Performance-Based Seismic Retrofit Procedure for Soft-Story Woodframe Buildings with Excessive Torsion

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1 Performane-Based Seismi Retrofit Proedure for Soft-Stor Woodframe Buildings with Exessive Torsion P. Bahmani & J. W. van de Lindt Colorado State Universit, Fort Collins, Colorado, USA T. N. Dao Universit of Alabama, Tusaloosa, Alabama, USA SUMMARY: In soft-stor buildings the relative stiffness of the soft-stor, tpiall the bottom stor, is signifiantl less than upper stories due to the presene of large openings whih redue the available spae for lateral fore resisting sstem omponents suh as shear walls. In man ases, the distane between the enter of rigidit and enter of mass (i.e. eentriit) of the soft-stor is signifiant whih produes a torsional moment in addition to the lateral fore aused b the earthquake. This paper presents the development and appliation of the Diret Displaement Retrofit (DDR) proedure to ensure a speified performane level for retrofitted soft-stor buildings under lateral fores and exessive torsional moments. The approah is validated using detailed finite element models of asmmetri buildings under a suite of earthquake ground motions and found to auratel reprodue the desired dnami strutural response. Steel frames and wood shearwalls are the two retrofit tehniques onsidered in this stud. Kewords: Soft-stor building; Torsion; Retrofit; Diret displaement design; earthquake 1. INTRODUCTION A soft-stor building, in general, is a building that has a stor with low relative stiffness ompared to its upper stories. In other words, a soft-stor building is a building with disontinuit in its lateral stiffness resisting sstem at the level of the soft stor. Insuffiient lateral stiffness or strength (i.e. disontinuit) of the building an result in failure of the building under a moderate to large earthquake due to large inter-stor drift at the level of the soft stor. In order to improve the seismi performane of soft-stor buildings, several retrofit tehniques an be emploed b appling a Performane Based Seismi Retrofit (PBSR) method based on diret displaement design, termed a diret displaement retrofit (DDR) proedure. In PBSR, the inter-stor drift due to lateral fores is redued b inreasing the lateral stiffness of the weak stor; whereas, the inter-stor drift due to torsional moments is redued b inreasing the torsional stiffness of the stor whih leads to lower displaements due to torsional moments. The first step in PBSR is identifing the target inter-stor drift and orresponding seismi intensit at whih that drift is not to be exeeded for the speifi building; then, in the seond step, the diret displaement design method (Bahmani et al, 01) is used to determine the ontribution of translational and torsional displaement in the overall stor drift; then, in the third step, the DDR proedure is emploed to determine the distribution of both lateral and torsional stiffness for eah stor suh that the target performane requirements are satisfied for 50% of earthquakes (i.e. a nonexeedane probabilit of 50%). Finall, the most eonomial multi-stor retrofit tehnique is seleted for the building and ma be different for eah stor.. SOFT STORY CLASSIFICATIONS Soft stories an be lassified into two maor ategories with regard to vertial irregularit riteria: (1)

2 stiffness-soft stor and () stiffness-extreme soft stor. Aording to ASCE7-10, Stiffness-soft stor is a stor in whih the lateral stiffness is less than 70% of that in the above stor or less than 80% of the average stiffness of the three stories above. Stiffness-extreme soft stor is a stor whose lateral stiffness is less than 60% of that in the above stor or less than 70% of the average stiffness of the three stories above (ASCE7-10, 010). Soft stories an also be lassified with regard to in plan irregularities (i.e., stor eentriit). Table.1 presents soft stor lassifiations based on the loation of the line of resistane and the stor eentriit for eah ategor. It an be seen from the floor plan onfigurations that a soft stor ma not onl lak stiffness in translation, but ma also lak enough torsional stiffness. Thus, in order to retrofit a soft-stor building, both lateral stiffness and torsional stiffness of the stor should be taken into onsideration. Table.1. Soft stor lassifiations Soft Stor Classifiation Resistane against lateral fore Strutural Desription Resistane against torsional moment Soft-stor Configuration A Three lines of resistane; Soft in one diretion Eentriit in one diretion; Soft in torsion CR CM B Two parallel lines of resistane; Soft in one diretion Eentriit in one diretion; Soft in torsion CR CM C Two perpendiular lines of resistane; Soft in both diretions Eentriit in both diretions; Soft in torsion (exessive torsion) CR CM D One line of resistane; Soft in both diretions Eentriit in both diretions; Soft in torsion (exessive torsion) CR CM. PERFORMANCE-BASED SEISMIC RETROFIT (PBSR) Performane-based seismi retrofit (PBSR) is essentiall the same as performane-based seismi design (PBSD) with the obvious exeption of the additional onstraints on the design due to existing strutural and non-strutural assemblies. The PBSD method is a design methodolog that seeks to ensure that strutures meet presribed performane riteria under seismi loads. In displaement-based design whih is a subset of PBSD, the stiffness of the struture is distributed along its height suh that a target displaement an be ahieved under a speifi seismi intensit. Displaement-based design was originall proposed b Priestle (1998) and later modified b Filiatrault and Folz (00) to be applied to wood strutures. Pang and Rosowsk (009) proposed the diret displaement design (DDD) method using modal analsis and later, Pang et al (009) proposed a simplified proedure for appling the DDD method whih was eventuall applied to a six-stor light-frame wood building and tested in Miki, Japan (van de Lindt et al., 010) validating the simplified DDD proedure. Finall Wang et al (010) extended the work of Pang et al to allow orretion as funtion of building height. The PBSR method presented herein an be used to retrofit existing buildings suh that all stories meet the performane riteria; and it an be used to retrofit buildings that are weak under both translational fores and torsional moments.

3 The DDD method developed in the previous studies is a reliable proedure for designing strutures, but in its present form it an onl be emploed for strutures whih have negligible in-plane torsional moments. In this paper, an approah to deouple the torsional and translational mode shapes that was formulated b Kan and Chopra (1977) is applied in order to find the ontribution of translational and torsional mode shapes for the overall lateral displaement at eah stor. In this approah, vibration periods and mode shapes of a torsionall oupled building were approximated as a linear ombination of three unoupled mode shapes resulting from modal analsis of the orresponding torsionall unoupled sstem. This method leads to a simpler proedure for appliation of the DDD method whih serves as the basis for the diret displaement retrofit (DDR) proedure proposed. The DDD and DDR methods proposed herein an be emploed to either design or retrofit buildings with an level of in-plane and vertial irregularit in order to meet the desired performane riteria and have been verified using a detailed -D finite element model. The performane riterion in this paper is defined b an inter-stor drift ratio alulated at the enter of mass of eah stor..1. DDD proedure for buildings under exessive torsion The obetive of this paper is to find the distribution of the stiffness of lateral load resisting sstem of a torsionall unbalaned building to ensure the maximum inter-stor drift experiened b the struture is less than the inter-stor drift expetation. For a smmetrial building (i.e., no torsion), onl the distribution of the lateral stiffness over the height of the building must be determined; whereas, in an unsmmetrial building (i.e. torsionall oupled building) the lateral stiffness must be defined both inplane of eah stor and over the height of the building. In order to find the ontribution of translational and torsional mode shapes to the overall lateral displaement, modal analsis with the aid of response spetrum analsis is used to evaluate the maximum response of a torsionall unoupled building. The global stiffness matrix has to be defined prior to ondut the modal analsis; however, in the DDD proedure the stiffnesses of lateral load resisting sstems are being sought whih eventuall leads to an iteration proess to alulate the stiffness matries during the design. In order to eliminate the iteration proess in onduting modal analsis, the vibrational mode shapes of the building should be standardized in suh a wa that their shape (but not their amplitude) are independent of the stiffness matrix of the building. In other words, the mode shapes should remain onstant regardless of the atual stiffness of the building. This an be ahieved b assuming that mass-to-stiffness ratio over the height of the building and stiffness ratios of lateral load resisting elements at eah floor remain onstant during the analsis. The optimal design (or retrofit) of the building an be ahieved b seleting the appropriate mass-to-stiffness ratios suh that all stories experiene almost the same inter-stor drifts Modal Analsis for torsionall oupled buildings Modal analsis, whih is a simple alternate method to time-histor analsis, an be emploed in order to alulate the displaements of a building due to lateral fores and torsional moments under ground exitation. The advantage of modal analsis over time-histor analsis is that it an be onduted b determining the global mass and stiffness matries of the struture, without the need for integration of the equation of motion. The maximum responses, then, an be obtained b means of the pseudoaeleration response spetrum whih is easil generated for the building loation. However, for a torsionall oupled sstem, alulating the global stiffness matrix is umbersome whih leads to the need to solve a high order eigenvalue problem; and therefore, weakens the advantages of using modal analsis (i.e. simpliit and time effiien) over a detailed finite element time-histor analsis. For a torsionall oupled N-stor building as shown in Figure.1 the irular vibration frequenies (i.e., ) and mode shapes (i.e., ) of the building an be determined b solving the following eigenvalue problem: 0 K M (.1)

4 where, K and M are global stiffness and mass matries of the building, respetivel. After deoupling translational and torsional mode shapes, the eigenvalue problem an be expressed as where, K l and l, or. M 0 K l (.) l l M are stiffness and mass matries in the l diretion whih an be substituted b x Figure.1. (a) N-stor building (after Kan & Chopra,1977) ; (b) Elevation view; () Plan view of i th floor Deoupling mode shapes an be onduted using the method that was proposed b Kan and Chopra (1977). B deoupling torsional modes from translational modes, the size of the stiffness matries redues from N N to N N (N= number of stories). In addition, there will be no need to define the oupled stiffness terms in the global stiffness matrix. After determining the deoupled mode shapes and the modal oupling parameters of the building, the response due to eah mode an be alulated with the aid of the pseudo- aeleration response spetra. Finall, the maximum response an be obtained b ombining the response due to eah mode shape using the well-known square-root-of-thesum-of-the-squares (SRSS) or omplete-quadrati-ombination (CQC) methods..1.. Normalized mass and stiffness matries In order to simplif the modal analsis and eliminate the iteration proess during modal analsis, the mass and stiffness matries in Equation (.) should be defined suh that the vibrational mode shapes of the building beome independent of the atual stiffness and mass of eah stor. In order to overome this problem, standard mass and stiffness matries an be defined as follows: m ~ M (.) ~ is total mass- remains where, M is the total mass matrix, m is the total lumped mass of the first floor, and ratio matrix. Sine the unit mass and area of eah floor is onstant during the analsis, ~ unhanged. (a) (b) () Aordingl, it an be assumed that the radius of gration of the i th stor about a vertial axis through the enter of mass of the floor an be defined as

5 r ~ R (.4) ~ is the global radius of gration matrix. ~ remain onstant. Thus, the mass matrix in Equation (.) for determining torsional mode shapes an be alulated as where, r is the radius of gration of the first floor and Sine the geometri properties of the floors do not hange during the analsis, R and ~ ~ M mr (.5) The unoupled lateral stiffness matries of the i th stor along the prinipal axes of resistane x and an be expressed as where, K i x k, x, ; K i, k (.6), K i, and x i K, are the total lateral stiffness of the i th stor along x and diretions, respetivel; and, x are the stiffness ratio of the th lateral load resisting element in the x and, diretions, respetivel, to the stiffness of the weakest resisting element of the first stor (i.e., k ) (Figure.1). The unoupled torsional stiffness matrix defined at the enter of mass of the i th floor an be expressed as K k, x) i, ( ( k, ) x (.7) where, K is the torsional stiffness about the enter of mass of the i th floor; and, x i, and are the distanes between the enter of mass of the floor to the entroid of the resisting element in x and diretions, respetivel. Thus, the unoupled stiffness matries an be defined as l k l l K ~ (.8) where, ~ l is the global stiffness ratio matrix of the building along the l diretion. k l is the total stiffness of resisting elements in l diretion at the first stor. Therefore, the eigenvalue problem for a torsionall deoupled sstem an be reformulated as k k ~ ~ m 0 1 x, x, ( ) ( ) ~, x, x mr 1 ~ ~ 0 (.9) (.10) Equations (.9) and (.10) an be used to find the unoupled translational and torsional mode shapes, respetivel. It an be seen from the above equations that the onl variables are k and m and all other terms are assumed to be onstant during the analsis; therefore, it an be onluded that the mode shapes and their orresponding frequenies onl depend on the value of k and m. The mass of eah stor an be estimated to a good level of aura before the design; thus, the response of the struture depends onl on the seant stiffness of the weakest element at the target drift in the first floor. If the maximum response of the struture is plotted against the period of the first stor (i.e. T / k M ), 1 l

6 then the k l and onsequentl k an be determined. B knowing k and the seant stiffness of the retrofitting elements or sub-assemblies at the target drift, the retrofits an be designed. 4. RETROFIT TECHNIQUES During a moderate to large earthquake, a soft-stor building an experiene a large inter-stor drift at the soft-stor level due to translation, rotation, or a ombination of translation and rotation, while the stories above behave almost rigidl. In order to improve the performane of a soft-stor building, the translational and torsional stiffness (and strength) of the soft stor should be inreased to prevent the exessive inter-stor drift. Translational fores an be redued b inreasing the stiffness of the building in both diretions, or the soft and weak diretion if onl one exists. For torsional moments, there are two retrofit options: (1) Option A: eliminating the torsional moment b adding the retrofits suh that the in-plane eentriit of the soft-stor diaphragm dereases whih onsequentl redues the torsional moment; or () Option B: designing for torsion (aommodating the design for the ontribution to displaement from the torsional moments) b inreasing the torsional stiffness of the soft stor whih is used to retrofit buildings in this stud. In this stud, Steel Frame and Columns and wood shearwalls with different nailing patterns are seleted as retrofit design options for the existing woodframe building. These retrofit options are quite pratial and an be implemented for a large number of woodframe buildings. Steel frames an be added over the garage door opening of the building and wood shearwalls an be added where there are non-strutural walls or nail patterns altered to provide stronger and stiffer walls Steel Frame and Columns Steel frames and olumns an be used to retrofit stories espeiall at the soft-stor level, i.e. the first stor. The steel frame an be modelled as a bilinear spring with initial stiffness, K 1 (Figure 4.1.a). The stiffness for three tpes of steel frame with different end supports has been evaluated in this paper. For eah tpe of steel moment frames, it is assumed that the stiffness is onstant (i.e. initial stiffness K 1 ) up to the ield fore, F, assoiated with the ield drift of Δ at whih point it redues to K. In this stud, the drift at the ield point is set equal to 1% and the ratio of the seondar stiffness to the initial stiffness is assumed to be Table 4.1 presents the relationship between lateral fore, displaement, and initial stiffness of three different tpes of steel frames. Table 4.1. Lateral stiffness and displaement for steel frames (after Silvia and Badie, 008) Support Condition Steel Frame Tpe Lateral Displaement* Lateral Stiffness* Fixed Support 6 4 P L 6 4 E I 6 K E I L Pinned Support P L 4 4 E I K1 4 E I L 4 Inverted Moment Frame (antilevered olumns) PL 6E I K1 6E I L * I, L = moment of inertial and height of olumn; I b, L b = moment of inertial and length of beam Ib Lb and I L In order to design the retrofits, the seant stiffness is known based on the PBSR analsis and the initial stiffness are being sought. Having assumed the bilinear spring for steel frame, the seant stiffness of a

7 single steel frame an be alulated using Equation 4.1. Then, the setion properties of beam and olumns an be alulated using equations presented in Table 4.1. It should be noted that the frames with horizontal beam an be used onl if the beams are braed against lateral torsional bukling. Sine it is diffiult to provide lateral braing for steel beams in a woodframe building, an inverted moment frame (IMF) (termed a antilevered olumn) is the onl pratial option for retrofitting woodframe buildings using steel frames as this time. K (1 r ) r 1 Y 1 T arg et se ant K (4.1) 1 T arg et 4.. Wood Shearwall In this paper, wood shearwalls are seleted as a retrofit design option for the upper stories. The wood shearwalls an be substituted for non-strutural walls or existing shearwalls an be modified to have a denser nail shedule, i.e. loser nail pattern. Wood shearwall modelling is based on a well-known tenparameter hstereti model (Folz and Filiatrault, 001). Figure 4.1.b presents the ten-parameter hstereti spring for wood shearwalls. The required seant stiffness at the target drift an be determined from the wood shearwall bakbone. Table 4. presents the seant stiffness orresponding to different levels of drift ratio for.44 meter (8 ft) tall standard wood shearwalls. Table 4.. Seant stiffness for standard.44 meter tall (8 ft) wood shearwall (NEESWood Report 5) Seant Stiffness, K s (KN/mm per m) Edge/Field Nail Spaing (mm) Wall Drift 0.50% 1.0%.0%.0% 4.0% Standard Wood Shearwall 51/ / / / (a) Figure 4.1. (a) Bilinear spring, (b) Ten-parameter hsteresis spring (after Folz and Filiatrault, 001) (b) 5. EXAMPLE: PBSR OF A THREE-STORY BUILDING A three-stor building with exessive torsion at all stories was retrofitted based on the proposed PBSR method. The floor plans of the building were designed suh that the first stor behaved as a soft-stor during an earthquake. The ratio of the seant stiffness of the first stor to the seond stor at the target drift of % (i.e. target drift orresponding to DBE level earthquake) is 50% in the X diretion. Therefore, the building fell into the stiffness-extreme soft-stor ategor. The in-plane eentriit

8 ratio in X and Y diretions for all stories were 1.5% and 16.7%, respetivel. Figure 5.1 presents the floor plan and elevation of the building. The seant stiffness of the walls in bold were assumed to be twie of other walls. This led to move the enter of rigidit (i.e. CR) toward the stiffer part of the building whih onsequentl inreased the in-plane eentriit. Figure 5.1. Plan view and elevation of the soft-stor building with exessive torsion In order to evaluate the seismi performane of the building before and after appling the retrofits, the probabilit of exeedane of the building for the presribed inter-stor drift was alulated under twent-two far-field earthquake reords (FEMA P695, 009) saled for the seismi intensit orresponding to spetral aeleration for DBE level earthquake in San Franiso, California. Figure 5. presents the probabilit of exeedane versus inter-stor drift ratio before and after adding retrofits to the building. It an be seen from Figure 5..a that the inter-stor drift ratio orresponding to 50% non-exeedane at the first stor is 4.65%; whereas, the inter-stor drifts for the upper stories are both less than %. It an be onluded that the first stor behaves as a soft-stor and the two upper stories move almost as a rigid bod thereb onl moderatel ontributing to the lateral resistane of the building against seismi loads. Further, this lak of ontribution would onl be exaerbated for more intense earthquake level. Thus, the building needs to be retrofitted. As mentioned earlier, there are two approahes for retrofitting soft-stor buildings with exessive torsion; (1) retrofitting buildings suh that it meets the performane riteria without ompletel eliminating the soft-stor, or () retrofitting buildings suh that all stories experiene the same drift (eliminating the soft-stor behavior). Figure 5..b and Figure 5.. present the probabilit of exeedane versus inter-stor drift ratio for the same building using the first and seond approahes in PBSR methodolog, respetivel. The figures show that the retrofitted building meets the performane riteria (i.e., 50% probabilit of nonexeedane for a % inter-stor drift at the DBE level earthquake). Table 5.1 presents the inter-stor drift and stiffness ratios of the stories over the height of the building. It an be seen that the both retrofit designs limit the maximum inter-stor drift of the building to %. In the retrofitted building using PBSR Method 1, the building after appling the retrofit is still soft at the first stor; however, the PBSR method in this stud meets the performane riteria. The building that is retrofitted using PBSR Method has no soft stor sine the stiffness ratios over the height of the building were alulated suh that all stories experiene almost the same drift (i.e. % drift in this ase) under earthquake exitation, and is thus onsistent with urrent design ode regulations in the U.S. suh as ASCE 7-10 (010).

9 1.1% 1.8% 1.79% 1.7% 4.65%.04% (a) Original building without retrofit (b) Retrofitted building - PBSR Method % 1.81%.0% () Retrofitted building - PBSR Method (elimination of soft stor) Figure 5.. Probabilit of failure of building before and after retrofit Table 5.1. Stiffness and drift ratios before and after appling PBSR retrofits % target drift at DBE level Retrofitted buildings Original Building PBSR - Method 1 PBSR - Method Stor Stiffness Drift (%) Stiffness Drift (%) Stiffness Drift (%) 1 K 4.65 K*.04 K** K K* K** K K* K**.0 K = Translational stiffness of the first stor in X-diretion in the original building K* = Translational stiffness of the first stor in X-diretion in the retrofitted building - PBSR Method 1 K** = Translational stiffness of the first stor in X-diretion in the retrofitted building - PBSR Method 6. SUMMARY AND CONCLUSION The proposed PBSR method, whih is based on the diret displaement design methodolog, an be used for retrofitting buildings that are weak in both torsion and translation b providing a simple et aurate wa for engineers and pratitioners to design retrofits for soft-stor buildings. In this stud, a logial retrofit option for soft-stor buildings with exessive torsion was evaluated. It was shown that the seismi performane of a soft-stor building under both lateral fores and torsional moments due to earthquakes an be sstematiall improved b using a multi-stor performane-based retrofit tehnique. Diret displaement design (DDD) was modified to design the retrofits not onl along the height of the building, but also in-plane b inluding the effet of torsional moments into the interstor drifts. It was shown that PBSR an be used to retrofit soft-stor buildings b ompletel and partiall eliminating the soft stor behavior suh that the building meets the desired performane

10 riteria. It should be noted that if the stiffness of the soft stor is muh greater than the stories above after adding retrofits, the soft-stor behavior will be transferred to the upper stories of the building. The PBSR method assures that the soft-stor behavior does not transfer to the upper stories b providing help to distribute stiffness both along the height of the building and in the plane of eah stor. ACKNOWLEDGEMENT This material is based upon work supported b the National Siene Foundation under Grant No. CMMI (NEES Researh) and NEES Operations. An opinions, findings, and onlusions or reommendations expressed in this material are those of the investigators and do not neessaril reflet the views of the National Siene Foundation. The authors kindl aknowledge the Co-Prinipal Investigators of the NEES-Soft proet: Mihael D. Smans at Rensselaer Poltehni Institute, WeiChiang Pang at Clemson Universit, Xiaoun Shao at Western Mihigan Universit, Mikhail Gershfeld at Cal Pol Pomona, and senior personnel David V. Rosowsk at Rensselaer Poltehni Institute, Andre Filiatrault at Universit of Buffalo, Gar Mohizuki at Strutural Solutions In., Shiling Pei at South Dakota State Universit, Douglas Rammer at U.S. Forest Produts Lab., David Mar at Tipping Mar, and Charles Chadwell at Cal Pol SLO. REFERENCES ASCE (010). Minimum Design Loads for Buildings and other Strutures. Amerian Soiet of Civil Engineering; Strutural Engineering Institute 7-05, Reston, VA. Bahmani, P., van de Lindt, J.W. and Dao, T.N. (01). Diret Displaement Design of Buildings with Torsion I: Theor and Verifiation, ASCE Journal of Strutural Engineering, Submitted in Ma 01. FEMA, Federal Emergen Management Agen. (009). Quantifiation of Building Seismi Performane Fators, FEMA P695. Washington (DC). Filiatrault A. and Folz B. (00). Performane-based seismi design of wood framed buildings, ASCE Journal of Strutural Engineering, 18(1): Folz, B. and Filiatrault, A. (001). Cli Analsis of Wood Shear Walls. ASCE Journal of Strutural Engineering, Vol. 17(4), Kan, C.L., and Chopra, A.K. (1977). Elasti Earthquake Analsis of Trosionall Coupled Multistore Buildings. Earthquake Engineering and Strutural Dnamis, Vol. 5, Pang, W.C., and Rosowsk, D.V. (009). Diret Displaement Proedure for Performane-based Seismi Design of Mid-rise Woodframe Strutures, Earthquake Spetra, 5(), Pang, W.C., Rosowsk, D. V., van de Lindt, J.W. and Pei, S. (009), Simplified Diret Displaement Design of Six-stor NEESWood Capstone Building and Pre-Test Seismi Performane Assessment., NEESWood Report NW-05. Priestle, M.J.N. (1998). Displaement-based approahes to rational limit states design of new strutures. Kenote Address, Pro., 11th European Conferene on Earthquake Engineering, Paris, Frane. Silvia, P., and Badie, S. S. (008). Optimum Beam-to-Column Stiffness Ratio of Portal Frames under Lateral Loads. Struture Magazine, Marh 008. van de Lindt, J.W., Pei, S., Pror, S.E., Shimizu, H. and Isoda, H. (010). Experimental Seismi Response of a Full-Sale Six-Stor Light-frame Wood Building, ASCE Journal of Strutural Engineering, 16(10): van de Lindt, J.W., Pror, S.E. and Pei, S. (009). Shake Table Testing of a Seven-Stor Mixed-Use Condominium at Japan s E-Defense. 009 SEAOC Annual Convention, San Diego, CA, September -6. Wang, Y., Rosowsk, D. V., Pang W. C. (010). Performane-Based Proedure for Diret Displaement Design of Engineered Wood-Frame Strutures. ASCE Journal of Strutural Engineering, Vol. 16(8),