Passive Energy Dissipation Systems in Structural Engineering

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title:Passive Energy Dissipation Systems in Structural Engineeringauthor:Soong, T. T.; Dargush, Gary F.publisher:John Wiley & Sons, Ltd. (UK)isbn10 | asin:0471968218print isbn13:9780471968214ebook isbn13:9780585165240language:EnglishsubjectStructural design, Structural dynamics, Force and energy.publication date:1997lcc:TA658.S634 1997ebddc:624.1/771subject:Structural design, Structural dynamics, Force and energy.

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1

Introduction

In the design of most buildings, the primary loads that must be considered are those due to the effects of gravity. These loads are always present and consequently must be resisted throughout the life of the building. Typically, the variation with time is slow compared to characteristic times of the structure. As a result, a static idealization is quite appropriate. Furthermore, the magnitudes can be readily determined based upon self-weight and occupancy requirements. This combination of factors greatly simplifies building design, and, in fact, allowed our ancestors to design and construct impressive structures prior to the development of rational scientific principles. The simplicity of the problem permits the use of a trial-and-error approach to design, particularly if one is not unduly constrained by material and labor costs.

In our modern era, resources are often severely limited. Efficient designs must be sought. Additionally, we demand protection from environmental forces, including winds, waves, and earthquakes, which are neither static nor unidirectional. For these types of loads inertial effects become important, resulting in dynamic amplification and cyclic response. Compared to gravity loads, the magnitudes are also much more difficult to predict, since the temporal and spatial scales of these phenomena are much smaller.

Despite these significant differences, there is a natural tendency to treat the environmental forces with the same methods used for gravity loads. For example, wind and earthquake forces are often idealized as lateral static loads of suitable magnitude that must be resisted by the structure. Utilizing this approach, the lateral loads corresponding to wind and small earthquakes are designed to be resisted by elastic action only, while those associated with moderate or severe seismic events are permitted to damage but not collapse the structure. This philosophy has provided the basis for a number of building codes since the early twentieth century, and results have been reasonably successful. Even an approximate accounting for lateral effects will almost certainly improve building survivability.

However, by considering the actual dynamic nature of environmental

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Figure2.3

AmplificationFactorforHarmonicLoading

factor becomes negligibly small since the load varies too rapidly to invoke a displacement response.

It is also instructive to consider the steady-state phase relationships. Figure 2.4 illustrates the dynamic balance of the forces associated with the applied load (p), inertia (f1), stiffness (fs), and damping (fD) in the complex plane. Of course, the actual force at any time t is the real component of the complex force shown in this Argand diagram. For the damped system, the spring force, and consequently the displacement response, lag behind the applied load by the phase angle q1. Meanwhile, the damping and inertia forces, which are in turn proportional to the velocity and acceleration, lead the displacement

Figure2.4

DamperForceBalanceforHarmonicExcitation


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and repeatable with rectangular hysteresis loops. Furthermore, the effect of loading frequency and amplitude, number of cycles, or ambient temperature on damper response was reported to be insignificant. Although the supportive component test data is not available in the literature, it would seem that a simple elastic-perfectly plastic hysteretic model, defined above in Table 4.1, is appropriate for structural analysis involving this device.

The final friction damper to be considered is the Energy Dissipating Restraint (EDR) manufactured by Fluor Daniel, Inc. and detailed in Fig. 4.1d. Superficially the design is similar to the Sumitomo concept, since this device also includes an internal spring and wedges encased in a steel cylinder. However, there are several novel aspects of the EDR that combine to produce very different response characteristics. A detailed presentation of the design and its performance is provided in Nims et al. (1993a). As indicated in Fig. 4.1d, the EDR utilizes steel compression wedges and bronze friction wedges to transform the axial spring force into a normal pressure acting outward on the cylinder wall. Thus, the frictional surface is formed by the interface between the bronze wedges and the steel cylinder. Internal stops are provided within the cylinder in order to create the tension and compression gaps that are illustrated in Fig. 4.1d. Consequently, unlike the Sumitomo device, the length of the internal spring can be altered during operation, providing a variable frictional slip force. Typical experimental hysteretic behavior is displayed in Fig. 4.12 for three different configurations. Figure 4.12a represents the response obtained with zero gaps and zero spring preload. Triangular shaped hysteresis loops result indicating slip force proportional to the device displacement. With non-zero spring preload and very large gaps, the device acts as a standard Coulomb damper as indicated in Fig. 4.12b. The model presented previously in Table 4.1 is obviously applicable for this second case. Finally, with a non-zero preload, but no initial gaps, the flag-shaped hysteresis loops of Fig. 4.12c are obtained.

Clearly, from Fig. 4.12, the repsonse characteristics of the EDR are quite different from those of the other friction dampers. Consequently, it is appropriate to briefly discuss the underlying mechanics. Consider the case associated with Fig. 4.12a having zero gaps and zero preload. This configuration corresponds to that depicted schematically in Fig. 4.13, except with G1 = 0. In its initial state, due to a zero internal spring force, there exists no normal contact pressure acting between the wedges and casing. However, once a force P is applied in either tension or compression, the spring, with stiffness Ks, is compressed and frictional resistance results. Let the spring displacement be represented by Ds, while the overall displacement of the device is D, which includes deformation of the rod and connections Dr. Thus,

D=Ds+Dr(4.3)

If the stiffness of the rod and connections equals K3, then


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Figure4.12

ExperimentalDataforEDR(Richteretal.,1990)

Figure4.13

EDRConfigurationSchematic(Nimsetal.,1993a)

P=K3Dr=K1D(4.4a,b)

where K1 is the effective overall stiffness of the device during initial loading. Furthermore, the spring force becomes

Ps=KsDs(4.5a)

and the corresponding frictional resistance during slippage can be written


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Pf=aKsDs(4.5b)

The positive factor a, which is less than one for practical designs, incorporates the geometric and Coulomb friction effects involved in transforming the action of the spring force through the wedges into a frictional resistance. For slippage during loading, equilibrium requires that

P=Ps+Pf(4.6)

Consequently, from Eqs. (4.3)-(4.6), one obtains the following expression for the effective stiffness:

This is simply the stiffness of a system featuring a parallel combination of internal spring and frictional elements, (1 + a)Ks, in series with the rod/connection spring K3.

Upon subsequent unloading of the device, the frictional force reduces immediately and further slippage is prevented. Thus, for the initial stage of unloading, the spring displacement remains constant. The stiffness of the device is then simply equal to the stiffness of the rod and connections K3. Eventually, as the applied force P is reduced, a level is reached at which slippage occurs in the unloading direction. In this regime, the frictional force now opposes the action of the internal spring. As a result, the effective stiffness of the device becomes

Note that in this configuration, the EDR device is self-centering. In the absence of external force, the internal spring will return to its initial zero preload state.

A detailed description of an appropriate hysteretic model is presented in Table 4.3. Results obtained from the model for displacement controlled cyclic loading are shown in Fig. 4.14a. It should be noted that this model also permits the simulation of response due to arbitrary loadings, which may include partial unloading-reloading cycles. Some care is required, however, in the numerical implementation, particularly for a 1. An extended version can also be developed to incorporate the effects of initial preload, indicated in Fig. 4.12c, by including an internal variable corresponding to Ds. While a detailed presentation is not included here, typical numerical results obtained from the model are provided in Fig. 4.14b. The device in this configuration is again self-centering.


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Figure4.14

HystereticModelforEDR;a)

NoGaps,NoPrelaod,b)

NoGaps,FinitePreload


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Before shifting attention to the overall analysis of structures that incorporate friction dampers, it is perhaps appropriate to mention a couple of aspects of damper response that have not been addressed adequately in the literature. In reviewing the available published component test data, one finds that nearly all dampers have been tested at a single, relatively low frequency. Classical Coulomb behavior is assumed, but not demonstrated. In particular, there have been no systematic attempts to investigate the effects of amplitude and frequency on response. Additionally, an examination of the consistency of damper response after long periods of inactivity has not been reported for any of the proposed dampers. Consequently, some care is needed in adopting one of the models presented above in Tables 4.1-4.3, since all assume Coulomb damping with a constant coefficient of friction.

4.4 Structural Analysis

After a hysteretic model has been validated for a particular friction damper that model can be readily incorporated in an overall structural analysis. Although some attempts have been made to introduce the concepts of equivalent viscous damping (e.g., Scholl, 1993), in general, a full nonlinear time domain analysis is required. The finite element methodologies outlined in Section 2.3.4 are directly applicable, and in fact have been used in a number of detailed numerical investigations involving friction dampers. The present section contains a review of the more prominent efforts, which attempt to highlight the benefits of incorporating various frictional devices into structural systems.

As a part of their initial work, Pall et al. (1980) performed parametric studies on a hypothetical panelized apartment building incorporating Limited Slip Bolted (LSB) joints. The nonlinear analysis utilized DRAIN-2D (Kanaan and Powell, 1973) to determine the response due to the 1940 El Centro S00E seismic ground motion scaled to various intensities. The primary structure was assumed to rest on a rigid foundation and remain elastic with 5% critical viscous damping, while the nonlinear model illustrated in Fig. 4.5b was used for the LSB joints. Design parameters varied in the analyses included number of building stories, LSB slip load, slot length, and joint stiffness. The last item was found to have little effect on response. However, sufficient slot length was needed to prevent the sudden increase in forces associated with bearing contact of the LSB joints. Both building height and slip load had a major influence on seismic performance. For example, Fig. 4.15a and b present the maximum wall normal stress at the base and the maximum displacement at the top, respectively, as a function of those two parameters. Ratios of less than unity indicate enhanced performance for the friction-damped structure. It is apparent that significant improvement is possible for the 15 and 20 story buildings, while the addition of LSB joints is not beneficial for the stiffer five


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and ten-story models. Unfortunately, this behavior is difficult to generalize, because the response is strongly influenced by the frequency content of the seismic signal.

Figure4.15

NumericalResultsofLSBJointfor

ElCentroGroundMotion,Ratioof

LBSJointedWalltoElastically

JointedWall(Palletal.,1980);

a)NormalStress,b)Deflection

Pall and Marsh (1982) presented similar numerical trends for a tenstory steel frame supported on a rigid foundation, again subjected to the 1940 El Centro earthquake. Results for three configurations, consisting of a moment resisting (MR) frame, a cross-braced moment resisting (BMR) frame, and a friction damped braced (FDB) frame, were compared. The DRAIN-2D analysis included consideration of tensile yielding and compressive buckling of primary frame members, along with their simple hysteretic friction damper model. Zero viscous damping was assumed for the structure in all


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three configurations. The resulting deflection and column force envelopes are reproduced in Fig. 4.16. The addition of friction dampers results in significant reductions in interstory drifts. Reduced column shear and bending moment are also apparent. On the other hand, axial forces are greater than those obtained for the moment resisting frame. For the particular case considered, plastic hinges form in beam members of the MR and BMR designs, while the primary members in the FDB with optimal slip loads remain elastic. The authors note, however, that results obtained for a single seismic record may not be conclusive.

Figure4.16

NumericalResultsofX-bracedFrictionDamperfor

ElCentroGroundMotion(PallandMarsh,1982)


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Filiatrault and Cherry (1987) considered several different earthquake inputs in their combined numerical and experimental investigation of a three-story, one-third scale steel FDB frame. In the numerical DRAIN-2D analysis, the model was subjected to 1940 El Centro S00E at 0.52g, 1966 Parkfield N65E at 0.52g, Newmark-Blume-Kapur artificial signal at 0.30g, and band-limited white noise at 0.50g. Optimal slip loads for the friction dampers were determined via a parametric study, and found to be reasonably independent of the seismic signal. Results were then compared with those obtained for the MR frame and BMR frame configurations, which correspond to the zero and infinite slip load cases, respectively. Two different friction damper models were considered in the analyses; the simple Pall-Marsh model of Fig. 4.5b, and the refined model depicted in Fig. 4.6. Although the latter more realistic model produced a significantly different response, the FDB frame still performed better than the traditional MR and BMR frames. For example, typical column shear force envelopes are illustrated in Fig. 4.17.

Figure4.17

NumericalColumnShearForceEnvelopesfor

Three-storyFrame(FiliatraultandCherry,1987)

Subsequently, Filiatrault and Cherry (1988) conducted a comparative numerical study of conventional, friction-damped, and base-isolated BMR steel frame structures. A typical ten-story building, with cross bracing in the even stories, was employed for the comparison. Optimal friction device slip loads were determined using DRAIN-2D for the 1940 El Centro S00E signal. In a similar manner, design parameters were established for the lead-rubber hysteretic bearing base isolation system. Mathematical models of all three systems were then subjected to signals from the 1977 Bucharest and 1985 Mexico City earthquakes, which have a very strong low frequency content. Damage predicted for the three structural configurations is identified in Fig. 4.18. The damage ratio (DR), included in that diagram, is defined as the ratio of the number of yielded members to total number of members. Both base isolated (BIBMR) and friction damped (FDB) frames performed well for the El Centro earthquake. However, only the FDB design was effective for


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the remaining two disturbances. As the authors note, this suggests that the proposed friction damped system may offer new opportunities in earthquake resistant design. Despite this observation, it is difficult to draw general conclusions concerning the relative merits of FDB and BIBMR designs. It can be argued that the BIBMR system was simply not designed to respond favorably to strong low frequency content earthquakes. In that regard, this study by Filiatrault and Cherry (1988) highlights the importance of optimizing structural performance, not for a single seismic signal, but rather for the entire range of earthquake inputs that can be expected to occur at a particular site. The computational effort required for such an approach is not beyond that available with modern engineering workstations.

Figure4.18

PredictedDamageinTen-story

Frame(FiliatraultandCherry,1988)


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In other related analysis work, Baktash and Marsh (1987) conducted a comparative study of the performance of friction damped braced frames (FDBF) and eccentric braced frames (EBF). The authors found that while both systems were adequate, the FDBF design produced smaller deflections, accelerations, and forces. An innovative friction damped timber shear wall concept was examined by Filiatrault (1990) and also found to be effective in reducing seismic response.

More recently, numerical and theoretical investigations on the response of structural systems incorporating EDR devices have appeared. Nims et al. (1993a) conducted parametric studies on idealized SDOF systems with added frictional elements that produce either the flag-shaped or triangular-shaped hysteresis loops discussed in Section 4.3. The parameters considered include the frequencies of the braced and unbraced structure, unbraced damping ratio z, EDR device initial slip load P1 as a percentage of the structural weight, and amplitude and frequency content of the seismic signal. Fig. 4.19 provides a typical set of results for devices with flag-shaped hysteresis loops. In those plots the acceleration response, due to the El Centro and Zacatula earthquakes, is plotted versus unbraced structural frequency with

Figure4.19

NumericalResponseofSDOFStructurewithEDR(Nimsetal.,1993a)


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response by phase angles of 90 and 180, respectively. At resonance, q1 = 90 and the applied loading is exactly balanced by the force in the damper.

Additional insight can be gained by examining the force-displacement curves as illustrated in Fig. 2.5 for the spring and damper. The energy stored in the spring at any time is equal to the area under the curve in Fig. 2.5a, while the energy dissipated via viscous action per cycle is equivalent to the area within the elliptical hysteresis loop shown in Fig. 2.5b. The elliptical shape is a direct result of the 90 phase difference between the damper force and displacement response, along with the constant amplitude nature of the motion. For a given structure, the area contained within the hysteresis loop is a function of the frequency ratio, with a maximum occurring near resonance. The specific case displayed in Fig. 2.5 has = 0.90 and z = 0.05.

Figure2.5

Force-displacementResponseforHarmonicExcitation;a)Spring,b)Damper

2.2.4 Transient Response

The environmental loads of most interest to us here are not pure harmonics, but rather the result of transient processes. With that in mind, consider the response of our SDOF model, initially at rest, to a general loading . The solution can be formally written in terms of a Duhamel integral. With zero initial displacement and velocity, this becomes

where


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unbraced damping ratio z = 0.05. The frequency of the braced structure is assumed, in all cases, to equal twice the unbraced frequency. With reference to Fig. 4.14b, the device stiffness ratio K1/K3 = 10. From Figs. 4.19a, c, it is apparent that the addition of frictional devices reduces response, except for structures in the low frequency range. (Results for an unbraced structure with z = 0.10 are also included in those figures to illustrate the effects of adding purely viscous damping mechanisms.) The variation of response with initial slip load is quantified in Figs. 4.19b, d.

The above EDR results are for an SDOF system. However, the response of a six-story, 0.3-scale steel MDOF structure, subjected to the El Centro and Zacatula ground motions, has been reported in Nims et al. (1993b). Comparisons, made with the corresponding unbraced and conventionally braced frames, indicate that the friction dampers effectively reduce displacements, while maintaining comparable acceleration levels.

Nonlinear analysis methods have been employed out of necessity in all of the efforts referred to in this section to describe the behavior of structural systems that incorporate friction dampers. In recent work, Inaudi et al. (1993a) have developed some interesting and potentially useful methods to approximate the response of systems that include EDR devices with triangular-shaped hysteresis loops. The authors note that although these frictional elements are nonlinear and the principle of superposition does not apply, the response is scale invariant. Thus, if a deformation history is scaled by a certain factor, the forces in the device are multiplied by that same factor. This permits the effective use of the techniques of harmonic linearization and statistical linearization (Inaudi et al., 1993a, b) to develop estimates of the actual nonlinear response. In general, very good results are obtained, indicating that these methods may be suitable for preliminary design calculations. It should be noted, however, that the use of discontinuous memory functions within a force-displacement model can lead to difficulties under arbitrary excitations which include partial unloading-reloading cycles.

4.5 Experimental Studies

As noted previously, the lack of well-developed theories necessitates significant reliance upon physical testing to establish the suitability of friction dampers. Component level testing has been reviewed in some detail in Section 4.3. Consequently, in the present section, the focus is on experimental studies at the structural level.

The first such investigation was conducted by Filiatrault and Cherry (1987), who evaluated the performance of the cross-braced friction dampers. Two identical three-story, one-third scale steel frame structures were fabricated in a manner that readily permitted transformation between MR, BMR and FDB frame configurations. Natural frequencies and damping ratios were


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measured at low amplitude for all three configurations. Then the structures were mounted on a shaking table and subjected to a series of earthquake records with varying magnitude and frequency content.

In general, the authors found that the friction-damped structures responded significantly better than the MR or BMR designs for high intensity signals. For example, beam bending moment envelopes for the 1952 Taft earthquake scaled to a peak acceleration of 0.60g are displayed in Fig. 4.20a. The moments are lowest for the FDB frame on all three floors. Meanwhile, deflections are shown in Fig. 4.20b. (Numerical predictions, which agree reasonable well with the experimental results, are also included in both of these plots.) Third floor acceleration for the same earthquake scaled to a magnitude of 0.90g is depicted in Fig. 4.21. Once again, the FDB design produces the lowest response. For this particular earthquake, the friction dampers dissipate over 90% of the input energy, and effectively protect the primary structure from damage.

Figure4.20

ResponseofThree-StoryTestFramefor

Taft0.60g(FiliatraultandCherry,1987)


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Figure4.21

MeasuredThirdFloorAccelerationsfor

Taft0.90gInput(FiliatraultandCherry,1987)

The experimental program designed by Filiatrault and Cherry (1987), and described briefly above, was well conceived and quite comprehensive. However, one minor point must be made concerning the use of full scale cross-braced friction devices in a one-third scale structure. Even though slip loads were adjusted to appropriate levels, this scaling imbalance reduces the contribution of any geometric nonlinearities that may be associated with the device. It is difficult to determine the significance of that contribution without further testing or detailed modeling.

An additional experimental study on the cross-braced dampers was conducted by Aiken et al. (1988). A three-bay, nine-story, one-quarter scale steel structure was extensively tested on an earthquake simulator, in both MR and FDB frame configurations. The dissipating elements in the FDB design utili

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Passive Energy Dissipation Systems in Structural Engineering