A new seismic testing method E. Kausel Professor of Civil and Environmental Engineering, Massachusetts 7-277, OamWd^e, ^ 027 JP,

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1 A new seismic testing method E. Kausel Professor of Civil and Environmental Engineering, Massachusetts 7-277, OamWd^e, ^ 027 JP, Introduction The bulleted enumeration that follows shows five experimental strategies to test the effects of earthquakes on structural components, structural models, or full scale structures; the first three are commonly used, the fourth one has recently been proposed but not yet implemented, and the last one is the subject of this paper. These five strategies are: Quasi-static Testing Method (QSTM) Shaking Table Testing Method (STTM) Pseudo-dynamic testing method (PDTM) * Effective Force Method (EFTM) Hybrid Shaking Table Testing method (HSTM) In the quasi-static testing method, a test specimen is subjected to slowly changing prescribed forces or deformations by means of hydraulic actuators without considering inertia forces within the structure. The purpose of this elementary test is to observe the material behavior of structural elements, components, or junctions when they are subjected to cycles of loading and unloading. A shaking table, on the other hand, allows ample opportunities to observe the effects of dynamic forces on structural test models. However, it is difficult to design a table capable of reproducing actual ground motions, particularly when simulating multi-axial earthquakes. Among the reasons are the deformability and inertia of the table, its characteristic modes of vibration, the

4 Earthquake Resistant Engineering Structures friction of the bearings, the physical capabilities of the hydraulic actuators, and (to a lesser extent) the limitations in the control devices.

2 4 Earthquake Resistant Engineering Structures friction of the bearings, the physical capabilities of the hydraulic actuators, and (to a lesser extent) the limitations in the control devices. For large scale structural models, additional problems develop because the table must be able to carry both the large dead weight of the specimen and the overturning moment caused by the inertia forces all of this without detriment to the functioning of the table. The pseudo-dynamic testing method resembles the quasi-static testing method in that it also consists in applying slowly varying forces to a structural model. During testing, however, the motions and deformations observed in the test specimen are used to divine the inertia forces that the model would have been exposed to during the actual earthquake; this information is then fed back into a control engine so as to determine and adjust the effective dynamic forces that must be applied onto the structure. These pseudo-dynamic forces are typically accomplished by means of actuators pushing against a large reaction wall. The effective force testing method is based on applying dynamic forces to a test specimen that is rigidly anchored to an immobile ground; these forces are proportional to the prescribed ground acceleration and the local structural masses. The deflections measured in this test correspond to the motions of the structural points relative to the ground that would have been observed had the specimen been subjected at its base to the actual test earthquake. While the theoretical basis for the effective force method is very well known, a proposal to develop and implement an actual testing device based on this principle has only recently been made [Leon et al, 1993]. As of this writing, however, there do not exist as yet exist any experimental facilities implementing this strategy. Finally, the hybrid shaking table testing method presented herein is a new technique which seeks to combine the advantages of shaking tables with those of the effective force method while avoiding some of the pitfalls in each of them. In this method, the test specimen is subjected to both a motion at its base by means of a shaking table, and to dynamic forces applied onto the masses by means of force actuators (reacting against either a stationary wall or against a support system moving with the table), or by thrust engines. The idea is to separate the ground motion into two arbitrary components, and to assign one component to the table and the other to the actuators. In fact, the characteristics of the components can be chosen so as to optimize the design of the testing system, as will be seen. While it is possible to show this method to be valid for complex multiple-degree of freedom systems, including inelastic deformations and large displacements, for the sake of brevity (and to avoid clouding the fundamental ideas behind a mass of obscure equations and concepts) only the essential aspects of the method will be presented and

3 Earthquake Resistant Engineering Structures 5 illustrated through a simple one degree-of-freedom system. A full proof of concept for multi-degree of freedom systems undergoing large displacements and/or deformations will be presented elsewhere (Kausel & Clark, 1996). Testing methods applied to a one degree-of-freedom (1-dof) system Consider a 1-dof (perhaps inelastic) system subjected to an arbitrary support motion. Let y be the relative displacement and u the absolute acceleration, as measured in the inertial system with respect to which the ground is moving with acceleration ii^, so that u = y + u^. The equation of motion is then m% + /(}',J/) = 0 (1) where f(y,y)is the restoring force in the member connecting the mass and the support. In general, this force is not only a function of the instantaneous values of the deformation y and the rate of deformation y, but the entire previous deformation history (i.e. the deformation path). For a linear system, the restoring force is given by the well-known expression f(y,y) = ky + cy, where k and c are the spring and dashpot constants. In terms of the relative displacement, the equation of motion is /) = -/%% (2) which describes the essence of the effective force method: apply fictitious forces -mu^ directly onto the structure while holding the base stationary. The left hand side contains the terms associated with the natural reaction of the system (i.e. that part which we do not control), while the right hand side contains the prescribed excitation (which we do control). Analogously, the left hand side of equation (1) represents the natural reaction of the system when mounted on a shaking table. By comparison, the equation of motion underlying the pseudo-static method is of the form /(;,,;,) = -m(^ + JP) (3) with the excitation term y obtained from the previous history of y by what amounts to a forward difference. To carry out the test, this equation is "slowed down" by appropriate time scaling (which requires neglecting the dependence of / on y ), and sacrifices are made in the estimation of y from past values of y to ensure dynamic stability.

4 6 Earthquake Resistant Engineering Structures Hybrid testing method The basic idea behind the hybrid testing method is best explained by means of a thought experiment: assume the structure to be resting on a shaking table that is in turn supported by another shaking table, as shown in Fig. 1. The bottom table 5, moves with acceleration u^ with respect to the inertial reference frame 5, while the top table ^ moves with acceleration u^ relative to the bottom table. Clearly, since the motions of the two tables are additive, their combined effect is equivalent to that of a single table with added motions u^ = u^ + u^. If one of the two tables, say the bottom one, is replaced by actuators exerting equivalent forces directly onto the structure, the response as far as structural deformations is concerned remains unaltered. In other words, as long as both excitations effectively add to the original ground motion, the structural response is indistinguishable from that obtained solely with a single shaking table, or solely with actuators. Let w, be the apparent absolute motion of the mass as seen from the (moving) reference frame 5,, and >>, = y^ = y the actual deformation of the member in either system. The true and apparent absolute motions are related by the equation u = u\ + u^ = y + u^ + u^ From equation (1), it then follows that which states that the response of the system can be obtained by applying a support motion u ^ underneath the (now single) top table simultaneously with fictitious forces -mii^ exerted by actuators. This equation reduces to either equation (1) or (2) when w^,or u^, respectively, go to zero (i.e. the HSTM method reduces then to either the STTM or the EFTM methods). Why hybrid testing? The proposed method could offer several potential advantages, including the possibility of optimizing the ground motion components from the point of view of the power or force demands on the table and actuators, or the mechanical characteristics of these devices. For example, one of the following criteria could be used: Separate the ground motion into low and high frequency components. Assign the low frequency components to the shaking table, and the high

5 Earthquake Resistant Engineering Structures 7 frequencies to the actuators. In fact, the separation need not strictly follow a Fourier decomposition. For instance, one could drive the shaking table with a quasi-sinusoidal component, modulated by an appropriate bellshaped window so as to simulate the ground displacement; the remainder would then be driven with actuators. Conceivably, this alternative could simplify considerably the design of the driving and bearing mechanisms of the table. At the same time, one could avoid the problems associated with low-amplitude table motions, which are often impeded by friction of the bearings. Separate again the ground motion into low and high frequency components. This time, however, simulate only the intermediate or high range of frequencies with the table. The remainder could be accomplished with actuators, including perhaps jet engines attached to the structure to simulate the low frequency components. This could have the advantage of limiting the stroke of the actuators and the maximum displacement that the table would have to accommodate; in addition, it could also reduce the total power requirements of the system. Expand by means of actuators the capabilities of an already existing table (or even a planned one) able to move in only one or two directions and use it to simulate fully three-dimensional earthquake forces. For example, model the strong translational components with the table, and the remaining components through actuators (particularly rotational ground motion components!). Split the components so as to minimize the instantaneous power demand and/or the total energy dissipated. As we shall see in the next section, shaking tables and actuators exhibit different mechanical behaviors and one could, in principle, find an optimal combination. Whatever the criterion used to separate the ground motion into additive components, this hybrid testing device would normally be supplemented with sophisticated control devices, which would measure the displacements of the table and the forces exerted by the actuators, and provide instantaneous feedback and correction to ensure a reliable simulation of the seismic excitation. Testing Systems and Power Demand The instantaneous power demanded by the experimental devices, while testing the 1-dof systems considered previously, is simply the product of the

6 8 Earthquake Resistant Engineering Structures net external force and the velocity of the point of application of this force. This power varies form system to system, as will be seen. From the previous section, and with reference to Fig. 2, the instantaneous mechanical power (excluding the power required to move the driving assembly, such as the table itself, or the actuators) is as follows. Shaking table: The net external driving force is p = mu, and the velocity is that of the ground. Hence, W = miiu (5) Force actuators: The force applied by the actuators is p = -mu^, and the velocity of the application point is y. Hence W = -mu^y (6) Hybrid system: The force exerted by the actuator is /?, = -mu^, which acts on the mass moving with velocity M, ; the driving force acting on the table, moving with velocity u^, is p^ = m(u\+u^) = mu (which is independent of how the ground motion is apportioned between the shaking table and the actuator). The total mechanical power delivered by the system is then W = /?, w, + p^u^, that is W = -mugm + muiigi = -mu^y + m(u - u^ )ii^ (7) In particular, if the earthquake is simulated only with the shaking table (u^ = 0, u^ =Mg, Wg2 =6,,), or only with actuators (u^ =0, u^ = 0, u^ = u^), then equation (7) reduces to equations (5) and (6), respectively. These two quantities are not equal. This is illustrated in Figs. 3, 4, which show a comparison of the two expressions for oscillators with unit mass, 5% structural damping, and resonant frequencies of 0.5 and 5 Hz, respectively, when subjected to the 1940 El Centro earthquake (SE component, normalized to 1 g). A can be seen, the shaking table requires less power for the soft spring-mass system, but much more for the stiff system. The converse is true for the force actuator system. Fig. 5, on the other hand, shows the power demand for a 1-Hz hybrid system in which the motion is represented 50% with a shaking table and 50% with

7 Earthquake Resistant Engineering Structures 9 actuators. Remarkably, the peak power demand is less then either system acting alone. We next split the motion into low and high frequency components by means of a low-passfilterthat rolls off smoothly in the band from 0.5 to 1.5 Hz.; the time histories for the two motion components are shown in Figs. 6 and 7. Fig. 8 gives the total power demand for a 1 Hz structure for the hybrid device, with the low components going into the shaking table, and the high components into the actuators. As can be seen, the hybrid system's peak power demand is half as large as that of the shaking table or the actuator system acting alone. Conclusion The new hybrid shaking testing concept presented in this paper is based on separating the ground motion components into two arbitrary additive parts; the simulation of the first part is accomplished with a conventional shaking table, while the second is carried out with actuators acting directly onto the structure. The concept was demonstrated here by means of a simple one degree-of-freedom system, but it can also be shown to be valid for system with many degrees of freedom, including those that exhibit material and/or geometric non-linearities. This strategy could offer several advantages in the design of a seismic testing device, particularly when the action of multiple ground motion components must be considered simultaneously. Among the potential benefits one could find: considerable reduction in the total power and energy requirements substantial decrease in stroke and thrust of the actuators needed to move the table or exert forces on the structural masses. simplification in the support mechanisms needed to shore up the structure and resist overturning moments when vertical and rotational components are simulated. possibility of using novel, low frequency force actuators (such as jet engines), which need not have the capacity of rapidly changing the thrust.

8 JO Earthquake Resistant Engineering Structures References Kausel, E. and Clark, A (1996): "A new hybrid method for earthquake testing", submitted for possible publication in Earthquake Spectra. Leon, R.T., Clark, A.J., French, C.W., and Bailey, F.N. (1993): "Development of an effective force technique for earthquake testing", presented at the U.S.- Japan Seminar on Development and Future Dimensions of Structural Testing Techniques", Ilikai Hotel Nikko Waikiki, June 28 to July 1 u Fig. 1

9 Earthquake Resistant Engineering Structures 11 a) Shaking Table S' b) Force Actuators c) Hybrid Testing System Fig. 2

10 12 Earthquake Resistant Engineering Structures Instantaneous power, 0.5 Hz test structure (5% damping) El Centro earthquake normalized to Ig 10 Shaking table Force actuators M> r. 4 --W-\//k/\--^/'f /1 / \ ' I \,/^: v\ \ I \l r Time (sec) 15 Fig. 3

11 Earthquake Resistant Engineering Structures 13 Instantaneous power, 5 Hz test structure (5% damping) El centro earthquake normalized to Ig GO Fig. 4

12 14 Earthquake Resistant Engineering Structures Instantaneous power, 1 Hz test structure 50% allocation between shaking table and force actuators Hybrid (50%) Shaking table Force actuators oo -5-15' Time (sec) Fig. 5

13 Earthquake Resistant Engineering Structures 15 Motion component 1 c o V\/\ _J Time (sec) Fig. 6

14 16 Earthquake Resistant Engineering Structures Motion component 2 e/5 04 s Time (sec) Fig. 7

15 Earthquake Resistant Engineering Structures Instantaneous power, 1 Hz test structure Ground motion separated into low and high frequencies Hybrid (0.5 Hz lowpass) Force actuators Shaking table Si- OJD Fig. 8

SHAKING TABLE DEMONSTRATION OF DYNAMIC RESPONSE OF BASE-ISOLATED BUILDINGS * Instructor Manual *

SHAKING TABLE DEMONSTRATION OF DYNAMIC RESPONSE OF BASE-ISOLATED BUILDINGS ***** Instructor Manual ***** A PROJECT DEVELOPED FOR THE UNIVERSITY CONSORTIUM ON INSTRUCTIONAL SHAKE TABLES http://wusceel.cive.wustl.edu/ucist/