Experimental and analytical studies on t

DOI: 10.1002/eqe.871Experimental and analytical studies on the response of freestanding laboratory equipment to earthquake shaking Dimitrios Konstantinidis1, ‡ and Nicos Makris2,3,∗,†,§,

Published online 10 December 2008 in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/eqe.871

Experimental and analytical studies on the response of freestanding

laboratory equipment to earthquake shaking

Dimitrios Konstantinidis1, ‡ and Nicos Makris2,3,∗,†,§,¶

1Department of Civil and Environmental Engineering , University of California, Berkeley, U.S.A.

2Department of Civil Engineering , University of Patras, Patras GR-26500, Greece

3Earthquake Engineering Research Center , University of California, Berkeley, U.S.A.

SUMMARYThis paper presents results of a comprehensive experimental program on the seismic response of full-scale freestanding laboratory equipment First, quasi-static experiments are conducted to examine themechanical behavior of the contact interface between the laboratory equipment and floors Based onthe experimental results, the response analysis that follows adopts two idealized contact friction models:the elastoplastic model and the classical Coulomb friction model Subsequently, the paper presents shaketable test results of full-scale freestanding equipment subjected to ground and floor motions of hazardlevels with corresponding displacements that can be accommodated by the shake table at the UC BerkeleyEarthquake Engineering Research Center For the equipment tested, although some rocking is observed,sliding is the predominant mode of response, with sliding displacements reaching up to 60 cm Numericalsimulations with the proposed models are performed Finally, the paper identifies a physically motivatedintensity measure and the associated engineering demand parameter with the help of dimensional analysis

Received 5 March 2007; Revised 10 September 2008; Accepted 15 September 2008

KEY WORDS: laboratory equipment; non-structural components; shake table experiments; rocking;

sliding; PBEE; fragility

∗Correspondence to: Nicos Makris, Department of Civil Engineering, University of Patras, Patras GR-26500, Greece.

†E-mail: nmakris@upatras.gr

‡Postdoctoral Scholar.

§Professor.

¶Senior Research Engineer.

Contract/grant sponsor: Earthquake Engineering Research Centers Program of the National Science Foundation;

contract/grant number: EEC-9701568

1 INTRODUCTIONDuring strong earthquake shaking, heavy equipment located at various floor levels of researchlaboratories, hospitals, and other critical facilities may slide appreciably, slide-rock, rock, or evenoverturn Rocking response is very sensitive to the geometry of the slender object and the kinematic

characteristics of the ground Minor variations in the input can result in overturning—catastrophe

[1–3] Even if overturning does not occur, the high acceleration spikes that develop during impact

of the rocking equipment are a major concern, since they can result in serious damage or loss ofthe equipment contents

Of the possible modes of response, sliding is the most favorable Nonetheless, excessive sliding

displacements may block a path or doorway that services evacuation Large displacements of

avoided, since the resulting acceleration spikes endanger the contents or even the equipment itself

In practice, excessive sliding is prevented by restraining the equipment—commonly by chaining it

to the framing of the nearby wall Although this may succeed in reducing sliding displacements,

it substantially amplifies accelerations The problem of equipment sliding has been studied in the

The research presented in this paper is part of a wider study that was set out to apply the

Earthquake Engineering Research (PEER) Center on a specific testbed: an actual science laboratory building, herein referred to as UC Science Building The UC Science Building is located on the

western part of the main UC Berkeley campus and is approximately 1 km west of the Haywardfault It is a modern structure, completed in 1988 in order to provide high-tech research laboratories[9] The PEER PBEE methodology consists of four stages [8]: hazard analysis, structural analysis,damage analysis and loss analysis

In this paper we present experimental and analytical studies that examine the seismic ability of freestanding and restrained laboratory equipment located in the UC Science Buildinglaboratories within several floor levels The equipment of interest includes low-temperature refrig-erators, freezers, incubators and other heavy equipment The study investigates the response ofequipment to moderately strong motions (50 and 10% probability of being exceeded in 50 years)which result to peak ground displacements or peak floor displacements that the Earthquake Engi-neering Research Center (EERC) shake table at UC Berkeley can accommodate Additional results

on the shake table were used to develop a dimensionless engineering demand parameter (EDP)

(a parameter that quantifies the response of the equipment), as a function of the intensity measure

(IM) (a parameter of the excitation that corresponds to a certain seismic hazard level) Since

taken An analysis was performed to generate fragility curves, which give the probability that the aforementioned EDP will exceed a specific limit c.

2 SEISMIC HAZARD, GROUND AND FLOOR MOTIONS

seismic hazard on the UC Berkeley campus is dominated by potential ground motions generated

from the Hayward fault, which is located approximately 1 km east of the site The Hayward fault

is a strike-slip fault that has a potential to generate earthquakes having magnitudes as large as

levels: (a) events with probability of exceedance (POE), equal to 50% in 50 years, (b) eventswith POE 10% in 50 years, and (c) events with POE 2% in 50 years For a hazard level equal

to 50% in 50 years, the largest contributions come from earthquakes in the magnitude range of

is noteworthy that the higher 2% in 50 years do not reflect larger magnitudes (as the Hayward fault

have been selected to satisfy (to the extent possible) the magnitude and distance combination from

10% in 50 years)

The seismic response of the UC Science laboratory building was analyzed by Lee and Mosalam[9, 12], who developed a sophisticated structural model of the building Their analyses resulted insimulated floor motions Floor motions are of unique interest in assessing the seismic response

of building contents since they differ appreciably from ground motions Table I lists the recordedground-acceleration motions and the simulated floor-acceleration motions that were used as inputfor the shake table experiments conducted in this study

All input motions used for shake table tests in this study were one-directional Preliminarydynamic analyses of a sliding block resting on a base subjected to horizontal and vertical earthquakemotion yielded peak sliding displacements that were only slightly amplified when the verticalcomponent of the excitation was included The same observation is made in a study by Shao and

with their lower amplitude renders them too feeble to impart a significant amplification of the peak

the horizontal and vertical components of the excitation may not be ignored

3 GEOMETRIC AND PHYSICAL CHARACTERISTICS OF THE TEST EQUIPMENT

3.1 Geometric properties

The equipment of interest included incubators, low-temperature freezers, refrigerators and otherheavy laboratory equipment of the UC Science Building at the UC Berkeley campus In particular,three pieces of equipment were obtained from the building laboratories in order to examine theirmechanical properties and to perform shake table tests Figure 1 shows pictures of the equipment,while Table II lists their geometric and physical characteristics Figure 2 is a schematic of a piece ofequipment that shows the geometric quantities that are listed in Table II Each piece of equipment

has two vertical faces, designated here by W for width and D for depth The stockiness angles

 W=tan−1



W H





D H



(1)

FORMA Incubator Kelvinator Refrigerator ASP Refrigerator

Figure 1 The three pieces of freestanding heavy laboratory equipment that were obtained from the UC

Science research facility for the purposes of this study

Table II Geometric and physical characteristics of the equipment

Weight H W (Wout) D (Dout) R W R D  W  D p W p D

larger the block (larger R), the smaller the p.

Figure 2 Schematic diagram of the experimental setup for the quasi-static pull tests.

pressboard surface covered with identical vinyl tiles was constructed Atop it rested the equipmentspecimen Figure 2 shows a schematic of the experimental setup of the quasi-static pull testsconducted on the equipment

Figure 3 plots load–displacement curves recorded during the quasi-static pull tests on the threepieces of equipment shown in Figure 1 The pre-yielding elasticity in the load–displacement curvesoriginates from the flexure of the legs of the equipment prior to sliding This pre-yielding elasticity

of the legs and the friction force that develops along the vinyl surface combine to a yieldingmechanism of the interface Simple idealizations of the yielding mechanism of each interface arethe elastoplastic models shown with dashed lines in Figure 3 The model parameters that define the

where Q is the post-yield constant force Another idealization of the contact interface is that of

slow-pull tests were conducted after the shake table tests in order to examine the validity of themechanical model The analyses yielded results that were in fair agreement with the experimentaldata from the shake table tests (presented in the following section) The predicted response of allthree pieces of equipment was appreciably improved when lower values of their respective frictioncoefficients were used The lower friction levels of the elastoplastic idealization are indicated inFigure 3 with solid lines The heavy solid lines shown in Figure 3 correspond to the Coulomb

best-fitting results from numerical simulations using the commercially available software Working

Model [14] to results obtained from shake table experiments Table III summarizes the values offriction coefficients and yield displacements that were obtained from the slow-pull tests and fromthe best-fitting procedure

Figure 3 Recorded load–displacement plots obtained from the slow-pull tests (wavy lines);

Table III Coefficients of friction and yield displacements obtained from slow-pull tests and from best-fitting

numerical simulation results to experimental results from the shake table tests

Elasto-plastic Model (Rigid-Plastic) Model

sinks into the surface of its base, as asperities deform, causing an increase in meniscus and

4 SHAKE TABLE TESTS OF FREESTANDING LABORATORY EQUIPMENTThe three pieces of equipment shown in Figure 1 were subjected to shake table tests at the UCBerkeley Earthquake Engineering Research Center’s (EERC) Earthquake Simulator Laboratory.The same type of pressboard surface that was used as the base for the slow-pull tests was built onthe shake table to support the equipment Figure 4 shows a photograph of one of the freestandingequipment resting on the shake table

The displacement of the shake table and the equipment were measured with wire transducersattached to a frame fixed on the laboratory floor Figure 4 shows the locations of the wire transducers

on the test specimen with heavy white lines Accelerometers were also installed on the positionsshown with black arrows in Figure 4 in order to capture horizontal and vertical accelerations The

experiments at full scale were run only for moderate ground motions (i.e with hazard level equal

to 50% in 50 years and 10% in 50 years)

In several occasions the equipment while shaken along the primary direction, exhibited rotationsabout its vertical axis In some cases these plane rotations were as small as 0.005 rad, while inothers as large as 0.33 rad, indicating that even when the excitation is one-directional, the response

is in fact in three dimensions

Table I lists the earthquake records that were used to test the freestanding equipment Also listed

Figure 4 The FORMA incubator resting atop the shake table at the UC Berkeley Earthquake EngineeringResearch Center The locations of the wire transducers are indicated with white lines, and the locations

of the accelerometers are indicated with dark arrows

occurs, the primary mode of response of the three pieces of equipment is sliding Criteria provided

 listed in Table II in conjunction with the values of s listed in Table III If the values of sobtained from the slow-pull tests are used, slide-rocking is anticipated to initiate for all three pieces

of equipment used in this study However, sliding dominates the response In fact, the maximum

uplift rotations than the other two specimens, these rotations were still well below the level for

incubator failed The resulting instability caused overturning of the specimen

Figure 5 (bottom window) plots the OTE FP ground-acceleration history recorded during the

1995 Aigion, Greece, earthquake The graph on the window above the acceleration record plots theresulting shake table displacement, and the third window from the top plots with a heavy solid linethe recorded sliding displacement of the FORMA incubator The recorded sliding displacementhistory shows that the equipment suddenly slides once a threshold table acceleration is exceeded(at about 3.8 s) The top two graphs in Figure 5 that plot with heavy solid lines the equipment upliftand the plane rotation (rotation about the vertical axis) show that the specimen does uplift andtwist just slightly even before the initiation of sliding (at about 3.65 s) In other cases, one mode ofresponse does not seem to trigger the other, but rather both happen simultaneously The responsemode coupling is less pronounced for the Kelvinator refrigerator which, although demonstrating

a slightly larger coefficient of friction during the slow-pull tests than the FORMA incubator

to uplift The Kelvinator refrigerator exhibited relatively small rotations, never exceeding 7% its

0 2 4 6 8 10 -1

equipment: FORMA incubator motion: Aigion, OTE FP

Figure 5 Response of the FORMA incubator subjected to the OTE FP motion recorded during the 1995Aigion, Greece, earthquake The heavy gray lines on the bottom two graphs plot a Type-B trigonometric

pulse that approximates the main pulse of the motion record

rotation about its vertical axis The maximum recorded plane rotation in all tests performed on theKelvinator refrigerator was 0.05 rad Figure 6 plots the response of the Kelvinator refrigerator to

1989 Loma Prieta, California, earthquake

the shake table tests performed on the ASP refrigerator in the Face configuration and the Profile

configuration is almost identical The maximum recorded uplift rotation did not exceed 0.005 rad

record of the 1979 Coyote Lake, California, earthquake

An interesting characteristic to note is the waviness of the heavy solid lines that plot the slidingdisplacement This wobbling is more pronounced for the FORMA incubator whose legs were veryflexible, less pronounced for the Kelvinator refrigerator whose legs are fairly stiff, and almostnon-existent for the ASP refrigerator whose legs are nearly rigid

0 2 4 6 8 10 -1

equipment: KELVINATOR refrigerator motion: Loma Prieta, Gavilan College FN 6th Floor (10% in 50yrs)

Figure 6 Response of the Kelvinator refrigerator subjected to the UC Science Building 6th-floormotion of the Gavilan College (10% in 50 years) record of the 1989 Loma Prieta, California,

approximates the main pulse of the motion record

5 REGRESSION ANALYSIS AND FRAGILITY CURVES

5.1 Governing parameters during sliding

Many parameters influence the full behavior of a piece of equipment subjected to seismic motion.However, since we are primarily concerned with sliding, the governing parameters become thosethat describe (a) the mechanical characteristics of the equipment–floor interface and (b) the kine-matic characteristics of the base motion From the slow-pull tests performed on the equipment, theload–displacement curves show that there is a pre-yielding elasticity due to the flexibility of the

which the equipment starts sliding with a relatively constant force (associated with the kinetic

Figures 5–7 that plot the results of the shake table tests on the freestanding equipment also plotthe results obtained by numerical simulations for two different models of the sliding interface:

an elastoplastic model (MATLAB) and a rigid-plastic (Coulomb friction) model (WM2D) It was