Seismic retrofitting with buckling restrained braces: Application to an existing non-ductile RC...

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Seismic retrofitting with buckling restrained braces: Application to anexisting non-ductile RC framed building

L. Di Sarno a,n, G. Manfredi b

a Department of Engineering, University of Sannio, Benevento, Italyb Department of Structural Engineering, University of Naples, Federico II, Italy

a r t i c l e i n f o

Article history:

Received 21 January 2010

Received in revised form

1 June 2010

Accepted 2 June 2010

a b s t r a c t

This paper assesses the seismic performance of typical reinforced concrete (RC) existing framed

structures designed for gravity loads only. The sample two-storey structural system exhibits high

vulnerability, i.e. low lateral resistance and limited translation ductility; hence an effective strategy

scheme for seismic retrofitting was deemed necessary. Such a scheme comprises buckling restrained

braces (BRBs) placed along the perimeter frames of the multi-storey building. The adopted design

approach assumes that the global response of the inelastic framed structure is the sum of the elastic

frame (primary system) and the system comprising perimeter diagonal braces (secondary system); the

latter braces absorb and dissipate a large amount of hysteretic energy under earthquake ground

motions. Comprehensive nonlinear static (pushover) and dynamic (response history) analyses were

carried out for both the as-built and retrofitted structures to investigate the efficiency of the adopted

intervention strategy. A set of seven code-compliant natural earthquake records was selected and

employed to perform inelastic response history analyses at serviceability (operational and damage-

ability limit states, OLS and DLS) and ultimate limit states (life safety and collapse prevention limit

states, LSLS and CPLS). Both global and local lateral displacements are notably reduced after the seismic

retrofit of the existing system. In the as-built structure, the damage is primarily concentrated at the

second floor (storey mechanism); the computed interstorey drifts are 2.43% at CPLS and 1.92% at LSLS

for modal distribution of lateral forces. Conversely, for the retrofitted system, the estimated values of

interstorey drifts (d/h) are halved; the maximum d/h are 0.84% at CPLS (along the Y-direction) and 0.65%

at LSLS (yet along the Y-direction). The values of the global overstrength O vary between 2.14 and 2.54

for the retrofitted structure; similarly, the translation ductility mD-values range between 2.07 and 2.36.

The response factor (R- or q-factor) is on average equal to 5.0. It is also found that, for the braced frame,

under moderate-to-high magnitude earthquakes, the average period elongation is about 30%, while for

the existing building the elongation is negligible (lower than 5%). The inelastic response of the existing

structure is extremely limited. Conversely, BRBs are effective to enhance the ductility and energy

dissipation of the sample as-built structural system. Extensive nonlinear dynamic analyses showed that

more than 60% of input seismic energy is dissipated by the BRBs at ultimate limit states. The estimated

maximum axial ductility of the braces is about 10; the latter value of translation ductility is compliant

with BRBs available on the market. At DLS, the latter devices exhibit an elastic behaviour. It can thus be

concluded that, under moderate and high magnitude earthquakes, the damage is concentrated in the

added dampers and the response of the existing RC framed structure (bare frame) is chiefly elastic.

& 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Framed systems have been extensively used for buildingstructures in earthquake-prone regions because of their seismicperformance (e.g. [1–5]; among many others). However, a numberof existing reinforced concrete (RC) framed building structureswere designed for gravity loads only and hence do not possess

adequate lateral stiffness and resistance; seismic details are alsolacking as observed during surveys carried out in the aftermath ofrecent earthquakes worldwide (Fig. 1).

It is, therefore, of paramount importance to retrofit suchexisting framed buildings and enhance their seismic performance.A number of intervention schemes, either traditional or innova-tive, are available (e.g. [6,7]; among many others), as shownpictorially in Fig. 2.

Existing framed structures may be suitably retrofitted by usingdiagonal braces, either traditional steel or innovative. Bracedsystems exhibit high lateral stiffness and strength under

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Soil Dynamics and Earthquake Engineering

0267-7261/$ - see front matter & 2010 Elsevier Ltd. All rights reserved.

doi:10.1016/j.soildyn.2010.06.001

n Corresponding author.

E-mail address: [email protected] (L. Di Sarno).

Soil Dynamics and Earthquake Engineering 30 (2010) 1279–1297


moderate-to-large magnitude earthquakes. The most commonstructural configurations for lateral-resisting systems are con-centrically brace frames (CBFs), which possess a lateral stiffnesssignificantly higher than that of unbraced frames, e.g. momentresisting frames. Nevertheless, due to buckling of the metalcompression members and material softening due to theBauschinger effect, the hysteretic behaviour of CBFs with tradi-tional steel braces is unreliable. Alternatively, buckling-restrainedbraces (BRBs) may be employed as diagonal braces in seismicretrofitting of steel and RC frames designed for gravity loads only.Such braces exhibit compressive strength, which is about 10–15%greater than tensile; the global buckling is inhibited (e.g., [8–10]).Frames with BRBs are being used for new and existing structures

worldwide (e.g. [11–13] among many others), especially fordamage controlled structures as shown pictorially in Fig. 3 andinitially formulated by Wada et al. [14].

The global response of the inelastic structural system can beassumed as the sum of the elastic frame (also termed primarystructural system) and the system formed by the diagonal braces(secondary system) that absorbs and dissipates a large amount ofhysteretic energy under earthquake ground motion.

The primary system is capable of withstanding vertical loadsand behaves elastically under earthquake loads. The secondarysystem includes the dissipative members and is thus designed todamp the seismic lateral actions and deformations. Dissipativemembers, such as BRBs, may be installed in the exterior frames of

Fig. 1. Typical failure modes observed in framed building structures in the 2009 L’Aquila (Italy) earthquake: collapse due chiefly to inadequate details of longitudinal and

transverse steel reinforcement (smooth bars) at beam-to-column connections (left) and extensive damage (buckled longitudinal ribbed bars) due to the lack of stirrups in

the column critical regions (right).

TRADITIONALSTRATEGIES

L OCAL INTERVENTION

GLOBAL INTERVENTION

COMBINED INTERVENTION

INNOVATIVESTRATEGIES

SEISMIC ISOLATION

SUPPLEMENTAL DAMPING

COMBINED INTERVENTION

HYBRIDINTERVENTION

SEIS

MIC

RE

TR

OF

ITT

ING

Fig. 2. Seismic retrofitting intervention schemes.

L. Di Sarno, G. Manfredi / Soil Dynamics and Earthquake Engineering 30 (2010) 1279–12971280


multi-storey buildings and can be thus easily replaced in theaftermath of a devastating earthquake. Primary and secondarysystems act as a parallel system; the lateral deformation of thestructure as a whole corresponds to the deformation of bothprimary and secondary systems. Fig. 4 compares the earthquakeresponse of a traditional frame and damage controlled structuralsystem. The response is expressed in terms of cyclic action–deformation relationships. When controlled damage strategy isadopted, the primary structure shows a linear elastic responseunder both moderate and high magnitude earthquakes. Theenergy dissipation is localized merely in the diagonal bracesacting as dampers. Conversely, traditional framed systemsdissipate seismic energy either within all members of thestructure or in the beams, if the capacity design rules areemployed.

This paper assesses the seismic structural performance of atypical RC framed school building retrofitted with BRBs. Theresults of comprehensive nonlinear (static and dynamic) analysesshowed that the use of BRBs is extremely cost-efficient.Notwithstanding, the design of such structural components isnot straightforward. A step-by-step procedure, compliant withthe performance-based (force- and displacement-based) frame-work, is outlined hereafter. A brief discussion of the pros and consof the use of the BRBs is presented in the next paragraph.

2. Buckling restrained braces (BRBs)

The disadvantages of traditionally braced frames may beprevented whether or not the occurrence of buckling for themetallic braces in compression is inhibited, e.g. using bucklingrestrained braces (BRBs). The energy dissipation capacity of atraditional brace is limited by the occurrence of buckling andhence stiffness reduction and strength degradation may occur.Conversely, buckling restrained braces exhibit large and stablehysteretic dissipation even at large amplitudes.

Buckling restrained braces may be employed for the design ofdamage controlled structures. BRBs thus form parallel systemswhere the bare frame behaves elastically and the braces absorband dissipate the seismic induced energy. Under high magnitudeearthquake ground motions the BRBs may exhibit large residualdeformations and should be replaced. Existing BRBs are chieflypatented systems and their layout may vary according to themanufacturer.

The devices assessed in the present study include a short-length BRB connected in series with a traditional metallic brace,as further discussed in the next sections. The short linkcomprising the BRB ends with a flanged bolted connection and apinned or a gusset plate. The detailing of the gaps between thejoint components is of paramount importance for the effective

Fig. 3. Damage controlled structure.

Fig. 4. Earthquake response of traditional framed (top) and damage controlled (bottom) structural system.

L. Di Sarno, G. Manfredi / Soil Dynamics and Earthquake Engineering 30 (2010) 1279–1297 1281


response under earthquake ground motions. The manufacturerprovides the geometrical and mechanical properties of thedissipative device.

3. Seismic retrofitting strategy

The design of new and existing structures with hystereticbuckling restrained braces generally comprises the following:

� the estimation of the optimum parameters for the dissipativebraces by using simplified methods;� the application of capacity design checks for all members of

the structure under the expected ultimate force induced by thedissipative braces, e.g. the yielding force of the BRBs;� the verification of the design performance, preferably through

nonlinear response history analyses.

Nonlinear dynamic analyses utilizing a suite of spectrum-compatible records, either artificial or natural, are yet not suitablefor design office use. Thus linear dynamic or nonlinear staticanalyses are generally employed for practical applications. In thepresent study nonlinear dynamic analyses are performed to assessthe reliability of the results derived through linear dynamicanalyses and nonlinear static pushovers.

The design methodology for damage controlled structuresutilized in the present study is an iterative strategy based onresponse spectra and an equivalent viscous damping (x) usedto quantify the effective hysteretic global response of theearthquake-resistant system. The selected damping can beutilized to estimate both design spectral accelerations anddisplacements. The design method formulated herein is a mixedforce- and deformation-based scheme employing an equivalentinelastic static approach. The evaluation of the spectral displace-ments is essential to ensure the elastic response of the structureto be retrofitted. The step-by-step design procedure is as follows:

1. Determine the seismic base shear (Vb) using the 5% dampedacceleration spectra.

2. Distribute the seismic horizontal forces along the buildingheight. For ordinary low-to-medium rise frames the distribu-tion can be assumed linear [15], e.g. compliant with the code-based formulation:

Fi ¼ VbziWiP

zjWjð1Þ

where W is the seismic mass and z is the storey height withrespect to the foundation level. Alternatively a modal analysiscan be carried out for the existing structure.

3. Determine the axial forces (Fbr) in the diagonal bracesassuming that the existing frame has pinned beam-to-columnand base-column connections and the braces are effective toresist earthquake loads:

Fbr ¼1

n

Vi

cos a ð2Þ

where Vi is the seismic storey shear at the ith floor, n thenumber of storeys and a is the angle of the braces withrespect to the horizontal beams.

4. Determine the cross-section of the core (Acore) of the dampersat each storey:

Acore ¼Fbr

fyð3Þ

where fy is the steel yield stress of the core element of theBRBs. Material overstrength may also be accounted for.

5. Perform nonlinear static analyses of the existing frame withthe added braces and determine the capacity curves of theearthquake-resistant system. The maximum displacementdemand is also computed by employing the equivalentviscous damping:

x¼ xiþxh ð4Þ

where the damping xh accounting for the hystereticbehaviour is

xh ¼Ep

4pEs¼

1

2pEp

dmaxFmaxð5Þ

with Ep being the hysteretic energy dissipated in a cycle andEs the elastic energy stored in the system. The value of Ep canbe computed by performing a cyclic pushover and assuming atarget displacement of the control point equal to themaximum lateral displacement demand of the structureretrofitted with the BRBs at collapse limit state. As a rule ofthumb, the latter displacement can be assumed equal to aglobal drift of 0.5–0.6% of the building height. The initialdamping xi accounts for all sources of dissipation in astructure which do not include hysteretic dissipation; itmay be assumed equal to 5%.

6. Determine the maximum displacement demand, using thedisplacement response spectrum and the equivalent damping.

7. Check that the existing frame responds elastically for thecomputed displacement demand; alternatively iterate fromsteps 1) to 7).

8. Compute the seismic forces by using the accelerationresponse scaled through the equivalent damping in Eq. (5).

9. Use the displacement demand estimated in 7) and thecapacity curve in 5) to compute the effective base shear inthe existing frame and the added braces. The latter may be re-designed and optimised by iterating steps 1) to 7).

10. Check the maximum axial loads in the braces at damage-ability limit state to prevent yielding under service loads.

The above design methodology quantifies the dissipationthrough the equivalent viscous damping, used to scale theacceleration and displacement response spectra. Alternatively,adequate response modification factors (R- or q-factors) may beemployed; values of R ranging between 4.5 and 6.5 have beenproposed [11]. The design method for BRBs has been applied to acase study as illustrated hereafter.

4. Case study

4.1. Building description

4.1.1. Geometry

The sample RC existing framed building is located near Naples,in South of Italy; the framed structure was built in the early 1960sand it was designed for gravity loads only. The plan layout of thebuilding comprises two T-shaped blocks (termed Building A andBuilding B) and a connecting rectangular block (namedBuilding C) as pictorially shown in Fig. 5. Buildings A and B areused for classrooms, while Building C is a sport hall. The total areaof the building is about 1400 sqm; the area of the Buildings A andB is about 610 sqm.

The structural system consists of three stories used forclassrooms, storage rooms and laboratories; the roof floor isutilized for insulation purposes. The ground floor is 3.08 m high



and includes laboratories; the first and second floors are 3.65 mhigh. The top floor has an inclined tiled roof; its height variesbetween 0.2 m (along the perimeter) and 1.90 m (at the centre).The structural system of the sample school building consists of amulti-storey RC frame with deep beams. The column cross-sections are summarised in Table 1; the frame employs30�65 cm deep beams. For the inclined roof, the deep beamsare 30 cm�50 cm. The floor slabs consist of 34 cm deep cast-in situ concrete and light brick decks at first and second levels; thethickness of the roof floor is 24 cm and the inclined roof is 20 cmthick. The solid slab thickness is 4cm at all floors; thusdiaphragmatic behaviour may be assumed for the sample frame.

The as-built framed system employs shallow foundationsconsisting of a grid of deep beams: T-shaped and rectangularcross-section beams are used for Buildings A and B; Building C hasonly deep rectangular beams. The height of the T-shaped beamsranges between 100 and 140 cm; rectangular beams in BuildingsA and C are 50�50, 40�90 and 100�90 cm. In Building C therectangular foundation beams are 40�65 cm.

The framed structural system employs superficial foundationwith rectangular beam grid. The typical cross-section of the deepfoundation beams is T-shaped (inner beams, web thickness of40 cm, height equal to 90 and 105 cm, width varying between120 and 220 cm) and rectangular (outer beams with 50�50 cmcross-sections).

4.1.2. Material properties

An extensive experimental test program (in situ and inlaboratory) was carried out to estimate the mechanical propertiesof the concrete and steel reinforcement in the existing RCbuilding. Additional in situ tests were carried out on the structuralsystem components, i.e. floor slabs and RC retaining walls of theunderground level.

Cylinder concrete samples with diameters of 100 and 60 mm weretested under compression to estimate the concrete

compression strength (fc). The latter is a function of the diameter(F) and the height (h) of the sample and the cylinder concretecompression strength (fcyl) of the test specimens. The concretestrength of the cylinder specimens with diameter f100 mm wasemployed to determine the average value of fc,mean¼18.60 MPa andfc,min¼13.55 MPa. Similarly, the compression strength of the cylinderspecimens with diameter f60 mm was employed to determine theaverage value of fc,mean¼22.42 MPa and fc,min¼19.89 MPa.

Ultrasonic tests were carried out on structural members wherethe cylinders with f100 mm were drilled. The results of theperformed ultrasonic tests provided characteristic compressionstrength fck of the concrete members. The mean values fc,mean ofthe resistance may be derived from fck through the followingrelationship [16]:

fc,mean ¼ fckþ8 MPa ð6Þ

The estimated mean value of the concrete cylinder compres-sion strength is thus 18.8 MPa; the latter value is close to thoseevaluated earlier with the crushing of the cylinders. Variations ofthe computed strength are in the range of 10%. The correlationbetween the concrete cylinder compression strength and thevelocity derived from the ultrasonic tests is provided in Fig. 6; theregression curve of the sample data shows a linear trend.

In the finite element modelling and performance assessment itis safely assumed that the characteristic concrete compressionstrength is fckffi15.7 MPa.

Tensile tests were carried out on steel reinforcement smoothbars; the laboratory tests on f20 mm straight bars showed yieldstrength fy¼296 MPa and ultimate strength fu¼435 MPa. Theestimated material overstrength is fu/fy¼1.47 and the ultimateelongation is esu¼37.1%. The latter values demonstrated the highplastic redistribution and ductility of the steel reinforcement ofthe RC cross-sections of the structural system. For the modelcalibration of the smooth rebars in the spatial frame finiteelement discretization it is assumed that fy¼285 MPa.

4.1.3. Structural details

The structural details of the beams and columns of the sampleframed structures do not comply with modern codes of practicefor seismic regions. The steel reinforcement comprises smoothbars and the spacing of the transverse stirrups is insufficient towarrant adequate shear resistance to beams, columns andstructural joints. The longitudinal steel reinforcement percentageis not appropriate to ensure ductile response of RC cross-sections.The typical layout of the steel reinforcement demonstrates that

Fig. 5. Plan layout of the sample as-built building (dimensions in metres).

Table 1Geometry of the columns of the sample frame (dimensions in metres).

1st floor 2nd floor 3rd floor 4th floor

0.35�0.30 0.35�0.30 0.30�0.30 0.30�0.30

0.35�0.40 0.35�0.35 0.30�0.35 –

0.40�0.40 0.30�0.40 0.30�0.40 0.30�0.40

0.40�0.55 0.40�0.45 0.40�0.40 –



beams may fail under shear actions, thus endangering the globalinelastic response of the structure, if any.

5. Earthquake input characterization

The construction site of the sample framed building is locatedin a moderate seismicity zone. The soil foundation can beclassified as ground type B, according to the classificationimplemented in the recently issued national seismic standards[17], which is also compliant with the European code provisions[16]. The available soil profiles of the site have shown that thelocal geology includes deposits of very dense sand and gravel withseveral tens of metres in thickness, characterized by a gradualincrease of mechanical properties with depth. The average shearwave velocity vs,30 defined ranges between 360 and 800 m/s.

In the present study, the seismic action is defined in terms of(horizontal) acceleration code response spectra and earthquakenatural records. The horizontal seismic action is described by twoorthogonal components assumed as being independent andrepresented by the same response spectrum. The verticalcomponent of the seismic action is not accounted for in theperformance assessment of the sample structure. This assumptioncomplies with the distance of the building site from active faults.It has been demonstrated by extensive field evidence (e.g. [18];among many others) that the structural response of framedstructures is significantly affected by the effects of the verticalcomponent of seismic ground motions in the near-field, i.e. at adistance of 10–50 km from the earthquake source.

The code horizontal input spectra was defined with referenceto the 5% damping acceleration response spectra evaluated for thefour limit states compliant with the recent Italian code of practice[17], namely the operational (OLS), damageability (DLS), lifesafety (LSLS) and collapse prevention (CPLS) limit states. Thereturn period TR of the earthquake loading is given by

TR ¼�VR

ln 1�PVRð Þð7Þ

where VR is the reference design life of the building, i.e. 75 years,and PVR the probability of exceedence of the seismic action,

expressed as a function of the limit state. The computed values ofTR are summarised in Table 2.

The design values of the peak ground accelerations (PGAs) onstiff soil vary between 0.066g (OLS) and 0.282g (CPLS) as shown inTable 2; the above values confirm that site of construction hasmoderate seismicity. The values of the parameters employed todefine the spectral shape of the horizontal acceleration anddisplacement components at different limit states are outlined inTable 3. These parameters include the coefficient of amplificationfor soil profile and topography (S), for system amplification (FO)and the periods (denoted TB, TC and TD) that correspond to thedifferent branches of the code spectral shape. The code-complianthorizontal acceleration and displacement response spectra aredisplayed in Fig. 7.

The suite of natural earthquake records employed to performinelastic response history analyses was selected in compliancewith the following rules [16,19]:

� A set of minimum three accelerograms was selected.� The mean of the zero period spectral response acceleration

values (calculated from the individual time histories) is notsmaller than ag S for the site of construction.� In the range of periods between 0.2T1 and 2T1, where T1 is the

fundamental period of the structure in the direction where theaccelerogram is applied. Values of the mean 5% damping

y = 0.014x - 23.166

0

5

10

15

20

25

30

1600Speed of Ultrasonic Waves (m/s)

Cyl

inde

r Stre

ngth

(MP

a)

Speed of Ultrasonic Waves vs Cylinder Strength

fck specimens - Speed of Ultrasonic Waves

2000 2400 2800 3200 3600 4000

Fig. 6. Correlation between the concrete cylinder compression strength and the velocity of the ultrasonic tests.

Table 2Parameters used to define the spectra of the horizontal earthquake components

Limit state (type) PVR (%) TR (year) PGA (g)

Serviceability

OLS 81 45 0.066

DLS 63 72 0.085

Ultimate

LSLS 10 712 0.223

CPLS 5 1472 0.282

Key: OLS¼operational limit state; DLS¼damageability limit state; LSLS¼ life

safety limit state; CPLS¼collapse prevention limit state; PVR¼probability of

exceedence; TR¼return period of the seismic action; PGA¼peak ground

acceleration.



elastic spectrum, calculated from all time histories, should begreater than 90% of the corresponding value of the 5% dampingelastic response spectrum.

A suite of seven natural records was selected for X- andY-direction of the sample frame. The normalized accelerationhorizontal response spectra of the selected records is shown inFig. 8 for X- and Y-direction.

Earthquake ground motions are generally characterized by thepeak ground parameters and accelerations and/or displacement

spectra. However, for ductile existing and new constructions theseismic response can be significantly affected by the duration andnumber of cycles of earthquake records. The bracketed, uniformand significant durations of the sample suite of accelerogramswere computed. The results are provided in Fig. 9. It is observedthat the selected records possess mean significant durations ofabout 15 s; the average of bracketed and uniform duration is 30 sand about 20 s, respectively.

The predominant periods, the Arias intensity of the samplerecords, are provided in Table 4, along with the scaling factorsemployed to fulfill the spectral compatibility. It is observed thatthe mean predominant is 0.37 s, which corresponds to thefundamental periods of vibration of the retrofitted structure, asdiscussed in the next paragraphs. The scaling factors vary with thelimit states; lower values correspond to serviceability limit states(OLS and DLS). The coefficient of variation is on average 0.30.

The three limit states usually utilized for existing structures,i.e. DLS, LSLS and CPLS, are further discussed in the nextparagraph; OLS is, in fact, of primary concern for critical facilitiesand hence was not accounted for the sample structure.

6. Analytical structural model

Refined three-dimensional (3D) finite element (FE) modelswere employed to discretize the sample framed as-built and

Table 3Parameters used to define the spectral shape of the horizontal earthquake

components

Limit state (type) S (dimensionless) FO (dimensionless) TB (s) TC (s) TD (s)

Serviceability

OLS 1.20 2.324 0.142 0.427 1.627

DLS 1.20 2.377 0.150 0.451 1.635

Ultimate

LSLS 1.19 2.406 0.167 0.501 1.691

CPLS 1.12 2.461 0.172 0.517 1.715

Key: S¼amplification factor for soil profile and topography; FO¼amplification

factor for earthquake horizontal component; TB,TC and TD are periods correspond-

ing to constant acceleration, velocity and displacement branches, respectively.

Fig. 7. Code-compliant horizontal acceleration and displacement response spectra.

0.0

1.0

2.0

3.0

4.0

5.0

0.0 1.0 2.0 3.0 4.0

Period (s)

Pseu

do-A

ccel

erat

ion

/ PG

A

196 198 232 290

879 5815 6144 Mean

0.0

1.0

2.0

3.0

4.0

5.0

0.0 1.0 2.0 3.0 4.0

Period (s)

Pseu

do-A

ccel

erat

ion

/ PG

A

196 198 232 290

879 5815 6144 Mean

Fig. 8. Normalized earthquake acceleration horizontal response spectra: X-direction (left) and Y-direction (right).



retrofitted structures and analyze the earthquake response. Bareframes were modelled as 3D assemblages of beam members.Shear deformability of beams and columns was also included inthe structural model. Panel zone strengths and deformations werenot considered. Fig. 10 displays the FE models utilized for theresponse analyses of the buildings. Such FE models employ a

refined fibre-based approach to estimate reliably the nonlinearresponse both at local and at global levels in the frames.

The FE package utilized to assess the seismic performance ofthe sample structures is SeismoStruct [20]. This program iscapable of predicting the large displacement response of spatialframes under static or dynamic loading, taking into account both

0 10 20 30 40

000196x

000198x

000232x

000290x

000879x

005815x

006144x

Acce

lero

gram

(lab

el)

Duration (seconds)

Uniform

Significant

Bracketed

Mean Bracketed

Mean Uniform

Mean Significant

0 10 20 30 40

000196y

000198y

000232y

000290y

000879y

005815y

006144y

Acc

eler

ogra

m (l

abel

)

Duration (seconds)

Uniform

Significant

Bracketed

Mean Bracketed

Mean Uniform

Mean Significant

Fig. 9. Duration of sample earthquake ground motions: components along X-direction (left) and Y-direction (right).

Table 4Predominant periods, Arias intensity and scaling factors computed for the sample records.

Earthquake record (label) Predominant period (s) Arias intensity (m/s) Scaling factor (dimensionless)

Limit state

OLS DLS LSLS CPLS

000196x 0.44 2.18 0.18 0.23 0.59 0.71

000196y 0.50 2.10 0.26 0.34 0.88 1.06

000198x 0.52 1.92 0.44 0.57 1.48 1.78

000198y 0.72 1.47 0.36 0.46 1.20 1.44

000232x 0.18 1.24 0.14 0.18 0.47 0.57

000232y 0.26 1.35 0.14 0.19 0.48 0.58

000290x 0.38 2.59 0.37 0.48 1.24 1.49

000290y 0.20 1.35 0.25 0.32 0.83 1.00

000879x 0.34 2.13 0.29 0.38 0.98 1.18

000879y 0.30 1.91 0.25 0.32 0.84 1.01

005815x 0.22 3.00 0.28 0.37 0.95 1.14

005815y 0.36 3.06 0.24 0.32 0.82 0.98

006144x 0.50 4.21 0.30 0.39 1.01 1.21

006144y 0.50 2.16 0.19 0.25 0.65 0.78

Mean 0.37 2.47 0.29 0.37 0.96 1.15

Stand. Dev. 0.15 0.82 0.09 0.11 0.29 0.35

COV 0.41 0.33 0.30 0.30 0.30 0.30

Fig. 10. Finite element model of the as-built (left) and retrofitted (right) sample framed building.



geometric nonlinearities and material inelastic. The spread ofinelasticity along the member length and across the section depthis explicitly modelled, allowing for accurate estimation of damagedistribution. Modelling of the local (beam-column effect) andglobal (large displacements/rotations effects) sources of geo-metric nonlinearity is carried out through the employment of aco-rotational formulation, whereby local element displacementsand resulting internal forces are defined with regard to a movinglocal chord system, referred to the current unknown configura-tion. Exact transformation of element internal forces and stiffnessmatrix, obtained in the local chord system, into the global systemof coordinates allows for large displacements/rotations to beaccounted for.

The interaction between axial force and transverse deforma-tion of the frame element (beam-column effect) is implicitlyincorporated in the element cubic formulation as implemented inSeismoStruct [20], whereby the strain states within the elementare completely defined by the generalized axial strain andcurvature along the element reference axis (x), whilst a cubicshape function is employed to calculate the transverse displace-ment as a function of the end-rotations of the element.

To evaluate accurately the structural damage distribution, thespread of material inelasticity along the member length andacross the section area is explicitly represented through theemployment of a fibre modelling approach. The distribution ofmaterial nonlinearity across the section area is accuratelymodelled, even in the highly inelastic range, due to the selectionof 200 fibres employed in the spatial analysis of the samplestructural systems. Two integration Gauss points per element arethen used for the numerical integration of the governingequations of the cubic formulation (stress/strain results in theadopted structural model refer to these Gauss Sections, not to theelement end-nodes). The spread of inelasticity along memberlength is accurately estimated because four 3D inelastic frameelements are utilized to model both beams and columns.Consequently, at least two Gauss points were located in theinelastic regions in order to investigate adequately the spreadingof plasticity in the critical regions and within structural members.

Five inelastic space frame elements were used to model bothbeams and columns of the bare RC frames. Two elements with alength of 0.10L of the member clear span (L) are located at thebeam ends; the remaining frame elements are 0.30L long.Inelastic truss elements were utilized to simulate the diagonalBRBs, as further discussed later.

Rod elements connecting in-plane slab nodes were used tosimulate the diaphragmatic action of the two slabs of the framedbuilding. The cross-section of the floor rod elements wascalibrated on the basis of the modal response of the system.

The structural models utilized to perform the dynamicanalyses employ masses lumped at structural nodes. The lumpedmasses were estimated by assuming the dead loads and part ofthe live loads in compliance with seismic code provisions.

6.1. Material modelling

Advanced nonlinear modelling was employed for concrete andsteel reinforcement in beams and columns and for the structuralsteel utilized for the diagonal braces.

A bilinear model with kinematic strain-hardening was utilizedto simulate the inelastic response of steel longitudinal bars of thecross-sections of RC beams and columns. Bilinear models aresimple to implement and computationally efficient. Such modelsrequire the definition of a limited number of parameters, namelythe Young modulus or modulus of elasticity (Es), the yieldstrength (fy) and hardening parameter (m). In the performed

analyses, it was assumed that Es¼200,000 MPa and fy¼280 MPa,in compliance with the experimental tests carried out on materialspecimens. The hardening parameter m is the ratio between thestiffness (Esp) of the post-elastic branch and the initial stiffness(elastic stiffness equal to the Young modulus Es). The post-elasticstiffness Esp is as follows:

Esp ¼fult�fy

eult�ey¼

fult�fy

eult�fy

Es

ð8Þ

where fult and eult are the ultimate (or tensile) strength andultimate elongation of the steel bars. It is assumed that fult¼

420 MPa and eult¼0.05. Note that the above value of the ultimateelongation is a conservative estimate of the actual materialresponse. It was adopted to derive a realistic value of the stainhardening. The stiffness Esp and the hardening parameter m are2880 and 0.014, respectively.

The concrete was modelled through a nonlinear constantconfinement model. This is a uniaxial nonlinear model thatfollows the constitutive relationships formulated by Manderet al. [21].

For the cross-sections of the RC sample structures, values ofthe confinement factor k were assumed equal to 1.2 and 1.0 forconfined (core) and unconfined (shell) concrete, respectively; thek-values were estimated with the formulation by Manderet al. [21].

A value of 19.0 MPa was adopted for the compressive strengthfck of concrete; this value was utilized for both core and shellconcrete.

The tensile strength was estimated through the followingrelationship:

ftk ¼ kt

ffiffiffiffiffifck

pð9Þ

where the coefficient kt ranges between 0.5 (pure tension) and0.75 (tension caused by flexure). The tensile strength of core andshell concrete is as follows:

ftk ¼ 0:75ffiffiffiffiffiffi19p

¼ 3:27 MPa ð10Þ

The strain ec at peak stress is 0.002 for confined andunconfined concrete, while the ultimate deformation eult is0.0035 and 0.0040 for shell and core concrete, respectively.

6.2. Brace modelling

The BRBs were modelled using 3D inelastic truss elements. Inparticular, the BRBs employed for the retrofitting of the sample RCframe are connected in series with traditional steel hollow sectionbraces, as shown pictorially in Fig. 11. Equivalent mechanicalproperties were thus derived to replace the BRBs and theconnected diagonal braces with equivalent steel inelastic trusselements. It was necessary to compute the equivalent elasticYoung modulus (Eel,EQ), the equivalent yield strength (fy,EQ), thehardening parameter (mEQ) and the equivalent maximum strain(emax,EQ).

The equivalent modulus Eel,EQ is given by

Eel,EQ ¼Kel,EQ ðLBRBþLBRACEÞ

ABRACEð11Þ

where LBRB is the length of the BRB, and LBRACE and ABRACE are thelength and the area of the brace, respectively.

The yield strength fy,EQ

fy,EQ ¼Fy,BRB

ABRACEð12Þ

where Fy,BRB is the yield strength of the BRB.



The hardening parameter (mEQ)

mEQ ¼Kpl,EQ

Kel,EQð13Þ

where

Kpl,EQ ¼1

1Kpl,BRBþ 1

Kel,BRACE

ð14Þ

and

Kpl,BRB ¼Fmax,BRB�Fy,BRB

Dmax,BRB�Dy,BRBð15Þ

The equivalent maximum strain (emax,EQ)

emax,EQ ¼Dmax,EQ

LBRACEþLBRBð16Þ

with

Dmax,EQ ¼Dmax,BRADþDel,BRACEðFmax,BRBÞ ð17Þ

and

Del,BRACEðFmax,BRBÞ ¼Fmax,BRB

Kel,BRACEð18Þ

The computed values of the Young modulus (Eel,EQ), theequivalent yield strength (fy,EQ), the hardening parameter (mEQ)and the equivalent maximum strain (emax,EQ) for the inelastic trusselements are summarised in Table 5. The latter table also providesthe variations of the aforementioned mechanical properties forthe diagonal braces employed for the seismic retrofitting of thesample existing structure.

In the present study the tensile and compression yieldstrengths of the BRBs are assumed similar; this assumption ison the conservative side as the BRBs possess compressivestrength, which is about 10–15% greater than tensile, asmentioned earlier.

7. Structural assessment

The seismic performance of the existing and retrofittedstructures was assessed through linear and nonlinear analyses,i.e. eigenvalue analysis, nonlinear static analysis and nonlineardynamic analysis. The results of the performed analyses arefurther discussed hereafter.

7.1. Eigenvalue analysis

Eigenvalue analysis is employed to identify the dynamicbehaviour of the as-built structure and investigate irregularresponse due to torsional deformability of the building layout.In so doing, a structural model with linear elastic behaviour ofelements was utilized; structural masses were located atstructural nodes; the mass distribution depends on the tributaryarea. Similarly, eigenvalue analysis is employed to estimate thedynamic response of the retrofitted structural system. Table 6provides the modal results for both existing and retrofittedbuildings, i.e. periods of vibration (T) of the first three modes andthe participation masses ( ~Mx and ~My) along the principaldirections of the structure of X and Y.

It is found that the existing building structure shows an irregulardynamic response. The second mode of vibration has 67.48% ofparticipation mass along the X-direction; the third mode of vibrationhas a participation mass of 20.49% along the X-direction. As a result,the existing structure exhibits coupled translation and torsionalmodes due to the concentration of lateral stiffness at the stairwells.The fundamental period of the retrofitted structure is significantlylower than the counterpart of the as-built system (0.397 s versus

0.612 s); the reduction is about 36%.The estimated values of the modal participation mass of the

retrofitted structure (see Table 6) show that the presence of bracesalong the perimeter is beneficial to achieve a regular dynamicresponse of the structure. The modal response of the retrofitbuilding shows that the first two vibration modes are puretranslations; these modes have participation masses of about 85%.For both existing and retrofitted structures the first three modesaccount for the total modal masses.

The comparison between the modal response parameters ofthe retrofitted and as-built structures shows the significantbenefits in utilizing the BRBs as retrofitting schemes. The dynamicresponse of the structures is considerably improved; overstress instructural members due to torsional modes are prevented in theretrofitted sample framed building.

7.2. Nonlinear static analyses

To estimate the expected inelastic mechanisms and thedistribution of damage in the sample framed buildings, nonlinear

Fig. 11. Typical sub-assemblage of the diagonal braces: buckling restrained component and traditional metallic tubular brace.

Table 5Summary of the equivalent mechanical properties of the diagonal buckling restrained braces.

Property Symbol Unit 1st Floor 2nd Floor

Min Max Min Max

Elastic modulus of equivalent system Eel,EQ N/mm2 159,082 166,451 171,022 176,5588

Equivalent yield strength fy,EQ N/mm2 86 107

Hardening parameter of equivalent system mEQ 0.0236 0.0286 0.0273 0.0335

Ultimate deformation of equivalent system emax,EQ 0.0041 0.0051 0.0042 0.0052



static (pushover) analyses were carried out for both the as-builtand retrofitted structural systems. In so doing, two lateral forcepatterns were employed for the seismic structural assessment:

� A modal pattern, proportional to lateral forces consistent withthe lateral force distribution in the direction under considera-tion determined in the elastic analysis.� A uniform pattern based on lateral forces that are parallel to

mass regardless of elevation (uniform response acceleration).

It is worth mentioning that for the existing structure, nonlinearstatic analyses were not compliant with the provisions imple-mented in the seismic codes of practice (e.g. [16,17]). Theparticipation mass of the mode of vibration along the X-directionis indeed lower than 75% (specifically 67.48%, as summarised inTable 6). Conversely, the retrofitted structure possesses participa-tion masses higher than 85% along both X- (85.50%) andY-direction (89.54%).

Figs. 12 and 13 provide the response curves of the as-built andretrofitted structures along the X- and Y-direction; results werecomputed for positive and negative directions of the lateralloadings. The performance points at operational (OLS), damage(DLS), life safety (LSLS) and collapse prevention (CPLS) limit statesare also included.

The computed results show that for the modal load distribu-tion the displacement demands relative to LSLS and CPLS causestructural instability. The maximum interstorey drift (d/h) atsecond floor is 2.43% along the X-direction; the correspondingdimensionless storey seismic shear (also termed seismic coeffi-cient) Vy/Wtot is 19.82%. Along the Y-direction, the maximum d/his 1.76% at the second floor; the dimensionless shear Vy/Wtot is21.46%. The above maximum values of the response parameterswere estimated both at CPLS. As a result, the selected seismicstrengthening strategy was aimed at enhancing the global lateralstability of the building. When subjected to the uniform loadpattern, the frame is severely damaged, but the system is stable.

Table 7 shows the ratios of top displacement and total height(also quoted as global or roof drifts, dtop/H) and the interstoreydrifts d/h for the first and second floors; such ratios werecomputed for all limit states discussed in Section 5, namely OLS,DLS, LSLS and CPLS. Both types of nonlinear static analyses (modaland uniform lateral force patterns) performed on the structuralmodel of the existing building were considered. The computedresults show that the as-built structure has a sufficiently lowlateral displacement along both X- and Y-direction. The damage ischiefly concentrated at the top floor of the structure; theinterstorey drifts either exceed the 2% or are very close to it

Table 6Modal response parameters of existing and retrofitted buildings

Mode Existing building Retrofitted building

Period (s) ~M x (%) ~M y (%) Period (s) ~M x (%) ~M y (%)

1 0.612 0.10 89.60 0.397 0.01 89.5

2 0.557 67.48 0.21 0.329 85.5 0.01

3 0.458 20.49 0.03 0.272 3.74 0.03

Fig. 12. Response (pushover) curves along the X-direction (left) and Y-direction (right) for the existing building.

Fig. 13. Response (pushover) curves along the X-direction (left) and Y-direction (right) for the retrofitted building.



(2.43% at CPLS and 1.92% at LSLS for modal distribution of lateralforces). The global drifts are on average higher than 1% both atCPLS and at LSLS; such response parameters do not varysignificantly with the lateral load patterns. As a result, roofdrifts should not be employed as reliable assessment responseparameters; they express the lateral deformation weighed alongthe building height. Conversely, the interstorey drifts are effectivefor damage identification and concentration for multi-storeyframes.

The total drifts and interstorey drifts estimated for theretrofitted structure are summarised in Table 8. The comparisonbetween the results obtained from nonlinear static analysisperformed on the structural models of the sample buildingsdemonstrate that both global and local lateral displacements aresignificantly lowered after the intervention of the seismic retrofitof the existing structure. The estimated values of interstorey driftsare halved; the maximum d/h drops to 0.84% at CPLS (along theY-direction) and to 0.65% at LSLS (yet along the Y-direction).Lateral drifts are uniformly distributed along height; in turn,damage localizations are inhibited, especially at ultimate limitstates, i.e. LSLS and CPLS.

The values of the interstorey drifts summarised in Tables 7 and8 are also shown pictorially in Figs. 14 and 15, where storeypushover curves are provided for X- and Y-direction. Such curvescan also be utilized to detect the storey seismic shear resistanceand storey mechanisms, if any. The demand displacements at OLS,DLS, LSLS and CPLS are also included in the curves.

The comparison between the storey response curves of the as-built and retrofitted structure demonstrates the significant

reduction of the interstorey drifts caused by the installation ofthe UBs at the first and second floors of the framed building. Thedesign approach utilized herein and illustrated in details inSection 3 was effective for the uniform distribution of damagealong the frame height. Concentration of interstorey drifts iseliminated and strength drops prevented, thus leading to a stableand reliable ductile response and hence augmented energydissipation. The latter dissipation is concentrated in the hystereticbraces, as also confirmed by the results of the comprehensiveinelastic dynamic response assessment, outlined in Section 7.3.

The global response curves were also utilized to assess thelateral strength of the sample structures at serviceability andultimate limit states. The dimensionless base shears Vb/W for bothexisting and retrofitted structure are outlined in Tables 9 and 10for all limit states and pushover analyses.

The computed results show the significant increase of the baseshear that can be withstood by the system strengthened withdiagonal braces. The values of Vb/W for the as-built frame are onaverage 30–50% of the values corresponding to the retrofittedbuilding. The variation is, however, dependent on the limit state.For serviceability limit states the variations are lower than for theultimate limit state counterparts.

The response curves (global pushovers) in Figs. 12 and 13 andhence the values summarised in Tables 9 and 10 can be employedto determine the translational ductility (mD), the system over-strength (O) and the all-encompassing response factor (R- orq-factor). The latter factor is computed as follows:

q¼OmD ð19Þ

Table 7Lateral drifts of the as-built structure derived by the pushover curves.

Limit state Lateral drifts Load distribution

+XFM +XM �XFM �XM +YFM +YM �YFM �YM

CPLS Top displacement/total height dtop/H (%) 1.21 1.20 �1.21 �1.20 1.37 1.29 �1.39 �1.29

Interstorey drift/interstorey height at first level d1/h1 (%) 0.47 1.03 �0.47 �1.03 0.98 1.37 �0.99 �1.37

Interstorey drift/interstorey height at second level d2/h2 (%) 2.43 1.37 �2.43 �1.37 1.76 1.21 �1.80 �1.21

LSLS Top displacement/total height dtop/H (%) 0.96 0.95 �0.96 �0.95 1.08 1.02 �1.10 �1.02



DLS Top displacement/total height dtop/H (%) 0.33 0.32 �0.33 �0.32 0.37 0.35 �0.38 �0.35



OLS Top displacement/total height dtop/H (%) 0.24 0.23 �0.24 �0.23 0.27 0.25 �0.27 �0.25



Table 8Lateral drifts of the retrofitted structure derived by the pushover curves

Limit state Lateral drifts Load distribution


CPLS Top displacement/total height dtop/H (%) 0.66 0.55 �0.66 �0.53 0.86 0.78 �0.86 �0.77



LSLS Top displacement/total height dtop/H (%) 0.53 0.44 �0.53 �0.42 0.68 0.62 �0.68 �0.61



DLS Top displacement/total height dtop/H (%) 0.19 0.16 �0.19 �0.15 0.23 0.21 �0.23 �0.21



OLS Top displacement/total height dtop/H (%) 0.14 0.12 �0.14 �0.11 0.17 0.15 �0.17 �0.15





For the retrofitted system the overstrength O and the mD arehigher than 2.0 as also outlined in Table 11. The response factor isthus nearly equal to 5.0; the latter values are implemented inmany seismic codes worldwide (e.g. [16]) for ordinary capacity-designed moment-resisting frames. The computed values of the

response factor are similar to those proposed for the design ofnew steel framed systems with BRBs [11].

Ductile and brittle mechanisms were also checked; deforma-tion-based analyses were carried out to establish the onset ofductile failure modes. Strength-based criteria were assessed to

Fig. 14. Storey response curve of the as-built structure relative to modal (left) and uniform (right) lateral force patterns: X-direction (top) and Y-direction (bottom).

Fig. 15. Storey response curve of the retrofitted structure relative to modal (left) and uniform (right) lateral force patterns: X-direction (top) and Y-direction (bottom).



estimate brittle mechanisms. Ductile mechanisms at CPLS wereperformed comparing the required rotations localized at the endsections of the structural elements with the ultimate availablerotation available yu. The formulation for yu implemented inEurocode 8 (EC8) [16] was adopted in the calculations.

The safety factors for columns and beams of the assessedstructures are provided in Fig. 16. The deficiencies of the existingstructure show that the safety factors are lower than unity for anumber of structural members. The lowest values are 0.67 forbeams and 0.74 for columns; such values were computed formembers located at the second floor of the as-built framedsystem.

The values provided in Fig. 16 also prove the significantincrease of the safety factor stemming from the enhanced seismicperformance of the retrofitted structure. The minimum safetyfactors are 1.14 for columns and 1.05 for beams at first floor of theretrofitted building.

7.3. Nonlinear dynamic analyses

The inelastic seismic performance of the as-built and retro-fitted structures was further investigated through nonlineardynamic analyses. Such analyses were conducted with respectto suites of seven different groups of earthquake natural recordsscaled linearly for each of the code-compliant limit states (see alsoTable 8).

Interstorey drift and floor acceleration response histories wereestimated for each set of records applied to the base of the

structure and each limit state. Lateral drift and floor accelerationsare fundamental response quantities to evaluate the structuraland non-structural performance of framed systems underearthquake loading (e.g. Bertero and Bertero [22], among manyothers).

Tables 12 and 13 summarize the maximum interstorey driftsfor the X- and Y-direction at damageability (serviceability) andcollapse prevention (ultimate) limit states. The tables provide alsothe average values of interstorey drift (s), the standard deviations(d) and coefficients of variation (COV).

The results provided in Tables 12 and 13 demonstrate that theinterstorey displacements estimated for the retrofitted structureare considerably lower than the counterparts values computed forthe existing structure, especially at the second floor, where thestorey mechanism is detected at ultimate limit state. Thesefindings confirm the outcomes of the seismic response assess-ment carried out through the inelastic static analyses (pushovers)and discussed earlier. At CPLS, the maximum d/h at the secondfloor of the as-built structure is 2.185% (along the X-direction) and2.032% (along the Y-direction). In the retrofitted system themaximum interstorey drifts are detected at the first floor; themaximum d/h is 0.801% (along the Y-direction). At the secondfloor the average d/h is 0.311% along the X-direction and 0.415%along the Y-direction.

It is also observed that the results summarised in Tables 12and 13 show a lower scatter for the structure equipped with BRBs;for such structure the response is not significantly affected by theearthquake input characteristics and hence the seismic perfor-mance is enhanced.

The inelastic response of the sample structures was alsoassessed through the period elongation of the framed system. Inso doing, the fast Fourier transform (FFT) of the accelerationresponse histories at first and second floor was employed todetermine the predominant period (inelastic period). It may beargued that the higher the period elongation, the higher theductile response of the structure. The FFT was utilized for the timehistories derived by using the suite of selected earthquake naturalrecords at ultimate limit states, i.e. LSLS and CPLS. The computedinelastic periods of vibrations are outlined in Tables 14 and 15 forexisting and retrofitted buildings.

Table 9Seismic base shear of the existing structure.

Load distribution


Vb (kN) Vb/W (%) Vb (kN) Vb/W (%) Vb (kN) Vb/W (%) Vb (kN) Vb/W (%) Vb (kN) Vb/W (%) Vb (kN) Vb/W (%) Vb (kN) Vb/W (%) Vb (kN) Vb/W (%)

CPLS 1649 14.6 2202 19.5 1649 14.6 2202 19.5 1839 16.3 2082 18.4 1839 16.3 2082 18.4

LSLS 1694 15.0 2153 19.0 1694 15.0 2153 19.0 1808 16.0 2049 18.1 1808 16.0 2049 18.1

DLS 1303 11.5 1537 13.6 1303 11.5 1537 13.6 1307 11.6 1424 12.6 1307 11.6 1424 12.6

OLS 1109 9.8 1308 11.6 1109 9.8 1308 11.6 1106 9.8 1198 10.6 1106 9.8 1198 10.6

Table 10Seismic base shear of the retrofitted structure.

Load distribution


Vb (kN) Vb/W (%) Vb (kN) Vb/W (%) Vb (kN) Vb/W (%) Vb (kN) Vb/W (%) Vb (kN) Vb/W (%) Vb (kN) Vb/W (%) Vb (kN) Vb/W (%) Vb (kN) Vb/W (%)

CPLS 4814 42.6 5066 44.8 4814 42.6 5066 44.8 3905 34.5 4172 36.9 3905 34.5 4172 36.9

LSLS 4602 40.7 4816 42.6 4602 40.7 4816 42.6 3738 33.0 4014 35.5 3738 33.0 4014 35.5

DLS 3168 28.0 3172 28.0 3168 28.0 3172 28.0 2671 23.6 2794 24.7 2671 23.6 2794 24.7

OLS 2527 22.3 2571 22.7 2527 22.3 2571 22.7 2149 19.0 2300 20.3 2149 19.0 2300 20.3

Table 11Global overstrength, translational ductility and response modification factor of the

retrofitted structure.

Response parameter Load pattern

XFM YFM XM YM

O 2.54 2.03 2.13 2.14

mD 2.17 2.36 2.07 2.27

q 5.51 4.79 4.40 4.86



1.290.74

1.07 0.88

3.97

1.42

2.081.65

0.00.51.01.52.02.53.03.54.04.55.0

Col

umn

Saf

ety

Fact

or

2.13 2.91 0.78 0.67

31.74

39.78

32.85 30.74

0

10

20

30

40

Bea

m S

afet

y Fa

ctor

1.40 1.771.14

1.84

3.17

6.69

2.43

4.45

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Col

umn

Saf

ety

Fact

or

S min S max

2.47 3.781.05 1.65

28.41

34.04

21.01

29.86

0

10

20

30

40

Bea

m S

afet

y Fa

ctor

Fig. 16. Minimum and maximum ratio between available and required rotations for columns (left) and beams (right) for the as-built (top) and retrofitted (bottom) structure.

Table 12Maximum interstorey drift at damageability limit state for existing and retrofitted buildings

Existing building Retrofitted building

X-direction Y-direction X-direction Y-direction

1st floor 2nd floor 1st floor 2nd floor 1st floor 2nd floor 1st floor 2nd floor

dr1/h (%) 0.259 0.389 0.272 0.387 0.094 0.098 0.156 0.159

dr2/h (%) 0.189 0.320 0.346 0.452 0.095 0.108 0.115 0.111

dr3/h (%) 0.162 0.227 0.263 0.284 0.082 0.090 0.124 0.110

dr4/h (%) 0.288 0.373 0.197 0.221 0.148 0.143 0.118 0.130

dr5/h (%) 0.161 0.232 0.258 0.277 0.173 0.188 0.132 0.135

dr6/h (%) 0.210 0.291 0.260 0.334 0.127 0.142 0.149 0.148

dr7/h (%) 0.273 0.417 0.380 0.468 0.100 0.109 0.164 0.164

s (%) 0.220 0.321 0.282 0.346 0.117 0.125 0.137 0.137

d (%) 0.049 0.070 0.057 0.086 0.031 0.032 0.018 0.020

COV (%) 22.30 21.80 20.20 24.90 26.50 25.40 13.20 14.60

Table 13Maximum interstorey drift at collapse prevention limit state for existing and retrofitted buildings

Existing building Retrofit building



dr1/h (%) 0.539 1.748 0.458 0.885 0.558 0.303 0.669 0.382

dr2/h (%) 0.501 1.050 1.294 1.446 0.387 0.306 0.801 0.434

dr3/h (%) 0.360 0.667 0.914 1.266 0.296 0.320 0.430 0.434

dr4/h (%) 1.593 1.864 1.056 1.222 0.527 0.337 0.288 0.349

dr5/h (%) 0.857 1.366 0.857 1.366 0.380 0.325 0.515 0.414

dr6/h (%) 0.916 1.159 0.911 1.075 0.418 0.334 0.575 0.362

dr7/h (%) 1.158 2.185 0.887 2.032 0.413 0.254 0.539 0.529

s (%) 0.846 1.434 0.911 1.327 0.426 0.311 0.545 0.415

d (%) 0.398 0.488 0.232 0.335 0.083 0.026 0.152 0.056

COV (%) 47.00 34.00 25.50 25.30 19.50 8.40 27.90 13.50



It is found that the inelastic periods are floor-dependent for theas-built structure; the top floor exhibits longer periods withrespect to the first floor. On average, the second floor exhibitsperiods that are twice the periods of the first floor, e.g., 0.39sversus 0.78s (along the X-direction) and 0.37 s versus 0.87 s (alongthe Y-direction) at LSLS. This outcome characterizes both the LSLSand the CPLS. Additionally, the periods computed for the latterultimate limit states are similar.

The comparison between the values of the period summarisedin Tables 14 and 15 with those in Table 6, computed througheigenvalue analysis as illustrated in Section 7.1, shows that theaverage elongation of the elastic periods of vibration for the as-built structure is negligible (the maximum variation is 4.6% alongthe X-direction at both LSLS and CPLS). Conversely, for theretrofitted structure the average period elongation is about 30%(28.5% for LSLS and 30.7% for CPLS) along the X-direction and 20%(18.5% for LSLS and 18.7% for CPLS) along the Y-direction. It canthus be argued that the presence of hysteretic BRBs is effective toaugment the ductility and energy dissipation of the system as awhole and hence enhance the global structural performanceunder moderate-to-high magnitude earthquakes.

The hysteretic brace response was also investigated throughresponse history analyses. The maximum axial displacementdemands and ductility were computed for the structure subjectedto the suite of natural records. The above response parametersare provided in Table 16 for both first and second floors. Themaximum demand is imposed at the ground floor, in compliancewith the assumption of the design approach illustrated in Section3. The target design mechanism is, in fact, a global failure modeand the lateral force patterns are derived from the force

distributions implemented in most seismic codes of practice.Such distributions are inverted triangular patterns. At designstage it is of paramount importance to check that the maximumaxial displacement demand of the BRB is compatible with itsultimate deformation and the layout of the brace-to-frameconnection. For the case study a device with 725 mm of strokeis deemed adequate for the second floor; a value of 715 mm maybe selected for the devices at the first floor.

The maximum axial ductility of the BRBs should also bechecked. For the case study, it can be assumed equal to 10 for bothfirst and second floors. The computed value of maximumtranslation ductility is compliant with BRBs available on themarket.

To further investigate the response of BRBs, the hystereticresponse was also assessed. The time history of two typicaldevices is provided in Fig. 17 with respect to the axial force andaxial displacement response. The computed results demonstratethe large amount of energy dissipation and its cyclic stabilityunder moderate-to-high magnitude earthquakes.

The type and layout of BRBs utilized for the retrofitting of theexisting sample structure are very effective for absorption andenergy dissipation. The energy time history, computed for DLSand CPLS, and displayed in Fig. 18, demonstrates that a largeamount (more than 60%) of input seismic energy is dissipated bythe BRBs. At DLS the latter device exhibits an elastic behaviour.

Finally, it is worth proving that the existing RC framedstructure (designed primarily for gravity loads) behaves linearly,thus fulfilling the design approach illustrated pictorially in Figs. 3and 4, namely retrofitting strategy based on damage controlledstructure schemes. In so doing, Fig. 19 provides the cyclic base

Table 14Inelastic periods of vibration at life safety limit state for existing and retrofitted buildings




Tinel1 (s) 0.44 0.66 0.50 0.50 0.44 0.44 0.50 0.50

Tinel2 (s) 0.30 0.54 0.30 0.72 0.46 0.38 0.56 0.46

Tinel3 (s) 0.32 0.64 0.28 0.96 0.38 0.38 0.52 0.46

Tinel4 (s) 0.44 0.64 0.32 1.02 0.44 0.44 0.32 0.44

Tinel5 (s) 0.34 0.88 0.32 1.24 0.34 0.34 0.46 0.42

Tinel6 (s) 0.38 0.96 0.36 1.12 0.50 0.38 0.54 0.36

Tinel7 (s) 0.50 1.12 0.50 0.50 0.50 0.50 0.52 0.52

s (s) 0.39 0.78 0.37 0.87 0.44 0.41 0.49 0.45

d (s) 0.07 0.21 0.09 0.30 0.06 0.05 0.08 0.05

COV (%) 18.99 27.25 25.23 34.21 13.58 13.21 16.52 11.68

Table 15Inelastic periods of vibration at collapse prevention limit state for existing and retrofitted buildings




Tinel1 (s) 0.44 0.66 0.50 0.50 0.46 0.44 0.50 0.50

Tinel2 (s) 0.32 0.54 0.36 0.72 0.52 0.52 0.54 0.46

Tinel3 (s) 0.32 0.64 0.26 0.96 0.38 0.38 0.54 0.46

Tinel4 (s) 0.44 0.64 0.32 1.02 0.44 0.44 0.32 0.44

Tinel5 (s) 0.34 0.86 0.32 1.24 0.34 0.34 0.46 0.42

Tinel6 (s) 0.38 0.96 0.36 1.12 0.38 0.38 0.56 0.36

Tinel7 (s) 0.50 1.12 0.50 0.50 0.50 0.50 0.52 0.52

s (s) 0.39 0.77 0.37 0.87 0.43 0.43 0.49 0.45

d (s) 0.07 0.21 0.09 0.30 0.07 0.07 0.08 0.05

COV (%) 17.91 27.16 24.63 34.21 15.57 15.44 16.76 11.68



Table 16Maximum axial deformations and ductility of the hysteretic diagonal braces.

BRB axial displacement BRB axial ductility



Dlmax1 (mm) 14.1 8.2 17.4 9.7 mmax1 12.2 6.8 15.1 8.1

Dlmax2 (mm) 10.0 8.2 18.6 11.7 mmax1 8.7 6.8 16.2 9.7

Dlmax3 (mm) 7.9 8.1 9.1 9.6 mmax1 6.9 6.7 7.9 8.0

Dlmax4 (mm) 12.4 8.7 8.9 8.5 mmax1 10.8 7.3 7.7 7.1

Dlmax5 (mm) 10.0 8.2 10.8 8.6 mmax1 8.7 6.9 9.4 7.1

Dlmax6 (mm) 11.1 8.8 11.6 9.1 mmax1 9.7 7.3 10.1 7.6

Dlmax7 (mm) 10.0 7.1 21.6 11.1 mmax1 8.7 5.9 18.8 9.2

s (mm) 10.8 8.2 14.0 9.7 s 9.4 6.8 12.2 8.1

d (mm) 1.8 0.5 4.7 1.1 d 1.6 0.4 4.1 0.9

COV (%) 17.0 6.0 34.0 12.0 COV 17.0 6.00 34.0 12.0

Fig. 17. Response history for typical hysteretic buckling restrained braces: hysteretic loop (top), force- (middle) and axial displacement (bottom) time histories.

100

75

50

25

0

Ene

rgy

(kJ)

3000

2500

2000

1500

1000

500

0

Ene

rgy

(kJ)

Time (s)0 5 10 15 20 25 30

Time (s)0 5 10 15 20 25 30

Fig. 18. Energy response history under earthquake loading in the retrofitted structure: damageability (left) and collapse prevention (right) limit states.



shear-roof displacement response computed for a typicalearthquake record illustrated in Section 5 and scaled at CPLS.The contributions of the added devices, i.e. diagonal UBs, and theresponse of the existing structure (RC framed system) are plottedseparately to demonstrate that the as-built RC system remains inthe elastic range.

The results of the time history analyses confirm that theenergy absorption and dissipation are concentrated in the addedbraces.

8. Conclusions

The present work focuses on the seismic performance assess-ment of typical reinforced concrete (RC) existing buildingstructures designed for gravity loads only. A refined fibre-basedthree-dimensional finite element model was implemented toassess the nonlinear earthquake response of a sample non-ductileRC multi-storey building. The existing two-storey framed struc-ture exhibits high vulnerability, i.e. low lateral resistance andlimited translation ductility; hence an effective strategy schemefor seismic retrofitting was employed. Such scheme comprisesbuckling restrained braces (BRBs) placed along the perimeterframes of the multi-storey building. The innovative BRBs possesscompressive strength, which is about 10–15% greater than tensile;the member buckling is prevented and hence the cyclic energydissipation is large and stable.

The adopted design approach assumes that the global responseof the inelastic structural system is the sum of the elastic frame(termed primary structural system) and the perimeter diagonalbraces (quoted as secondary system); the latter braces absorb anddissipate a large amount of hysteretic energy under earthquakeground motion. This design approach is effective for damagecontrolled structures and can be utilized for performance-basedseismic retrofitting.

A simplified step-by-step procedure, compliant with theperformance-based (force- and displacement-based) framework,was illustrated and applied to the framed structure of the existingnon-ductile school building. Equivalent viscous damping orresponse modification factors may be adopted for the design ofnew steel frames with BRBs or for existing RC frames retrofittedwith BRBs.

Extensive nonlinear static (pushover) and dynamic (responsehistory) analyses were carried out for both the as-built andretrofitted structures to investigate the efficiency of the adoptedintervention strategy. A set of seven code-compliant naturalearthquake records were selected and employed to performinelastic history analyses at serviceability (operational anddamageability limit states, OLS and DLS) and ultimate limit states(life safety and collapse prevention limit states, LSLS and CPLS).

The comparison between the results obtained from nonlinearanalyses demonstrate that that both global and local lateraldisplacements are notably reduced after the seismic retrofit of theexisting system. In the as-built structure, the damage is primarilyconcentrated at the second floor (storey mechanism); thecomputed interstorey drifts are 2.43% at CPLS and 1.92% at LSLSfor modal distribution of lateral forces. Conversely, for theretrofitted structure, the estimated values of interstorey drifts(d/h) are halved; the maximum d/h are 0.84% at CPLS (along theY-direction) and 0.65% at LSLS (yet along the Y-direction).Furthermore, lateral drifts are uniformly distributed along theheight; in turn, damage localizations are inhibited, especially atultimate limit states, i.e. LSLS and CPLS.

The response curves were utilized to estimate the globaloverstrength O, translation ductility mD and the all-encompassingresponse factor (R- or q-factor). The values of O vary between 2.14and 2.54 for the retrofitted structure; similarly, the mD-valuesrange between 2.07 and 2.36. The estimated response factor is onaverage equal to 5.0, which corresponds to the value utilizedin many seismic codes worldwide for ordinary RC capacity-designed moment resisting frames. The computed R-factorsare similar to those proposed for the design of new steelframed structures equipped with BRBs, i.e. values rangingbetween 4.5 and 6.5.

The structural performance of the bare and retrofitted systemsis also assessed with respect to the elongation of the fundamentalperiod of vibration with respect to the values derived by modalanalysis. The higher the period elongation, the higher the ductilityof the system. It is found that, for the braced frame, undermoderate-to-high magnitude earthquakes, the average periodelongation is about 30%, while for the existing building theelongation is negligible (lower than 5%). As a result, BRBs areeffective to enhance the ductility and energy dissipation of thesample structural system.

Dire

ctio

n X

= = +

+D

irect

ion

Y

= = +

Fig. 19. Cyclic response (left) and energy dissipation (right) of the retrofitted framed structure: hysteretic response of the structure with braces (left), existing structure

(middle) and buckling restrained braces (right).



The above results were derived from inelastic static analysesand were confirmed by detailed nonlinear dynamic responsehistories. The latter proved also that more than 60% of inputseismic energy is dissipated by the UBs at ultimate limit states.The estimated maximum axial ductility of the braces is about 10;the latter value of translation ductility is compliant with BRBsavailable on the market. At DLS the latter device exhibits anelastic behaviour. It can thus be concluded that, under moderateand high magnitude earthquakes, the damage is concentrated inthe added dampers and the existing RC framed structure (bareframe) has an elastic behaviour.

Acknowledgements

This work was financially supported by the Italian ConsortiumTecnologie per il Recupero Edilizio (Technologies for the Restora-tion of Structures), under the project TELLUS-STABILITA (Testing of

innovative technologies and devices to protect the structures from the

environmental-induced vibrations, with emphasis on earthquake

loading), funded by the Ministry of Education, University andResearch—FAR art.5 D.M.8/8/2000, no. 593. Any opinions, find-ings and conclusions or recommendations expressed in this paperare those of the authors and do not necessarily reflect those of theConsortium RELUIS. The numerical simulations were carried outby Mr. Pasqualino Costa; his immense efforts and enthusiasticdedication are vividly appreciated.

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