EQSpect Wood Numerical.pdf

8/10/2019 EQSpect Wood Numerical.pdf

http://slidepdf.com/reader/full/eqspect-wood-numericalpdf 1/32

Seismic Behavior of Wood-framedStructures with Viscous Fluid Dampers

Michael D. Symans,a)M.EERI, William F. Cofer,b) Ying Du,b)

and Kenneth J. Fridleyc)

The suitability of viscous fluid dampers for seismic protection of light-framed wood buildings is investigated in this paper. Nonlinear finite-elementmodels of wood building components (shear wall) and systems (three-dimensional buildings) are developed and numerical analyses are performed to evaluate their response to seismic loading. For both the single wall and the

building system, seismic protection is provided by installing viscous fluid dampers within the wall cavities. The results of the numerical analyses dem-onstrate the ability of fluid dampers to dissipate a significant portion of seis-mic input energy, reducing the inelastic strain energy demand on the wood

framing system. In addition, the study revealed some important practical is-sues associated with implementation of fluid dampers within light wood-framed buildings. [DOI: 10.1193/1.1731616]

INTRODUCTION

During the past decade, base isolation systems and supplemental damping systemshave seen a steadily increasing number of applications in large steel and concrete build-ings. However, to date, within the United States there is only one application of a seis-mic protection system to wood-framed structures (Symans et al. 2002a). The research

presented herein seeks to expand the number of applications of seismic protection sys-tems to wood-framed structures by investigating the suitability of a particular supple-mental energy-dissipation system for application to wood-framed structures. It has been

recognized that the seismic response of a building can generally be reduced by introduc-ing a supplemental damping system within the framing of the building. However, theargument has been made that wood-framed buildings would not benefit from a supple-mental damping system since the effective damping ratio of such structures is quite high(on the order of 7 to 15%). However, one must recognize that such levels of effectivedamping are the result of appreciable inelastic behavior associated with structural dam-age. A supplemental damping system would dissipate a portion of the seismic input en-ergy, thereby reducing the amount of energy dissipated via inelastic behavior within thestructural framing.

Relatively few studies have been conducted on the application of seismic protectionsystems to wood-framed structures. This may be partially due to a number of impedi-ments to the implementation of base isolation and supplemental damping systems in

a) Department of Civil and Environmental Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180 b) Department of Civil and Environmental Engineering, Washington State University, Pullman, WA 99164c) Department of Civil and Environmental Engineering, University of Alabama, Tuscaloosa, AL 35487

451

Earthquake Spectra, Volume 20, No. 2, pages 451–482, May 2004; © 2004, Earthquake Engineering Research Institute





The aforementioned supplemental damping systems are attractive for offering seis-mic protection to wood-framed structures. However, the potential benefits of viscousfluid dampers, the dominant type of damper used in practice today, have not yet beenexplored. This study seeks to fill this gap in knowledge by performing a numericalevaluation of the seismic response of wood-framed shear walls and building systemswith fluid dampers. A unique feature of viscous fluid dampers is that they are capable of

providing a high energy-dissipation density (i.e., the energy dissipated is very large in

comparison to the physical size of the damper). As a result, the dampers can be conve-niently located within the walls of a wood-framed structure. Practical issues associated with the required capacity of such dampers and their installation within wood-framed shear walls are also presented herein. To the knowledge of the authors, the research pre-sented herein represents the first study on the application of viscous fluid damperswithin wood-framed structures for seismic energy dissipation.

MODEL OF WOOD-FRAMED SHEAR WALL

DESCRIPTION OF WALL

The wall model developed herein is similar to a series of walls that were experimen-tally tested by Dolan (1989). The dimensions of the shear wall were 2.44 m2.44 m

(8 ft8 ft) (see Figure 1). The framing of the wall consisted of 38.1 mm88.9 mm(nominal 2 in.4 in.) lumber with the vertical studs spaced at 60.96 cm (24 in) on cen-ter. Single end studs and top and bottom plates were used. The wall was sheathed with1.22 m2.44 m (4 ft8 ft) plywood sheathing panels having a thickness of 9.53 mm(3/8 in). The connections between the sheathing and framing consisted of 6.35 cm (2.5in) 8d galvanized common nails with field and perimeter nail spacing of 15.24 cm (6 in).

Figure 1. Schematic of wood shear wall used for numerical analysis (nail location shown is notrepresentative of actual nail position). 25.4 mm1.0 in

SEISMIC BEH AVIOR O F WO OD-FRAMED STRUC TURES WITH VISCO US FLUID DAMPERS 453



Note that, to duplicate the walls that were experimentally tested by Dolan (1989), thestud spacing and field nail spacing of 24 and 6 in. on center, respectively, differ from thespacing of 16 and 12 in., respectively, that is commonly used in practice. The difference

in lateral load resisting behavior of the wall with these two different spacing conditionsis probably not very significant since the number of field nails differs by only two.

The weight at the top of the wall was 44.5 kN (10 kips), which is intended to rep-resent the tributary weight if the wall were located at the first story of a three-storyapartment building in North America. The weight was distributed at the nodes along thetop plate (i.e., at the top of each stud). The bottom plate was assumed to be fixed to thefoundation. Thus the effects of uplift and sliding of the bottom plate are not explicitlyconsidered. However, these effects are implicitly considered as a result of calibration of the model using experimental test data in which these effects may be present to somedegree. It should be noted that, as per previous research studies on the application of seismic dampers to wood-framed shear walls, the wall depicted in Figure 1 does not in-clude finish materials. However, recent experimental testing performed by Fischer et al.

(2001) and Gatto and Uang (2002) indicate that the finish materials used on structuralwalls and partitions can make a considerable difference in system behavior; the effect

being to increase the stiffness and generally reduce the story drifts. It is anticipated thatfuture studies by the authors will explore the influence of finish materials on the seismicresponse of wood-framed structures incorporating damping systems.

FINITE ELEMENT MODEL

A nonlinear finite-element model of a wood-framed shear wall was developed for thenumerical analyses using the commercial program ABAQUS (ABAQUS 1998). A totalof 415 nodes were used to define the model. The framing members and sheathing panelswere modeled as two-dimensional isoparametric, isotropic, elastic cubic beam elementsand two-dimensional isoparametric, orthotropic, elastic linear plane stress elements, re-

spectively. Elastic framing members and sheathing panels are used since, as is com-monly understood, the hysteretic behavior of the wall is considered to be dominated bythe hysteretic behavior of the sheathing connections. The initial clearance between thesheathing panels was assumed to be 7.94 mm (5/16 in). The interaction between the twosheathing panels was accounted for via a softened contact pressure-clearance relation-ship with an exponential law.

The sheathing connections associated with each nail were modeled as two orthogo-nal (one vertical and one horizontal) uncoupled nonlinear springs whose characteristicswere defined by a modified hybrid Stewart-Dolan connector model consisting of a seriesof straight-line segments (Stewart 1987) and an exponential backbone curve (Dolan1989). The hysteresis loop for the connection model is shown in Figure 2b for the staticcyclic loading protocol shown in Figure 2a. For qualitative comparison, a hysteresis loop

obtained from experimental testing of a similar sheathing connection is shown in Figure2c. The idealized hysteretic loop shown in Figure 2b is generated using a rule-based model for loading/unloading behavior. The connector model includes an exponential

backbone curve that represents the monotonic resistance to lateral displacement and serves as an envelope for the force developed during cyclic motion. In addition, the

454 M. D. SYMANS, W. F. COFER,Y. DU, AND K. J. FRIDLEY



model includes linear loading/unloading segments and a linear pinching region. The backbone curve is given by the following expression relating the connection shear force,P, and the connection displacement, u:

PPo K 2u1exp K ou

Po (1)

where Po is the force intercept corresponding to the slope of the backbone curve at theultimate displacement, K o is the initial elastic stiffness of the connection (i.e., the initialslope of the backbone curve), and K 2 is the stiffness of the connection at the ultimatedisplacement (i.e., the slope of the backbone curve at the ultimate displacement). Theremaining parameters that define the hysteretic behavior are as follows (see Figure 3): P1

is the force intercept within the pinching region, uult is the displacement corresponding

to the ultimate force (i.e., the displacement at which stiffness degradation initiates), K 3 isthe stiffness of the connection beyond the ultimate displacement (i.e., the degradingstiffness), and K 4 is the stiffness of the connection within the pinching region.

Four of the seven parameters of the sheathing connection model (Po , P1 , K o , and K 2) were obtained from experimental test data produced by Dolan (1989). The other

Figure 2. Hysteretic behavior of sheathing connection: (a) static cyclic loading protocol, (b)response from numerical analysis, and (c) experimental test data (Figure 2c adapted from Dolan1989). 25.4 mm1.0 in; 4.45 kN1.0 kip]




three parameters ( K 3 , K 4 , and uult) were determined via a calibration procedure (dis-

cussed below) in which experimental monotonic and cyclic test data was compared withthe results of numerical analyses. The values of the parameters defining the sheathingconnection model are provided in Table 1.

The pinched shape of the hysteresis loops of Figure 2b for small displacements isdue to the crushing of the wood sheathing and framing along with nail yielding as theconnections are cycled. Note that the commonly observed strength and stiffness degra-dation for repeated cycles at the same displacement was neglected. Beyond the displace-

ment uult (corresponding to the ultimate load Pult) the nail begins to withdraw from theframing and sheathing, resulting in a rapid reduction in load-carrying capacity. Thus, inthis study, it is assumed that the connection has essentially failed if the displacementexceeds uult . Any possible failure from nail tear-out has not been considered. It should

be noted that the simplifications mentioned above were made for purposes of efficientanalysis and were deemed acceptable since the purpose of this study was to demonstrate

Figure 3. Illustration of sheathing connection parameters defining monotonic and cyclic force-displacement behavior.

Table 1. Values of parameters defining sheathing connection model

Po P1 K o K 2 K 3 K 4 uult

915 N(206 lb)

180 N(40 lb)

1320 N/mm(7536 lb/in)

39 N/mm(220 lb/in)

3.0 N/mm(17.1 lb/in)

29.5 N/mm(168.4 lb/in)

15.24 mm(0.6 in)

Note: Values of Po , P1 , K o , and K 2 taken from experimental data (Dolan 1989) thatrepresents average results from static-monotonic, static-cyclic, and dynamic cyclic tests

of plywood sheathing connections with framing grain parallel and sheathing grain per- pendicular to load.




the effects of supplemental damping in a representative wood-framed shear wall, not toaccurately model all of the details associated with the dynamic behavior of the shear wall.

CALIBRATION OF SHEAR WALL MODEL

Since the shear wall model was not developed with the intent of accurately repro-ducing the behavior of any particular shear wall, a calibration procedure was performed so as to ensure that the monotonic and cyclic behavior of the wall was reasonable. Spe-cifically, the shear wall model was calibrated by adjusting the value of the three sheath-ing connection parameters K 3 , K 4 , and uult so as to obtain a reasonable match between

static monotonic and static cyclic experimental test data and results from numericalanalyses. The static monotonic analysis was performed in a manner similar to the ASTME564-76 Standard, in which a linearly increasing displacement is applied at the top platewhile holding the bottom plate fixed (see Figure 4). Similarly, a static cyclic analysis was

performed using the static cyclic loading protocol shown in Figure 5a. As shown in Fig-ure 4 and 5, the comparison between the analytical and experimental data is reasonablygood for both monotonic and cyclic motion, indicating that the parameters of the modelare adequate for capturing the salient behavior of a plywood-sheathed shear wall.

FLUID DAMPER BEHAVIOR AND CONFIGURATION WITHIN SHEAR WALL

DESCRIPTION AND DYNAMIC BEHAVIOR OF DAMPER

As mentioned previously, viscous fluid dampers were selected for investigation inthis study primarily due to their high energy-dissipation density (i.e., their ability to dis-sipate large amounts of energy in comparison to their size), a feature that is importantdue to the relatively narrow confines of a typical wood-framed shear wall. A cross-sectional view of a typical fluid damper is shown in the exploded view of Figure 6. Thedamper consists of a cylinder filled with low-viscosity fluid (silicone oil). The fluid is

Figure 4. Calibration of shear-wall finite-element model via static monotonic pushover analysiswith P-delta effects removed (experimental test data taken from Dolan 1989). 4.45 kN

1.0 kip




Figure 5. Calibration of shear-wall finite-element model via static cyclic analysis: (a) static cy-clic loading protocol, (b) hysteresis loop from numerical analysis, and (c) experimental hyster-esis loop (Figure 5c adapted from Dolan 1989). 25.4 mm1.0 in; 4.45 kN1.0 kip]

Figure 6. Schematic of fluid damper and orientation within shear wall.




forced to pass through orifices either within or around the piston head as the attached single-ended piston rod is cycled. Due to the relatively small size of the piston head ori-fices, the fluid passes through the orifices at high speeds, resulting in the development of heat energy, which is transferred to the environment via convection and conduction. Inthe design shown in Figure 6, a fluid accumulator is used to account for the volume of fluid displaced by the single-ended piston rod as it enters the cylinder, thus minimizingthe development of stiffness due to fluid compression (Symans and Constantinou 1998).An alternative design omits the accumulator and utilizes a double-ended piston rod (i.e.,a piston rod that extends outward from the piston head in both directions and exits thedamper at both ends). For either design, the damper behaves essentially as a pureenergy-dissipation device. The design of structures that incorporate such dampers be-comes simplified since the dampers may be regarded as simply adding additionalenergy-dissipation capacity to the structure. Of course, one must recognize that the in-

stallation of supplemental dampers will alter the load path for the transfer of forceswithin the structure.

The hysteretic behavior of an 8.9-kN (2-kip) capacity fluid damper subjected to sinu-soidal input motion is presented in Figure 7 for room temperature conditions (23 C) and frequencies of 1, 2, and 4 Hz (Symans and Constantinou 1998). As is evident from Fig-ure 7, in this range of frequencies, typical of the fundamental mode of light-framed resi-dential wood construction, the fluid damper exhibits insignificant restoring force and its

behavior is essentially linear viscous (i.e., the shape of the hysteresis loops is essentiallyelliptical with negligible slope). Thus an appropriate mathematical model for the damper is given by that of a simple linear viscous dashpot:

Pt Cu̇t (2)

where P is the damper force, C is the damping coefficient, u̇ is the velocity of the pistonhead with respect to the cylinder, and t is time. Note that, in spite of the relatively lowviscosity of the silicone oil within the damper, such dampers are often referred to asviscous fluid dampers, giving the impression that the fluid within the damper is highlyviscous. The term viscous is the result of the hysteretic behavior of the damper that is

Figure 7. Hysteretic behavior of 8.9-kN (2-kip) capacity fluid damper subjected to harmonicmotion at three different frequencies. 25.4 mm1.0 in; 4.45 kN1.0 kip]




equivalent to a linear viscous dashpot. The hysteretic behavior is primarily controlled bythe shape of the piston head orifices, not the viscosity of the fluid. In fact, the shape of the piston head orifices is often altered to produce nonlinear viscous dashpot behavior as

given by:

Pt C u̇t sgnu̇t (3)

where the velocity exponent varies from about 0.5 to 2 and sgn• is the signum func-tion. At a given frequency and amplitude of harmonic motion, the nonlinear damper withvelocity exponent of 0.5 produces a more rectangular loop than a linear damper, result-ing in an increase in energy-dissipation capacity of approximately 11% (Symans and Constantinou 1998). In this study, the linear damper model is utilized, although it is an-ticipated that future studies by the authors will explore the effects of nonlinear dampers.

DAMPER CONFIGURATION WITHIN SHEAR WALL

The authors believe that fluid dampers offer promise for application within wood-

framed buildings due to their high energy-dissipation density, which allows the dampersto be conveniently located within the walls of a wood-framed structure. For example, inthis study, the damper was positioned along the diagonal of the wall (see Figure 6). Inthe configuration shown in Figure 6, dual let-in rods are used to connect the lower corner of the wall to one end of the damper. One rod is located on each side of the wall and small metal straps are used to prevent the rod from buckling outward. One advantage tothis configuration is that the damper force lies concentrically within the plane of the walland thus there are no bending moments applied to the wall at the corner connections.Furthermore, this configuration maintains a certain level of gravity load-carrying capac-ity and does not interfere with the installation of sheathing on either side of the wall.However, a possible disadvantage to this configuration is that it may be difficult toimplement. Also, the effectiveness of the damper is reduced by 50% due to the diagonal

orientation. Although the damper shown in Figure 6 is located in the upper corner of thewall, this is not necessary; instead the damper may be positioned at the lower corner,which may offer improved access to the damper for periodic inspection.

To improve constructability, an alternate installation configuration was proposed byProfessor Daniel Dolan and refined by Professor Andre Filiatrault. It involves a reorien-tation of the studs, as shown in Figure 8, in which they are rotated 90 with two studslocated at each original stud location. The damper is located near one of the lower cor-ners of the wall and is connected, through a steel tube, to the opposite upper corner of the wall. Wood spacers are used to connect the two rows of side studs in order to in-crease their lateral stability under gravity loads. The tube fits snugly between the studsso as to inhibit lateral buckling of the tube. Special steel anchorages are utilized at thelower and upper corners of the wall to effectively transfer the damper force through the

wall and into the foundation. Panels of this configuration could be manufactured offsiteand installed as a modular unit. Note that this bracing configuration does not interferewith the transfer of gravity loads or with the placement of sheathing on both sides of theframing. Although the installation configurations shown in Figures 6 and 8 require thatthe damper be installed within the confines of the wall framing, this is not necessary. The




damper and its bracing system could be cantilevered out such that they lie in a plane parallel to the plane of the wall. Of course, this configuration would introduce bendingmoments at the connections to the wall.

EFFECT OF FLUID DAMPER ON WOOD-FRAMED SHEAR WALL BEHAVIOR

DYNAMIC PROPERTIES OF SHEAR WALL

The dynamic properties of the wall were determined via an undamped eigenvalueanalysis using the initial elastic stiffness of the wall (i.e., the properties are associated with low amplitudes of motion). The resulting natural frequencies in the fundamentaland second modes of vibration were 4.18 and 22.8 Hz, respectively, with correspondingmode shapes as shown in Figure 9 (the undeformed configuration is also shown). Notethat the mode shapes shown in Figure 9 include deformations of both the sheathing pan-els and framing. The inherent damping in the wall was accounted for via a Rayleigh

damping formulation wherein, for low amplitudes of vibration, the damping ratio in thefirst two modes of vibration was assumed to be 2% and 8%, respectively.

For the wall with a fluid damper installed, the fundamental frequency is essentiallyunchanged since the damper may be regarded as providing a source of pure energy dis-sipation and thus does not increase the stiffness of the wall. Two different dampers were

Figure 8. Schematic of alternate fluid damper intallation configuration. (Drawing courtesy of Professor Andre Filiatrault; used with permission.)




considered in this study, one having a damping coefficient of 17.5 kN-s/m (100 lb-s/in)

and the other having a damping coefficient of 87.6 kN-s/m (500 lb-s/in). Considering asimplified SDOF representation of the wall, wherein the fundamental frequency is takenas 4.18 Hz (as given above) and the lumped weight is 44.5 kN, the addition of thedamper results in an increase in the fundamental mode damping ratio from 2% to 5.7%and 20.4% for C 17.5 kN-s/m and 87.6 kN-s/m, respectively. Note that the smaller damping coefficient was selected since the principal author had previously performed experimental testing on such a damper and recognized that the size of the damper wassuch that it could readily be installed in a wood-framed shear wall (see Figure 7 for cy-clic test data obtained by the principal author on the aforementioned damper). The larger damping coefficient was selected after it was recognized that the smaller capacitydamper was not adequate for resisting strong near-field motions. Furthermore, based onconsultation with a leading manufacturer of seismic fluid dampers, it was confirmed that

the damper with the larger damping coefficient could be readily manufactured at a suit-able size for installation within a wood-framed shear wall.

SEISMIC RESPONSE

The mathematical model of the shear wall was subjected to the following two his-torical earthquake ground motions: (1) 1952 Kern County earthquake, Taft record– Lincoln School Tunnel (S69E comp.) and (2) 1994 Northridge earthquake, Newhallrecord–LA County Fire Station (90 comp.). For regions of California that are regarded as having a high seismic risk, the probability of exceedance for the Taft record would beon the order of 50% in 50 years which may be regarded as a relatively frequent event.For the Newhall record, the probability of exceedance would be on the order of 10% in50 years, which may be regarded as a code level event. The recorded acceleration for

these two ground motions for the first 30 seconds is shown in Figure 10 and the 5%-damped acceleration response spectra (actual, not pseudo) are shown in Figure 11. Thetwo records were selected since, as is readily evident in Figures 10 and 11, the recordsare disparate (i.e., the Taft record is a weak, far-field motion while the Newhall record isa strong, near-field motion). The fluid dampers proved to be beneficial for both types of ground motion in that, for the weak, far-field motion, the shear wall remained essentially

Figure 9. Fundamental and second mode shape of shear wall without dampers.






The effectiveness of the damper is clearly depicted in the hysteresis loops shown inFigure 12 where the two loops are plotted to the same scale. For this relatively weak earthquake, the wall alone (i.e., no damper) experiences inelastic behavior. Although theinelastic response is not strong, the wall has been weakened in terms of resisting after-shocks and future earthquakes. In contrast, the wall with the damper experiences sig-nificantly smaller drifts (peak reduction of 54%) and shear forces (peak reduction of 34%), implying much less damage to the wall. The peak damper force, velocity, and stroke are 3.87 kN (868.6 lb), 4.41 cm/s (1.74 in/s), and 0.265 cm (0.104 in), respec-tively. As will be explained subsequently, a damper with such behavior can be readilymanufactured. Furthermore, one may note the somewhat larger forces that developwithin the small displacement region of the pinching zone for the case of the wall withthe damper. This is the result of the damper force being proportional to velocity, thusleading to large damper forces in the region of the pinching zone where the displace-ments are small and the velocities are large. The development of larger forces in the

pinching region is one of the reasons that the dampers are so effective. Note that, for thewall with the damper, the hysteresis loop consists of a combination of damper behavior and wall behavior and thus it is not readily apparent how the wall itself (i.e., the wood framing system) performed. However, as shown in Figure 13, the hysteresis loop can bedecomposed into its contributions from the wall and damper, allowing one to visualizethe performance of the wall itself.

The potential for damage to the wall can be conveniently characterized by the driftratio. According to the NEHRP Guidelines for the Seismic Rehabilitation of Buildings(ATC 1997), for light-framed wood shear walls, the transient drift ratios corresponding

to the structural performance levels of Immediate Occupancy (IO), Life-Safety (LS),and Collapse Prevention (CP) are 1%, 2%, and 3%, respectively (see Table 2). A de-scription of the damage state for these performance levels is also provided in Table 2.

Note that the drift ratios provided in Table 2 do not represent drift limit requirements;rather they provide a measure of the overall structural response associated with various

performance levels. As mentioned previously, the shear wall analyzed herein does not

Figure 12. Hysteresis loops of shear wall without and with fluid dampers subjected to Taftrecord ( plotted to same scale). 25.4 mm1.0 in; 4.45 kN1.0 kip]




include the effects of finish materials. The inclusion of finish materials increases thestiffness of wood framing systems, which generally reduces the drift ratios.

The response-history of drift ratio for the wall without a damper and with a damper having a damping coefficient of C 87.6 kN-s/m is shown plotted to the same scale in

Figure 14a and 14b, respectively. Evidently, even for the wall without dampers, the Im-mediate Occupancy objective is met. However, as noted above, there is more damage tothe wall. The peak drift ratio for the two response-histories shown in Figure 14a and 14b,

Figure 13. Decomposition of hysteresis loop into wall and damper contributions for shear wallsubjected to Taft record.

Table 2. Structural performance levels for light-framed wood shear walls

Damage State Wall Condition Performance Level Transient Drift Ratio

No damage — O–Operational —

Slight damage Minor cracking IO–ImmediateOccupancy

1%

Moderate damage Large cracks at corners of

door/window openings

— —

Extensive damage Large cracks acrossshear walls

LS–Life Safety 2%

Complete damage Large permanentdisplacements

CP–CollapsePrevention

3%

Collapse — — —




as well as the case of the wall with a damper having a damping coefficient of C 17.5 kN-s/m, are plotted in Figure 14c. Recall that the fundamental mode dampingratio for the wall without a damper is 2%. For the two cases with a damper, the dampingratio based on a SDOF idealization of the wall is 5.7% and 20.4% for C 17.5 kN-s/m and 87.6 kN-s/m, respectively. Thus an increase in the damping ratiofrom 2% to 5.7% (a 185% increase) results in a 28.8% reduction in peak drift while anincrease in the damping ratio from 5.7% to 20.4% (a 258% increase) results in an ad-ditional 25.2% reduction in peak drift. In general, one can expect diminishing returns asthe damping ratio is increased to higher levels.

The performance of the fluid dampers may also be evaluated by considering the en-ergy distribution within the wall during the earthquake. The response-histories of vari-

ous energy quantities are shown in Figure 15 for the wall with and without the fluid damper having a damping coefficient of C 87.6 kN-s/m. Note that the two plots shownare plotted to the same scale. Figure 15a indicates that, without a fluid damper, essen-tially all of the seismic input energy is eventually dissipated via inelastic behavior in thewall. In contrast, Figure 15b demonstrates a significant reduction in energy-dissipationdemand on the wall (reduction of approximately 78% compared to no damper case)

Figure 14. Drift ratio for wall with and without dampers when subjected to Taft record: (a)response-history for no damper, (b) response-history for C 87.6 kN-s/m, and (c) summary of

peak values. 25.4 mm1.0 in; 4.45 kN1.0 kip]






performance of the wall itself (see Figure 17). A careful examination of the two loopsshown in Figure 16 reveals that the peak drift was reduced to 0.37% (a reduction of 88%from the failure drift ratio of 3%) when the damper was utilized. Thus, the dampers areeffective in preventing failure and minimizing damage to the wall. The peak damper force, velocity, and stroke are 8.66 kN (1.95 k), 9.88 cm/s (3.89 in/s), and 5.99 mm(0.236 in), respectively. As will be discussed subsequently, a damper with such behavior

Figure 16. Hysteresis loops of shear wall without and with fluid dampers subjected to Newhallrecord ( plotted to same scale). 25.4 mm1.0 in; 4.45 kN1.0 kip]

Figure 17. Decomposition of hysteresis loop into wall and damper contributions for shear wallsubjected to Newhall record.






proach was too refined to reasonably analyze an entire structure. Therefore, as described below, a simplified shear wall model was developed and calibrated using previous experimental and numerical results.

DESCRIPTION OF BUILDING

The geometry of the building model was similar to the full-scale, two-story, light-

framed wood residential building recently tested as part of the CUREE-Caltech Wood-frame Project by Fischer et al. (2001). The building was tested in various configurations(e.g., with and without finish materials) on a shaking table at the University of Californiaat San Diego (UCSD). The plan dimensions of the UCSD building are 16 ft20 ft(4.88 m6.10 m) with nominal story heights of 9 ft (2.44 m).

For the numerical analyses described herein, the plan dimensions and story heightsof the UCSD building were modified to 19 ft24 ft (5.79 m7.32 m) and 8 ft (2.4 m),respectively, to facilitate the direct use of the 8 ft8 ft (2.4 m2.4 m) shear wall model

previously described. Elevation and plan views of the building model are shown in Fig-ures 19a and 19b, respectively. Two different versions of the building were analyzed; onewith symmetric placement of wall panels in the first story and the other with asymmetric

placement (to simulate the effects of asymmetry due to, for example, a large garage door

opening). In both cases, the numerical analyses were performed for the case of seismicexcitation in the east-west direction only (see Figure 19a). The window and door open-ings were accounted for in an approximate manner by omitting full-height wall panels atthe approximate location of these openings. The effects of wall finish materials and in-terior partition walls were not considered. Although the building used for the numericalanalyses was not developed with the intent of accurately representing the UCSD build-

Figure 19. Geometry of building model: (a) isometric view of both symmetric and asymmetric building and (b) plan views of symmetric and asymmetric building (solid rectangles indicatelocation of shear walls). 1.0 m3.28 ft




ing, it may be regarded as adequate for capturing the global behavior of a building withsimilar characteristics to that of the UCSD building while simultaneously permitting ef-ficient analyses.

FINITE ELEMENT MODEL

A nonlinear finite-element model of the wood-framed building was developed for thenumerical analyses using the commercial program ABAQUS (ABAQUS 1998). Based on both experimental and numerical observations, the hysteretic behavior of shear wallsis primarily characterized by the behavior of the connections. In other words, the shapeof the base shear versus drift hysteresis loops for a shear wall is qualitatively of the sameform as the force versus deflection hysteresis loops for the connections (e.g., compareFigures 2c and 5c). Therefore, the same form of backbone curve and hysteretic algo-rithm used for the connection element can be used to model the shearing behavior of anentire shear wall. A simplified equivalent representation of the shear wall was thus de-veloped as explained below:

• Studs, which have high axial stiffness relative to their shear stiffness, are de-

signed to carry the vertical load in the wall. Resistance to shearing is provided by the sheathing panels. Without sheathing panels, the studs, top plate, and bot-tom plate form a mechanism, essentially connected with hinges. Therefore, trusselements were used to form the framework of the simplified equivalent shear wall. The two vertical elements of the framework were assigned an axial stiff-ness equal to that of half of the studs in the detailed shear wall model.

• Shear resistance of the simplified equivalent shear wall is provided by two diag-

onal bracing elements. The hysteretic behavior of the bracing elements was based upon the connection element of the detailed wall model. The values of the parameters that define the hysteretic behavior of the simplified shear wall weredetermined via a calibration procedure in which the response of both the sim-

plified wall and the detailed wall model were matched when subjected to bothstatic and dynamic loading. A comparison between the response of the simpli-fied wall model and the detailed wall model is presented in Figure 20 for static

pushover analysis and Figure 21 for seismic analysis. For the static loading, thecomparison is quite good. For the dynamic loading, the response-histories arequalitatively of the same form but with peak drift and base shear values that donot match (12.4% error in peak force and 23.0% error in peak displacement).Although the peak values are not in complete agreement, the frequency contentof the response-histories appears to be in reasonable agreement. Clearly, the sim-

plified model, while not an exact representation of the detailed shear wall model,may be deemed adequate for the purpose of evaluating the effect of fluid damp-ers on the seismic response of the building model.

• The roof and floor diaphragms were modeled using four-node, isoparametricshell elements. Stiffness properties were based upon typical housing construc-tion, with the intention of producing diaphragms that are very stiff in plane rela-tive to the in-plane stiffness of the shear walls.

• The mass of the roof and floor diaphragms was accounted for via a consistent




mass matrix in which the assigned weight density was typical of the weight for design of floors and roofs (Ambrose and Vergun 1987). The contribution to massfrom the walls was lumped to the nodes at the perimeter of the diaphragms onthe basis of tributary area and typical weight values for walls. The resulting totalmass of the symmetric building was 8,344 kg (47.6 lb-s2/in) with 3,353 kg(19.13 lb-s2/in) being assigned to the roof level, 3,811 kg (21.74 lb-s2/in) as-signed to the second floor level, and the remaining 1,180 kg (6.73 lb-s2/in) as-signed to the first floor (ground) level. The mass associated with the additionalshear wall in the first story of the asymmetric building (3.5% of the total weightof the symmetric building) was regarded as insignificant and thus was not ac-counted for in the mass of the asymmetric building.

Figure 20. Comparison of static pushover response for detailed wall model and simplified wallmodel. 25.4 mm1.0 in; 4.45 kN1.0 kip]

Figure 21. Comparison of response-histories for detailed wall model and simplified wall modelwhen subjected to Taft record: a) drift ratio and b) base shear coefficient.




EFFECT OF FLUID DAMPER ON WOOD-FRAMED BUILDING BEHAVIOR

DYNAMIC PROPERTIES OF BUILDING

The dynamic properties of the building were determined via an undamped eigen-value analysis using the initial elastic stiffness properties of the building model (i.e., the

properties are associated with low amplitudes of motion). The natural frequencies in thefirst three modes of vibration are 4.38 Hz (east-west translation), 6.21 Hz (north-southtranslation), and 8.29 Hz (torsion) for the symmetric building and 5.03 Hz (east-westtranslation), 6.21 Hz (north-south translation), and 8.71 Hz (torsion) for the asymmetric

building. The inherent damping in the building was accounted for via a Rayleigh damp-ing formulation wherein, for low amplitudes of vibration, the damping ratio in the firstand second modes of vibration were assumed to be 2% and 10%, respectively.

SEISMIC RESPONSE

Both the symmetric and asymmetric building were subjected to seismic excitation in

the east-west direction using the two earthquake excitations described previously. For thecase of the building with dampers, dampers having a damping coefficient of C 87.6 kN-s/m were located along the diagonal of all of the shear walls of the first story.Thus, there are six dampers located within the first story of the symmetric building and seven dampers within the first story of the asymmetric building. No dampers were lo-cated in the second story since preliminary analyses revealed that, for the particular structure analyzed herein, the effects of the dampers were most significant when theywere located in the first story. Note that, for the asymmetric building, no attempt wasmade to distribute the dampers so as to control the torsional response. For the Taft earth-quake record, the building response without dampers was at the Operational to Imme-diate Occupancy performance level with minimal damage (peak drift ratio of walls wasapproximately 0.25%). Thus, this case is not of significant interest and is presented else-

where (see Symans et al. 2002b). Note that the building performance level was obtained from Table 2 using the drift ratios of the walls. Due to limited computer storage capacity,the response of the building subjected to the Newhall earthquake record was determined for only the first 15 seconds of the record shown in Figure 10. This limitation was con-sidered to be acceptable since the strongest portion of the record occurs within the first15 seconds.

Symmetric Building—Newhall Earthquake Record

The hysteresis loops for the first and second stories are shown in Figure 22 for thesymmetric building with and without dampers. Note that the second story shear is nor-malized with respect to the total weight of the building. For the no damper case, only the

portion of the predicted response prior to failure is shown wherein failure occurs at ap-

proximately 5.6 seconds into the earthquake. Based on the damage levels described inTable 2 and indicated in Figure 22, it is evident that, for the no damper case, the firststory would likely collapse (peak drift ratio exceeds 3%) while at the same time the sec-ond story would have experienced minor damage (peak drift ratio less than 1%). Itshould be noted that, since collapse is actually quite rare for wood-framed buildings,collapse would likely not be predicted if the effects of wall finish materials, interior par-




titions, and interaction among the numerous elements of wood-framed buildings wereconsidered. For the building with dampers, the effect of the dampers is to increase the

peak base shear in the first story by 46%. This is not surprising since the dampers in-troduce additional forces that must be transferred through the lateral force resisting sys-tem. In addition, the inclusion of the dampers reduced the peak drift ratio in the firststory by 58% in comparison to the Collapse Prevention drift ratio of 3%. The peak force,velocity, and stroke in a single damper was 25.3 kN (5.69 kips), 28.9 cm/s (11.4 in/s),and 2.14 cm (0.844 in), respectively. Based on the damage levels described in Table 2, itis evident from Figure 22 that, for the building with dampers, the first story would ex-

perience slight to moderate structural damage while the second story would experienceessentially no damage. Finally, it is pointed out that the presence of the dampers resultsin significantly larger forces within the small displacement region of the pinching zone,leading to increased energy-dissipation capacity for the building with dampers. The per-formance of the fluid dampers can also be evaluated via examination of the time-dependent energy distribution within the building during the earthquake. The response-histories of various energy quantities are shown in Figure 23 for the building with and without the fluid dampers. For the building without dampers, only the portion of the en-

Figure 22. Hysteresis loops for symmetric building with and without dampers subjected to Newhall record.






Figure 24. Hysteresis loops for first story of asymmetric building with and without damperssubjected to Newhall record.






The performance of the fluid dampers may also be evaluated by considering the en-ergy distribution within the asymmetric building during the earthquake. The response-histories of various energy quantities are shown in Figure 26 for the building with and without fluid dampers. Note that the two plots shown are plotted with different scales onthe vertical axis. Figure 26a indicates that, without fluid dampers, essentially all of theseismic input energy is eventually dissipated via inelastic behavior in the wall framingsystem. In contrast, Figure 26b demonstrates a significant reduction in energy-dissipation demand on the wall framing system (reduction of 63% compared to nodamper case) while the viscous energy dissipated by the fluid dampers represents a sig-nificant portion (56%) of the final seismic input energy. Thus the fluid dampers effec-tively provided for a transfer of energy-dissipation demand from the building to the

dampers.

IMPLEMENTATION ISSUES

For the shear wall and building model analyzed herein, the peak force, velocity, and stroke demand on a single damper was 25.3 kN (5.7 kips), 28.9 cm/s (11.4 in/s), and 2.14 cm (0.844 in), respectively. These peak values define the capacity requirements for a damper having a damping coefficient of 87.6 kN-s/m. According to the dominantdesigner/manufacturer of seismic fluid dampers in the United States, a damper with suchcharacteristics can be readily manufactured. However, a number of issues remain to beaddressed before fluid dampers will find implementation in light-framed wood buildings.

Prior to implementation, experimental testing needs to be performed to validate thegeneral results presented herein. In particular, testing should be performed on full-scale

wood-framed shear walls and three-dimensional building systems with and without bothlinear and nonlinear fluid dampers. Experimental tests are critically important for iden-tifying sources of error in mathematical and computational models utilized in numericalsimulations.

Figure 26. Energy distribution within asymmetric building subjected to Newhall record.

25.4 mm1.0 in; 4.45 kN1.0 kip]




It is recognized that typical light wood-framed structures are primarily constructed inthe field. To aid in the installation of fluid dampers in such structures, it is likely that thedamper would need to be installed within a prefabricated modular wall unit that can be

installed in strategic locations in a wood-framed building in order to act as the primarylateral load-resisting system (similar to the recently developed Simpson Strong-TieStrong-Wall® Shearwall). The modular wall units would be constructed in a controlled manufacturing environment with damper connections that produce essentially no slip

prior to damper engagement. Minimizing slip will be important for controlling the levelof damage during earthquakes; particularly for frequent, weak earthquakes that, while

producing damage in the structure, generate relatively small wall displacements. In ad-dition, construction tolerances may be such that, prior to damper engagement, the build-ing deforms sufficiently to cause wall finish damage. Note that the use of modular wallunits would result in changes in the load path and the torsional resistance of the build-ing, leading to a potentially more complex design and analysis process for both the wood framing system and the fluid dampers.

Although a rigorous evaluation of the optimal damper locations (both plan-wise and elevation-wise) within a general wood-framed structure was not performed, the seismicanalysis performed herein on a particular two-story building model indicated that thedampers were more beneficial when located in the first story rather than the second. Thismay be partially attributed to the larger mass that drives the first story (i.e., second floor

plus roof) as compared to the mass that drives the second story (i.e., roof only). Assum-ing that placement of the dampers in the first story is generally more beneficial than

placement in the second story, for a typical two-story residential building with a floor area of, say, 92.9 m2 per floor (1,000 ft2) and four external walls, it is expected that oneor two dampers per external first story wall would provide sufficient supplemental damp-ing to significantly reduce the inelastic response of the building when subjected to strongearthquakes. If the prefabricated modular wall units were to be mass-produced, a con-

servative estimate of the cost of each damper within a wall unit would be approximately$600 based on consultation with a fluid damper manufacturer. Thus, for one or twodampers per external wall, the cost for the supplemental dampers would be approxi-

mately $1.2/ft2 to $2.4/ft2 (note that this does not include any additional cost associated with fabrication and construction of the prefabricated modular wall unit).

Although not explored in this study, recently developed amplification systems for stiff structures (Berton and Bolander 2002, Constantinou et al. 2001) may be well suited to light-framed wood buildings that experience inelastic deformations at relatively lowdisplacements.

As noted previously, recent experimental testing (Fischer et al. 2001, Gatto and Uang2002) indicates that the effects of wall finish materials and interior partitions on the dy-namic response of building systems can be significant. The results presented herein did

not include the effects of wall finish materials or interior partitions and thus further study is warranted with regard to these issues.

For multistory building systems, consideration needs to be given to the developmentof suitable load paths and the plan-wise and elevation-wise distribution of dampers.






suited to providing superior protection of structures subjected to strong earth-quakes and thus of meeting the potentially stringent requirements of

performance-based earthquake engineering specifications.

Issues that remain to be addressed to further the potential for implementation of fluid dampers in light-framed wood structures include the need for experimental testing, theconsideration of a comprehensive set of earthquake ground motion records, the consid-eration of the effects of construction tolerances, an evaluation of the effects of wall fin-ish materials and interior partitions, an evaluation of the effects of damper installation onload paths, an evaluation of the optimal distribution of dampers for torsional resistance,an evaluation of the effectiveness of linear versus nonlinear dampers, the need for sim-

plified design and analysis procedures, and the need for cost-benefit analyses.

ACKNOWLEDGMENTS

This research was carried out under contract to the Consortium of Universities for Research in Earthquake Engineering (CUREE) as part of the CUREE-Caltech Wood-frame Project (‘‘Earthquake Hazard Mitigation of Woodframe Construction’’), under agrant administered by the California Office of Emergency Services and funded by theFederal Emergency Management Agency (FEMA). The authors are solely responsiblefor the information contained herein. No liability for the information contained herein isassumed by Consortium of Universities for Research in Earthquake Engineering, Cali-fornia Institute of Technology, California Office of Emergency Services, or the FederalEmergency Management Agency.

The authors would like to thank Professor Andre Filiatrault, project manager of thecomponent Testing and Analysis of the CUREE-Caltech Woodframe Project, for his sup-

port of this particular task within the Woodframe Project. In addition, Kelly Cobeen, project manager of the Building Codes and Standards component of the CUREE-Caltech Woodframe Project, raised many insightful questions regarding practical issuesrelated to the implementation of fluid dampers within wood-framed buildings. Finally,the authors would like to thank the anonymous reviewers who provided many usefulcomments and suggestions that improved the manuscript.

REFERENCES

ABAQUS, 1998. Standard User’s Manual (Version 5.8), Hibbitt, Karlsson, and Sorenson, Inc.,Pawtucket, RI.

Ambrose, J., and Vergun, D., 1987. Design for Lateral Forces, John Wiley & Sons, New York.

Applied Technology Council (ATC), 1997. NEHRP Guidelines for the Seismic Rehabilitation of

Buildings, prepared for the Building Seismic Safety Council, published by the Federal Emer-gency Management Agency, FEMA-273, Washington, D.C.

Berton, S., and Bolander, J. E., 2002. Amplification system for passive energy dissipation de-vices in seismic applications, Proceedings of 7th U.S. National Conf. on Earthquake Engi-

neering, Boston, MA, July.

Constantinou, M. C., Tsopelas, P., Hammel, W., and Sigaher, A. N., 2001. Toggle-brace-damper seismic energy dissipation systems, J. Struct. Eng., ASCE, 127 (2), 105–112.

Dinehart, D. W., and Lewicki, D. E., 2001. Viscoelastic material as a seismic protection system




for wood-framed buildings, Proceedings of 2001 Structures Congress and Exposition,ASCE, Edited by P. C. Chang, Washington, D.C., May.

Dinehart, D. W., and Shenton, H. W., 1998. Comparison of the response of timber shear walls

with and without passive dampers, Proceedings of Structural Engineers World Congress, San Francisco, CA, July, Paper T207-5.

Dinehart, D. W., Shenton, H. W., and Elliott, T. E., 1999. The dynamic response of wood-frameshear walls with viscoelastic dampers, Earthquake Spectra 15 (1), 67–86.

Dolan, J. D., 1989. The Dynamic Response of Timber Shear Walls, Ph.D. dissertation, Univer-sity of British Columbia, Vancouver, B.C.

Filiatrault, A., 1990. Analytical predictions of the seismic response of friction damped timber shear walls, Earthquake Eng. Struct. Dyn. 19, 259–273.

Fischer, D., Filiatrault, A., Folz, B., Uang, C-M., and Seible, F., 2001. Shake table tests of atwo-story woodframe house, CUREE Publication No. W-06 , Consortium of Universities for Research in Earthquake Engineering (CUREE), Richmond, CA.

Gatto, K., and Uang, C-M., 2002. Cyclic response of woodframe shearwalls: Loading protocoland rate of loading effects, CUREE Publication No. W-13, Consortium of Universities for Research in Earthquake Engineering (CUREE), Richmond, CA.

Goel, R. K., 1998. Effects of supplemental viscous damping on seismic response of asymmetric-plan systems, Earthquake Eng. Struct. Dyn. 27, 125–141.

Higgins, C., 2001. Hysteretic dampers for wood frame shear walls, Proceedings of the 2001

Structures Congress and Exposition, ASCE, edited by P. C. Chang, Washington, D.C., May.

McMullin, K. M., and Merrick, D., 2002. Seismic performance of gypsum walls—experimentaltest program, CUREE Publication No. W-12, Consortium of Universities for Research inEarthquake Engineering (CUREE), Richmond, CA.

Stewart, W. G., 1987. The Seismic Design of Plywood-Sheathed Shearwalls, Ph.D. dissertation,University of Canterbury, Christchurch, New Zealand.

Symans, M. D., Cofer, W. F., and Fridley, K. J., 2002a. Base isolation and supplemental damp-ing systems for seismic protection of wood structures: Literature review, Earthquake Spectra

18 (3), 549–572.Symans, M. D., Cofer, W. F., Du, Y., and Fridley, K. J., 2002b. Evaluation of fluid dampers for

seismic energy dissipation of woodframe structures, CUREE Publication No. W-20, Consor-tium of Universities for Research in Earthquake Engineering (CUREE), Richmond, CA.

Symans, M. D., and Constantinou, M. C., 1998. Passive fluid viscous damping systems for seis-mic energy dissipation, J. Earthquake Tech., ISET, Special Issue on Passive Control of Struc-

tures, 35 (4), 185–206.

(Received 15 January 2003; accepted 8 September 2003)


Documents

EQSpect Wood Numerical.pdf