Incremental Dynamic Analysis of Woodframe Buildings

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EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICSEarthquake Engng Struct. Dyn. 2009; 38:477496Published online 2 December 2008 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/eqe.864

Incremental dynamic analysis of woodframe buildings

Ioannis P. Christovasilis1,, Andre Filiatrault1,,, , Michael C. Constantinou1,

and Assawin Wanitkorkul2,

1Department of Civil, Structural and Environmental Engineering, State University of New York at Buffalo,

Buffalo, NY 14260, U.S.A.2Connell Wagner (Thailand), Bangkok 10110, Thailand

SUMMARYThe collapse of wood buildings was one of the main contributors to the heavy death toll and economiclosses during the 1995 Hyogo-ken Nanbu (Kobe) earthquake in Japan. In California, half of the propertyloss from the 1994 Northridge earthquake was attributed to wood construction. Based on damage observedin recent earthquakes, the seismic vulnerability of existing wood buildings under maximum credibleseismic events is uncertain. The main objective of this study is to quantify the seismic collapse fragilitiesand collapse mechanisms of a two-story townhouse and three-story woodframe apartment building throughnumerical analyses. Three construction quality variants (poor, typical and superior) were considered foreach building in order to assess the effects of construction qualities on seismic collapse fragilities. Thebuildings were also re-designed according to the 2006 edition of the International Building Code toquantify the seismic fragilities of modern woodframe construction. The results obtained suggest that theconstruction quality, excitation direction and wall finish materials can influence significantly the collapsefragilities of woodframe buildings. Copyright q 2008 John Wiley & Sons, Ltd.

Received 6 November 2007; Revised 8 September 2008; Accepted 8 September 2008

KEY WORDS: collapse; incremental dynamic analysis; seismic; wood structure

1. INTRODUCTION

Observations from significant earthquakes in the last two decades, such at the 1989 Loma Prieta andthe 1994 Northridge earthquakes in California and the 1995 Hyogo-ken Nanbu (Kobe) earthquake

Correspondence to: Andre Filiatrault, Department of Civil, Structural and Environmental Engineering, State Universityof New York at Buffalo, Buffalo, NY 14260, U.S.A.

E-mail: [email protected], [email protected] Student Researcher.Professor. Senior Structural Engineer.

Contract/grant sponsor: Department of Homeland Securitys Federal Management Agency (FEMA)

Copyright q 2008 John Wiley & Sons, Ltd.


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478 I. P. CHRISTOVASILIS ET AL.

in Japan, have demonstrated that seismic hazards pose a credible threat to residential woodframebuildings. The 1994 Northridge earthquake in California demonstrated that both existing and newwoodframe buildings are vulnerable to strong ground shaking. More than half of the $40 billionproperty loss that occurred in the Northridge earthquake was attributed to wood construction [1].

In Japan, the collapse of residential wood buildings was one of the main contributors to the heavydeath toll (more than 6400) and economic losses (more than $100 billion US) during the 1995Kobe earthquake [2].

While seismic provisions included in current building codes [3, 4] govern the seismic designof new engineered wood construction in the US, the performance of traditionally nonengineeredwall finish materials, such as gypsum wallboard or stucco, is not accounted for in the designprocess. Additionally, many older existing woodframe buildings were poorly designed to resistearthquake shaking. For example, thousands of woodframe, multi-unit residential buildings havebeen constructed in California with tuck-under parking at the ground level. This type of wood-frame construction usually includes a soft-story configuration that may lead to severe damage andeven collapse under strong earthquake shaking. Several buildings of this structural type, typicallyconstructed in the 1960s or 1970s, experienced ground story collapses during the 1994 Northridgein California.

In order to develop consistent performance-based seismic design procedures for woodframebuildings, their global system-level seismic fragilities under the complete range of seismic hazardsmust be evaluated. This study attempts to shed some light on these issues by quantifying the seismiccollapse fragilities and collapse mechanisms of woodframe buildings using uni- and bi-directionalincremental inelastic time-history dynamic analyses.

2. DESCRIPTION OF ORIGINAL BUILDING MODELS

Two different woodframe residential building models, a townhouse and an apartment building,are considered in this study. These buildings are part of a suite of prototype index buildingsdeveloped under the recently completed FEMA-funded CUREE-Caltech Woodframe Project inCalifornia for use in loss estimation and benefit-to-cost ratio analysis [5]. Detailed modeling onthese index buildings has been conducted by Isoda et al. [6]. Two design alternatives of thesetwo index buildings are considered: (1) the original buildings designed according to earlier coderequirements and (2) the re-designed buildings according to the requirements of the 2006 editionof the International Building Code [3]. The construction details of the two original index buildingmodels are summarized in Table I. Figure 1 shows architectural rendering and plan views ofthe original index building models. The major structural components of the building models areidentified in Figure 1 and are described in detail in [7].

2.1. Original townhouse building

This two-story townhouse contains three units, each having approximately 170m2 of living spacewith an attached two-car garage, as shown in Figure 1. The building is assumed to be foundedon a level lot with a slab-on-grade and spread foundations. The original building is assumed tohave been built as a production house in either the 1980s or 1990s, located in either Northern orSouthern California. The design is based on the 1988 edition of the Uniform Building Code [8]

Copyright q 2008 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 2009; 38:477496DOI: 10.1002/eqe


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INCREMENTAL DYNAMIC ANALYSIS OF WOODFRAME BUILDINGS 479

Table I. Construction details for original index woodframe buildings.

Components Construction details

Exterior walls Stucco (22 mm thick) over 11mm oriented strand board (OSB) on outside

Gypsum wallboard 12 mm thick on insideFurring nails (9 mm head) spaced at 150 mm on center along vertical studs used toattach wire mesh of stucco finish to wood framingEight-penny common nails (diameter=3.3 mm, length=76.2 mm) spaced at 150,100 or 75 mm along edges and 300 mm on field used to attach OSB panels toframing

Interior walls Gypsum wallboard (12 mm thick) on both sidesDrywall nails (38 mm long) spaced at 175 mm on center along vertical studs(spaced at 400 mm on center) used to attach gypsum walls to framingGypsum wallboard panels positioned vertically

for engineered construction. The height of the townhouse building from the first floor slab to theroof eaves is 5.5 m and its total dead weight is 980 kN.

Seismically relevant characteristics that were intentionally featured in this townhouse include theintegral garage and for the end units, the imbalance in plan stiffness between the solid longitudinalwall with gypsum wallboard at the common wall side versus the perforated walls with stucco ororiented strand boards (OSB) on the exterior wall side.

2.2. Original apartment building

This index building represents a three-story, rectangular apartment with ten units (each with 85m2

of living space) and space for mechanical and common areas, as shown in Figure 1. All wallsand elevated floors are light woodframe. It has parking on the ground floor. Each unit has twobedrooms and one assigned parking stall. The building is assumed to have been constructed prior

to 1970 in Northern or Southern California, designed according to the 1964 edition of the UniformBuilding Code [9] and engineered to a minimal extent. The height of the apartment buildingfrom the first floor slab to the roof eaves is 8.2 m and its total dead weight is 1550 kN.

2.3. Construction variants

Three deterministic construction variants are considered for each index building in order to assessthe effects of construction qualities on the seismic fragilities and collapse mechanisms. The vari-ants are representative of poor-quality, typical-quality and superior-quality construction and weredeveloped as part of the CUREE-Caltech Woodframe Project [5]. The managers of the CUREE-Caltech Woodframe Project, Element 3 (Building Codes and Standards), assisted by a group ofstructural engineers familiar with the seismic design of light-frame wood buildings in California,

selected four key characteristics that contribute most strongly to repair cost, and defined, basedon their experience, these characteristics for a poor-quality, typical-quality and superior-qualityvariant. The characteristics of each construction variant are summarized in Table II.

The superior quality construction variant has good nailing of shear walls good connectionsbetween structural elements, good quality stucco and good nailing of gypsum wallboard (allcomponents are assumed to exhibit strength and stiffness comparable with high-quality laboratorytest specimens). The typical quality variant has average nailing of shear walls and diaphragms



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Figure 1. Index woodframe building models: (a) architectural rendering; (b) plan views of townhousebuilding; (c) architectural rendering; and (d) plan views of apartment building, after [7].

(5% increase in average nail spacing), average connections between structural elements (10%reduction in shear wall stiffness and strength), average quality stucco (10% reduction in stiffnessand strength) and average nailing of interior gypsum wallboard (15% reduction in stiffness andstrength). The poor-quality variant has poor nailing of shear walls (20% increase in average nailspacing) and poor vapor barrier installation (5% supplemental reduction in stiffness and strength),poor connections between structural elements (20% reduction in shear wall stiffness), poor quality



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Table II. Summary of construction variants for original woodframe index buildings, after [6].

Components Superior quality Typical quality Poor quality

Shear walls Good nailing of shear

walls, stiffness andstrength equal to thatobtained in high-qualitylaboratory tests

Average nailing of shear

walls, nail spacing 5%greater than that ofsuperior quality

Poor nailing of shear

walls, nail spacing 20%greater than that ofsuperior quality plus 5%supplemental reductionin stiffness and strengthdue to water damage

Connections Good connectionsbetween structuralelements, stiffness andstrength equal to thatobtained in high-qualitylaboratory tests

Typical connectionsbetween structuralelements, 90% ofstiffness and strengthobtained in high-qualitylaboratory tests

Poor connectionsbetween structuralelements, 80% ofstiffness and strengthobtained in high-qualitylaboratory tests

Exterior wall finish Good quality stucco,

stiffness and strengthequal to that obtained inhigh-quality laboratorytests

Average quality stucco,

90% of stiffness andstrength obtained inhigh-quality laboratorytests

Poor quality stucco, 70%

of stiffness and strengthobtained in high-qualitylaboratory tests

Interior wall finish Superior nailing ofinterior gypsumwallboard, stiffness andstrength equal to thatobtained in high-qualitylaboratory tests

Good nailing of interiorgypsum wallboard, 85%of stiffness and strengthobtained in high-qualitylaboratory tests

Poor nailing of interiorgypsum wallboard, 75%of stiffness and strengthobtained in high-qualitylaboratory tests

stucco (15% reduction in stiffness and strength) and poor nailing of interior gypsum wallboard(15% reduction in stiffness and strength). Further details on how the constructions variants wereincorporated in the numerical model can be found in [6].

3. DESCRIPTION OF RE-DESIGNED PROTOTYPE BUILDING MODELS

Both original index woodframe buildings described above were designed according to earlierbuilding code requirements and may not be completely representative of current seismic designpractices in California. In order to evaluate the seismic response and collapse mechanisms ofwoodframe buildings designed according to current building code requirements, both original indexbuildings were re-designed according to the seismic requirements contained in the 2006 edition of

the International Building Code [3]. Figure 2 shows plan views of the re-designed index buildingmodels.

In the re-design of the index woodframe buildings, the architectural layouts of the buildingswere maintained but only wood sheathed shear walls were considered for the lateral load-resistingsystem in each principal direction of each building. The lateral stiffness and strength of exteriorand interior nonstructural wall finish materials were not considered in the re-design of the indexwoodframe buildings. The analyses, however, are conducted with and without consideration of



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Figure 2. Plan views of re-designed index woodframe building models: (a) townhousebuilding and (b) apartment building.

these nonstructural wall finishes. In addition, only the typical quality construction variant (seeTable II) is considered in the analyses of the re-designed index woodframe buildings.

The re-design of the townhouse building to the 2006 IBC resulted in two important differences:(1) the shear capacity of the narrow wall piers along the first-level garage line had to be reducedby a factor equal to 2bs / h, where bs is the width of each wall pier (0.9 m) and h is the height(2.4 m), which caused a reduction of the edge nail spacing for these walls (this clause did notexist in the 1988 edition of the UBC) and (2) new double wood shear walls between units in theeastwest direction were introduced to satisfy fire resistance requirements of the 2006 IBC. Forthe re-designed apartment building, the long eastwest interior wall on the first-level-incorporatednew wood sheathing, which also caused a significant increase of the lateral strength of the buildingalong that direction.

4. NUMERICAL MODELING

In this study, the numerical prediction of the seismic collapse of the index woodframe buildingswas based on bi-directional (horizontal) nonlinear time-history dynamic analyses; the vertical

acceleration component was not captured. For this purpose, a pancake structural model wasadopted [10]. This modeling approach simulates the three-dimensional seismic response of abuilding through a degenerated two-dimensional planar analysis. The computer program SAWSSeismic Analysis of Woodframe Structures [10, 11], developed within the recently completedCUREE-Caltech Woodframe Project in California, was used to analyze the prototype buildings.

In the SAWS model, the building structure is composed of two primary components: rigidhorizontal diaphragms and nonlinear lateral load-resisting shear wall elements, as illustrated



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Shear Element-to-DiaphragmAttachment Point

Origin: (0,0)

A B C

3

2

1xU

V

y

Generic Point on the RigidDiaphragm: (x, y )

SDOF Shear Element(Zero-Height), typ.

Foundation, typ.

f

fp

x

y

Global Degrees-of-FreedomFor Rigid Diaphragm

1

2

3

B CA

Foundation

Shear Wall, typ.

Diaphragm (Rigid)

Partition Wall, typ.

(a) (b)

Figure 3. SAWS model: (a) components of woodframe buildings considered in the SAWS program and(b) structural model of woodframe buildings, after [10].

O

A

B

D

E

F

G

H

I

C1

1

1(u,Fu)

r2K0K0

r4K0

r3K0

FI 1

Kp

1

F0

120

Force

Displacement

NonlinearBackbone Curve



Capping StrengthCapping Strength

Pinching andRe-Loading Stiffness

Pinching andRe-Loading Stiffness

In-CycleDegrading Strength

In-CycleDegrading Strength

r2k0 DegradingCapping Strength

DegradingCapping Strength

FailureDisplacement

f

Figure 4. Hysteretic behavior of shear spring element included in the SAWS Program, after [10, 11].

in Figure 3(a). The actual three-dimensional building is degenerated into a two-dimensionalplanar model using zero-height shear wall spring elements connected between the diaphragmsand the foundation, as shown in Figure 3(b). The hysteretic behavior of the walls can becharacterized from cyclic test results on full-scale wall units or by an associated numericalmodel [12] that predicts the walls loaddisplacement response under general quasi-static cyclic

loading. In the SAWS model, the hysteretic behavior of each wall panel (wood, interior gypsumor exterior siding) can be represented by an equivalent nonlinear shear spring element. Thehysteretic behavior of this shear spring element includes pinching, stiffness and strength degra-dation and is governed, in total, by ten physically identifiable parameters [10, 11], as shown inFigure 4.

The monotonic racking response (backbone curve) of the wall model, shown in Figure 4, isexpressed in terms of the top-of-wall force Fand corresponding top-of-wall horizontal displacement



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by the following nonlinear relationship:

F=

sgn() (F0+r1 K0||)[1exp(K0||/F0)], |||u|

sgn()

Fu+

r2 K0[

sgn()

u], |

u|< |||

F|

0, ||>|F|(1)

This forcedeformation model for the backbone curve is characterized by six parameters:F0, K0,r1,r2,u and F, each identified in Figure 4. With this representation, the displacement uis associated with the ultimate load Fu (capping strength), while failure of the wall occurs at thedisplacement F.

The basic unloading and reloading rules defining the hysteretic wall model are also shownin Figure 4. The forcedeformation paths OA and CD follow the monotonic envelope curve asexpressed by Equation (1). All other paths are assumed to exhibit a linear relationship betweenforce and deformation. Unloading of the envelope curve follows a path such as AB with stiffnessr3 K0. Here, the wall unloads elastically. Under continued unloading, the response moves onto path

BC that is characterized by a reduced stiffness r4 K0. The very low stiffness along this path typifiesthe pinched hysteretic response displayed by wood shear walls under cyclic loading. For woodshear walls, this behavior is the result of previous crushing of the framing members and sheathingpanels around the connectors (in this case as the wall followed the path OA). First time loadingin the opposite direction forces the response onto the envelope curve CD. Unloading of this curveis assumed elastic along path DE, followed by a pinched response along path EF, which passesthrough the zero-displacement intercept FI, with slope r4 K0. Continued re-loading follows pathFG with degrading stiffness Kp, as given by

Kp =K0

0

max

(2)

with 0=(F0/K0) and a hysteretic model parameter, which determines the degree of stiffnessdegradation. Note from Equation (2) that Kp is a function of the previous loading history through thelast unloading displacementun of the envelope curve (corresponding to point A in Figure 4), so that

max=un (3)

where is another hysteretic model parameter. A consequence of this stiffness degradation is thatit also produces strength degradation in the response. If on another cycle the shear wall is displacedto un, then the corresponding force will be less than Fun, which was previously achieved. Thisstrength degradation is shown in Figure 4 by comparing the force levels obtained at points A and G.In addition, with this model under continued cycling to the same displacement level, the force andenergy dissipated per cycle are assumed to stabilize beyond the second loading cycle.

With the simple approach adopted by the SAWS model, the response of the building is definedin terms of only three-degrees-of-freedom per floor level. The capabilities of the SAWS computerprogram have been investigated previously by comparing its response predictions with the shaketable tests of a large-scale, two-story, woodframe house under the CUREE-Caltech WoodframeProject [11]. During this investigation, the test structure experienced maximum top-of-roof driftlevels of the order of 2%. At this response level, the SAWS model provided good agreementwith the test results. The capability of the SAWS program to predict the global seismic collapse



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intensities and the associated collapse mechanisms of wood buildings has not been investigatedyet and is the focus of this study.

In undertaking this collapse study, a number of limitations in the formulation of the SAWSmodel must be recognized at the outset. First, the degenerated planar model utilized by SAWS

suppresses the vertical dimension of the building. Consequently, SAWS has no capability to capturethe vertical excitation of the test structure. Second, this degenerated planar model does not takeaccount of P effects, which are not expected to become significant until near global instabilityfor low-rise short period wood buildings supporting light gravity loads.

5. ANALYSIS PROCEDURES

5.1. Incremental dynamic analyses

A collapse analysis procedure that is based on incremental dynamic analysis (IDA) [13] is usedin this study to predict the seismic response and collapse mechanisms of the woodframe index

buildings. Only global side-sway collapse mechanisms of light-frame wood buildings, caused byexcessive lateral wall deformations, are considered in this study, as illustrated in Figure 5.

In the IDA approach, nonlinear time-history dynamic analyses are performed for an ensembleof earthquake ground motions scaled to a given intensity level. The scaling of the ground motionsintensity can take several forms. Because the index woodframe buildings considered in this studyexhibit short fundamental periods, the scaling is based on the median spectral acceleration of theensemble of ground motion records considered for the analyses at a period of 0.2 s. This meansthat a single amplitude scaling factor is used for all records such that the median spectral valuetaken across all records at a period of 0.2 s is equal to a target value.

From the results of each dynamic analysis, the peak inter-story drift experienced by any wallline in the woodframe building model is retained. For each ground motion record, the analysesare repeated for increasing intensities. The intensity of the ground motion causing collapse of thewoodframe building is defined as the point on the intensity-drift IDA exceeding a peak inter-storydrift of 7% in any of the wall line of the structure. This arbitrarily selected collapse drift valuedoes not affect the collapse intensities since (as it will be shown later) the IDA plots are essentiallyhorizontal for this drift value. The process is then repeated for all ground motions and a series of

Figure 5. Examples of global side-sway collapse mechanism of light-framewood buildings (USGS photos).



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intensity-displacement (IDA) plots can be obtained. The probability of collapse for a given intensitylevel can then be estimated by counting the number of ground motion records causing collapseand dividing this value by the total number of records considered in IDAs. In turn, a fragilitycurve giving the relationship between the probability of collapse and the intensity measure can be

obtained and a lognormal cumulative probability distribution can be fitted to the data. In this study,the fragility curves are computed in terms of empirical and lognormal cumulative distributionfunctions (CDF) as a function of the median spectral acceleration across the earthquake groundmotion ensemble at a period of 0.2 s. The lognormal CDF of a random variable y is defined bythe median (50%) value of y my and by the dispersion parameter expressed as the standarddeviation of the log of the values of y.

5.2. Earthquake ground motions

The suite of 22 pairs of scaled bi-directional historical ground motion records (44 records total)considered for the ATC-63 Project [14] were used as an input to IDAs conducted in this study. Theselection of these records was based on representing extreme ground motions. Minimum limits were

imposed on the earthquake magnitude (M>6.5) and on the peak ground velocity and acceleration(PGA >0.2 g or PGV>15cm/s). These limits were chosen to select large motions, while ensuringthat enough motions will meet the selection criteria. Another limitation of the ground motionensemble is that all records were recorded at a significant distance from the fault (distance >10km)and on firm soils (shear wave velocities >180m/s). Therefore, dominant near-field and soft soileffects are not considered by this suite of records.

Each earthquake record pair was normalized in order to maintain a fairly constant variability inspectral values across a wide period range. Table III lists the main characteristics of the groundmotion records along with the amplitude scale factor applied to each record, while Figure 6presents 5% damped absolute acceleration response spectra for these 44 scaled records along withthe median spectral value. The design basis earthquake (DBE) and maximum credible earthquake(MCE) intensity levels associated with these earthquake records correspond to a scaled median

spectral acceleration at a period of 0.2 s of 1.0g and 1.5g, respectively.

5.3. Directional effects

Uni-directional IDAs were carried out for each principal direction of each index building (northsouth and eastwest) as well as bi-directional IDAs. For the bi-directional IDAs, each pair of groundmotions was used twice by rotating their components 90 degrees with respect to the principaldirections of each index woodframe building, thereby generating 44 analysis results per definedspectral intensity. An increment of the 0.2 s spectral acceleration intensity measure of 0.10g wasused in the IDA. Approximately 30 000 nonlinear time-history dynamic analyses were performedin this study.

6. ANALYSIS RESULTS

6.1. Pushover analysis results

Figure 7 presents the uni-directional pushover curves for both principal directions of each originalindex woodframe building predicted by the SAWS program based on inverse triangular lateral load



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Table III. Characteristics of strong ground motions, after [14].

Seismic event Records

Pair Epicentral Amplitude

No. Magnitude Year Name Recording station distance (km) Scale factor

1 6.7 1994 Northridge Beverly Hills14145 Mulhol 13.3 0.7552 6.7 1994 Northridge Canyon Country-W Lost 26.5 0.8323 7.1 1999 Duzce, Turkey Bolu 41.3 0.6294 7.1 1999 Hector Mine Hector 26.5 1.0925 6.5 1979 Imperial Valley Delta 33.7 1.3116 6.5 1979 Imperial Valley El Centro Array #11 29.4 1.0147 6.9 1995 Kobe, Japan Nichi-Akashi 8.7 1.7188 6.9 1995 Kobe, Japan Shin-Osaka 46.0 1.0999 7.5 1999 Kocaeli, Turkey Duzce 98.2 0.68810 7.5 1999 Kocaeli, Turkey Arcelik 53.7 1.36011 7.3 1992 Landers Yermo Fire Station 86.0 0.98712 7.3 1992 Landers Coolwater 82.1 1.07313 6.9 1989 Loma Prieta Capitola 9.8 0.822

14 6.9 1989 Loma Prieta Gilroy Array #3 31.4 0.88015 7.4 1990 Manjil, Iran Abbar 40.4 0.78716 6.5 1987 Superstition Hills El Centro Imp. Co. Cent 35.8 0.87017 6.5 1987 Superstition Hills Poe Road (temp) 11.2 1.36218 7.0 1992 Cape Mendocino Rio Dell Overpass-FF 22.7 1.51619 7.6 1999 Chi-Chi, Taiwan CHY101 32.0 0.63620 7.6 1999 Chi-Chi, Taiwan TCU045 77.5 0.56321 6.6 1971 San Fernando LA-Hollywood Stor FF 39.5 2.09622 6.5 1976 Driuli, Italy Tolmezza 20.2 1.440

distributions. The results are presented for each construction quality of each building. The vertical

axis of each plot is expressed by a seismic coefficient defined as the total lateral load applied (baseshear) divided by the total dead weight of each building. The design seismic coefficient for eachbuilding is also indicated. The horizontal axis of each plot is expressed by the roof drift ratio,defined as the lateral displacement at the center of the building roof divided by the height fromthe first floor (ground) slab to the roof eaves of each building.

For both original index buildings, the peak lateral loads are reached at small roof drift ratios(0.30.5%). This is the result of the high lateral stiffness and limited ductility of the wall finishmaterials, particularly exterior stucco, included in the models. These stiffer and brittle finishmaterials fail before the underlying wood shear wall reaches its capacity. Note, however, that thelateral deformed shape of both buildings is influenced by soft-story mechanisms, for which a largeportion of the roof drift ratio is mobilized in the first story (as it will be seen later). Compoundedby the significant plan eccentricity of both buildings, the drift ratios of the first-level wall lines

(first story drift) experiencing the maximum deformations are 2 to 3 times larger than the roofcentral drift ratios shown in Figure 7. For both buildings, the lateral strength in the (long) eastwest direction is higher than in the (short) northsouth direction. The construction quality has asubstantial influence in both the stiffness and strength of both buildings but has only a minor effectin their displacement capacities. Increasing the nail density along wood panel edges increases thelateral stiffness and strength but has little effect on the displacement at failure that is governed bythe global kinematics of the wall assembly.



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0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0 0.51 1.5 2 2.5 3

Period (sec)

SpectralAcceleratio

n,

Sa

(g)

Median Spectrum

5% Damping

Figure 6. Acceleration response spectra at 5% damping of scaled ground motion records.

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Roof Drift Ratio (%)

SeismicCoefficient

Typical Quality

Superior Quality

Poor Quality

East-West

Design Seismic Coefficient = 0.183

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1


SeismicCoefficient

Typical Quality

Superior Quality

Poor Quality

North-South


0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1


SeismicCoefficient

Typical Quality

Superior Quality

Poor Quality

East-West


0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1


SeismicCoefficient

Typical Quality

Superior Quality

Poor Quality

North-South


(a)

(b)

Figure 7. Pushover curves of original index woodframe buildings: (a) townhousebuilding and (b) apartment building.

Figure 8 presents the uni-directional pushover curves for both principal directions of the typicalquality construction variant of each index woodframe building re-designed to 2006 IBC. Theresults are presented with and without consideration of the wall finish materials and are also



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East-West

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4Roof Drift Ratio (%)

SeismicCoefficient

Re-Designed Typical Quality with Wall Finishes

Original Typical Quality with wall Finishes

Re-Designed Typical Quality without Wall Finishes

1988 UBC Seismic Design Coefficient = 0.183

2006 IBC Seismic Design Coefficient = 0.154

North-South

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4


SeismicCoefficient


Original Typical Quality with Wall Finishes




East-West

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4Roof Drift Ratio (%)

SeismicCoefficient


Original Typical Quality with wall Finishes




North-South

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4


SeismicCoefficient


Original Typical Quality with Wall Finishes




(a)

(b)

Figure 8. Pushover curves of typical quality original and re-designed index woodframe buildings with andwithout wall finishes: (a) townhouse building and (b) apartment building.

compared with the pushover curves obtained for the typical quality construction of the originalindex woodframe buildings. The re-design of both buildings increases their lateral strength inthe eastwest direction but has very little effect in the northsouth direction. For both originalbuildings, wood shear walls were already present along the wall lines in the northsouth direction.For the townhouse building, the re-design involved new double wood shear walls between units inthe eastwest direction, which causes a significant increase in the lateral strength of the buildingin that direction. For the re-designed apartment building, the long eastwest interior wall on thefirst-level-incorporated new wood sheathing, which causes also a significant increase of the lateralstrength of the building along that direction.

Note that when the wall finishes are not considered, the wood structure exhibits lower strengthvalues with peak lateral loads being reached at much larger roof drift ratios (1.52.5%) than theratios obtained for the re-designed structures incorporating the wall finishes (0.30.5%). This isas a result of the stiffness and strength incompatibility between the wall finish materials (stuccoand gypsum wallboard) and the wood sheathed walls.

6.2. Free vibration analysis results

Table IV presents the computed first two initial natural periods (under elastic conditions, that is,each shear spring element in the SAWS model had initial stiffness) of each construction variant



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Table IV. Initial natural periods of original and re-designed index buildings.

Natural period (sec)

Building Mode/direction Poor quality Typical quality Superior quality

Original 1/northsouth 0.189 0.173 0.161Townhouse 2/eastwest 0.169 0.155 0.144Original 1/northsouth 0.276 0.249 0.233Apartment 2/eastwest 0.245 0.222 0.222

With wall finishes Without wall finishes

Re-designed 1/northsouth 0.176 0.429Townhouse 2/eastwest 0.151 0.347Typical qualityRe-designed 1/northsouth 0.245 0.514Apartment 2/eastwest 0.219 0.486Typical quality

for both original and re-designed index woodframe buildings considered in this study. The naturalperiods of each original building are increased by approximately 10% for each lower qualityconstruction (i.e. increment of 10% from superior quality to typical quality and another incrementof 10% from typical quality to poor quality). This increase in natural periods is approximately thesame for each mode of vibration.

The fundamental periods of the re-designed buildings are essentially identical as that of theoriginal typical quality construction. On the other hand, the fundamental period for each re-designedbuilding is more than doubled when the wall finishes are removed from the structural model. Thisresult clearly indicates the important contribution of the wall finishes to the lateral stiffness anddynamic characteristics of the index woodframe buildings.

6.3. IDA results

Figure 9 illustrates typical IDA results for the typical quality variant of the original townhousebuilding subjected to bi-directional excitations. The IDA plots shown in Figure 9(a) are monotonicand essentially bi-linear, which greatly simplifies the evaluation of the collapse level for individualground motion. The empirical collapse fragility curve constructed from these IDA plots is shownin Figure 9(b) along with the best-fit lognormal CDF. The median collapse value and the dispersionfactor are also shown. The collapse probabilities at the DBE and MCE levels are also identifiedfrom the fragility curve.

Fragility information extracted from all IDA results is presented in Tables V and VI for theoriginal and re-designed index woodframe buildings, respectively. Listed in these tables are themedian and values for all the computed lognormal CDFs along with the probabilities of collapse

associated with the DBE and MCE levels.The construction quality has a significant influence on the computed collapse fragility of both

original buildings (Table V). For the bi-directional analyses on the original townhouse building, themedian collapse intensity (expressed in terms of the median spectral acceleration of the ensembleof ground motion records considered for the analyses at a period of 0.2 s) increases by 15% whenthe construction quality is upgraded from poor to typical and by 9% from typical to superior. Thecorresponding increases in median collapse intensities are 13 and 10% for the original apartment



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Bi-Directional

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0 1 2 3 4 5 6 7 8 9 10

Maximum Interstory Drift (%)

Median

Probabilityofco

llapse

Saat0.2sec(g) Collapse

Limit-State

Bi-Directional

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7

Median Sa at 0.2 sec (g)

Empirical CDF

Lognormal CDF

Median =1.81 g

= 0.38P[Collapse/MCE] = 0.31

P[Collapse/DBE] = 0.06

(a) (b)

Figure 9. Results of bi-directional IDAs for typical quality original townhouse building: (a) IDA plotsand (b) collapse fragility curves.

Table V. Fragility information for original index woodframe buildings.

LognormalCDF Probability of collapse

DBE MCEExcitation Median level level

Building Variant direction (g) (Sa0.2 =1.0g) (Sa0.2 =1.5g)

Original townhouse Typical Eastwest 2.26 0.39 0.02 0.15Northsouth 2.26 0.44 0.03 0.17Bi-directional 1.81 0.38 0.06 0.31

Poor Eastwest 1.92 0.37 0.04 0.25Northsouth 1.92 0.42 0.06 0.28

Bi-directional 1.58 0.34 0.09 0.43Superior Eastwest 2.53 0.39 0.01 0.09

Northsouth 2.44 0.45 0.02 0.14Bi-directional 1.97 0.38 0.04 0.24

Original apartment Typical Eastwest 1.79 0.44 0.09 0.34Northsouth 1.65 0.43 0.12 0.41Bi-directional 1.40 0.33 0.15 0.58

Poor Eastwest 1.63 0.39 0.11 0.41Northsouth 1.52 0.42 0.16 0.49Bi-directional 1.24 0.33 0.25 0.71

Superior Eastwest 2.04 0.43 0.05 0.24Northsouth 1.77 0.43 0.09 0.35Bi-directional 1.54 0.32 0.09 0.47

building. The dispersion parameter remains almost constant around 0.40 for all cases since onlythe variation in ground motion characteristics is captured by IDAs. The excitation direction has alsoa significant influence on the collapse fragility of both original buildings. The bi-directional analysesreduce the median collapse levels obtained from the uni-directional analyses by approximately20% for all three construction variants of both original buildings. This reduction can be attributed



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Table VI. Fragility information for typical quality construction of re-designed index woodframe buildings.

LognormalCDF Probability of collapse

Wall Excitation DBE level MCE levelBuilding finishes direction Median (g) (Sa0.2 =1.0g) (Sa0.2 =1.5g)

Re-designed townhouse Included Eastwest 2.60 0.33 0.01 0.05Northsouth 2.15 0.36 0.02 0.16Bi-directional 2.00 0.40 0.04 0.24

Not included Eastwest 2.15 0.46 0.05 0.22Northsouth 1.90 0.48 0.09 0.31Bi-directional 1.70 0.43 0.11 0.39

Re-designed apartment Included Eastwest 2.38 0.36 0.01 0.10Northsouth 1.65 0.44 0.13 0.41Bi-directional 1.47 0.36 0.14 0.52

Not included Eastwest 2.15 0.46 0.05 0.22Northsouth 1.88 0.44 0.08 0.31

Bi-directional 1.52 0.32 0.12 0.49

to the fact that, when a pair of bi-directional motions is rotated along each principal direction ofa building, the larger component is applied in both analyses along one of the directions of thebuilding, which increases its likelihood of collapse compared with uni-axial IDAs, where the largecomponent is applied only once. In addition, construction quality and excitation direction influencesignificantly the resulting collapse probabilities at the MCE level.

The seismic weakness of tuck-under parking structures is evident from the fragility informationpresented in Table V. The probability of collapse of the poor quality original apartment buildingis more than 70% under the bi-directional MCE level ground motions. Even the superior qualityvariant has a corresponding collapse probability near 50%.

The collapse fragility of the typical quality re-designed townhouse with wall finishes (Table VI)is reduced substantially in the eastwest direction compared with the collapse fragility of thetypical quality original townhouse building (see Table V). This is the direct result of the re-designedparallel wood shear walls between units in the eastwest direction. The same observation canbe made between the typical quality re-designed and original apartment buildings in the eastwest direction as a result of the incorporation of wood sheathing in the long interior wall of there-designed apartment. When wall finishes are excluded from the structural models, the collapsefragility of both re-design buildings is increased in both directions compared with the typicalquality original buildings.

6.4. Collapse mechanisms

Figures 10 and 11 illustrate the collapse mechanisms associated with the uni- and bi-directionalIDAs on the original index woodframe townhouse and apartment building, respectively. Each figureshows the percentage of collapse cases initiated in a given wall line (i.e. having maximum inter-story drift at collapse) in the building. Each percentage value shown in the figures was obtainedby the number of earthquake records causing a particular wall line to reach its collapse limit statefirst in the building divided by 44 records; therefore, the sum of the percentages shown for a givenbuilding is equal to 100%. All collapse mechanisms are associated with wall lines located on the



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Figure 10. Distribution of collapse mechanisms, original townhouse: (a) uni-directionalIDAs and (b) bi-directional IDAs.

Figure 11. Distribution of collapse mechanisms, original apartment: (a) uni-directionalIDAs and (b) bi-directional IDAs.



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Figure 12. Distribution of collapse mechanisms, typical construction quality re-designed index buildingswith wall finishes: (a) townhouse uni-directional IDAs; (b) townhouse bi-directional IDAs; (c) apartment

uni-directional IDAs; and (d) apartment bi-directional IDAs.

first story of each original building (weak story collapse). For both original buildings, the collapse

mechanism associated with uni-directional IDAs (Figures 10(a) and 11(a)) corresponds to the samewall line for all ground motions (100% collapse) and is independent of the construction quality.For bi-directional IDAs, a variety of collapse mechanisms occur. This distribution of collapsemechanisms is also influenced by the construction quality although the majority of collapses occuralong the same first story wall lines (north for the townhouse, east for the apartment).

Figures 12 and 13 illustrate the collapse mechanisms associated with the uni-directional andbi-directional IDAs on the typical construction quality re-designed index woodframe buildingswith and without wall finishes, respectively. For both re-designed buildings with wall finishes(Figure 12), all collapse mechanisms are associated with wall lines located on the first story(weak story collapse). For the re-designed townhouse with and without wall finishes, all collapsemechanisms associated with uni-directional IDAs in the northsouth direction occur along the westwall line (Figures 12(a) and 13(a)) as opposed to the east wall for the original townhouse building

(see Figure 10(a)). This migration of the collapse mechanism from the east to the west wall isdue to the narrow wall piers along the east garage wall of the townhouse building that triggers aspecial clause of the 2006 IBC leading to closely spaced nailing of the wood shear walls alongthe east wall of the re-designed townhouse.

For both re-designed buildings without wall finishes, second-level collapse mechanisms areobserved (see Figure 13) indicating a more uniform distribution of lateral displacements amongthe various floor levels.



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Figure 13. Distribution of collapse mechanisms, typical construction quality re-designed index buildingswithout wall finishes: (a) townhouse uni-directional IDAs; (b) townhouse bi-directional IDAs; (c) apartment

uni-directional IDAs; and (d) apartment bi-directional IDAs.

7. CONCLUSIONS

This study conducted incremental dynamic analyses on two original and re-designed index wood-frame buildings with and without wall finishes: a townhouse and an apartment building. Threedeterministic construction variants (poor, typical and superior) were considered for each originalindex building in order to assess the effects of construction qualities on the seismic fragilitiesand collapse mechanisms. The re-designed buildings were based on the seismic requirements ofthe 2006 Edition of the International Building Code. Only the typical construction quality wasconsidered for these re-designed index buildings, but models with and without wall finishes wereincluded. Based on the results obtained, the following conclusions can be drawn:

The construction quality had a substantial influence on the stiffness and strength of both originalbuildings, but had only a minor effect in their displacement capacities.

The construction quality had a significant influence on the collapse fragility of both originalbuildings. For the bi-directional analyses on the townhouse building, the median collapseintensity increased by 15% when the construction quality was upgraded from poor to typicaland by 9% from typical to superior. The corresponding increases were 13 and 10% for theapartment building.



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The collapse fragility of the typical quality re-designed townhouse with wall finishes wasreduced substantially in the eastwest direction compared with the collapse fragility of thetypical quality original townhouse building. The same observation can be made betweenthe typical quality re-designed and original apartment buildings in the eastwest direction.

When wall finishes were excluded from the structural models, the collapse fragility of bothre-design buildings was increased in both directions compared with the typical quality originalbuildings.

The excitation direction had a significant influence on the collapse fragility of both original andre-designed buildings. The bi-directional analyses reduced the median collapse levels obtainedfrom the uni-directional analyses by approximately 20%.

ACKNOWLEDGEMENTS

The material described in this paper was developed as background material for the ATC-63 ProjectQuantification of Building System Performance and Response Parameters, which was funded by theDepartment of Homeland Securitys Federal Management Agency (FEMA). The authors kindly acknowl-

edge Dr Charles Kircher, Chair of the ATC-63 Project Management Committee, Mr Christopher Rojahn,ATC-63 Project Executive Director, and Mr John Heinz, ATC-63 Project Quality Coordinator, for theirguidance and support during the course of this project. The authors acknowledge also Kelly Cobeen fromCobeen and Associates Structural Engineering, who re-designed the index buildings considered in thisstudy.

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Incremental Dynamic Analysis of Woodframe Buildings