “Assessment of the seismic vulnerability of art
objects: The ‘Galleria dei Prigioni’ sculptures at the Accademia Gallery in Florence.” J. Cult. Herit., 13(1), 7-21.
Nigbor, R.L. (1989). “Analytical/experimental evaluation of seismic mitigations measures for art objects.” Ph.D. thesis.,
University of Southern California.
Rosetto, T. et al. (2012). The 20th May 2012 Emilia Romagna Earthquake. EPICentre Field Observation Report EPI-FO-
200512, London, UK.
Thomas, H., Bowes, W., and Nelson, B.S. (1960). “Geologic report on the effects of the earthquake of 22 May 1960 in
the city of Puerto Varas.” Bull. Seismol. Soc. Am., 53(6), 1347-1352.
Wittich, C.E., Hutchinson, T.C., Wood, R.L., & Kuester, F. (2012). A Methodology for Integrative Documentation and
Characterization of Culturally Important Statues to Support Seismic Analysis. Progress in Cultural Heritage
Preservation: Proceedings of 4th International Conference, Euromed 2012 (pp. 825-832). Berlin: Springer.
Wittich, C.E. & Hutchinson, T.C. (2013). Computing Geometric and Mass Properties of Culturally Important Statues for
Rigid Body Rocking. Proceedings of the 2013 ASCE International Workshop on Computing in Civil Engineering.
Renton, VA: ASCE Press.
Figure 1: (left) Captain Scott Statue at Scott Reserve in Christchurch, NZ before the February 2011
Christchurch Earthquake. (right) Captain Scott Statue after the February 2011 Christchurch Earthquake.
Note that the statue was unrestrained with a stone-stone interface and that it overturned during the
earthquake. [“Fallen Captain Scott Statue.” (2011). Christchurch City Council.]
The response of eccentric rigid bodies to seismic loading is of paramount
importance for the protection of culturally important statues and can be
easily extended to building contents and mechanical equipment. The
analysis of cultural heritage artifacts, statues in particular, has been a
historically neglected area of structural and earthquake engineering with
advances only being made in the past decade or so (Nigbor, 1989). Yet,
their high cultural, national, and religious significance combined with
observations of toppling from recent earthquakes gives impetus to their
study (Thomas, 1960; Berto, 2012; Rosetto, 2012). Culturally important
statues have been observed to be typically constructed out of a single
piece of marble and to be resting unrestrained on a stone pedestal with a
high coefficient of static friction. As a result, they are expected to respond
to seismic loading in the predominant rigid body modes of rocking, sliding,
and slide-rocking. To date, few experiments have been conducted to
understand the dynamics of typical rigid bodies.
FIELD SURVEY A field survey was conducted in Italy
which included obtaining three-
dimensional reconstructions of 25
culturally important statues. These
reconstructions are used to obtain the
geometric parameters that theoretically
govern rocking and sliding responses.
Light detection and ranging (LiDAR)
and structure-from-motion (SfM) were
used in the field to obtain the point
clouds which were then triangulated
into the fully enclosed meshes. (Wittich
et al. 2012; Wittich & Hutchinson 2013)
An example is seen in the figure at
right.
ACKNOWLEDGEMENTS
REFERENCES
SPECIMEN DESIGN
Each configuration of the
specimen is subjected to a suite
of 12-15 input motions (Figure 4).
Two near-fault pulse-type ground
motions were selected along with
the corresponding transient and
extracted pulse motions. A
broadband motion was selected
for use in an experimental
incremental dynamic analysis. An
increasing sinusoidal protocol
was also developed in order to
induce many cycles of rocking
and sliding behavior.
Guided by the results of the field survey, the experimental specimen is
designed such that a consistent set of weight plates can be arranged to
shift the center of mass in three directions. This will vary the critical
geometric parameters for rocking: center of mass and slenderness. As
such, the specimen can represent 84% of statues surveyed. Furthermore,
the specimen is fixed to a marble base which rests unattached to another
piece of marble on the shake table. This maintains the in-situ frictional
interface and rebound properties. Figure 3 contains an image of this
experimental specimen and setup in the UCSD Powell Laboratory as well
as image of the specimen post-shaking with the catch system engaged.
0 1 2 3 40
1
2
3
4
Period, T [s]
Psuedo-S
pectr
al A
ccele
ration [
g]
1999Duzce,Bolu
1999Duzce transient
1999Duzce pulse
1989LP,Gavilon Col
1989LP transient
1989LP pulse
1994Northridge,UCLA
Figure 4: Pseudo-spectral acceleration (5% damped of critical)
of the selected ground motions including transient motions and
extracted pulses.
In order to record the observed three-dimensional rotation, sliding, slide-
rocking, accelerations due to impact, and angular accelerations, a large
network of sensors was used: (7) string potentiometers, (22)
accelerometers, (8) high definition cameras for motion tracking using grid
and circle patterns on specimen.
Figure 2: Three dimensional reconstructions of
a surveyed statue by LiDAR and SfM
GROUND MOTION SELECTION
INSTRUMENTATION
PRELIMINARY RESULTS
The following is a sequence of rotational time history responses of the
specimen in its tallest configuration with varying degrees of in-plane
eccentricity. The effect of the pulse-like ground motion is clearly seen with
comparison to the response of the transient motion. In addition, the
eccentricity, as expected, one-sidedly accentuates the response and leads
to overturning.
Symmetric
Eccentric 1
Eccentric 2
Figure 3: (left) Experimental setup in the UCSD Powell Laboratory uniaxial shake table with marble base
attached to shake table, steel specimen with marble base and attached weight plates, and safety catch
system to allow the specimen to rotate through 35°. The grid and circle patterns on the specimen are
used for camera motion tracking (see Instrumentation section). (right) Experimental specimen post-
shaking for a tall configuration with minor eccentricity in-plane of shaking (Eccentric 1 in Preliminary
Results section) in an overturned state with the safety system fully engaged.
Figure 5: Rotational time histories of the tall configuration with three levels of
eccentricity subjected to Duzce, Bolu ground motion as an original motion, transient
motion, and extracted pulse.