1. Principal of Simpson Gumpertz & Heger Inc., 41 Seyon Street, Waltham, Massachusetts 02453, djkelly@sgh.com

2. President of S. K. Ghosh Associates Inc., 334 E Colfax Street, Unit E, Palatine, Illinois 60067, skghoshinc@gmail.com

D. J. Kelly, S. K. Ghosh, Diaphragm Response to and Design for Earthquake Ground Motions, Proceedings of the 10th National Conference on Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

Tenth U.S. National Conference on Earthquake EngineeringFrontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska 10NCEE

DIAPHRAGM RESPONSE TO AND DESIGN FOR EARTHQUAKE GROUND MOTIONS

Dominic J. Kelly1 and Satyendra K. Ghosh2

ABSTRACT Analytical studies, shake table test results, and accelerations from instrumented buildings indicate that floor and roof diaphragm response to earthquake ground motion is substantially different than currently accounted for by seismic design provisions used in the U.S. For design purposes, diaphragms may be grouped in terms of whether the overall response of the building is dominated by the response of the vertical elements of the seismic force-resisting system or the response of the diaphragm. Two initiatives regarding the response of diaphragms to earthquakes are underway: one that applies to buildings for which the response to an earthquake is dominated by the response of the vertical elements, and the second that applies to single-story buildings for which the response is dominated by that of the diaphragm. For buildings in which response of the vertical elements of the seismic force-resisting system dominates the overall behavior, analytical studies and test results of structures loaded by simulated earthquakes using a shake table indicate that the magnitude of diaphragm forces is significantly larger and the relative magnitudes of diaphragm forces over the height of a building are more constant than those computed using current design provisions in the U.S. For single-story buildings with stiff vertical elements such as steel-braced frames and shear walls and with flexible wood panel or steel deck diaphragms, the response to an earthquake is more likely to be dominated by the diaphragm response than the vertical element response. For these one-story buildings with a flexible diaphragm, the yielding and energy dissipation is often in the diaphragm rather than in the vertical elements, as current U.S. code provisions assume. This paper describes the initiative of Issue Team 6 – Diaphragms (IT-6) of the Provisions Update Committee for the 2015 NEHRP Provisions and the initiative of a project working group for the Simplified Seismic Design project of the Building Seismic Safety Council.

1. Principal of Simpson Gumpertz & Heger Inc., 41 Seyon Street, Waltham, Massachusetts 02453, djkelly@sgh.com

2. President of S. K. Ghosh Associates Inc., 334 E Colfax Street, Unit E, Palatine, Illinois 60067, skghoshinc@gmail.com

D. J. Kelly, S. K. Ghosh, Diaphragm Response to and Design for Earthquake Ground Motions, Proceedings of the 10th National Conference on Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

Tenth U.S. National Conference on Earthquake EngineeringFrontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska 10NCEE

Diaphragm Response to and Design for Earthquake Ground Motions

Dominic J. Kelly1 and Satyendra K. Ghosh2

ABSTRACT Analytical studies, shake table test results, and accelerations from instrumented buildings indicate

that floor and roof diaphragm response to earthquake ground motion is substantially different than currently accounted for by seismic design provisions used in the U.S. For design purposes, diaphragms may be grouped in terms of whether the overall response of the building is dominated by the response of the vertical elements of the seismic force-resisting system or the response of the diaphragm. Two initiatives regarding the response of diaphragms to earthquakes are underway: one that applies to buildings for which the response to an earthquake is dominated by the response of the vertical elements, and the second that applies to single-story buildings for which the response is dominated by that of the diaphragm. For buildings in which response of the vertical elements of the seismic force-resisting system dominates the overall behavior, analytical studies and test results of structures loaded by simulated earthquakes using a shake table indicate that the magnitude of diaphragm forces is significantly larger and the relative magnitudes of diaphragm forces over the height of building are more constant than those computed using current design provisions in the U.S. For single-story buildings with stiff vertical elements such as steel-braced frames and shear walls and with flexible wood panel or steel deck diaphragms, the response to an earthquake is more likely to be dominated by the diaphragm response than the vertical element response. For these one-story buildings with a flexible diaphragm, the yielding and energy dissipation is often in the diaphragm rather than in the vertical elements, as current U.S. code provisions assume. This paper describes the initiative of Issue Team 6 – Diaphragms (IT-6) of the Provisions Update Committee for the 2015 NEHRP Provisions and the initiative of a project working group for the Simplified Seismic Design project of the Building Seismic Safety Council.

Introduction

Analytical studies and shake table test results indicate that floor and roof diaphragm response to earthquake ground motion is substantially different than currently accounted for by the design provisions of Minimum Design Loads of Buildings and Other Structures (ASCE/SEI 7-10) [1]. To address this inconsistency, two initiatives regarding the response of diaphragms to earthquakes that could lead to significant changes to diaphragm design provisions in the U.S. are underway. Issue Team 6 – Diaphragms (IT-6) of the Provisions Update Committee for the 2015 NEHRP Recommended Seismic Provisions for New Buildings and Other Structures [2] is assembling and reviewing analytical studies and test data. The efforts of IT-6 are applicable to diaphragms of buildings for which yielding of the vertical elements of the seismic force-resisting system is the primary source of inelastic response and energy dissipation. The goal of IT-6 is to develop diaphragm design provisions that more accurately account for forces developed and the

strength and ductility of diaphragms. A project working group (PWG-3) of the Simplified Seismic Design Project for the Building Seismic Safety Council (BSSC) is studying the response of one-story buildings with flexible diaphragms to earthquake ground motions. The goal of PWG-3 is to develop design provisions applicable to one-story buildings with flexible diaphragms for which the response of the diaphragm dominates the response of the building. The efforts of these initiatives and the findings to date are described in this paper.

Current Requirements for Diaphragm Design Forces

Current design requirements for diaphragms in ASCE/SEI 7 are based on empirical considerations. In contrast to the design for vertical elements for which forces are reduced due to expected inelastic action, diaphragm design forces are not reduced due to expected inelastic action of the diaphragm. Instead, diaphragm forces are a function of the design forces acting on the vertical elements, with added minimum and maximum caps on the forces. Because the diaphragm forces are a function of the design forces for the vertical elements, the magnitude of the diaphragm design force is dependent on the reduction by the R-factor that applies to the vertical elements. The diaphragm design force is computed using Eq. 1 and the minimum and maximum limits on the diaphragm design force are provided by Eqs. 2 and 3. = ∑∑ (1)

Where

Fpx is the diaphragm design force at level x. Fi is the portion of the seismic base shear, V, induced at Level i. wi is the weight tributary to Level i. wpx is the weight tributary to the diaphragm at Level x.

≥ 0.2 (2) Where SDS is the design spectral response acceleration parameter at short periods. Ie is the seismic importance factor. ≤ 0.4 (3)

Diaphragm design forces obtained from Eq. 1 are directly related to the design forces for the vertical elements, which includes force reduction accounting for inelastic response through the use of the R factor. Also, Eq.1 does not account for over-strength of the vertical elements, so design of diaphragms using this approach does not prevent yielding of the diaphragm. This empirical approach has been generally satisfactory as evidenced by a lack of severe damage to many diaphragm types in earthquakes. Material-specific factors related to diaphragm over-strength and deformation capacity may account for the adequate diaphragm performance in past earthquakes.

An exception to satisfactory performance is large diaphragms for precast concrete

garages that have experienced significant damage in earthquakes. Other diaphragm types may also be susceptible to damage, such as flexible diaphragms with longer spans for which diaphragm yielding is likely and transfer diaphragms. Transfer diaphragms transfer seismic forces from the vertical resisting elements above the diaphragm to other vertical resisting elements below the diaphragm due to offsets in the placement of the elements or to changes in relative lateral stiffness of the vertical resisting elements.

Results using analysis tools, which were not available when the empirical rules were first

established, indicate that the level of force required for diaphragm design of new code-compliant buildings may not ensure development of inelastic mechanisms in the vertical elements of the seismic force-resisting system. This phenomenon was dramatically illustrated by the response of several shear wall structures during the Northridge Earthquake. Diaphragms in Buildings with Inelastic Behavior Concentrated in Vertical Elements For buildings in which response of the vertical elements of the seismic force-resisting system dominates the overall behavior, analytical studies and test results of structures loaded by simulated earthquakes using a shake table indicate that the magnitude of diaphragm forces is significantly larger and the relative magnitudes of diaphragm forces over the height of building are more constant than those computed using current design provisions in the U.S. To address this difference, IT-6 proposed a change to the diaphragm design procedure of ASCE/SEI 7 for consideration by BSSC’s Provisions Update Committee, which passed, and will soon be considered as a proposed change to ASCE/SEI 7. The proposed change is intended to be mandatory for the design of precast concrete diaphragms in buildings assigned to Seismic Design Category (SDC) C and above and, at least initially, it would be optional for the design of other diaphragms. The proposed provisions enable the greater forces observed in near-elastic diaphragms and the anticipated over-strength and deformation capacity of diaphragms to be directly considered in the diaphragm design procedure. This should result in an improved distribution of diaphragm strength over the height of buildings and among buildings with different types of seismic force-resisting systems. Proposed Procedure The proposed equation for diaphragm design force is Eq. 4. The minimum design force of Eq. 2 is also applicable. The variation of diaphragm design force over the height of the building is represented in Fig. 1.

pxpx px

s

CF = w

R (4)

Where

Cpx is the diaphragm design acceleration coefficient at Level x. Rs is the diaphragm design force reduction factor. Cp0 is the diaphragm design acceleration coefficient at the structure base. Cpn is the diaphragm design acceleration coefficient at the top of the structure.

Figure 1. Floor acceleration envelopes for calculating the design acceleration coefficient Cpx in buildings with n ≤ 2 and in buildings with n ≥ 3

The elastic diaphragm design force is proposed as the square root of the sum of the

squares of the first mode effect and higher mode effects [3], which is apparent in Eq. 5 used to calculate Cpn, which is the diaphragm design acceleration coefficient at the top of the structure. In Eq. 5, the first term within the square root is for the first mode effect and the second term is for higher mode effects. For the diaphragm design force, the first mode effect is reduced by the response modification factor, R, of the seismic force-resisting system. This is not directly apparent in Eq. 5 because the reduction by R is accounted for in the coefficient Cs, which is the coefficient used to compute the base shear for the design of the seismic force-resisting system. The first mode force term also includes the over-strength factor, Ωo. The combination of dividing the force by R and amplifying it by Ωo recognizes that an inelastic mechanism in the first mode is anticipated and accounts for diaphragm forces being limited by the expected strength of the vertical elements.

( ) ( )Γ Ω Γ2 2

pn m1 0 s m2 s2C = C + C (5)

Where

Γm1 and Γm2 are first and higher modal contribution factors, respectively. Cs is the seismic response coefficient used to compute the base shear. Ωo is the system over-strength factor. Cs2 is the higher mode seismic response coefficient

The effect caused by higher mode response is included in the second term within the

square root. The equations for Cs2, which are not include herein, do not include a reduction in force from the R-factor, because higher mode accelerations typically do not lead to yielding of the vertical elements. Diaphragm accelerations for higher modes should not be extracted from a modal analysis in lieu of the proposed equations for Cs2, because higher mode contribution to floor accelerations can come from a number of modes, particularly when there is torsional-lateral

coupling of the modes. Although the equations for Γm1 and Γm2 are not presented herein, they depend on the number of stories and a mode shape factor that is system-dependent.

The diaphragm design acceleration coefficient at the base of the building, Cp0, is

computed in accordance with Eq. 6. In this equation, the short-period spectral acceleration parameter, SDS, is multiplied by 0.4, which approximates converting the spectral acceleration to peak ground acceleration.

0.4p0 DS eC = S I (6)

For buildings three or more stories tall, the diaphragm design acceleration coefficient

between the base of the building and 80% of the building height is equal to the diaphragm design acceleration at the base of the building, Cp0. This value reflects that at about 80% of the structural height, floor accelerations are largely, but not solely, contributed by the first mode of response.

Diaphragm Force Reduction Factor In recognition that diaphragms have over-strength and inelastic displacement capacity and that some yielding of the diaphragm is acceptable, the elastic diaphragm force from the first and higher modes of response may be reduced by dividing the elastic diaphragm force by a diaphragm force reduction factor, Rs, as Eq. 1 allows. With the modification by Rs, the proposed design force level may not be significantly different from the current diaphragm design force level of ASCE 7-10 for many practical cases. For some types of diaphragms and for some locations within structures, the proposed diaphragm design forces will change significantly, resulting in noticeable changes to resulting construction. Based on testing and analysis data and building performance observations, it is believed that these changes are warranted.

For diaphragm systems with inelastic deformation capacity sufficient to permit inelastic response under the design earthquake, the diaphragm design force reduction factor, Rs, is typically greater than 1.0, so that the design force demand (Fpx) is reduced relative to the force demand for a diaphragm that remains linear elastic under the design earthquake.

Diaphragms with Rs values greater than 1.0 shall have the following characteristics: (1) a well-defined, specified yield mechanism, (2) global ductility capacity for the specified yield mechanism, which exceeds anticipated ductility demand for the maximum considered earthquake, and (3) sufficient local ductility capacity to provide for the intended global ductility capacity, considering that the specified yield mechanism may require concentrated local inelastic deformation to occur. For diaphragm systems that do not have sufficient inelastic deformation capacity, Rs should be less than 1.0 and as low as 0.7, so that linear-elastic force-deformation response can be expected if shaken by ground motions equivalent to that of the maximum considered earthquake (MCE). Diaphragm force reduction factors, Rs, have been developed for some commonly used diaphragm systems. The derivation of factors for each of these systems is explained in detail in the proposed commentary.

Validation of Proposed Approach

To validate the proposed approach, coefficients Cpx were calculated for various buildings tested on shake tables. Fig. 2 plots the floor acceleration envelopes and the floor accelerations predicted from Eq. 4 with Rs = 1 for a bearing wall building built at full-scale and tested on a shake table [4]. A similar plot for a concrete moment frame building will also appear in the commentary [5].

Figure 2. Comparison of measured floor accelerations and accelerations predicted by Eq. 4 with Rs = 1 for a seven-story bearing wall building [4].

The procedure was also compared to the measured floor accelerations of a structure with steel buckling restrained braced frames and a structure with special steel moment-resisting frames. The procedure requires diaphragm forces that are in good agreement near the bottom and top of buildings. The procedure may not require high enough forces for intermediate levels. The provisions are not entirely final and revisions may be made to the proposal to better represent the diaphragm force of the intermediate levels. Collectors The proposed provisions require that diaphragm collectors be designed for 1.5 times the force level used for diaphragm in-plane shear and flexure, rather than amplifying the force by the over-strength factor, Ωo, as current provisions for Seismic Design Categories C through F require. The intent of this requirement is to increase collector forces to help ensure that collectors will not be the weak links in the seismic force-resisting system. Because this proposal specifically includes Ωo in the formulas for calculating diaphragm design forces and diaphragm forces are more accurately identified, a smaller multiplier, 1.5, than has been used in the past, Ωo, is justified. Other Issues Issues such as how to treat transfer diaphragms and how to address significant changes in story

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.5 1.0 1.5

Rela

tive

heig

ht

Cpx / Cpo

Measured EQ4

Proposed

mass over the height of the building are considered in the proposed provisions and commentary. The provision requiring a 25% increase in design forces for certain diaphragm elements in building with certain irregularities is proposed for deletion because the diaphragm design force level in this alternative proposal is based on a realistic assessment of anticipated diaphragm behavior.

Single-Story Flexible Diaphragm Buildings For single-story buildings with stiff vertical elements such as steel-braced frames and shear walls and with flexible wood panel or steel deck diaphragms, the response to an earthquake is more likely to be dominated by yielding and energy dissipation of the diaphragm than yielding and energy dissipation of the vertical elements as ASCE/SEI 7 assumes. If the stiff vertical elements are precast concrete, either plant-cast or site-cast, or masonry walls, the buildings are often referred to as rigid wall-flexible diaphragm (RWFD) buildings or box buildings. In California and the Southwest, the diaphragms of these buildings are usually wood structural panels attached to wood framing or attached to wood nailer plates bolted to steel bar joists. East of the Rockies, the diaphragms are almost exclusively steel deck attached to steel bar joists with welds, powder- actuated fasteners, or screws. The steel deck diaphragms are also used in California and the Southwest, but less frequently than the wood diaphragms.

For diaphragm spans that are several hundred feet long, the diaphragm deflections in these buildings is often many times the deflections of the vertical elements. For these buildings, design for yielding of the vertical elements prior to yielding of the diaphragm is difficult to achieve, so PWG3’s effort has been focused on developing a design approach in which inelastic response of the diaphragm is expected. The current design approach and two proposed approaches are being studied using nonlinear analyses of prototype buildings. The goal of PWG3’s efforts is to develop stand-alone provisions that apply to this type of buildings that are still relatively simple to use. Performance in Previous Earthquakes Single-story buildings with rigid walls have generally performed poorly in past earthquakes. References describing the poor performance are listed in Koliou et al. [6]. As described in a paper by Lawson et al. [7], the main issue has been with failure of the top-of-wall to diaphragm connections. The buildings that experienced this type of damage have had wood panel diaphragms. As a result, the design forces for these connections have increased in several codes since the issue was first identified as a result of the 1964 Anchorage, Alaska, Earthquake. Buildings with heavy perimeter walls and steel deck diaphragms have not been a common building type in regions of the U.S. that have experienced strong earthquake ground shaking. Therefore, the lack of reported damage to these buildings from damaging earthquakes should not be mistaken for good performance. Issues to Consider In studying this building type, several issues have been identified. Confirming that the ASCE/SEI 7 top-of-wall connection forces are adequate is a priority, given that inadequate

strength and ductility of these connections has led to numerous failures. Determining the available ductility of the diaphragm connections and how local connection ductility relates to global ductility of the diaphragm is necessary because the performance of these buildings is dependent on the ductility and energy dissipation of the diaphragm. The diaphragm’s strength, ductility, and energy dissipation demands are considered along with P-Δ effects to determine whether proposed design approaches result in adequate stability of these structures. Design approaches are discussed in Lawson et al. [7]. The effect on the building behavior of yielding of tall walls due to out-of-plane force is also a consideration. An issue specific to RWFD buildings with steel deck is how out-of-plane wall forces combine with diaphragm shears. This is an important issue for the steel deck diaphragms because out-of-plane wall anchorage forces that are oriented parallel to the length of the deck panels are transferred directly into the deck. These forces must be transferred from panel end-to-panel end as much as one-half the diaphragm’s depth unless others means of transferring these loads into the diaphragm are provided, such as providing ties oriented parallel to the deck panel lengths. Numerical Framework for Collapse Assessment To determine whether the design approaches result in structures with adequate resistance against collapse, nonlinear time-history analyses consistent with the approach of FEMA P695 [8] were used. Using detailed models that include all framing members, diaphragm panels, and connections is computationally intensive and would have taken too long to implement so a numerical framework was developed to capture the response of these buildings with less computational effort. The numerical framework used to assess the risk of collapse is presented in a paper by Koliou et al. [6]. The main steps are: (1) assembling a connector database, (2) creating detailed inelastic roof diaphragm models from which hysteretic models of portions of diaphragms are developed for use in step 3, and (3) creation of simplified nonlinear analysis models. The nonlinear analysis models account for the location of the mass of the walls, possible nonlinear behavior of walls in the out-of-plane direction, P-Δ effects, and spread of plasticity within the diaphragms. Archetype buildings are being modeled using this numerical framework. The archetypes include buildings with 30 ft tall walls, footprints of 100 ft x 100 ft to 400 ft x 400 ft, and diaphragm aspect ratios of 1:2, 1:1, and 2:1. Diaphragms are nailed wood structural panels and steel deck welded, screwed, or nailed with powder actuated fasteners to steel joists. The steel panels are connected along their sides with button punches, screws, or welds. Further description of the archetypes is provided in Lawson et al. [7]. Findings to Date Findings to date include the following:

• The current design approach of using R equal to 4 for an intermediate precast concrete shear wall and the approximate period in the code results in archetype designs with wood structural panel diaphragms that pass the P695 criterion for individual archetypes but fail the criterion for performance groups. Many of the archetypes designed with steel deck

diaphragms do not pass the P695 criterion for individual archetypes and none of the performance groups studied pass the applicable P695 criterion.

• Using the current design approach for a steel deck diaphragm but weakening the interior portions of the diaphragm improves the margin against collapse by reducing ductility demands near the perimeter and spreading the inelastic behavior of diaphragm over a larger portion of the diaphragm length. This leads to a possible design approach of designing diaphragms with a stronger perimeter and a weaker interior.

• A design approach is proposed in which diaphragms are designed using an R factor of 4.5 for the interior 80% of the diaphragm dimension and amplifying the diaphragm shears computed using R of 4.5 in the outer 10% of the diaphragm dimensions by 1.5. For this approach, the period is based on the flexibility of the diaphragm and vertical elements. The results of incremental dynamic analyses of archetypes with wood structural panel or steel deck diaphragms designed using this proposed approach pass the P695 criteria both as individual archetypes and as performance groups.

• Analyses indicate that the forces on connections that support the tops of walls loaded in the out-of-plane direction are higher for walls being loaded parallel to the long diaphragm direction and smaller for walls being loaded parallel to the short diaphragm direction.

• The ASCE/SEI 7 connection design forces for support of walls in the out-of-plane direction are appropriate in the long diaphragm direction and conservative in the short diaphragm direction.

• Incorporating the out-of-plane yielding of walls in the models improved the margin against collapse. The effect can be conservatively be incorporated into the modeling by assuming the wall is pinned at its base and at the diaphragm level and accounting for yielding near mid-height of the wall.

Conclusions

Current design procedures used in the U.S. underestimate the diaphragm design forces for buildings in which yielding is primarily in the vertical elements of the seismic-force-resisting system and do not address the design of a diaphragm that is the primary yielding element of a seismic-force-resisting system. To address the first shortcoming of the current code requirements, a diaphragm design procedure is presented in this paper that more accurately accounts for forces developed in diaphragms for buildings with the nonlinear response concentrated in vertical elements. In recognition that diaphragms have generally performed well in earthquakes, the procedure allows reductions of diaphragm forces that are a function of a diaphragm’s over-strength and ductility. To address the second shortcoming, a study addressing One-story buildings in which the diaphragm is the primary yielding element is described and findings are described. This study will eventually lead to design provisions for one-story building in which the diaphragm response dominates the overall response of the building to earthquake ground motions.

Acknowledgments

The portion of the paper regarding the efforts of Issue Team 6 (IT-6) of the Provisions Update Committee for development of 2015 NEHRP Recommended Seismic Provisions for New Buildings and Other Structures is supported by the Federal Emergency Management Agency (FEMA) through its contract with the Building Seismic Safety Council (BSSC) HSFEHQ-09-D-0147 Task Order HSFE60-12-J-001C. The study regarding rigid wall-flexible diaphragm buildings is conducted as part of a project directed by the National Institute of Building Sciences (NIBS) and funded by the Federal Emergency Management Agency (FEMA) under DHS/FEMA Contract HSFEHQ-09-D-0147, Task Order HSFEHQ-09-J-0002. The main objective of the project is to develop simplified seismic design procedures for Rigid Wall-Flexible Diaphragm (RWFD) buildings. Any opinions, findings, conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the NIBS and FEMA.

References

1. ASCE. Minimum Design Loads for Buildings and Other Structures. Reston, Virginia: American Society of

Civil Engineers 2010. 2. FEMA. NEHRP Recommended Seismic Provisions for New Buildings and Other Structures.

Washinghton, DC: Federal Emergency Management Agency, 2015. 3. Rodriguez, M, Restrepo, J. I. and Carr, A. J., 2002 “Earthquake induced floor horizontal accelerations in

buildings”, Earthquake Engineering - Structural Dynamics, 31 693-718. 4. Chen, M., Pantoli, E., Astroza, R., Ebrahimian, H., Mintz, S., Wang, X., Hutchinson, T., Conte,

J.,Restrepo, J.,Meacham, B., Kim, J., and Park, H., Draft 2013 Full-scale structural and nonstructural building system performance during earthquakes and post-earthquake fire: Specimen design, construction and test protocol. Structural Systems Research Project Report Series. University of California San Diego, San Diego, CA.

5. Panagiotou, M, Restrepo, J, and Conte, J.P. 2011, “Shake-Table Test of a Full-Scale 7-Story Building Slice. Phase I: Rectangular Wall”, ASCE J. Struct. Engr., 137(6), 691-70

6. Koliou, M, Filiatrault, A., Kelly, D.J, and Lawson, J., “Numerical Framework for Seismic Collapse Assessment of Rigid Wall-Flexible Diaphragm Structures”, Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

7. Lawson, J, Kelly, D. J., Koliou, M, Filiatrault, A., “Development of Seismic Design Methodologies for Rigid Wall – Flexible Diaphragm Structures”, Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

8. FEMA P695. Quantification of Building Seismic Performance Factors. Washinghton, DC: Federal Emergency Management Agency; 2009.