improved external device for a mass-carrying sliding system for shaking table testing

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICSEarthquake Engng Struct. Dyn. 2011; 40:393–411Published online 30 July 2010 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/eqe.1026

Improved external device for a mass-carrying sliding systemfor shaking table testing

Julian Carrillo1,2,∗,† and Sergio Alcocer2

1Departamento de Ingeniería Civil, Universidad Militar Nueva Granada, Cra. 11 No. 101-80, Bogotá, Colombia2Instituto de Ingeniería, Universidad Nacional Autónoma de México, Ciudad Universitaria,

Coyoacán 04510, D.F., México

SUMMARY

Shaking tables are suitable facilities to assess and validate the behavior of structures and nonstructuralcomponents under actual seismic actions. Because of the size and weight limitations of the tables,some approaches, like testing reduced-scale models or testing only the main structural components, aredeemed necessary. In these cases, to comply with modeling requirements, large amount of extra-massshould be added to the specimen. Therefore, to avoid the risk of lateral instability of models, to maintainthe weight of test specimens within table payload, while maintaining the amount of mass needed, anexternal device for transmitting the inertia forces to the models using an improved sliding system isproposed. Although friction devices for similar purposes have been developed using sliding bearings(Teflon pads or rollers), the measured coefficient of dynamic friction and the energy dissipated by frictionhave been very high. In order to drastically diminish the damping added to the specimen response whena friction device is used, the improved device employs a linear motion guide system (LMGS) withvery low friction. Shaking table tests to collapse of reinforced concrete walls were used to evaluate theeffectiveness of the proposed device. Measured dynamic friction coefficients, spectral accelerations andhysteresis loops show that friction developed in the LMGS did not add any significant amount of dampinginto the specimen response. Thus, the proposed device is a reliable and suitable mass-carrying slidingsystem (MCSS) for dynamic testing using medium-size shaking tables. Copyright � 2010 John Wiley &Sons, Ltd.

Received 8 December 2009; Revised 28 April 2010; Accepted 30 April 2010

KEY WORDS: dynamic response; mass; shaking table testing; structural models; test equipment

1. INTRODUCTION

In earthquake engineering research, shaking tables are a valuable tool for assessing the behavior ofstructural systems and components, as well as of nonstructural components under seismic actions.Shaking table tests are used to validate a design and/or analysis concept, in addition to studying thedynamic effects on the performance of a specimen. However, mainly due to financial constraints,the size of the majority of shaking tables is small in comparison with real structures [1]. Then, it isnecessary to formulate simplifications like constructing reduced-scale models or testing the maincomponents of a structural system. If reduced-scale models are used, specimen ought to complywith the laws of similitude. This involves scaling dimensions and/or mechanical characteristics of

∗Correspondence to: Julian Carrillo, Departamento de Ingeniería Civil, Universidad Militar Nueva Granada, Cra. 11No. 101-80, Bogotá, Colombia.

†E-mail: [email protected], [email protected]

Copyright � 2010 John Wiley & Sons, Ltd.

394 J. CARRILLO AND S. ALCOCER

materials. When dimensions are scaled down, while maintain the same prototype materials (i.e.the specific gravity of materials), additional mass is often required. Furthermore, it is not rare thata large amount of mass is needed to set the natural period of the specimen corresponding to that ofthe prototype structure or in the case of tests aiming at assessing the performance near collapse oreven at the collapse performance level. Additional mass has its own drawbacks because it increasesthe weight acting on the table platform, thus making the control of movements more complexand difficult [2]. Additional mass has led to the development of devices specially designed andconstructed for its support [3]. One shortcoming of such devices when built or mounted on thetable is the undesirable noise and extra signals introduced to the specimen, which become a partof the specimen’s response. For these reasons, it is advisable to use a setup so that additional massis located outside the simulator. In this way, the total payload capacity of the shaking table canbe used for the specimen itself, while the risk associated with mass resting directly on the modelsconsiderably decreases.

Currently, three types of mass-carrying systems located outside the shaking table have beenused: a linear sliding system, a rotational system and a pendulum system. When the additionalmass moves on a sliding surface, the effectiveness of the mass-carrying system can be measuredusing, as reference parameters, the dynamic friction coefficient of the sliding system, the equivalentviscous damping added to the specimen response, the ratio of the energy dissipated by frictionto the total input energy and evidently, the load carrying capacity of the system. If the dynamicfriction coefficient is high, large damping is introduced into the specimen’s response. This, in turn,causes a low dynamic amplification factor which is artificial and then, low spectral quantities aregenerated. Some experimental programs have reported the use of this type of devices for addingmass to the models. However, taking a closer look into the measured dynamic friction coefficientsor the reported ratio of the energy dissipated by friction to the total input energy, their effectivenessis questionable.

In this paper, an improved external device for safely and adequately carrying additional inertialmass for shaking table testing is presented. Device characteristics are discussed in detail and thedynamic equations of motion of the external device and the shaking table are developed. Theproposed device has been used successfully in the dynamic testing of six reinforced concrete (RC)wall models: four squat walls [4] and two walls with openings [5]. Experimental verification ofthe device performance is presented herein by analyzing the results of test of walls with openings.Similar performance was obtained for the RC squat walls tested [4]. In the experimental program itwas found that the maximum damping added by the proposed device corresponds to only 2% of thetotal damping developed in the model dynamic response. Additionally, the spectral accelerationscalculated using a damping equal to the effective damping plus the damping added by the proposeddevice are nearly the same as the actual spectral accelerations. Based on the observed and themeasured performance, it can be concluded that the proposed external device is suitable for dynamictesting of models.

2. EXTERNAL DEVICES

When tests are performed using medium-size shaking tables and small quantities of mass aredirectly attached to the test specimens, small inertia forces result. Low-magnitude inertia forcesare often too small to cause significant damage to the specimen, thus hindering the possibilityof studying the performance at the near-collapse or collapse levels. If reduced-scale models withhigh-scale factors (i.e. miniature models) are planned, extrapolation of the prototype behaviorfrom the measured behavior of specimen becomes more difficult and, often, is unreliable. Externaldevices are an efficient solution to the challenge of transmitting large inertia loads to specimens.Using such devices, the additional mass is placed on a supporting structure that is adjacent tothe shaking table platform and which is linked to the top of the specimen by means of a pinnedconnection. Different configurations of mass-carrying systems located outside the shaking tablehave been used: linear sliding systems, rotational systems and pendulum systems. All of these

Copyright � 2010 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 2011; 40:393–411DOI: 10.1002/eqe

IMPROVED EXTERNAL DEVICE FOR A MCSS 395

present diverse advantages and drawbacks, providing a wide range of solutions to different typesof research programs.

2.1. Linear sliding systems

In this case, a storing structure, where the additional mass is piled up, is allowed to slide horizontallyon a fixed supporting structure located outside the shaking table. The method requires a low-frictionsliding surface between the storing and supporting structures. In the past, two types of slidingbearings have been used: Teflon pads and roller bearings. The main drawbacks associated withsuch schemes are the high friction of the sliding bearings, as well as the need for an additionalout-of-plane restraining mechanism when either the pinned connection between the specimen andthe mass-carrying device allows rotations with respect to all directions or when the sliding bearingspermit transverse movement.

Using Teflon pads: In this system, the additional mass is placed on sliding bearings made ofTeflon pads coated with lubricant to reduce friction (Figure 1(a)). However, during tests reportedby Pinho [6] and Elnashai et al. [7], the level of friction was high, reaching values of 8.5%, thusintroducing strong damping into specimen’s response. Further, this type of sliding system led toa rough response of the models. Small-frequency vibrations, not present in the input motion andnot caused by vibrations of the models, were recorded. It is likely that material deterioration ofTeflon pads could have been the main reason of the large measured values of the dynamic frictioncoefficient. The main disadvantage associated with such damping is the resulting small dynamicamplification factors, which in turn reduces the seismic demand on the models. In addition, thenatural period of vibration of the models, prior to and after each test, cannot be estimated usinghammer impact testing (or similar methods), since any small displacement demand on the modelsis damped to zero almost instantaneously. Owing to the observed high friction levels betweenTeflon pads and the additional mass, a dynamic amplification factor of 1.8 was assumed duringanalytical modeling, corresponding to an equivalent viscous damping of 10% [6]. In addition,because Teflon pads allows for transverse movements, an out-of-plane restraining system had tobe implemented.

Using roller bearings: In this case, the additional mass is placed on rolling steel carts (Figure 1(b)).This method is reported by Bachmann et al. [8] and Lestuzzi and Bachmann [9]. To laterally guidethe specimens and restrain the out-of-plane movement, additional lateral frames were constructed.Two steel beams resting on lateral frames were used to guide the specimen at the top slab. Tominimize the friction between the top slab and the steel guides, layers of Teflon attached to thesteel beams were used [8]. Using the experimental results reported by Lestuzzi and Bachmann [9],Chuang et al. [10] modeled the response of the additional mass and rolling device by assuming asteel material with 10% as additional damping. However, the comparison between the numericaland the experimental results suggests that the damping developed in the experiment was higherthan that assumed. Chuang et al. [10] concluded that the damping added by the device to themodel response was probably higher than 10%. Furthermore, Lestuzzi and Bachmann [9] used theratio of the energy dissipated by friction to the total input energy as a key parameter to measurethe effectiveness of the device. The portion of energy dissipated by friction particularly appears inthe rolling of the device. During testing, using earthquake records, the mean value of the energydissipated by friction in the device was close to 24% of the total input energy. Higher values (closeto 50%) were observed for small-intensity earthquakes [9].

2.2. Rotational systems

In the experimental program carried out by Laplace et al. [11], a rotational system for supportingthe additional mass was used. The system, depicted in Figure 1(c), consists of a pinned structurewhich gets its stability from the specimen. For allowing the axial load to be applied throughtwo center-hole rams, a steel beam was bolted at the top of the specimen. Restraining cables



Figure 1. Typical external devices.

were provided to limit the translation of the additional mass. During specimen failure, the devicewould translate until the limit displacement of the restraining cables is reached and the additionalmass would stop. Using this device, out-of-plane displacements are restrained and then, additionaldevices for this purpose are not required. However, this device has an impact on the loading andoverall stiffness of the system (specimen-device) through the P-delta effect. The P-delta effectis defined as an equivalent lateral force due to overturning moment that is equal to the verticalforce multiplied by the lateral drift. There are two components contributing to the P-delta in thisscheme. The largest effect was created from the overturning moment of the device, which wasdue to the location of the device along the height from the lab floor as compared with the shakingtable platform. The second P-delta effect was produced when the described axial load system wasused. The latter becomes difficult to calculate due to pivoting of the axial load line-of-force nearthe base of the footing. Moreover, in this system, friction developed at the hinges of the pinnedstructure cannot be easily determined and, therefore, included in the dynamic equations.

2.3. Pendulum systems

The main features of this experimental setup are characterized by hanging the additional massfrom the outside of the shaking table (Figure 1(d)). In this case, some extra devices are needed toprevent out-of-plane displacements. A coil spring can be installed between the pinned connectionand the additional mass as shown in Figure 1, in order to reproduce the natural period of any partof the structure from which the test specimen had been taken out. For example, when a structuralelement or structural sub-assemblage taken out from a building structure (wall, column or partialframe) is used as a test specimen, the spring properties are established to match the natural periodof the device with the fundamental period of the building structure. However, it is noted that thespring exerts a force within the elastic behavior that is only applied to the upper part of the building.According to a literature review, the use of an elastic spring has been only applied for the schemedepicted in Figure 1(d) (Yamada et al. [12]). Evidently, a spring may be used for other schemesillustrated in Figure 1. Also, when using schemes depicted in Figures 1(c) and (d), rotation of theadditional mass will generate additional vertical forces atop the specimen. These are caused by



the inclination of the pinned connection during movement; as the model displacements increase,vertical forces will be higher.

3. PROPOSED DEVICE

3.1. Full description

An improved mass-carrying system that allows horizontal sliding on a supporting structure, locatedoutside the shaking table, was planned for carrying the additional mass blocks. Main componentsare shown in Figure 2(a). Additional mass blocks were placed in a steel storing box which is, inturn, supported by a linear motion guide system (LMGS) with a very low friction. Testing deviceshown in Figure 2(b) was designed for a total inertial weight of about 245 kN, where 196 kNcame from additional blocks and 49 kN from the self weight of auxiliary components (load beam,pinned connections, connection beam, load cell and storing box). For reducing the mass volumein the storing box, lead ingots were used. Specific gravity of lead is close to 111kN/m3, whichis roughly 1.5 times the specific gravity of steel (76kN/m3). Also, lead ingots were bolted tothe load beam for applying the vertical load to the models; this mass was also accounted for thecalculation of the additional mass required for adequate modeling. The supporting structure of theLMGS is a steel-braced frame made of wide-flange sections for the columns and beams, and ofbox-section members for the bracing elements. The additional mass is piled up inside a steel boxmade of wide-flange sections. Connection between the storing box and the specimen consisted ofa connection beam with pinned ends (i.e. roller swivels with free in-plane rotations) and a loadingbeam to be bolted to the top of the model. To measure the partial load acting on specimens, a loadcell was placed between the connection beam and the loading beam. To restrain any movement oflead ingots during testing, steel beams and winch straps were used (see details depicted in Figure 2).To avoid out-of-phase displacements, the mass-carrying system needs a sliding mechanism with avery low dynamic friction coefficient between the storing box and the fixed support (main beams).From discussion in Section 2.1, it is apparent that the sliding mechanisms based on Teflon padsor roller bearings are not an adequate solution for dynamic testing because of their high friction.For the research reported herein, several options for the additional mass-carrying sliding system(MCSS) were studied. In the following, the solution that was implemented will be described.

To assure a dynamic friction coefficient near zero, an LMGS was used (Figure 3). This equipmentcomprises a steel rail machined with high precision and sliding blocks. In turn, high-precision steelballs roll within four rows of two raceways, which are precision-ground on a linear-motion (LM)

Figure 2. Test setup: (a) main components and (b) perspective.



Figure 3. Linear motion guide system (LMGS): (a) main components and (b) rail with two blocks.

block and slide on a rail. The end-plates attached to the LM block allow the balls to circulate. TheLM rail has a sectional shape with high flexural rigidity and self-adjusting capability. The racewaysare arranged at 45◦ in relation to one another so that each train of balls bears an equal load rating inall four directions: radial, reverse-radial and two lateral directions. The LMGS was manufacturedby THK Company [13]. Taking into account the design parameters of the experimental program(amount of additional mass and maximum expected acceleration, velocity and displacement), tworails (Model JR55) with three blocks in each one (Model JR55A1SS) were used. According tothe LMGS manufacturer, for ideal working conditions, the maximum dynamic friction coefficientshould be close to 0.5%. This value is much lower than the friction coefficient reported in similarstudies. According to manufacturer charts, the dynamic load carrying capacity of each block is89 kN; therefore the dynamic load carrying capacity of the LMGS was approximately 534 kN(6×89kN).

3.2. Main advantages and drawbacks

There are important advantages of the proposed device: (a) Table performance: shaking tableperformance depends on the weight acting on its test platform. Hence, excluding the additionalmass acting on the platform, the performance and total capacity of the shaking table can be used.Suppose testing of a specimen with 28 kN of self weight and 168 kN of additional weight is beingplanned. If additional mass (weight) is expected to be supported by the table, like in tests reportedby Liao et al. [3], the total weight to be carried by the platform is 196 kN. If one assumes themaximum acceleration of the shaking table system to be 9.8m/s2 (1.0g), when the table is loadedto its limit payload, the maximum base shear will be 196 kN. In contrast, if the additional mass(weight) is placed outside the platform of the table, the only weight acting on the table would bethe specimen’s self weight, which is equal to 28 kN. Suppose that for such a load on the table, themaximum acceleration that could be applied is near to 3.0g. Therefore, for this case, the maximumbase shear would be close to 588 kN. From this simple example, it is clear that by planning theadditional mass outside the table, larger accelerations and base shears might be applied, and thus,specimens could be subjected to much higher damage, or even collapse; (b) Safety under collapseperformance level: if the specimen is tested to collapse performance level, additional mass outsidethe table poses minimal risk to the lateral stability of models. Then, safety of laboratory staff,equipments and specimen instrumentation is also greatly improved. If specimen collapses duringthe test, the support frame restricts the displacement of the additional mass using shock absorbers(Figure 2). In contrast, if the additional mass were placed directly on the specimen, in case offailure of specimen and fall of the mass, permanent damage to specimen instrumentation andeven probably, to shaking table components (hydraulic jacks, platform, internal instrumentation,etc.) can be caused; (c) Simplicity: if the proposed device is used, a special auxiliary structureon the platform to support additional mass is not necessary. Such an auxiliary structure could bequite complex and may very well introduce unwanted signals during severe shaking conditions;



(d) Factor of amplification: because in the proposed device the effect of friction is not significant,the specimen’s dynamic amplification factor and thus the specimen response would not be changed;(e) Low distortion: distortion of signals is greatly reduced; (f) Overturning moment: overturningmoment is one movement that imposes a significant challenge for proper control in closed-loopsystems. By taking the additional mass out from the table, overturning moments are reduced; (g)Preparation time: due to the simple connection system between the specimen and the additionalmass, time necessary for assembling and disassembling of test setups decreases. For preparing thespecimen for testing, it is only necessary to connect the load beam to the top of the specimen.Therefore, for experimental programs in which a large number of tests are expected, research timedecreases considerably; (h) Small out-of-plane displacement: using pinned connection with onlyfree in-plane rotations allowed (transverse rotation restrained), the out-of-plane displacements arediminished or almost eliminated. However, to assure pure in-plane behavior, it was necessary torestrain the out-of-plane model displacements. The out-of-plane restraining system was designed sothat transverse displacements were restrained while allowing the longitudinal (in-plane) and verticaldisplacements to really take place [14]. The main drawback associated with external devices,including the proposed device, is that high axial forces on the specimen are not applied. However,to overcome this problem, it is possible to place small weights at the top of the specimen or touse external post-tensioning bars. When the latter method is used, springs should be connected inseries to post-tensioning bars to control any change of the post-tensioning force from relaxationor during testing. This is because cracking of the specimen would alter the post-tensioning force.As it was mentioned earlier, for applying the vertical load to the models in the proposed device,the method employed was placement of lead ingots bolted to the load beam.

3.3. Equations of motion

As it was discussed in the previous sections, the device used for placing the additional massrequired for the test, and thus for applying inertia force to the models, greatly simplified the testsetup, assembly and preparation of specimens. Nevertheless, it has an effect on the force, stiffnessand damping of models because of the friction developed within the LMGS (rails and blocks).The relevance and magnitude of this effect can be analyzed through the equation of motion for thewhole system, i.e. the MCSS and the shaking table. The equation of motion for a nonlinear singledegree of freedom oscillator with constant viscous damping, in response to horizontal earthquakemotion, can be written as [15]

mx(t)+cx(t)+k(t)x(t)=−mxs(t) (1)

where m is the mass of the oscillator, c is the damping coefficient, k is the stiffness, x , x and x aredisplacement, velocity and relative acceleration of the oscillator, respectively, and xs is the groundacceleration. For the system shown in Figure 2(a), Equation (1) can be rewritten as:

mx(t)+cx(t)−�dW ′+k(t)x(t)=−mxs(t) (2)

In this case, m is the effective lateral mass of the system and can be calculated as (Figure 2(a))

m =m1 +m2 +m3 +m4 +m5 +m6 +m7�1 (3)

where m1 is the added mass (lead ingots placed in the storing box); m2 is the mass of the storingbox for piling up the added mass, the mass of the restraining system and the mass of the LMblocks; m3 is the mass of the pinned connection system (roller swivels, connection beam and loadcell); m4 is the mass of the loading beam; m5 is the mass of the vertical load system (optional);m6 is the mass of the top component of the specimen for connecting the loading beam; m7 is thespecimen mass; and �1 is the fraction of m7 contributing to the effective inertia. Factors �d andW ′ are the dynamic friction coefficient and the normal force acting on the LMGS, respectively.W ′ can be, in turn, calculated as

W ′ =m′g =(

m1 +m2 + m3

2

)g (4)



where g is the gravity acceleration (9.81m/s2). The absolute displacement of the system, xabs, isdefined as

xabs(t)= x(t)+xs(t) (5)

where x is the relative specimen displacement and xs is the shaking table displacement.

3.4. Calculation of effective acceleration

Friction of the LMGS developed during seismic excitation modifies the basic equation of motion.Rearranging Equation (1):

mx(t)+cx(t)+k(t)x(t)=−m

(xs(t)− �dW ′

m

)(6)

Therefore, the effective acceleration of the shaking table acting on specimen is:

xs(t)ef = xs(t)− �dW ′

m(7)

3.5. Calculation of effective lateral force

Lateral force acting on the specimen (Fsp) is the sum of the damping (Fd) and spring (Fs) forces:

Fsp(t)= Fd(t)+ Fs(t)=cx(t)+k(t)x(t) (8)

The force on the specimen, Fsp, may be obtained by applying one of two procedures: (a) using aload cell or (b) via equation of motion.

Using a load cell: The connection beam (Figure 2(a)) was instrumented with a load cell whichwas placed just before the pinned connection. The load cell measured the lateral force acting onthe specimen caused by the inertia force from the additional mass device. Besides this force, it isnecessary to include the inertia force from the mass of the connection system between the load celland the specimen, and that from the load beam mass and from the contribution of the specimenmass. Then, the effective lateral force can be calculated as

Fsp(t)=−[Flc(t)+ xabs(lb)(t)(m3�2 +m4 +m5 +m6 +m7�1)] (9)

where Flc is the measured force by the load cell, xabs(lb) is the absolute acceleration measured inthe loading beam and �2 is the fraction of mass of the connection system between the load celland the specimen. Fsp and xabs(lb) are taken as positive in the direction toward the MCSS.

Using the equation of motion: The second option for calculating Fsp is through the equation ofmotion. Replacing Equation (8) in Equation (6), we obtain:

Fsp(t)=−m[xs(t)+ x(t)]+�dW ′ (10)

According to Equation (5), Equation (10) can be rewritten as:

Fsp(t)=−[mxabs(t)−�dW ′] (11)

If the absolute acceleration of the storing box, xabs(sb), is measured using an accelerometer, Equa-tion (11) can be rewritten as:

Fsp(t) = −{xabs(sb)(t)[m1 +m2 +m3(1−�2)]

+xab(lb)(t)[m3�2 +m4 +m5 +m6 +m7�1]−�dW ′} (12)

As shown in Figure 2(a), the specimen is connected to the storing box through a pin-endedconnection beam. In theory, the absolute lateral displacement of the specimen is equal to the



displacement of the storing box. This means that the absolute acceleration is the same as thosein the storing box and load beam (top of the specimen). However, slack in the swivels, smallmisalignment and specimen vertical displacements can lead to small differences between specimenand storing box displacements and accelerations. Because of these differences, accelerations weremeasured in the storing box (xabs(sb)) and loading beam (xabs(lb)) so that they are included inEquation (12).

3.6. Calculation of dynamic friction coefficients

From Equation (9), it is possible to calculate the effective lateral force acting on the specimenwithout knowing the coefficient of the dynamic friction. However, for estimating the effectivedamping of the specimen, it is required to evaluate the level of friction being developed in theLMGS during the test. When the level of friction is high, strong damping is added into thespecimen’s response. This, in turn, leads to a lower dynamic amplification factor. Two types ofCoulomb’s friction coefficients may be measured in the LMGS device: static friction (�s) anddynamic friction (�d). In the series of tests herein presented, interest was concentrated on estimatingthe coefficient of dynamic friction. In a simple way, this coefficient can be estimated by applyinga known excitation onto the additional mass system and therefore by measuring the required forcefor moving such system. When the motion applied has a constant velocity, the force due to dynamicfriction, (Fdf), can be expressed as a function of the coefficient of dynamic friction (�d), and theweight to be moved (N ):

Fdf =�d N (13)

Applying Equation (13) to the system shown in Figure 2(a) or making equal Equation (9) withEquation (12), the resulting equation for calculating the coefficient of dynamic friction during adynamic high velocity excitation is:

�d(t)= xabs(sb)(t)[m1 +m2 +m3(1−�2)]− Flc

W ′ (14)

Considering that Equations (9) and (12) were equalized for calculating �d, the numerical resultfor calculating Fsp will be the same when using any of the two proposed procedures (i.e. using aload cell or using the equation on motion).

3.7. Energy dissipated in friction device

The energy dissipated by Coulomb friction, in one cycle of vibration with displacement ampli-tude x0, is the area within the hysteresis loop enclosed by the friction force—displacementdiagram. Damping may be expressed through an equivalent viscous damping, ��eq, in whichenergy dissipated, ED , should be substituted for the energy dissipated by Coulomb friction, EF , inEquation (15):

��eq = 1

4�

ED

ESO= 1

4�

EF

ESO(15)

where the strain energy, ESO =kx20/2, is calculated from the specimen stiffness k, determined by

the experiment.

3.8. Calculation of effective damping ratio

According to Chopra [15], the natural period of vibration of a system with Coulomb dampingis the same as for a system without damping. Hence, the device has no effect on the period ofvibration of the specimens. However, for calculating the effective equivalent viscous damping ratioin the specimen, it is necessary to subtract the damping generated in the LMGS, ��eq. Thus, theeffective damping ratio, �′

eq, must be calculated as

�′eq =�eq −��eq (16)



where �eq is the equivalent viscous damping ratio computed using, for example, the amplitudeof the transfer function or the hysteresis curve in terms of effective lateral force versus totaldisplacement.

4. EXPERIMENTAL VERIFICATION

Aimed at better understanding the seismic behavior of RC walls typically used in low-rise housingin Mexico, a large research program has been underway between the Institute of Engineering atUNAM and Grupo CEMEX. Characteristics of prototype walls are their small thickness (100 mm),clear height of 2400 mm, concrete compressive strength of the order of 15 MPa and amounts ofweb reinforcement smaller than 0.0025. For the shaking table tests, the selected prototype was atwo-story house with RC walls in the two principal directions. Owing to limitations in the testingcapacity of the shaking table of UNAM, the experimental program consisted of testing isolatedwall models. Wall thickness and height of prototype walls were those in the prototype house.Similar models had been tested under quasi-static cyclic loading. However, for studying wallbehavior under more representative seismic actions, lightly reduced-scaled models were built andtested under shaking table excitation. The experimental program of dynamic tests included squatwalls, without and with openings (door and window). In this paper, results of the experimentalprogram of walls with openings are presented. Results from testing of squat RC walls may befound elsewhere [4].

4.1. Geometry and reinforcement

Owing to limitations in payload capacity of the table, lightly scaled models were designed (SL =1.25). Because the size of the specimens was very similar to the isolated wall prototypes, thesimple law of similitude was chosen. In this type of law of similitude, the models are built with thesame material as the prototype (i.e. materials properties are not changed) and only the dimensionsof the models are altered. Main scale factors for simple law of similitude are presented in Table I.The wall specimens were built on a stiff strong beam (3.5 m long × 0.6 m wide × 0.4 m high)bolted to the platform of the shaking table.

The geometry and the reinforcement layout of the two specimens tested are illustrated in Figure 4.The Longitudinal and transverse reinforcement at the boundary elements were the same in bothspecimens: 4 No. 4 longitudinal deformed bars (12.7 mm diameter= 4

8 in) and No. 2 smooth barstirrups (6.4 mm diameter= 2

8 in) at 180 mm spacing. Specimen MVN100D was reinforced for webshear with a single layer of No. 3 vertical and horizontal deformed bars (9.5 mm diameter= 3

8 in)with spacing of 320 mm. The amount of web reinforcement corresponds approximately to theminimum web steel ratio prescribed in ACI-318 [17] building code, which is equal to 0.25%.Specimen MVN50mD was reinforced for web shear with a single mesh (6×6− 8

8 ) of No. 8 wires

Table I. Main scale factors for the simple law of similitude [16].

Quantity Equation Scale factor

Length (L) SL = L P/L M SL =1.25Strain (ε) Sε =εP/εM 1Stress (�) S� = fP/ fM 1Specific weight (�) S� =�P/�M 1Force (F) SF = S2

L S f S2L ≈1.56

Time (t) and Period (T ) St = SL (S�Sε/S f )1/2 SL =1.25Displacement (d) Sd = SL Sε SL =1.25Velocity (v) Sv = Sε(S f /S�)1/2 1Acceleration (a) Sa = S f /SL St 1/SL =0.80Mass (m) Sm = S�S3

L S3L ≈1.95



Figure 4. Geometry (mm) and reinforcement layout of walls: (a) MVN100D and (b) MVN50mD.

(4.1 mm diameter) with spacing of 150 mm (∼6in). The web steel ratio was approximately 50%of the minimum ratio prescribed in ACI-318 [17].

4.2. Mechanical properties of materials

For design, nominal concrete compressive strength was 15 MPa, and nominal yield strength of barsand wire reinforcement were 412 MPa (mild steel) and 491 MPa (cold-drawn wire reinforcement),respectively. Mean value of the measured compressive and tensile splitting strengths of concreteof wall models were 24.7 and 2.09, respectively. For similar walls tested under quasi-static cyclicloading, these values were 16.0 and 1.55 MPa. These properties were obtained at the time oftesting. Mean value of the measured yield strength of No. 3 bars (9.5 mm diameter) and wirereinforcement (4.1 mm diameter) were 435 MPa and 630 MPa, respectively.

4.3. Additional inertial mass

For adequately extrapolating specimen’s response to the prototype response, isolated specimenswere designed considering the fundamental period of vibration of the prototype house. For estab-lishing such a dynamic characteristic, analytical models were developed and calibrated throughambient vibration testing. The fundamental period of vibration of the two-story house was esti-mated at 0.12 s [4]. Taking into account the scale factor for period, ST =1.25 (Table I), isolatedwall models were designed to achieve an initial in-plane vibration period (Te), close to 0.10 s(approximately equal to 0.12 s/1.25). In design, it was supposed that walls would behave as asingle degree of freedom system. The dynamic weight, Wd (mass × gravity acceleration) necessaryto achieve the desired design period Te, was calculated as

Wd = KeT 2e

4�2g (17)

where Ke is the in-plane stiffness of the wall that was calculated from the measured mechanicalproperties of materials (Ke =75.7kN/mm). To account for shrinkage cracking, the moment ofinertia of the wall section was reduced by 25%. As a result, the dynamic weight was 188.2 kN.The masses and dynamic weights of the specimens during testing, as well as value of factors �1and �2 are presented in Table II. In the analysis of the specimens, the upper half of the wall masswas assumed to contribute to the effective inertia, and then �1 =0.5. Factor �2 was calculatedas the ratio of the weight of the connection system between the load cell and the specimen (oneroller swivel and half of the load cell) and the total weight of the pinned connection system; inthis case, �2 =0.35 (2.2 kN/6.2 kN).



Table II. Masses and dynamic weights of the system.

Type Mass (kg) Dynamic weight (kN)

m1 11356 111.4m2 3425 33.6m3 632 6.2m4 754 7.4m5 1305 12.8m6 887 8.7m7 795 7.8m′ 15097 148.1m 18756 184.0m (nominal) 19185 188.2�1,�2 0.50, 0.35

4.4. Test setup and instrumentation

For testing the specimens shown in Figure 4, the external device designed for placing the additionalmass (Figure 2) and the out-of-plane restraining system were used. The complete test setup forspecimen MVN100D is shown in Figure 2(a). The moving platform of the shaking table is 4 msquare size. The medium-size shaking table was designed for a payload of up to 196 kN and isconfigured to produce two translational components, horizontal and vertical, plus three rotationalcomponents of motion. However, the tests were carried out only in the horizontal direction. Themaximum acceleration of the shaking table system is 9.8m/s2 (1.0g), when the table is loaded toits limit payload. An axial compressive stress of 0.25 MPa was applied at the top of the walls. Theaxial load was kept constant during the test and was exerted through the weight of the load andconnection beams, as well as through the lead ingots bolted to the load beam. Although lead ingotsresulted in a triangular load distribution, the addition of the weight of the connection beam resultedin a final distribution of the axial load on the walls that was uniform across the wall cross-section.Specimens were instrumented using accelerometers, displacement transducers and strain gauges.Also, an optical displacement measurement system (with Light Emitting Diodes—LED’s) wasused. Details may be found elsewhere [14].

4.5. Input motions

In order to study wall performance under different limit states (or performance levels), from onsetof cracking to collapse, specimens were subjected to three earthquake hazard levels using bothnatural and artificial acceleration records. An earthquake record from an epicentral region in Mexico(Mw =7.1, CALE-71) was used for the seismic demand in the elastic limit state. The earthquakewas recorded in Caleta de Campos station, in January 11, 1997. This record was considered asa Green function (basic event) to numerically simulate larger-magnitude events, i.e. with largerinstrumental intensity and duration [18]. Two earthquakes with Mw magnitudes 7.7 (CALE-77) and8.3 (CALE-83) were numerically simulated for the strength and ultimate limit states, respectively.Time history accelerations for prototypes are presented in Figure 5. According to the simple lawof similitude, acceleration and time scale factors were applied to these records for the actual tests(Sa =0.80 and St =1.25, Table I). Specifically, accelerations were amplified using a factor equalto 1.25 ( 1

0.8 ) and the scale of time was reduced to 80% of the real scale ( 11.25 ). Models were

tested under progressively more severe earthquake actions, scaled up considering the value of peakacceleration as the reference factor, until the final damage stage was attained. The tests startedwith a sine-curve (SN) and ramp (RM) signals, which were used to evaluate the level of friction ofthe LMGS during low-velocity excitations. At the beginning and at the end of the seismic tests, arandom acceleration signal (white noise—WN) at 10cm/s2 (0.01g) RMS was applied to identifydynamic properties.



Figure 5. Time history accelerations for the prototype house: (a) CALE-71;(b) CALE-77; and (c) CALE-83.

Figure 6. Coefficients of the dynamic friction using low-velocity excitations: (a) sine curve and (b) ramp.

4.6. Test results—response of the MC SS

Performance using low-velocity excitations: As mentioned earlier, prior to starting the tests, lowfrequency SN (0.5 Hz) and RM (0.02 Hz) signals were applied to the platform. The maximumdisplacement of both signals was equal to 10 mm. These input motions, applied at low velocity(31.4 mm/s for SN and 0.8 mm/s for RM), induced negligible response of the models. Therefore,any source of resistance to the applied motion would originate only from the friction beingdeveloped in the LMGS. To reduce, and almost remove, the noise in recorded signals, accelerationand force time-histories were filtered with a band-pass Butterworth filter of 0.1–2.0 Hz and 0.004–0.5 Hz for SN and RM input signals, respectively. The lower corner frequencies were 20% ofthe frequency of the input signals. Using Equation (14), the coefficient of dynamic friction wasthen quantified. Typical time histories of the coefficient of dynamic friction are shown in Figure 6for both SN and RM excitations. For describing statistically the observed coefficient of dynamicfriction, the 75th percentile or the third quartile (P75) was used. This value states that 75% ofthe time histories data is below this value. The P75 limit is depicted at both sides, positive andnegative, in Figure 6. The damping added by Coulomb friction was calculated using Equation (15).Calculation required to initially obtain the energy dissipated by friction in one cycle of vibrationduring the low-velocity SN and RM signals (EF ). Typical hysteresis loops enclosed by the frictionforce–displacement diagram are shown in Figure 7. Strain energy, ESO =kx2

0/2, was calculatedfrom the measured initial stiffness of specimen, k, and the maximum displacement measured duringSN and RM signals, x0.

The dynamic friction coefficients and the equivalent viscous damping ratios added by theLMGS obtained using low-velocity excitations are presented in Table III (data are presentedin percentage). For comparison, results for four other specimens tested in a previous phase ofthe experimental program are shown. Information of these four tests may be found elsewhere[4]. Using low-velocity excitations, the arithmetic mean of these parameters (�d and ��eq) was0.62 and 0.08%, respectively. In other experimental studies where devices for similar purposeshave been used [6, 7], the coefficient of dynamic friction using low-velocity excitations hasbeen very high (close to 8.5%), almost 14 times larger than the value measured in the deviceproposed herein, and therefore, it had not been possible to isolate the actual response of themodels.



Figure 7. Hysteresis loops of the LMGS using low-velocity excitations: (a) sine curve and (b) ramp.

Table III. Dynamic friction coefficients and damping ratios in the LMGS using low-velocity excitations.

�d (%) ��eq (%)

Specimen Sine curve Ramp Mean Sine curve Ramp Mean

M1∗ 0.56 0.65 0.61 0.09 0.09 0.09M2∗ 0.66 0.62 0.64 0.10 0.05 0.07M3∗ 0.56 0.62 0.59 0.10 0.10 0.10M4∗ 0.61 0.64 0.63 0.10 0.10 0.10MVN50mD 0.52 0.68 0.60 0.06 0.07 0.07MVN100D 0.56 0.74 0.65 0.06 0.07 0.07

X† 0.62 0.08S‡ 0.02 0.02V (%)§ 3.5 18.7

∗Additional wall tested [4].†Arithmetic mean.‡Standard deviation.§Coefficient of variation= S/X .

Performance using high-velocity excitations: As it is shown in Table III, the dynamic frictioncoefficient and the equivalent damping ratio depend on the characteristics of the excitation, partic-ularly, on the peak velocity in the LMGS. Then, using Equations (14) and (15), the coefficientsof dynamic friction and the equivalent damping ratios added by the LMGS during earthquakerecords were also calculated. The peak velocity (vmax), the dynamic friction coefficients (�d) andthe damping added by the LMGS (��eq) are presented in Table IV. The observed coefficients ofdynamic friction also correspond to the 75th percentile (P75) of the time histories data. The peakvelocity corresponds to the maximum velocity in the LMGS during each record, which was inturn calculated from the acceleration record at the storing box, where the additional mass wasplaced.

As mentioned earlier, the ideal magnitude of the damping added by the additional mass-carryingsystem should be close to zero. This was the case for the device proposed herein. Test datapresented in Tables III and IV are plotted in Figure 8, where a fitted regression curve is shown. Asit was expected, the damping added by the device depended on the peak velocity in the LMGS.However, damping ratios added by the proposed device were very low. For instance, for the highestvelocity observed in the LMGS (0.42 m/s), the highest value was equal to 0.20%. Consequently,modification of the specimen response through the damping added by the LMGS used for testingis negligible. The fitted curve shows a suitable correlation with the test data as can be observedfrom the correlation coefficient, r [19]. If the peak velocity in the LMGS is a known parameter,the nonlinear regression can be used for estimating the damping added by the proposed device.



Table IV. Dynamic friction coefficients and damping ratios in the LMGS using high-velocity excitations.

vmax (m/s) �d (%) ��eq (%)

Specimen 1∗ 2† 3‡ 4§ 1∗ 2† 3‡ 4§ 1∗ 2† 3‡ 4§

M1 0.14 0.27 0.42 ¶ 0.53 0.68 1.31 ¶ 0.08 0.10 0.20 ¶

M2 0.14 0.25 0.35 0.42 0.53 0.66 1.04 1.04 0.06 0.08 0.12 0.12M3 0.11 0.27 0.36 ¶ 0.58 0.83 1.16 ¶ 0.10 0.14 0.20 ¶

M4 0.12 0.28 0.35 0.41 0.60 1.03 1.14 1.24 0.10 0.17 0.19 0.20MVN50mD 0.12 0.25 0.34 ¶ 0.67 0.88 1.43 ¶ 0.07 0.10 0.16 ¶

MVN100D 0.11 0.26 0.40 0.36 0.65 0.92 1.57 1.61 0.07 0.09 0.16 0.16

∗CALE-71-50%.†CALE-71-100%.‡CALE-77-75%.§CALE-77-100%.¶Data not included—failure of specimen.

Figure 8. Damping added by the LMGS using high-velocity excitations.

4.7. Test results—RC wall specimens

Overall performance: The overall performance of walls tested was assessed through the hysteresiscurves expressed in terms of the normalized shear strength, V/Vnormal or shear stress, and lateraldrift ratio. The shear strength (V = Flateral) was calculated using Equation (9). The shear strengthpredicted using equations proposed by Carrillo et al. [20], Vnormal, was utilized to normalize themeasured lateral force, V . Predicted shear strength was calculated using measured wall dimensionsand mechanical properties of materials. The drift ratio, R, was obtained by dividing the relativedisplacement measured at mid-thickness of the top slab, by the height at which such displacementwas measured. The hysteresis curves for specimens MVN100D are shown in Figure 9(a). Forcomparison purposes, results of similar wall tested under quasi-static cyclic loading are shownin Figure 9(b). Most important measured results are summarized in Table V: peak shear strength(Vmax) and shear stress (�max), normalized peak shear strength (Vmax/Vnormal), drift ratio at peakshear strength (Rmax), drift ratio at ultimate shear strength (Ru) and failure mode. In the presentstudy, Ru corresponds to a 20% drop in the peak strength. Vmax, �max, Rmax and Ru represent theaverage for the two directions of in-plane displacement (i.e. push and pull directions).

Walls reinforced with welded wire mesh and with 50% of the minimum code prescribed steelratio exhibited diagonal tension failures, DT. Failure was brittle because of the limited deformationcapacity of the wire mesh. In contrast, in walls reinforced with deformed bars and with 100% ofthe minimum steel ratio, a combined failure mode, diagonal tension and diagonal compression,DT-DC (i.e. yielding of some bars of reinforcement in the web and noticeable crushing of concrete),



Figure 9. Hysteresis curves for wall MVN100: (a) dynamic loading and (b) quasi-static cyclic loading.

Table V. Measured response parameters—Dynamic and quasi-static tests.

MVN50m MVN100

Parameter Dynamic Quasi-static Dynamic Quasi-static

Vmax (kN) 184.4 252.0 226.2 383.4�max (MPa) 1.44 1.19 1.75 1.81Vmax/Vnormal 1.05 1.00 1.03 1.18Rmax (%) 0.40 0.40 0.49 0.67Ru (%) 0.44 0.40 0.82 1.09Failure mode DT∗ DT∗ DT-DC† DT-DC†

∗Diagonal tension.†Combined: Diagonal tension and diagonal compression.

was observed. As it was expected, there were some differences between the performance of thespecimen tested using real dynamic actions (earthquake records) and the specimen tested underquasi-static loading. Differences in behavior are related to the loading rate effect, the number ofcycles and the cumulative parameters such as ductility demand and energy dissipated [14].

Estimation of equivalent damping ratios: Equivalent damping ratios calculated from the responseof wall specimens are presented in Table VI. Included in the table are the equivalent viscousdamping, �eq, the equivalent damping added by the LMGS, ��eq, and effective equivalent dampingratio, �eq’. The ratio between the damping added by the LMGS and the equivalent viscous dampingdeveloped during the measured response of the specimen (��eq/�eq) is also shown. The effectivedamping ratio, �′

eq was calculated using Equation (16) by subtracting the value of the dampinggenerated in the LMGS, ��eq (Table IV), from the equivalent viscous damping involved in themeasured response of the specimen, �eq. The latter was derived from the fitted curve of the ratiosof spectral amplitudes between the acceleration recorded at the top of specimens and that recordedat the base (shaking table), particularly in the vicinity of the peak at the fundamental frequencyof vibration of the specimen. In this calculation, the procedure proposed by Rinawi and Clough[21] was followed. In this approach, the theoretical transfer function of a single degree of freedomsystem is fitted to the experimental shape of a similar transfer function; the identification of thedamping coefficient is then based on the amplitude of the function for the vibration mode underconsideration. Measured and fitted curves of transfer functions for specimen MVN100D duringtwo earthquake records (initial and final damage stage) are shown in Figure 10. In quasi-statictesting, parameter ��eq is not a relevant quantity because the lateral loads are applied directlyby hydraulic actuators. Using the quasi-static hysteresis curve in terms of effective lateral forceversus total displacement, �eq was derived by calculating the dissipated and strain energies in eachcycle of loading [15]. The experimental energy dissipated was determined by integrating the areasbounded by all the hysteresis loops.



Table VI. Damping ratios.

MVN50m MVN100

Record (%) �eq (%) ��eq (%) �′eq (%) ��eq/�eq (%) �eq (%) ��eq (%) �′

eq (%) ��eq/�eq (%)

CALE-71-50 7.27 0.07 7.20 1.0 5.66 0.07 5.59 1.2CALE-71-100 8.28 0.10 8.19 1.2 6.60 0.09 6.51 1.4CALE-77-75 9.26 0.16 9.10 1.7 9.33 0.16 9.17 1.7CALE-77-100 10.88 0.19 10.68 1.8 9.45 0.16 9.29 1.7CALE-83-75 — — — — 10.52 0.21 10.31 2.0

Quasi-static∗ 12.28 10.93

∗�eq is the maximum value calculated for every loading cycle applied in a quasi-static test.

Figure 10. Ratios of spectral amplitudes for wall MVN100D: (a) CALE-71-50% and (b) CALE-83-75%.

It is readily apparent from Table VI that the maximum effective damping factors of specimensderived from the dynamic tests (�eq) were quite similar but smaller than those obtained from quasi-static tests. For example, in specimen MVN100, maximum damping factors under dynamic andquasi-static testing were 10.52 and 10.93%, respectively. Although these factors are not theoreticallycomparable, the similarity in the magnitude of such factors is relevant for verifying the small-magnitude damping generated in the LMGS (Table IV). Moreover, the maximum value of the ratio��eq/�eq indicates that only 2.0% of the total damping developed in the model response was addedby the friction being developed in the LMGS. When the additional mass was placed on rollingsteel carts, Lestuzzi and Bachmann [9] used the ratio of the energy dissipated by friction to thetotal input energy as a key parameter to measure the effectiveness of their device. As mentionedearlier, using earthquake records, the mean value of the energy dissipated by friction in the devicewas close to 24% of the total input energy [9]. This ratio is considerably higher and detrimentalfor specimen response, when compared with that of the proposed device.

Effect of damping added by the device: In order to assess the effect of damping added by theproposed device, response spectra for the time history accelerations measured by an accelerometerplaced on the shaking table platform were calculated. The effective damping, �eq’ (labeled as‘actual’) as well as the damping equal to the effective damping plus the damping added by thedevice, �eq, were used. The spectral accelerations related at Tm(Sa) and the ratio between thespectral acceleration and the ‘actual’ spectral acceleration (Sa/Sa(Actual)) for the earthquake recordCALE71-50% are presented in Table VII. Tm corresponds to the period of vibration measured priorto this test stage. For comparison, results for the other devices developed for similar purposes,using Teflon pads and roller bearings, are also included in Table VII. Although the value of thedamping added by a particular device should be evaluated accurately, values reported by Pinho [6]and Chuang et al. [10] were used for estimating �eq.

From results presented in Table VII, it is readily apparent that the spectral accelerations calculatedusing a damping equal to the effective damping plus the damping added by the proposed device(‘LMGS’) are almost the same as that in the ‘actual’ spectral acceleration. The latter confirms thatthe very minor amount of damping added by the device proposed herein did not modify in any



Table VII. Comparison of spectral accelerations.

MVN50m MVN100

Device Sa (g) Sa/Sa(Actual) Sa (g) Sa/Sa(Actual)

Actual 0.361 1.00 0.389 1.00LMGS—Proposed 0.360 1.00 0.387 0.99Teflon pads 0.300 0.83 0.285 0.73Roller bearings 0.267 0.74 0.242 0.62

significant way the actual response spectra. On the contrary, differences are obvious when Teflonpads or roller bearings are used for carrying additional mass. Consequently, the damping added bythese devices significantly modify the seismic response of the test specimen and, in some cases,may very well hinder the possibility of inflicting large damage, or even collapse, of the specimen.Further, it is apparent from Figure 9, that using the device presented herein, it was possible toachieve hysteresis curves typical of RC walls governed by seismic shear demands. If the equivalentviscous damping added by the LMGS had been higher, the dynamic loops had been wider and morestable and, probably, the expected pinching had not been observed. Structures with wider loops andless pinching exhibit, on the average, lower seismic response, thus leading to erroneous estimationof response parameters, as compared with structures with narrow and pinched loops [22].

5. FINAL REMARKS

An improved external device for a MCSS for dynamic testing using medium-size shaking tableswas developed and presented. In order to assess the effects of the coefficient of dynamic frictionon the force, stiffness and damping properties of specimens, the dynamic equation of motion ofthe shaking table and the device was developed. The external device was used in shaking tabletesting of six RC squat wall models, four without openings and two walls with openings. Althoughwalls were built using a scale factor close to 1.0 (1:1.25), tests were carried out successfully tocollapse. Most important test results of wall models with openings have been shown to provideevidence on the effectiveness of the proposed device.

Dynamic friction coefficients, spectral accelerations and hysteresis loops have shown that frictiondeveloped in the LMGS, did not add any significant amount of damping into the specimen response.Although the dynamic friction coefficient depends on the maximum velocity in the LMGS, it wasobserved that the maximum damping added by the proposed device corresponded to only 2.0%of the total damping involved in the earthquake model response. Moreover, the ratio of spectralaccelerations calculated using the damping equal to the effective damping plus the damping addedby the proposed device, and the actual spectral acceleration was equal to 1.0. Therefore, based onthe observed behavior and the advantages identified (stable table performance, safety for attainingcollapse performance level, small out-of-plane displacements and reduced time for test preparation),the external device can be used suitably as a MCSS for dynamic testing using medium-size shakingtables.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the financial support from Grupo CEMEX and the extensive assistancein the experimental testing from staff and students of the Shaking Table Laboratory of the Instituto deIngeniería at (UNAM).

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improved external device for a mass-carrying sliding system for shaking table testing

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