Seismic vulnerability evaluation of RC moment …scholar.cu.edu.eg/?q=medial_sector/files/1016_ftp.pdfA multi-level seismic vulnerability assessment of reinforced concrete moment frame

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICSEarthquake Engng Struct. Dyn. 2011; 40:215–235Published online 13 May 2010 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/eqe.1016

Seismic vulnerability evaluation of RC moment frame buildingsin moderate seismic zones

H. A. El Howary1 and S. S. F. Mehanny2,∗,†,‡

1Structural Engineer, DAR Al-Handasah, Cairo, Egypt2Structural Engineering Department, Cairo University, Cairo, Egypt

SUMMARY

A multi-level seismic vulnerability assessment of reinforced concrete moment frame buildings locatedin moderate seismic zones (0.25g) is performed on a set of ductile versions of low- to mid-rise two-dimensional moment frames. The study is illustrated through application to comparative trial designs oftwo (4- and 8-story) buildings adopting both space- and perimeter-framed approaches. All frames aredimensioned as per the emerging version of the seismic design code in Egypt. These new seismic provisionsare in line with current European norms for seismic design of buildings. Code-compliant designs (CCD),as well as a proposed modified code design relaxing design drift demands for the investigated buildings,are examined to test their effectiveness and reliability. Applying nonlinear inelastic incremental dynamicanalyses, fragility curves (FC) for the frames are developed corresponding to various code-specifiedperformance levels. Code preset lower and upper bounds on design acceleration and drift, respectively,are also addressed along with their implications, if imposed, on the frames seismic performance andvulnerability. Annual spectral acceleration hazard curves for the case study frames are also generated.Estimates for mean annual frequency (MAF) of exceeding various performance levels are then computedthrough an integration process of the data resulting from the FC with the site hazard curves. The studydemonstrates that the proposed design procedure relaxing design drift demands delivers more economicbuilding designs relative to CCDs, yet without risking the global safety of the structure. The relaxed designtechnique suggested herein, even though scoring higher, as expected by intuition, MAF of exceedingvarious code-limiting performance levels expressed in terms of interstory drift ratios, still guarantees areasonably acceptable actual margin against violating code limits for such levels. Copyright � 2010 JohnWiley & Sons, Ltd.

Received 1 December 2009; Revised 29 March 2010; Accepted 5 April 2010

KEY WORDS: RC moment frames; ductile; moderate seismic zones; codes; fragility curves; hazard

1. INTRODUCTION

Earthquake hazards generally cause mild to significant damage to structures and may even some-times result in a widespread failure throughout buildings. Moment-resisting frames are widelyused as prominent lateral load-resisting systems to carry seismic demands during earthquakeswhen sufficient ductility is to be met. Emerging performance-based design approaches currentlypromoted in modern seismic provisions worldwide, when applied to these promising moment framesystems seek to enable more accurate and transparent assessment of both LS risks and damagecontrol through the use of advanced analysis models and design criteria. A critical element towardachieving this vision is through an accepted framework that integrates the results of sophisticatedinelastic static and dynamic analyses with a seismic hazard analysis in a probabilistic format.Such step, when accomplished, will help deliver answers to typical questions such as: ‘how safeare code-conforming moment-framed structures?’ and ‘how much more likely are these moment

∗Correspondence to: S. S. F. Mehanny, Structural Engineering Department, Cairo University, Cairo, Egypt.†E-mail: [email protected]‡Associate Professor.

Copyright � 2010 John Wiley & Sons, Ltd.

216 H. A. EL HOWARY AND S. S. F. MEHANNY

frames able to tolerate different levels of damage corresponding to various code expected, andset a priori, performance levels?’ Some answers to these questions and others alike are furnishedin recent documents, e.g. [1] aiming at quantifying building system performance and responseparameters for use in performance-based seismic design/evaluation.

Several researchers in the past have investigated the performance and responses of RC moment-resisting frames through a probabilistic assessment framework and the list is fairly long. Focusingherein though on presenting only recent efforts in this direction, it is worth reporting the work doneby Haselton [2]. Haselton studied 30 different ductile RC moment frames located in high seismiczones and further evaluated the collapse capacity of these frames. The frames cover varying heights(1–20 stories) and were designed according to recent building code seismic provisions in the UnitedStates. On the other hand, Ramamoorthy [3] studied generic low- to mid-rise (up to 10 stories) RCframe buildings located in eastern and mid US regions. He used a Bayesian methodology to developprobabilistic demand models to predict the maximum interstory drift associated with various codepre-specified performance levels. Fragility estimates with confidence bounds are developed for thegeneric buildings using the predicted drift demands and structural capacity values. In a more recentresearch building upon the work in [2], Liel [4] have conducted detailed assessments of collapserisk of RC moment frame buildings in high seismic zones, including both ‘ductile’ frames thatconform to current building code requirements in the US, and ‘non-ductile’ frames that are designedaccording to out-dated (pre-1975) building codes. The study presents a probabilistic assessmentof structural collapse risk through nonlinear response history simulation, which incorporates theuncertainties associated with ground motions and structural modeling.

The present paper is an additional effort along the same frontier looking into the seismicvulnerability assessment of RC moment-framed buildings but through an evaluation of the currentEgyptian seismic code provisions. Code-Compliant design (CCD) versions of RC ductile moment-resisting frame buildings (4- and 8-story, adopting perimeter- and space-frames configurations)are developed using ECP 201 [5] Force-Based Design (FBD) provisions. All case study momentframes are located in moderate seismic zones. Moderate seismic zones refer to sites with a designPGA, ag , of approximately 0.25g. As per [5], the design PGA pertains to seismic events with aprobability of exceedance of 10% in 50 years (or a return period of 475 years). Note that thisag =0.25g is among the highest values expected in Egypt, with only one other higher design PGA(0.3g) assigned to very local regions. Using the results of a series of nonlinear inelastic incrementaldynamic time-history analyses under a suite of 20 multi-level scaled records, fragility curves (FC)for the frames are developed. FC generated correspond to various code-specified performancelevels encompassing, for example, Immediate Occupancy (IO), Life Safety (LS) and CollapsePrevention (CP) as identified by ASCE 41-06 [6]. A Modified Code Design (MCD) procedurerelaxing design drift demands for the investigated buildings is then proposed for reasons that will bedemonstrated in the sequel and is further examined to test its effectiveness and reliability. Annualspectral acceleration hazard curves describing the seismic hazard in Egypt are also developedfor each case study frame and for each design technique (CCD versus MCD). Data from thesehazard curves are then integrated with data extracted from FC resulting in estimates—for eachcase study frame—of Mean Annual Frequency (MAF) of exceeding various code performancelevels identified above. These final integrated (i.e. modified by the hazard) probability values andtheir relative magnitudes are important to evaluate the trade-off between safety and reliability ofthe ‘as-designed’ frames at one side and their economy at the other side. This has been illustratedfor the CCD versus the proposed MCD procedure when applied to RC moment-framed buildingslocated in moderate seismic zones featuring a design PGA of approximately 0.25g.

2. OUTLINES AND SPECIFICS OF THE SEISMIC DESIGN PROCEDURES—ECP 201VERSUS OTHER CODES

The main design requirements specified in [5] are the ‘no-collapse’ and the ‘damage limitation’requirements. Satisfying the ‘no-collapse’ requirement depends not only on the strength of the

Copyright � 2010 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 2011; 40:215–235DOI: 10.1002/eqe

SEISMIC VULNERABILITY EVALUATION 217

designed elements to resist all expected stress resultants that occur due to seismic actions, butalso on providing adequate ductility capacity through strictly following all code’s relevant specialdetailing and other pertinent (ductility-related) design criteria. Design seismic actions correspondto the reference seismic hazard associated with a reference probability of exceedance of 10% in 50years (or a reference return period of 475 years). In a complementary step, and in line with EC8[7] regulations, the structure shall also be checked to withstand a seismic action having a largerprobability of occurrence (minor earthquake) than the design seismic action associated with the‘no-collapse’ requirement, without occurrence of damage to structural and non-structural elements.Such a seismic action is used to verify the ‘damage limitation’ requirement. It has a probability ofexceedance of 10% in 10 years (or a return period of 95 years) and is almost equal to half [5, 7] ofthe design seismic action for the ‘no-collapse’ limit state taking into account the important factorof the building. As per code, the ‘damage limitation’ requirement is satisfied if the interstory driftsare limited to a given fraction of the story height depending on the type and fixation form ofthe non-structural elements. The interstory drift associated with the design seismic action for the‘no-collapse’ limit state has thus to be first reduced to take into account the lower return period ofthe seismic action associated with the ‘damage limitation’ requirement. Implicit in the use of thisreduction is the assumption that the response spectrum of the seismic action for the ‘no-collapse’requirement has the same shape as the spectrum of the seismic action for ‘damage limitation’requirement (i.e. the latter is a scaled down replica of the former). For buildings investigated herein,this reduction factor, �, is taken equal to 2.0 [5, 7] and the interstory drift limit is set to 0.005 ofthe story height associated with non-structural elements of brittle materials that are attached to thestructure. On the other hand, in other similar seismic provisions commonly adopted worldwideespecially in the US practice (such as in [8–10]), the drift and strength checks are rather performedfor one same design level earthquake of 10% in 50 years (equivalent to two-thirds of the maximumconsidered earthquake (MCE) or two-thirds of the 2% in 50 years earthquake). The design drift istherefore checked versus a magnified interstory drift limit compatible with this 10% in 50 yearsevent level. The term ‘magnified’ is used in the previous statement to describe this limit with respectto the reduced interstory drift limiting value set in [5, 7] corresponding to the ‘damage limitation’requirement (i.e. corresponding to the minor/lower 10% in 10 years event). This magnified limitis roughly equal to the limit set by Eurocode (as a ratio of the story height) times the � factormentioned above. In other words, even though different codes apparently approach the same taskfrom different perspectives, they are basically more-or-less heading towards the same target.

Note that, furthermore, in order to avoid excessively low design acceleration values (and hencepotentially un-conservative designs) at medium to long periods that may arise from inaccuratemodeling of structures, and again similar to Eurocode directions in that concern, ECP 201 [5]is imposing a constant minimum design acceleration of 0.2ag . Such an enforced lower boundsometimes introduces too much conservatism into the design.

Two seismic design scenarios are performed in this paper on four case study buildings. Thebuildings consist of 4- and 8-story moment-framed ductile RC structures adopting either space orperimeter frames systems. The two seismic design procedures are depicted below:

CCD: It is a design procedure where (1) ‘no-collapse’—in terms of satisfying both strengthand ductility requirements of different structural elements considering second-order effects—and(2) ‘damage limitation’—in terms of satisfying code interstory drift limits under reduced hazard—requirements are jointly satisfied. ECP 201 Design Response Spectrum (DRS) modified by theresponse modification factor, R, as shown in Figure 1 and featuring the constant acceleration lowerbound of 0.2 ag is adopted.

MCD: It is a modified (more relaxed) seismic design procedure through ignoring the codepre-specified constant acceleration lower bound when checking drift demands. In other words,checking drift is carried out for a scaled down version of ECP 201 acceleration Elastic ResponseSpectrum (ERS) associated with 10% in 50 years hazard as shown in Figure 1 by directly dividingits ordinates by the R factor, as well as by a reduction factor of 2.0 accounting for the lowerreturn period (corresponding to a 10% in 10 years hazard) of the seismic action associated with thecode ‘damage limitation’ requirement, then magnifying it back by a displacement behavior factor,Rd , approximately equal to 0.7R as per [5]. This proposed step entirely discards any effect on



Figure 1. ECP 201 elastic and design acceleration response spectra.

seismic design drift demands that may arise from the lower bound of 0.2ag imposed on the designacceleration specified by code and reflected into the code DRS. A Modified Elastic ResponseSpectrum (MERS) used for checking drift developed in the context of this step is thus also shown inFigure 1 for comparison purposes. However, it is worth pointing that the ‘no-collapse’ requirementis still verified under the code acceleration DRS with the lower bound on the design acceleration.Note that this is not uncommon; the concept of not applying the minimum base shear used for strengthdesign to drift analysis has been already done in the US [8–10] for the past 20 years. MCD procedure,despite being a code non-compliant design procedure, is promoted herein since it provides potentiallyeconomic versions of the case study buildings yet without risking safety as will be demonstrated later.

In order to clarify the threshold behind initiating the proposed MCD procedure, it is worthnoting that both codes [5, 7] rely on linear analysis to estimate the actual expected displacement,ds , induced by the design seismic action at a given point within the structure through the followingsimplified expression:

ds = Rdde (1)

where de is the displacement of the same point as determined by a linear analysis based on theDRS; and Rd is a displacement behavior factor. Rd (or qd in [7]) is approximately assumed by theEurocode equal to R in line with the commonly recognized ‘Equal Displacement Rule (EDR)’,whereas ECP 201 is assigning to Rd a reduced value of 0.7R. The MCD procedure outlinedabove draws its threshold from the note spelled out in EC8 stating that ‘the value of ds does notneed to be larger than the value derived from the elastic spectrum’. The fundamental role of thisnote—missing out in [5]—for buildings with relatively medium to long periods is to avoid theeffect of the 0.2ag lower bound enforced in the code acceleration DRS that produces increasinglylarger (and erratic) spectral displacements when compared with the case of simply adopting theERS. Such unboundedly increasing displacements are physically not possible [11]. Among themajor objectives of this paper is therefore to assess the effect that the proposed MCD procedure(or, more simply such upper bound note stated in EC8 regarding drift estimation) may have onthe reliability/safety versus economy of ductile RC moment frames of either the space or theperimeter type when located in moderate seismic zones.

To conclude on seismic design parameters adopted herein, it is worth noting that ECP 201 [5] ismore liberal than EC8 [7] in selecting the R factor that is set to a value of 7 in the former for ductileRC moment frames. EC8 assumes instead a value of 5.85 for the behavior, q , factor (equivalentto R factor in [5]). This value of 5.85 is calculated for a multi-story multi-bay moment-resistingframe system pertaining to the high ductility class (DCH) as per the terminology used in [7]. Onanother issue, the notion for reducing the displacement factor, Rd , as adopted in [5]—and thus notfollowing the EDR—is likewise followed by other world-widely recognized seismic provisionsand standards such as [8–10]. These latter documents set this factor equals to approximately0.69(= [Cd =5.5]/[R =8]) times R for RC special (i.e. ductile) moment-resisting frames. Although



ECP 201 [5] draws most of its background from EC8 [7], it may nevertheless have set Rd =0.7R(and thus literally violating the EDR adopted in EC8 provisions) to counter-account for the largervalue of R =7 assigned a priori in [5] for the design of ductile RC moment frames. However, ina separate study conducted by the authors, it has been recommended to modify ECP 201 seismicregulations to always adopt the EDR (i.e. Rd = R) for better estimation of the inelastic displacementdemands relying on the elastic demands.

It is further important to state that the MCD procedure promoted herein is a modification—ina performance-based seismic design format—to the FBD method proposed in [5] in line with thewell-perceived seismic design provisions in [7]. This is in order to achieve more economic, yetwith reliable performance, structures (especially medium- to long-period moment frames) underdifferent seismic hazard levels corresponding to various preset code performance levels. The overallprocedure developed and illustrated herein is therefore not originally intended to provide a generaland conclusive methodology similar to that given in [1] for either (a) setting minimum acceptabledesign criteria and response parameters for standard code-approved seismic-force-resisting systemsor (b) providing a basis for the evaluation of current code-approved systems for their ability toachieve intended seismic performance objectives. This may have been however a bi-product of theproposed procedure as will be demonstrated in the sequel.

3. CASE STUDY BUILDINGS DESIGN AND ANALYTICAL MODELS

The case study building is developed according to the general layout of a theme structure proposedfor this research work [12]. It is designed as a 4- and 8-story building in moderate seismic region(0.25g) according to appropriate portions of relevant codes and standards [5, 13]. RC ductile-framed designs are developed first employing a space frame configuration, where the lateral systemconsists of five similar moment frames in each direction. Another framed design is then developedusing a perimeter frame approach as common, for example, in the US practice [14] where onlyperimeter frames constitute the lateral load-resisting system.

A typical floor height of 3 m is adopted, whereas the ground floor is 5-m high. Building’slayout is essentially bi-symmetric in plan, square in shape with a typical bay width of 6 m inboth directions, and is a representative of benchmark typical office buildings in current practicein Egypt. For gravity load design, dead loads include the self weight of the structure, a typicalfloor cover of 1.5kN/m2 and partition (wall) loads intensity of 1.5kN/m3 including plasteringand assuming typical walls thickness of 250 mm. A live load of 5.0kN/m2 is also considered. Onthe other hand, for seismic design purposes, a total seismic mass including self weight and floorcover plus 50% of live load is considered. The seismic design has been carried out assuming animportant factor of 1.0 and a seismic zone 5 (as per Egyptian zoning system) with a design PGA,ag , of 0.25g associated with the code reference probability of exceedance of 10% in 50 years.Acceleration ERS type 1 is adopted as per [5]—known as type 2 in [7]—and is shown in Figure1 for the case study buildings. For comparison purposes, also shown in Figure 1 is the code DRSused for elastic analysis of the buildings after introducing the lateral force reduction factor R of 7.

A solid slab is used at all floors with a designed constant thickness of 140 mm. All columnsand beams dimensions and reinforcement are as shown in Tables I and II. Reinforcing steelused has a minimum guaranteed (i.e. nominal) yield strength of 360 MPa, and concrete has aminimum specified cube characteristic strength in compression of 30 MPa. For design purposesusing FBD methodology and linear elastic analysis, cracked members properties are adopted asper recommendations in ECP 201; 70% of the gross inertia is used for columns whereas 50%of the gross inertia is used for beams. Furthermore, the current trial designs have considered thefirst interior frame in the Space Frame Building (SFB) configuration (i.e. the one adjacent tothe edge frame) believed to be the vulnerable frame of interest worth to be studied when only atwo-dimensional analysis of a single representative ‘critical’ frame is sought for this SFB. As aresult, and as per the recommendations in [5] (similar to requirements set in [7]) for the design forminimum accidental eccentricity, the design base shear for this selected frame has been increasedby 15%, whereas the design base shear for the perimeter frame in the Perimeter Frame Building



Table I. Sizes and reinforcement of structural members of CCD case study moment frames∗.

Outer columns Inner columns Beams

Building Size Size Sizetype Story # (mm) Reinf. Story # (mm) Reinf. Story # (mm) Reinf.

4S-PFB 1–4 600×600 12�20 1–2 400×1100 7�20 1–4 300×1000 4�253–4 400×1000 6�20

4S-SFB 1–4 400×400 12�16 1–2 700×700 16�20 1–4 250×800 4�203–4 600×600 12�20

8S-PFB 1–8 500×500 12�16 1–3 500×1500 8�25 1–4 300×1100 6�254–6 500×1400 7�25 5–8 250×900 6�207–8 400×1300 5�25

8S-SFB 1–8 500×500 12�16 1–3 800×800 20�20 1–4 250×1000 5�204–6 700×700 16�20 5–8 250×900 4�207–8 600×600 12�20

∗Reinforcement shown in Tables for all columns with a square cross section represents the total number ofre-bars to be distributed equally along the four sides, while that for columns with a rectangular cross sectionrepresents the number of main re-bars per each of the two opposite shorter sides of the cross section, i.e. inthe direction resisting the bending moment in the frame direction; additional secondary re-bars are placedalong the longer sides. Reinforcement given for beams represents the number of re-bars used per each side(top and bottom) of the beam’s cross section. Beams have symmetric reinforcement to accommodate expectedreversible bending moments during seismic events.

Table II. Sizes and reinforcement of structural members of MCD case study moment frames∗.

Outer columns Inner columns Beams

Building Size Size Sizetype Story # (mm) Reinf. Story # (mm) Reinf. Story # (mm) Reinf.

4S-PFB 1–4 600×600 12�20 1–2 400×900 6�20 1–4 300×900 7�203–4 400×800 6�20

4S-SFB A replica of the 4S-CCD-SFB moment resisting frame8S-PFB 1–8 500×500 12�16 1–3 400×1100 8�20 1–4 300×1000 8�20

4–6 300×900 7�16 5–8 250×700 7�207–8 300×600 5�16

8S-SFB 1–8 500×500 12�16 1–3 800×800 24�20 1–4 250×800 7�204–6 600×600 16�20 5–8 250×700 6�207–8 400×400 12�16

∗Reinforcement shown in Tables for all columns with a square cross section represents the total number ofre-bars to be distributed equally along the fou sides, while that for columns with a rectangular cross sectionrepresents the number of main re-bars per each of the two opposite shorter sides of the cross section, i.e. inthe direction resisting the bending moment in the frame direction; additional secondary re-bars are placedalong the longer sides. Reinforcement given for beams represents the number of re-bars used per each side(top and bottom) of the beam’s cross section. Beams have symmetric reinforcement to accommodate expectedreversible bending moments during seismic events.

(PFB) configuration also investigated in this research has been increased by 30%. Such a factorwill add to the intrinsic (actual) static overstrength of the various moment frames considered hereinbut with different magnitudes and effects thereof as will be highlighted in the sequel.

Detailing requirements for ductile RC moment frames in Egypt as per [5, 13] are in line with (andmore-or-less similar to) EC8 [7] requirements in what concerns (1) minimum and maximum valuesof longitudinal reinforcement ratio; (2) confinement reinforcement and (3) stirrups shapes, detailsand spacing in columns, beams and connections. In addition, seismic provisions in [13] related toductile RC moment frames, and again similar to [7], have set explicit requirements to determinemaximum design values for shear in beams and columns in accordance with a capacity design



Table III. Period and associated modal mass ratio for fundamental and second mode of vibration for casestudy moment frames from modal analysis.

Fundamental mode of vibration Second mode of vibration

Building type Period (s) Modal mass ratio (%) Period (s) Modal mass ratio (%)

Moment Frames as per CCD Procedure4S-CCD-PFB 1.01 92.9 0.31 5.84S-CCD-SFB 0.83 92.9 0.24 5.98S-CCD-PFB 1.52 81.2 0.54 12.98S-CCD-SFB 1.37 86.9 0.49 9.4

Moment Frames as per MCD Procedure4S-MCD-PFB 1.22 93.5 0.38 5.44S-MCD-SFB 0.83 92.9 0.24 5.98S-MCD-PFB 2.01 80.6 0.80 14.68S-MCD-SFB 1.65 82.6 0.63 11.2

rule corresponding to a preset plastic hinge formation. On the other hand, the strong column–weakbeam factor in ECP 201/203 [5, 13] is however less stringent than its equivalent in EC8 (a valueof 1.2 is required in the former instead of 1.3 in the latter).

All designed case study moment frames satisfy the minimum strength, ductility, stiffness (drift)and strong column–weak beam requirements specified in [5, 13]. Members’ (columns and beams)sizes in both CCD and MCD procedures were controlled nearly exclusively by drift requirements,whereas only the design of the 4-story SFB frame has been marginally controlled by the strengthrequirements under gravity loads fundamental ultimate combination. This resulted in having the4-story MCD SFB frame a replica of the 4-story CCD SFB frame. Calculated fundamental periodof vibration (and second lateral mode period) along with the associated modal mass ratios relativeto the total considered seismic mass for all case study frames are given in Table III for both CCDand MCD procedures for future relevance in the seismic assessment study.

In order to perform inelastic nonlinear static pushover and dynamic time-history analyses,computer models of the ‘as-designed’ buildings are required. The structural analysis platformOPENSEES (Ver. 1.7.0) [15] is used to determine structural response of the case study moment-resisting frames. Among the main features of the analytical models adopted in this research are(1) the use of nominal (minimum specified) material property values rather than expected ones;(2) confined concrete response as per the uni-axial Kent–Scott–Park model with degraded linearunloading/reloading stiffness according to the early work of Karsan and Jirsa [16] with no tensilestrength, and using confined concrete parameters as illustrated in [17]; (3) steel reinforcementuni-axial bilinear material model with kinematic strain hardening; and (4) hysteretic behavior in theform of distributed plasticity integrated along the length of two-dimensional beam–column elementsusing a fiber-element model available in OPENSEES library that does not capture strain-softeningassociated with re-bar buckling. Beam–column element with a displacement-based formulation isadopted to model both beams and columns of the two-dimensional moment-resisting frames studiedherein. P-� (i.e. second-order geometric) transformation is activated. Rayleigh mass and stiffnessproportional damping is also adopted. A damping ratio of 5% has been assigned to the first twomodes of vibration for all case study frames. A dummy column (commonly known by a ‘leaningcolumn’) is introduced in all PFB frames to account for p–� effects from the tributary gravityloads carried by the non-seismically designed interior ‘gravity-only’ columns in this buildingconfiguration. For more data related to these issues, the reader may be referred to [12].

4. SELECTED GROUND MOTION RECORDS AND ANNUAL SPECTRALACCELERATION HAZARD CURVES

A bin of 20 ground motions is selected for the seismic evaluation study presented in this paper.The 20 records pertain to the large database of records gathered in [18] and are originally extracted



from the Pacific Earthquake Engineering Center (PEER) Strong Motion Database (PEER StrongMotion Catalog). The ground motions represented by the records are characteristic of non-near-fault motions recorded in California. They all have magnitudes Mw less than 6.5 and have beenidentified by the PEER database as Small Magnitude (SM) records. Furthermore, the selectedrecords considered herein feature a distance R to the fault that is larger than 30 km, and are hencerecognized by the PEER database as Large Distance (LR) records. In brief, this bin of records hasbeen referred to by the PEER as a Small Magnitude Large Distance (SMLR) bin. All 20 groundmotions were recorded on NEHRP soil types C or D (stiff soil or soft rock) sites. These records wereextensively used in several earlier studies related to building structures [18, 19] as well as to bridges[20]. For specific details of the records including earthquake names, sensor location, magnitude,distance, soil type, faulting mechanism and peak waveform ordinates, one may be referred to [18].

On the other hand, the seismic hazard is generally characterized by one of two ways: either (1)through an explicit probabilistic seismic hazard analysis of a particular site or simply (2) usingspectral acceleration hazard maps or hazard information from building code provisions [21]. Thesecond (simplified) alternative to obtain the hazard curve is followed in this research. It is inferredfrom reported spectral and site coefficients provided by the seismic design provisions of ECP 201[5] and a relevant seismic hazard document prepared for a performance-based design frameworkfor LNG Damietta project in Egypt [22]. A spectral acceleration hazard curve—to be used in thisresearch—of the form given by

HSa(Sa′)= P[Sa>Sa′]=koSa−k (2)

is obtained simply by fitting a line (in log–log scale) to the points defined by two pre-determinedannual exceedance probabilities and the corresponding spectral accelerations. Note that −k is aconstant for a given site with a given seismology, irrespective of the dynamic characteristics ofthe structure; ko is on the other hand a constant that is structure-specific and is depending on Saat T 1 of a given structure, where T 1 is the fundamental period of vibration of the structure; andHSa thus gives the probability of exceeding a given Sa(T 1) at a particular site of interest. Oneof the two points used to develop the hazard curve is simply extracted from the ERS providedin [5] corresponding to an event with 10% probability of exceedance in 50 years (i.e. having areturn period of 475 years corresponding to no-collapse limitation as per [5] terminology, or tothe design level earthquake as per [8] terminology). The second point is determined as the onecorresponding to an event with a return period of 10 000 years (i.e. having approximately 1%probability of exceedance in 100 years). This point is associated with a so-called Safe ShutdownEarthquake set in the seismic hazard report mentioned above [22]. Once the hazard curve is fullydefined using the form given by Equation (2) along with the two Sa values (10% in 50 yearsand 1% in 100 years), Sa corresponding to any other exceedance probability (for instance, 2% in50 years referred to in [8] as the MCE) could be easily determined. The 2% in 50 years earthquake(with a 2475-year return period) is the one included in the hazard maps of [8] for sites in the USand roughly corresponds to the near-collapse performance level.

Relying on the fact that the ratio between any two Sa values corresponding to any two differentexceedance probabilities is always constant, the log–log slope of the spectral acceleration hazardcurve, −k, is determined to be −2.77 for all case study frames located in Egypt. However, the otherconstant ko takes different values depending on Sa(T 1) for each structure of interest. A hazardcurve for each of the 4 CCD frames investigated herein is developed and is shown in Figure 2.Also given in the same figure are different hazard levels of interest for the current study. Hazardcurves for the MCD versions of the case study frames are likewise developed [12] but are notprovided herein for space limitations. It is worth mentioning that similar hazard curves have beenlikewise generated but for actual long span bridges crossing the river Nile in Egypt in a previousprobabilistic seismic assessment study [23].

A final point to highlight is that, referring to Figure 2, the highest spectral acceleration annualhazard is for the 4S-CCD-SFB frame having the highest—among all investigated frames—Sa(T 1)associated with the particular code design hazard level of 10% in 50 years as a result of its lowestfundamental period T 1 of 0.83 s (Table III). Conversely, the lowest spectral acceleration annual



0.000001

0.00001

0.0001

0.001

0.01

0.1

1

0.0 0.4 0.8 1.2 1.6 2.0

Sa (T1) [g]

HSa

(Sa'

) =

P[S

a>Sa

'] 4S-CCD-PFB

4S-CCD-SFB

8S-CCD-PFB

8S-CCD-SFB

10%in10yrs

10%in50yrs

2%in50yrs

Figure 2. Annual spectral acceleration hazard curves for CCD frames (5% damping).

hazard is scored for the 8S-CCD-PFB frame having the lowest Sa(T 1) associated with the samehazard of 10% in 50 years as a result of its highest T 1 of 1.52 s (Table III).

5. STATIC INELASTIC PUSHOVER ANALYSIS

Displacement-controlled inelastic pushover analyses with geometric nonlinearity (P–� effects) areconducted on two-dimensional base line models for the case study frames using OPENSEES [15].Pushover analysis consists of first applying the distributed gravity load (full dead loads and 50%of the design live load) to the structure and then applying incremental displacements to the top ofthe frame with a given pre-specified distribution as per [5] at different floor levels until reaching agiven target displacement. Note that for the frames of the PFBs, a leaning column as introducedabove is modeled in the 2D pushover analysis to account for the interior gravity columns of thePFB that are not part of the lateral load-resisting system. The percentage of the design base shearfor each of the case study frames is plotted versus the Roof Drift Ratio defined as the lateraldrift at the top of the frame divided by the frame total height. The maximum value scored bythis percentage simply defines the so-called static actual built-in overstrength, �o, for each frameas designed. Figure 3(a) gives this relationship for 4- and 8-story SFB and PFB frames designedaccording to the CCD approach. Figure 3(b) shows the same relationship for the four MCD casestudy frames for comparison purposes. A summary of �o values for all case study frames is givenin Table IV.

As a result of having same design base shear for strength calculations in both CCD and MCDprocedures in conjunction with the adoption of larger cross sections for the CCD frames to satisfyrestrictive code interstory drift requirements as previously mentioned, the MCD approach usuallyyields more flexible (and further less strong) frames than these developed using the CCD approach.It may be also generally observed that the actual intrinsic static overstrength, �o, for space framesis usually larger than that for perimeter frames as expected by intuition. This is mainly due togravity load design dominance for the former thus increasing their lateral resistance. Moreover,the significant influence of considerable gravity loads mobilizing more detrimental P–� effectsfor the case of the perimeter frames (captured through the leaning column technique) results in aconsiderable loss in their lateral capacity relative to the space frames of same height. This is aswell a proof of the strength dominance in the design, and hence in the lateral capacity, of the spaceframes compared with the perimeter frames for which drift requirements are more importantlycontrolling the seismic lateral design. Furthermore, it has been noted that when following theproposed MCD procedure, �o, of the 8-story PFB largely decreased from 1.88 to 1.16 due to thereduced cross-sections dimensions, and thereafter the magnified detrimental effects of the P–�phenomenon. However, on the other hand, �o for 8S-SFB remains almost constant for both CCDand MCD approaches (refer to Table IV). Such an observation shows the relatively lower P–�



0

50

100

150

200

250

300

350

0.000 0.005 0.010 0.015 0.020Roof Drift Ratio, RDR

% D

esig

n B

ase

Shea

r

4S-CCD-PFB 4S-CCD-SFB

8S-CCD-PFB 8S-CCD-SFB

0

50

100

150

200

250

300

350

0.000 0.005 0.010 0.015 0.020Roof Drift Ratio, RDR

% D

esig

n B

ase

Shea

r

4S-MCD-PFB 4S-MCD-SFB

8S-MCD-PFB 8S-MCD-SFB

(a) (b)

Figure 3. Static inelastic displacement-controlled pushover analysis results for case study frames: (a) CCDFrames and (b) MCD Frames.

Table IV. Summary of pushover analysis results for static built-in overstrength factors.

Building type �o �T �∗o =�o ×�T

Moment Frames as per CCD Procedure4S-CCD-PFB 2.54 1.30 3.304S-CCD-SFB 3.28 1.15 3.778S-CCD-PFB 1.88 1.30 2.448S-CCD-SFB 2.29 1.15 2.63

Moment Frames as per MCD Procedure4S-MCD-PFB 1.93 1.30 2.514S-MCD-SFB 3.28 1.15 3.778S-MCD-PFB 1.16 1.30 1.518S-MCD-SFB 2.30 1.15 2.65

effects on the lateral capacity of the SFBs compared with the PFBs for these mid-rise RC framesdesigned for moderate seismic regions, and further reinforces the fact that such a proposed relaxeddesign technique (MCD) does not penalize the built-in overstrength (i.e. the strength reserve) forthe SFBs. On the other hand, as shown in Table IV, the inherent static overstrength remarkablyincreases with the decreasing number of stories for the space frame construction when followingthe same design procedure (i.e. either CCD or MCD), while it increases less sharply for perimeterframes. This observation is justified since it could be again directly related to the decrease in therole of the P–� effects for low-rise buildings along with the gravity dominance in design relative tolateral drift demands. It is finally worth keeping in mind that the design of almost all frames (except4S-CCD- and MCD-SFB) is controlled by drift limitations and not by strength requirements. It isalso important to report that occasionally unexpected differences in response could be attributedto human factor involving some minor changes in design decisions made throughout the designprocess. An additional point that could be of some importance to justify many of the resultspresented herein is that the ratio of gravity to lateral tributary area for the space frame in anSFB is 1.0, whereas this ratio is much smaller (=0.25) for the perimeter frame in a PFB. In thelatter configuration, the gravity load of half of the building is in addition mobilizing P–� effectsplacing extra demands on this perimeter frame (captured through the leaning column technique).The current study nonetheless ignores including the intrinsic stiffness and lateral strength of thegravity-only frames in the analysis of investigated PFBs, and hence ignores their expected beneficialcontribution to the lateral load resistance and collapse capacity of these buildings.

Generally speaking, the results of pushover analyses presented in this paper reflect the followingsources of overstrength: (1) minimum stiffness (drift) criteria, (2) structural redundancy, (3) strong



column–weak beam criterion, among other sources commonly identified in the literature andrecognized by seismic provisions worldwide. In addition to reported �o values in Table IV, there isan inherent overstrength factor included in the design base shear calculation in this research. Thisfactor is attributed to the accidental torsion specified by the code as has been previously pointed outin the literature [24]. Accordingly, the actual overstrength of the frames is higher than the values,�o, previously presented. Updated (i.e. adjusted) overstrength value, �∗

o, for each case study frameis determined as the product of �o and �T and is also presented in Table IV. �T simply refersto the additional overstrength introduced by the accidental torsion. This updated �∗

o is the actualoverstrength and is the one affecting the response since all assessment static pushover and timehistory analyses herein are based on a 2D configuration (with no torsional effects). Note that �Ttakes different values for SFBs and PFBs since, in the current research, the first interior frame isthe one considered for the former, whereas the perimeter frame is the one investigated for the latteras mentioned earlier. This will further contribute to the final conclusions made in this research.

6. INCREMENTAL DYNAMIC ANALYSIS, TARGET PERFORMANCE LEVELSAND FRAGILITY CURVES

Seismic performance is further assessed through nonlinear time history analyses using the set of 20SMLR ground acceleration records presented above. For multi-level seismic hazard analyses, it isassumed that the acceleration component of the records can be linearly scaled based on the spectralacceleration computed at the fundamental period of the structure, Sa(T 1). Shome and Cornell [25]have demonstrated that, compared with other approaches, scaling based on Sa(T 1) will reducethe record-to-record dispersion in the response data and will not bias the results especially whenthe response of interest is the Interstory Drift Ratio, IDR. The spectral accelerations of the scaledearthquake records, Sa(T 1), can be related to the maximum IDR, IDRMAX, depicting the peakresponse from corresponding time-history analyses providing what is referred to in the literatureas Incremented Dynamic Analysis (IDA) curves [26]. To summarize, IDA is a parametric analysismethod that involves subjecting a structural model to one (or more) ground motion records, eachscaled to multiple levels of intensity, thus providing one (or more) curves of response (e.g. IDRMAX)parameterized versus intensity level (Sa(T 1) herein).

FC constitute a representation of the relationship between (a) the probability of a set of Perfor-mance Levels (PL), or limit states, being reached or exceeded at a prescribed system demand and(b) the system demand itself. For a conventional performance-based seismic analysis, the systemdemands are typically represented by (or, are corresponding to) various ground motion severi-ties or Intensity Measures (IM). A recently promoted efficient IM is typically represented by thespectral acceleration at the fundamental period of the structure, Sa(T 1) as previously highlighted.On the other hand, the structural performance limit states of interest can vary from IO, to LS,to CP as per ASCE 41-06 [6] definitions, and even up to complete failure of the structure. PLsare generally represented in the literature by a given Engineering Demand Parameter (EDP) orDamage Measure (DM). The DM adopted in the current study is a semi-global measure givenby IDRMAX. The fragility function is basically thus giving the probability that a particular PL isexceeded (reflected by recorded IDRMAX exceeding a pre-specified IDRTARGET set by specializedseismic provisions as will be clarified in the sequel) conditioned on Sa(T 1) (simply referred toby P[IDRMAX�IDRTARGET|Sa(T 1)]). Characterized by a lognormal distribution, FC developedin this paper represent a cumulative distribution function defined by the median IM correspondingto exceeding a given PL, Sa(T 1), and the dispersion given by the standard deviation of the naturallog, � (lnSa(T 1)), both of which are obtained from IDA data. In brief, FCs in this research arebased on the two-parameter lognormal distribution function to get an S-shape curve. This approachwas used by several researchers in the literature, e.g. [19, 27] and proved to give precise results.

Qualitative structural performance levels: IO, LS and CP mentioned above are reported in ASCE41-06 [6]. For RC frame structures, ASCE 41-06 recommendations further give a quantitativeformat for these PLs through assigning to them deterministic interstory drift limits of 1, 2 and 4%



of the story height for IO, LS and CP performance levels, respectively. Although these suggestedlimits are approximate, they are deemed fairly reasonable for buildings designed for seismicloading [3]. For the sake of the current study of low- to mid-rise ductile RC moment-resistingframes located in moderate seismic zones, it is practically adequate to further assume that checkingconformity with IO performance level corresponding to IDRMAX =0.01 could be associated withthe 10% in 10 years hazard of ECP 201[5] and EC8 [7]. Similarly, the 10% in 50 years (i.e. thedesign level earthquake as set by most seismic codes worldwide) and the 2% in 50 years eventscould hence represent the hazard associated with LS and CP performance levels correspondingto IDRMAX =0.02 and 0.04, respectively [24]. However, as per [2], an IDRMAX =0.04 could begenerally considered a conservative assumption/limit for CP performance level for the case studyductile frames.

Figure 4 shows samples of developed FCs for 8-story SFB and PFB frames designed accordingto both CCD and MCD approaches for various PLs introduced above. For similar data related tothe 4-story case study frames—not given herein due to space limitations—one could refer to [12].Note that the values of the horizontal axis of the FCs given in Figure 4 are normalized by thespectral acceleration referring to the 2% in 50 years hazard at the fundamental period T 1 of eachframe. As such, values in the different presented FCs could be compared across various investigatedbuildings with different periods. Moreover, the median of this normalized value (or, dimensionlessratio) provides directly an estimate for the margin against satisfying the CP performance level(corresponding to an IDR=0.04) as listed in the last column of Table V.

The smaller (i.e. milder) slopes of FCs depict more uncertainty in the system. From Figure 4,it could be thus easily observed that there is much more uncertainty associated with CP limit

0.0

0.2

0.4

0.6

0.8

1.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

Normalized IM, Sa(T1)/Sa(2in50)(T1)

IDR = 0.01 (IO)

IDR = 0.02 (LS)

IDR = 0.03

IDR = 0.04 (CP)

0.0

0.2

0.4

0.6

0.8

1.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0


P [

IDR

MA

X ≥

ID

RT

AR

GE

T |S

a]

IDR = 0.01 (IO)

IDR = 0.02 (LS)

IDR = 0.03

IDR = 0.04 (CP)

0.0

0.2

0.4

0.6

0.8

1.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0


IDR = 0.01 (IO)

IDR = 0.02 (LS)

IDR = 0.03

IDR = 0.04 (CP)

0.0

0.2

0.4

0.6

0.8

1.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

Normalized IM, Sa(T1)/S (T1)a(2in50)

IDR = 0.01 (IO)

IDR = 0.02 (LS)

IDR = 0.03

IDR = 0.04 (CP)

(a) (b)

(c) (d)

Figure 4. Fragility curves for investigated 8-story CCD- and MCD-PFB and SFB frames: (a) 8S-CCD-PFBframe; (b) 8S-CCD-SFB frame; (c) 8S-MCD-PFB frame; and (d) 8S-MCD-SFB frame.



Tabl

eV

.Su

mm

ary

ofSa

(PL

)/Sa

(haz

ard)

ratio

sfo

rca

sest

udy

fram

esfo

rva

riou

spe

rfor

man

cele

vels

.

IOPe

rfor

man

ceL

evel

LS

Perf

orm

ance

Lev

elC

PPe

rfor

man

ceL

evel

Bui

ldin

gty

peSa

(10%

in10

)(g

)Sa

(IO

)Sa

(10%

in10

)Sa

(10%

in50

)(g

)Sa

(LS)

Sa(1

0%in

50)

Sa(2

%in

50)

(g)

Sa(C

P)Sa

(2%

in50

)

Mom

ent

Fra

mes

aspe

rC

CD

Pro

cedu

re4S

-CC

D-P

FB0.

118

2.97

0.21

12.

840.

383

3.13

4S-C

CD

-SFB

0.14

12.

840.

252

2.98

0.45

72.

848S

-CC

D-P

FB0.

077

1.95

0.13

72.

920.

249

3.41

8S-C

CD

-SFB

0.08

23.

050.

147

3.06

0.26

73.

45

Mom

ent

Fra

mes

aspe

rM

CD

Pro

cedu

re4S

-MC

D-P

FB0.

097

2.49

0.17

32.

770.

314

3.12

4S-M

CD

-SFB

0.14

12.

700.

252

2.98

0.45

72.

848S

-MC

D-P

FB0.

059

1.19

0.10

51.

140.

191

1.15

8S-M

CD

-SFB

0.06

92.

310.

123

2.44

0.22

32.

29



state, as expected, followed by LS performance level, and then finally by IO reporting the leastuncertainty. Moreover, it is obvious from Figure 4 that MCD frames are more vulnerable todamage than their corresponding CCD frames at a given IM reflected by a particular Sa(T1),especially at severe PLs such as CP; and similarly, PFB frames are more prone to damage thantheir equivalent SFB frames for either CCD or MCD approaches. One should however note thatFCs of the type shown in Figure 4 only reflect (and consider) record-to-record variability and donot account for modeling (epistemic) uncertainties and other aspects of the ground motions suchas consideration of the spectral shape (ε parameter) first introduced in [28]. Owing to the lack ofa large data base of recorded ground motions in Egypt, the ε parameter, although important, is notconsidered in the current investigation. FCs accounting for these additional sources of uncertaintieshave been developed in the literature by different researchers either for RC ductile and ordinarymoment frames [2, 4] or for actively and passively controlled structures composed of Steel ductilemoment-resisting frames [29]. These studies concluded the importance of the inclusion of suchuncertainty sources for an accurate performance prediction of structures located in high seismiczones. Not accounting for modeling uncertainties in the fragility analysis in the current research isamong the adopted assumptions and may be accepted as a traditional approximation. Moreover,considering capacity and modeling uncertainties in the FCs only changes the slope of the curvewhile its center (i.e. the median Sa(T 1) corresponding to P[PL|Sa(T 1)]=0.5) remains unalteredas per [29]. This is basically relying on the classic first-order assumption identified in [30] whichmay be customarily considered a valid approximation. It is finally also worth pointing that theapproximation arising from not considering such epistemic uncertainties would be definitely lesscritical for limit states related to IO and LS performance levels (especially for moderate seismiczones) than for CP performance level.

6.1. Margins against satisfying various code expected performance levels

For this section of the paper, two previously highlighted hazards are considered. A brief importantdescription of these two hazard levels is presented below, whereas Table V reports the actualnumbers depicting these hazard levels in terms of Sa(T 1). Sa(T 1) will be referred to from now onby Sa for brevity. The first hazard level is Sa(10% in 50 years) that is specified by ECP 201 [5] andother similar worldwide building codes seismic provisions as the design-basis earthquake in whichthe performance objectives for a given building are limited to structural damage (i.e. LS). The valueof Sa(10% in 50 years) is directly extracted from ERS in Figure 1 (or alternatively from the hazardcurves in Figure 2) for each case study frame. On the other hand, the second hazard level of interest isSa(2% in 50 years) as specified in US seismic provisions (e.g. [8]) referring to the MCE in which theperformance objectives for a building are near collapse (or in brief, the associated implied behavioris that the structure will maintain CP for this 2% in 50 years hazard). Values of Sa(2% in 50 years)are similarly derived for case study frames from the annual hazard curves in Figure 2. Relying oninformation provided by IDA results and generated FCs, median Sa (LS) values corresponding toIDRMAX reaching or exceeding IDRTARGET =0.02, as well as median Sa (CP) values correspondingto IDRMAX reaching or exceeding IDRTARGET =0.04, may be easily determined. For completeness,Sa (IO) values that could be related to IDRTARGET =0.01 (and hence associated with a 10% in10 years hazard) could also be retrieved, although relating this IO performance level to a specificearthquake hazard and to a particular IDRTARGET is not as apparent as LS and CP levels. Toexamine the implications of these data on the safety/reliability of trial designs developed in thisresearch, three limit state ratios are reported in Table V comparing Sa (IO,) Sa (LS), and Sa(CP) to the hazard accelerations Sa(10% in 10), Sa(10% in 50), and Sa(2% in 50), respectively.Presented margins against satisfying IO performance level may however reveal some degree ofapproximation due to not fitting Equation (2) explicitly around the 10% in 10 years hazard level.

Note that the Sa (PL)/Sa(hazard) ratios simply furnish margins against satisfying various codeexpected performance levels associated with different hazards of interest. These ratios fairly exceed1.0 for all frames which indicates that all case study frames perform well in excess of codeexpectations at the various PLs investigated herein. One should realize that a lower value for this



ratio (or for this margin) for any particular frame at one PL relative to the other (e.g. LS versus CP)indicates that this PL governs the design of the frame. A general note worthy point is that referringto Table V, all case study frames (irrespective of the height, frame type or design procedure)feature almost consistent value of that margin at the three PLs of interest, except for one or twoframes. Such an exception even only occurs for the IO performance level whereas the consistencyin that margin still holds for the other two (LS and CP) levels. Such observation points to a certainhomogeneity and uniformity preserved by the code seismic design procedure as well as by theMCD procedure proposed in this paper. Moreover, relying on such more-or-less uniformity in thesereported margin values, one could further draw some global conclusions based on average values ofthese margins calculated for the three considered performance levels (IO, LS and CP) for each casestudy frame. One could then notice that the lowest average margin is scored for the 8S-MCD-PFB(1.16); whereas it was on average 2.76 for the same frame in the CCD procedure (i.e. roughly 2.4times larger). This reflects the effect of the significant reduction in the concrete dimensions due tothe MCD procedure, and hence the magnified detrimental P–� effects. Enforcing ECP 201 currentrestrictive limitations on design interstory drifts (by imposing the 0.2ag lower bound to the codeDRS while checking drifts in the design procedure, whereas ignoring the upper bound on ds similarto that set in EC8 [7] and explained in Section 2) will apparently resolve this issue and restore alarger margin, but this is not the correct approach. It has been previously demonstrated [11] that sucha lower bound on acceleration in the absence of the upper bound on ds results in unrealistic spectraldisplacement values for medium to long period structures. Furthermore, these displacements seemeven unbounded with the increase of the period of vibration which is physically impossible.Therefore, it is still beneficial to follow the proposed MCD procedure but performing alternativelythe design considering, a priori, lower R values. Such a step is recommended in order to guaranteea reasonably larger margin of safety against exceeding code LS and CP performance levels forthese mid-rise perimeter-framed buildings. On the other hand, other case study frames (4-storySFB and PFB buildings and 8-story SFB buildings) reveal that following the MCD procedure withcode-specified R value of 7 is still a good option that keeps a more economic design than theCCD procedure yet with an adequate margin of safety against exceeding different code limitingperformance levels. Determining suitable lower R values that work well with the MCD procedure,especially for mid-rise (i.e. somehow long period) moment-framed buildings, is part of an ongoingresearch by the authors. It is however important to acknowledge in the presented research theimportance of such needed reduced R values to be compatible with the proposed MCD procedurefor designing structures with reliable performance at different limit states (or performance levels).Other additional options to improve the MCD procedure are also currently under scrutiny. Amongthem are (1) enhancement of P-Delta design criteria through generating adequate (and efficient)P-Delta factors to be considered in the design phase in line with the MCD technique presentedherein and (2) investigating more suitable design values for strong column–weak beam criterion.It is also worth mentioning the current effort in the US [1, 31] aiming at determining period-dependent R-factors (as also equally implied by the results presented in the current investigation)to be included in future versions of seismic design codes.

Moreover, it may be noted from Table V that Sa (PL)/Sa(hazard) ratios associated with LSand CP performance levels remain practically unaltered for the studied 4-story frames (either SFBor PFB) irrespective of the adopted design method (CCD or MCD). This is loosely a proof thatlow-rise structures are less prone to damage that may result from detrimental P–� effects.

Nonetheless, it is important to highlight that (1) the adoption of only rectangular sections alongall beams in the current computer models of the investigated frames when performing inelasticpushover and dynamic analyses rather than L- or T-sections where deemed appropriate based onthe continuously changing direction of the bending moment demands, along with (2) the use ofminimum specified (i.e. nominal) materials strength properties instead of expected values, may havecontributed to a relatively low value of actual built-in overstrength, �o (or �∗

o), and furthermore toan underestimation of retrieved actual Sa(PL) values. The first point was though adopted in analysisto avoid overly complicated models along with further ad hoc assumptions related to the effectiveflange width to be considered with L- or T-beams, that at best would have added extra uncertaintyto the subject instead of improving modeling and actual structure realization. In addition, regarding



the second point related to material properties, it was decided by the authors to rather rely onminimum specified values to account for occasionally poor production of construction materialsin the local market. The decisions made herein for these couple of modeling issues will add someconservatism to the current estimation of Sa(PL)/Sa(hazard) values reported in this paper thatcould be generally accepted for design codes evaluations/studies.

7. MEAN ANNUAL FREQUENCY (MAF) OF EXCEEDING VARIOUSPERFORMANCE LEVELS

Once an FC is computed and hazard information for the site is available, the MAF of exceedinga given PL, �(PL), can be computed as follows [18, 32]:

�(PL)=∫ ∞

0FPL,SaPL(Sa′)|dHSa(Sa′)| (3)

where PL could equally refer to either CP or LS performance level or to any other PL of interestincluding collapse limit state; FPL,SaPL(Sa′) represents the probability of Sa corresponding to agiven PL, SaPL, exceeding Sa′(or in other words it corresponds to the value of the FC at spectralacceleration Sa′, for a given limit state or performance level as given in Figure 4); and the spectralacceleration hazard, dHSa (Sa′), is the MAF of Sa exceeding Sa′ (ground motion hazard such asthat given in Section 4).

It is worth stating that FCs in Figure 4 obtained as previously described in Section 6 areimplemented in Equation (3) (the first term of the integral) in order to compute MAF values throughnumerical integration with the relevant spectral acceleration hazard curve (given in Figure 2). Thisprocedure is traditionally termed in the literature [33] the indirect method and is identified to bean Intensity Measure (IM)-based method as per the naming adopted in [34].

�(PL) values for each case study frame are thus computed through a numerical integrationprocess of FC corresponding to a given PL with hazard curves pertaining to the specific site.

7.1. Disaggregation of MAF (i.e. joint probability)

To better understand the spectral acceleration levels contributing most to MAF of exceeding agiven PL, �(PL), Figure 5 shows a disaggregation of � (PL) for an exemplar case correspondingto (near) collapse, or CP, performance level (i.e. once IDRMAX exceeds the limiting value of 0.04conservatively delineating CP level in the current research). The disaggregation diagrams given inFigure 5 are simply created by keeping track of each term of Equation (3) during the process of

Figure 5. Disaggregation of MAF data corresponding to the CP performance level (IDR=0.04)for selected case study frames.



numerical integration. Data in these plots could also be simply referred to as the ‘joint probability’given by P[Demand � Capacity, Sa]; which is basically the probability of IDRMAX exceeding agiven IDRTARGET corresponding to a particular PL conditioned on Sa(T1) then modified by thehazard, i.e. modified by the MAF for Sa(T1) of that frame exceeding a given value Sa′.

Figure 5 shows that for 4S-CCD-PFB, ground motions with Sa(T 1=1.01s) ranging from 0.7 to2.0g (with a spreading plateau-like peak extending from 1.0 to 1.4g) dominate the (near)collapsehazard, or the CP performance level corresponding to exceeding an IDR value of 0.04. Similarly,and again referring to Figure 5, it may be shown that for 8S-CCD-PFB and 8S-MCD-PFB, groundmotions with Sa(T 1=1.52sec) for the former, and Sa(T 1=2.01sec) for the latter, ranging from0.4 to about 1.4g (with peak between 0.6 and 0.8g) and from 0.1 to roughly 1.0g (with a sharpobvious peak at 0.2g), respectively, dominate the side sway (near)collapse hazard.

Referring to Table V, median values, Sa (CP), could be determined as 1.2, 0.85 and 0.22gfor 4S-CCD-PFB, 8S-CCD-PFB and 8S-MCD-PFB case study frames, respectively. This revealsthat these median values corresponding to CP performance levels originally based on exceedinga pre-set target IDR of 0.04 as per ASCE 41-06 recommendations are consistently close to theground motion intensity level that most dominates the side sway (near)collapse hazard, namely:1.0–1.4g plateau-like peak, 0.6–0.8g plateau-like peak, and 0.2g sharp peak, respectively, for thethree frames cited above, as per Figure 5. Similar observations made for other investigated frames[12] are not shown herein due to space limitations.

7.2. Estimates of MAF for case study frames

MAF of exceeding a given PL obtained by integrating the relevant FC with the site hazard curve asexplained above can be interpreted as a rate of exceeding (i.e. violating) this particular performance,or in other words, the number of times this PL is breached in any given year. MAFs of exceedingvarious PLs investigated herein are given in Table VI for all case study frames.

Looking at the CP level (i.e. IDR�0.04) as an illustrative example, one could notice from resultsin Table VI that for the low-rise 4-story frames, the SFB has a total probability (i.e. MAF) ofexceeding this PL that is about 28% larger than that for the PFB for CCD version of the buildings,while it is to the contrary about 18% lower for the MCD version. One could therefore state thatthe 4-story SFB frames are generally speaking more prone to collapse than their correspondingPFB frames when the CCD procedure is followed, while, conversely, the PFB frames are moreprone to collapse if the MCD is instead adopted. On the other hand, the conditional probability(directly extracted from relevant FCs without being modified by, or integrated with, the estimatedprevailing hazard in Egypt) for exceeding this CP level for the PFB is consistently higher than thatfor the SFB as expected by intuition for this low-rise configuration. This is due to more pronouncedP–� effects in the PFB construction. One could note that modifying the conditional probabilityby integrating it with the site-specific acceleration hazard did not alter the expected result for the

Table VI. MAF×10−6, �(PL), of exceeding various performance levels (or damage limitstates) for case study frames.

IDR�0.01 IDR�0.02 IDR�0.04Building type (IO) (LS) IDR�0.03 (CP)

Moment Frames as per CCD Procedure4S-CCD-PFB 1554 163 64 324S-CCD-SFB 1072 172 72 418S-CCD-PFB 3031 320 52 388S-CCD-SFB 888 160 63 32

Moment Frames as per MCD Procedure4S-MCD-PFB 1819 342 76 504S-MCD-SFB 1072 172 72 418S-MCD-PFB 3832 1880 1066 9088S-MCD-SFB 2275 638 478 265



low-rise 4S-PFB being in a global sense more vulnerable than the 4-story SFB for the case of theproposed MCD procedure.

On the other hand, although the annual spectral acceleration hazard for the 8-story SFB isconstantly higher than that for the 8-story PFB for both CCD and MCD procedures (e.g. Figure 2),MAF of exceeding CP level for the PFB is larger than that for the SFB (about 1.2 and 3.4 timesfor CCD and MCD, respectively). This reflects the significantly higher drifts and interstory driftsin the perimeter frames, especially as the height of frames increases. This additional vulnerabilityof the PFB relative to the SFB has not been hindered by the higher annual spectral accelerationhazard of the latter frames relative to the former for this mid-rise 8-story building, especiallyfor the MCD procedure generally entailing more flexible designs with higher contribution fromP–� effects.

Another way of looking at MAF, or in other words �(P L), data provided in Table VI arethrough reporting instead 1/� values which give the return period for exceeding a particular PL.For example, the return period for exceeding the CP level is simply (1/38×10−6 ≈) 26 315 yearsand (1/908×10−6 ≈) 1100 years for 8S-CCD-PFB and 8S-MCD-PFB, respectively. From suchresults, one could conclude that the 8S-MCD-PFB frames designed and analyzed herein are moreprone to exceed IDRTARGET value of 0.04 corresponding to ASCE 41-06 CP performance levelthan the 8S-CCD-PFB. Similar illustrations could be carried out for other case study frames.

From another perspective, and in order to evaluate the adequacy of the two design techniques(CCD versus MCD), it is constructive to report the ratio �(CP)MCD/�(CP)CCD corresponding toexceeding an IDR value of 0.04 as an illustrative example. This ratio scores approximately 1.6,8.3 and 23.9 for 4S-PFB, 8S-SFB and 8S-PFB, respectively. The highest retrieved ratio is byfar pertaining to the 8S-PFB frame as a result of the negative effect on the drift demand of thehigh tributary seismic mass inherent to these perimeter frames for mid- to high-rise construction.The significant reported value of 23.9 is an expected outcome of the remarkable reduction incolumns and beams concrete dimensions for the 8S-MCD-PFB relative to the 8S-CCD-PFB (referto Tables I and II) as a result of introducing a more relaxed process in checking IDRs for designpurposes through the use of MERS instead of DRS (refer to Figure 1 and Section 2). On the otherhand, �MCD/�CCD ratio of 8.3 reported for the 8S-SFB frames is fairly moderate with respect tothat scored for 8S-PFB frames. This could be attributed to still having smaller structural memberscross-sections for SFBs while adopting the MCD procedure but not with the same magnitude ofreduction in cross sections encountered in the 8S-MCD-PFB frames. Finally, a rather low value of1.6 for the ratio �MCD/�CCD for 4S-PFB frames is a direct proof that this low-rise perimeter-framedbuilding type has its design more-or-less still controlled by drift more than by strength. However,relaxing design drift calculations within the MCD procedure was not that influential in largelyincreasing the vulnerability of these MCD frames relative to their CCD counterparts. One couldalternatively say that these 4-story buildings belong to the low-rise construction for which theseismic design is nearly equally affected by strength and drift demands, and accordingly the changein their vulnerability by modifying their design procedure (CCD versus MCD) is fairly marginal.

8. SUMMARY AND CONCLUSIONS

Different trial designs of ductile low- to mid-rise (4- and 8-story) RC moment-resisting frameslocated in moderate seismic zones (0.25g) have been implemented using both space and perimeterframe configurations according to emerging Egyptian seismic code that is in line with Eurocode8 seismic provisions. Code’s controlling design criteria (including strength versus stiffness criteria,as well as currently imposed constant lower bound on design acceleration and missing upper boundon calculated actual expected displacement) have been addressed along with their implications onthe ‘as-designed’ frames seismic performance/vulnerability. A series of static inelastic pushoveranalyses have been performed on the case study frames. In addition, nonlinear incremental dynamicanalyses have been carried out for each investigated frame under a bin of 20 small-magnitude-large-distance ground records in a multi-level analysis context. FC are hence developed for the



case study frames corresponding to the probability of exceeding various performance levels ofinterest including IO, LS and CP levels conditioned on an efficient Intensity Measure definedby Sa(T 1). CCDs as well as a proposed MCD relaxing design drift demands are examined totest their effectiveness and reliability. Annual spectral acceleration hazard curves describing theseismic hazard in Egypt are developed for each case study frame and for each design technique(CCD versus MCD). Data from these hazard curves are then integrated with data extracted fromfragility curves resulting in estimates—for each case study frame—of MAF of exceeding variousperformance levels commonly set by seismic design codes. These final integrated (i.e. modifiedby the hazard) total probability values and their relative magnitudes are important to evaluate thetrade-off between safety and reliability of the ‘as-designed’ frames at one side and their economyat the other side for the CCD versus the proposed MCD procedures applied to RC moment-framedbuildings located in moderate seismic zones.

In brief, the current research has a dual aspect/goal. The first is to present the outcome ofan evaluation of the current Egyptian seismic code provisions through performing a seismicvulnerability assessment of ductile RC moment-framed buildings. This step is complemented bypromoting a proposed MCD technique that features some corrective measures to the design coderelated to drift calculation. Such corrective measures overcome a specific deficiency in the currentECP 201 seismic provisions, and hence improve these provisions to be fully compatible withother international well- and long-established codes such as in the US and Europe. The otheraspect (or benefit) of the current study that is by all means not less important than the first oneis to check the ability of performance-based design techniques (the proposed MCD method beingone example of such techniques) to cross-examine available traditional and widely adopted force-based seismic design procedures. This task is particularly carried out in the present study forductile moment-resisting frames located in moderate seismic zones and dimensioned as per currentEgyptian seismic provisions that are fairly in line with Eurocode seismic design requirements.Such an effort is indispensable in order to (1) assess the validity of current force-based seismicdesign codes in satisfying the performance objectives/levels set forth in performance-based codes,and/or (2) propose enhancement measures—in case needed—for such codes.

Some important conclusions that further confirm the aforementioned twofold aspect of thecurrent investigation could be summarized as follows:

1. The paper shows that although the MCD frames do not generally perform as good as the CCDframes (as reflected by MAF values in Table VI) especially for the mid-rise 8-story buildings,both design procedures result in moment frames that are—as per Table V—life-safe, andthat literally satisfy various seismic performance levels (e.g. IO, LS and CP) correspondingto relevant hazard levels implied by the design code [5]. Moreover, retrieved margins againstsatisfying various code expected performance levels (IO, LS and CP) associated with differenthazards of interest exceed 1.0 for all case study frames. These reported margins further showconsistency across all performance levels of interest for each investigated frame thus pointingto reasonable uniformity and homogeneity furnished by the two design procedures adoptedherein.

2. Furthermore, it has been proven that it would be better to impose the constant lower boundof 0.2ag on the design acceleration only when designing for strength of different structuralelements. If this bound on the design acceleration response spectrum is equally enforced whilechecking drift, it will result in unrealistically large values of drift demands unless an upperbound to the expected (actual) displacements is implemented. In other words, the expectedactual displacement, ds , need not be larger than the value derived from the elastic spectrum.Such an upper bound on displacement set in EC8 is more-or-less equivalent to the MCDprocedure proposed in this research as an enhancing modification to ECP 201 seismic designrecommendations. This bound is of primary importance when estimating actual drifts since itguarantees realistic displacement values for medium- to long-period structures especially incase the 0.2ag constant lower limit to the design acceleration response spectrum is enforcedin the design procedure. However, such a recommendation shall be complemented with acode decision to assign lower R values than the current ones for the design of mid-rise



(8-story and most probably higher) moment frames either of the space or of the perimetertype. A special emphasis shall be to reduce this R value for the perimeter frame configurationparticularly if the proposed MCD procedure is adopted. It is though worth noting that theproposed relaxation in the drift design constraints through the MCD procedure entails ageneral increase in the fragility of moment-framed buildings, especially for the 8-story PFBs,which means an increase in the MAF of exceeding various code expected performance levels.However, reasonable actual margins against violating code limits for these performance levelsare still guaranteed complemented by achieving a good economy of the resulting designs.

3. When only relying on FC of different studied frames providing results of a seismic responseassessment in a probabilistic format without including any modification to account for thespecific seismic hazard prevailing in the site of interest in Egypt, it was demonstrated thatthe perimeter frames are consistently more vulnerable and more prone to exceed LS andCP performance levels than the space frames; the former having steeper FC than the latter.This observation is valid for both CCD and MCD procedures for both 4-story and 8-storybuildings (i.e. low- to mid-rise moment-framed construction).

It is nonetheless important to realize that this study and the conclusions thereof are so far onlyvalid for ductile low- to mid-rise moment-resisting-framed buildings up to 8-story high locatedin moderate seismic zones (0.25g). Further testing of the proposed MCD procedure for (andextrapolation of the results presented herein to) other seismic zones, other frame configurations,various design ductility levels (e.g. the so-called limited-ductility as per [5, 7] terminology), andhigher moment-framed buildings shall be the subject of a similar effort before this promoted PBDmethodology—and the results thereof—are either widely (and conclusively) applied or denied.

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Seismic vulnerability evaluation of RC moment …scholar.cu.edu.eg/?q=medial_sector/files/1016_ftp.pdfA multi-level seismic vulnerability assessment of reinforced concrete moment frame