Engineering Structures 76 (2014) 295–312

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Engineering Structures

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Seismic demand on brace-intersected beams in two-story X-bracedframes

http://dx.doi.org/10.1016/j.engstruct.2014.07.0220141-0296/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +1 (515) 294 6473.E-mail address: jshen@iastate.edu (J. Shen).

Jay Shen a,⇑, Rou Wen b, Bulent Akbas c, Bilge Doran d, Eren Uckan e

a Department of Civil, Construction and Environmental Engineering, Iowa State University, IA, USAb Sharma & Associates, Inc., Countryside, IL, USAc Department of Earthquake and Structural Engineering, Gebze Institute of Technology, Turkeyd Department of Civil Engineering, Faculty of Civil Engineering, Yıldız Technical, Turkeye Department of Earthquake Engineering, Kandilli Observatory and Earthquake Research Institute (KOERI), Bosphorus University, Istanbul, Turkey

a r t i c l e i n f o

Article history:Received 30 December 2013Revised 11 June 2014Accepted 18 July 2014

Keywords:Brace-intersected beamConcentrically braced frameTwo-story X-braced frameDuctility demand

a b s t r a c t

A study on the seismic demand on braced-intersected beams in two-story X-braced frames is presentedto address a major concern: whether or not the beam is likely to become inelastic during the designearthquake ground motion, and if so, how such inelastic deformation affects the seismic behavior ofthe frames as a whole. Typical 6- and 12-story buildings using two-story X-braced frames with strongand weak braced-intersected beams were subjected to a set of 20 earthquake ground motions, and result-ing seismic responses were discussed in terms of seismic strength and deformation demands on beamsand the impact of inelastic deformation in weak beams on critical components in two-story X-bracedframes. In addition, the 6- and 12-story buildings with inverted V-braced frames were also studied forcomparison. The study concludes that brace-intersected beams in two-story X-braced frames designedwith the minimum possible required strength permitted by the current design provisions would undergosignificant vertical inelastic deformation when the frames experience the expected 0.02–0.04 story driftratio response, and the inelastic deformation in the middle spans of brace-intersected beams substan-tially increases ductility demands on braces and beam-to-column connections. This study also finds thatthe use of story drift ratio as sole deformation response index fails to reveal actual seismic response ofcritical components in two-story X-braced frames when beams experience inelastic deformation withintheir own spans.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

The current seismic design specification [1] requires that thebeams intersected by braces in a special concentrically bracedframe (SCBF) with V-type or inverted V-type configurations shallremain elastic under the design earthquake. This requirement indi-cates that a brace-intersected beam has required design strengthunder a large unbalanced force from the difference in yieldingand buckling strengths at about 2–4% of story drift, always result-ing in deep beam sections in braced bays. Experimental and analyt-ical studies [2,3] have shown that deep girders in the SCBF mightimpose significant flexural stress on columns at beam-to-columnconnections, potentially leading to fracture in columns. With anattempt to reduce the beam size, practicing engineers have beenusing the two-story X-braced frames, having Inverted V-type

braces in one story and V-type braces of the same sizes above it.Some structural engineers believe that there is no need to considerunbalanced force in the brace-intersected beams since unbalanceforces below and above the beam would have same quantity butopposite directions in the two-story X-braced frame. Such practiceassuming no or little unbalanced force on the brace-intersectedbeam in two-story X-braced frames appears to be encouraged bysome design examples in AISC [4].

The literature survey by the authors has found little that providessubstantial basis to support such widely spread practice. The onlywork referred by AISC 341 [1], related to two-story X-braced frames,Khatib et al. [5] studied seismic behavior of concentrically bracedframes with V-, inverted V-, X-, tie-bar-to-ground, zipper, andtwo-story X-type braces. Overall seismic response of a six-storytwo-story X-braces frame subject to a recorded earthquake groundmotion was presented with no information on brace-intersectedbeams. Chen and Mahin [6] conducted a comprehensive assessmenton performance-based seismic demand of 2-, 3-, 6-, 12- and

(a) Typical floor plan with locations of SCBF Frames 5

@ 3

0 ft

5 @ 30 ft

SCB

F

6 @ 13 ft

(b) Elevation for frames having two-story X bracing configuration

6 @ 13 ft

(c) Elevation for frames having chevron bracing configurations

Fig. 1. Plan and elevation of the studied 6-story steel braced frames.

296 J. Shen et al. / Engineering Structures 76 (2014) 295–312

16-story special concentrically braced frames and buckling-restrained braced frames that were designed based on ASCE 7-05and AISC 341-05. The two-story X-braced frame was selectedbecause of its popularity in practice, and designed with small unbal-anced loads on the brace-intersected beams. But it is not clear howthe beams behaved during earthquake ground motion excitations.Yoo et al. [7] conducted a numerical simulation study to examinethe influence of gusset plate, framing members and floor slab oncyclic behavior of two-story X-braced frames. The inelastic behaviorof gusset plates and potential brace fracture were investigated bystatic nonlinear analysis using a typical first-mode loading patternwith three beam sizes included. No information was provided onhow the beams were selected, and the response of brace-intersectedbeams was not discussed. It should be noted that the static analysis,particularly with the first-mode loading pattern, is unlikely to revealactual seismic demand on the brace-intersected beams in two-storyX-braced frames during earthquake ground motions. A recent workby Hsiao et al. [8] included two-story X-braced frames in a series ofthree-story and nine-story special concentrically braced frames toquantify the response modification coefficient through nonlinearanalysis. The paper does not include any information about thebrace-intersected beams, such as how they were designed, theiractual sizes used, and their response during earthquake groundmotions.

According to AISC 341 seismic design provisions, the requiredstrength of beams shall be determined from an analysis in whichall braces in tension are assumed to resist forces correspondingto their expected strength and all braces in compression areassumed to resist their expected post-buckling strength. This anal-ysis is based on an expected inelastic inter-story deformation limitstate within one story, from which the maximum possible requireddesign strength for the brace-intersected beam in an inverted v-, orv-braced frame can be determined. However, the expected inelas-tic deformation limit state in a two-story X-braced frame withcombined inverted V- and V-type braces intersecting the samebeam is not necessarily the same as for individual inverted V-, orV-type braces. Applying the maximum possible design loadingfor inverted V-, or V-type braces cases directly to the two-storyX-type braces is to assume that the inverted V-type braces belowand V-type braces above the beam reach their inelastic deforma-tion limit at the same time. This assumption is inconsistent withthe fact that story drift ratio time histories of any two adjacentfloors are in general different from each other, and for the bracesin both floors to reach their inelastic deformation limit at the sametime is a rare occasion. It is obvious that such a rare occasion pro-duces the lowest required design strength on the beam, and anydeviation from such occasion would result in higher loads on thebeam. Consequently, the brace-intersected beam designed withthe lowest seismic load assuming the rare occasion might becomeinelastic during the design earthquake. Furthermore, it is not clearhow an inelastic brace-intersected beam would influence overallstructural behavior of the two-story X-braced frame.

In this paper, we present a study of the seismic demand onbraced-intersected beams in two-story X-braced frames. Typical6-story and 12-story buildings with two-story X-braced frameswere designed based on two different interpretations of the designprovisions on brace-intersected beams in AISC 341: (i) the X-typeconfiguration might be considered as separate inverted V-typeand V-type with only one of them creating the unbalanced loadon the beam, leading to strong beams; and (ii) both inverted V-typeand V-type braces reach their unbalanced loads, leading to weakbeams. In addition, the 6- and 12-story inverted V-braced frameswere also designed for comparison. These three types of frameswith 6 and 12 stories, a total of six frames, were subjected to aset of 20 earthquake ground motions. The results are presentedin terms of seismic demands on brace-intersected beams and the

impact of inelastic behavior of such beams on overall seismic per-formance of the structures.

2. Structures and earthquake ground motions

2.1. Design of two-story-X-braced frames (TSXBFs)

Modal frames investigated in this study were designed followingprovisions in ASCE 7 [9] for required design strength and AISC 341[1] for seismic design requirements. Figs. 1 and 2 show the floorplans and elevations of 6-, and 12-story office buildings, respec-tively. Special concentrically braced frame (SCBF) with V- andinverted V-braces in alternating stories, forming X-braces overtwo stories, named as ‘‘two-story X-braced frame (TSXBF)’’, isarranged on the perimeter as seismic force resisting systems in bothorthogonal directions. The floor system consists of a 3–1/2 in. thickconcrete on the metal deck with steel shear studs welded to floorbeams and cast in concrete decking, which is considered to have a‘‘non-flexible’’ diaphragm for the purpose of transferring lateralforces to the TSXBFs. The columns along other lines are connectedto girders with shear beam-to-column connections, forming‘‘gravity-only frames’’ to carry gravity loads. The contribution fromthe gravity-only frames to resisting lateral forces is not included inthis study. Dead and live loads of 80 psf and 50 psf, respectively,

(a) Typical floor plan with locations of SCBF frames

12 @ 13 ft

(c) Elevation for frames having inverted V bracing Configurations

(b) Elevation for frames having two-story X-bracing configuration

12 @ 13 ft

5 @

30

ft

5 @ 30 ft

Bra

ced

Fram

e

Fig. 2. Plan and elevation of the studied 12-story steel braced frames.

J. Shen et al. / Engineering Structures 76 (2014) 295–312 297

were assumed in the design. The buildings were located at a sitewith Ss and S1 equal to 2.0 and 1.0, respectively. The total base shearwas 2400 kips (22% of total building weight) in the 6-story building,and each braced bay was designed by a quarter of the total baseshear. The 12-story building was designed with the total base shearof 4100 kips (19% of total building weight) and each of six bracedbays was designed for 1/6 of base shear.

The brace sizes were determined by the basic load combinationin ASCE 7 [9]: (1.2 + 0.2SDS)DL + qQE + 0.5LL, where redundancy fac-tor q was taken as 1.3. The same size of round or square hollowsteel section was used for the braces intersecting the same beam.In addition, the effort was made to select the lightest section pos-sible to keep the design and required strengths close to each other.

All braces satisfy the width-to-thickness ratio requirement forhighly ductile members stipulated in AISC 341 [1].

The columns in braced bays were designed using amplified seis-mic load. The amplified seismic load on columns was determinedbased on various possible inelastic deformation scenarios in bracesto create maximum possible required design strength for columns.The typical procedure in so doing was to replace all braces withassumed axial forces, and apply these axial forces at brace connec-tions to find the maximum possible amplified seismic load on col-umns. Three analytical cases (two primary and one additionalcases), were conducted following the provisions stipulated explic-itly in AISC 341 [1] for the column strength in SCBF. In the first pri-mary case, the braces were assumed to reach their expectedstrength in tension and compression, respectively. In the secondprimary case, the braces in tension were replaced with theirexpected strength in tension, and braces in compression with30% of their expected strength in compression. In the additionalcase, the ASCE 7 load combination with an over-strength factorof 2.0 was applied to the SCBF structures with all braces in com-pression removed. The forces in the columns from this case wereconsidered as upper bound of required strengths of columns, asindicated in AISC 341 [1]. It was found that the required strengthfor column design was governed by the results from the additionalcase in both 6-story and 12-story frames. Note that the tensileforces in the braces exceeded their design strength in this addi-tional analysis case, but the braces were kept elastic for the ampli-fied seismic load on columns.

The required design strength of brace-intersected beams isrelated to the main objective of this study, and was given a specialattention. The provisions in AISC 341 [1] (F2) require that theamplified seismic load on such beams be based on ‘‘the larger forcefrom the following two analyses:

(i) An analysis in which all braces are assumed to resist forcescorresponding to their expected strength in compression orin tension.

(ii) An analysis in which all braces in tension are assumed toresist forces corresponding to their expected strength andall braces in compression are assumed to resist theirexpected post-buckling strength.

Fig. 3 illustrates possible loading types on the beams in a two-story X-braced frame (TSXBF) in (a) and (b). Also included in Fig. 3are the beams in an inverted-V and V type braced frames, in (c) and(d), respectively, for comparison. Two types of beams in a TSXBF,the beam intersected by braces (Type a), and the beam not inter-sected by braces (Type b), are shown in Fig. 3a and b, respectively.Note that amplified seismic lateral force Fi in Fig. 3 will be deter-mined after the brace resistances are specified for each of thetwo above-mentioned analyses (i) and (ii) for the entire TSXBFstructure. Referring to Fig. 3a and b, one can observe the followingfacts:

� The required seismic design strength of ‘‘Type a’’ beamwould be very small for both analyses. In fact, they areequal to zero if the braces below and above the beam havethe same size. As a result, the governing design strength of‘‘Type a’’ beams would be from the gravity loads.

� The required seismic compressive strength of ‘‘Type b’’beam would be governed by the analysis case (ii) whenall braces resist forces corresponding to their expectedstrength in tension and post-buckling strength incompression.

It appears that the required strength for the brace-intersectedbeam in the TSXBF is less than that in either inverted V- or

Fig. 3. Types of amplified seismic loads on brace-intercepted beams in a braced bay with two-story X (TSXBF), inverted -V (InVBF), and V (VBF) configurations.

298 J. Shen et al. / Engineering Structures 76 (2014) 295–312

V-braced frames. But, it would be un-conservative to consider norequired seismic strength on brace-intersected beam, a criticalseismic-resisting component. In order to assess the seismicdemand on the brace-intersected beams, two TSXBFs, one (TypeA frame) with the strongest brace-intersected beams possible,and the other (Type B frame) with the weakest brace-intersectedbeams possible, were selected. For comparison, an inverted-Vframe (Type C frame) was also included for each of the 6- and12-story buildings. In Type A frame, the brace-intersected beamswere designed as if the V braces above the beam did not exist. InType B frame, the brace-intersected beams were designed basedon the assumption that the sum of braces intersecting a beamwas negligible. Type C is an inverted-V CBF, and has the samebrace-intersected beams as Type A. The member sizes are summa-rized in Tables 1 and 2 for the 6-story and 12-story braced frame,respectively.

2.2. Finite element modeling of concentrically braced frames

Two dimensional (2D) finite element structural models weredeveloped within RUAUMOKO 2D [10] framework. RUAUMOKO2D includes a type of element, REMENNIKOV Steel Brace, to modelsteel braces. REMENNIKOV Steel Brace element was developedusing plastic hinge concept and empirical formula for tangentmodulus to simulate post-buckling inelastic behavior of braces.The brace element in RUAUMOKO 2D appears to simulate selectbraces under cyclic inelastic deformation well, but has not been

Table 1Member sizes of the 6-story braced frames.

Level Braces Columns inbraced bay

Beam

Typeframe

6 HSS 8.625 � 0.500 (KL/r = 82, D/t = 18.5) W12 � 65 W215 W334 HSS 10.000 � 0.625 (KL/r = 71, D/t = 17.2) W12 � 136 W213 W332 HSS 9 � 9 � 5/8 (KL/r = 70, b/t = 12.5, h/t = 12.5) W12 � 252 W211 W33

Notes: (1) Round and rectangle brace shape have been used to keep the brace design strenused for braces and columns, and moderately ductile members for the beams intercept

used extensively in the earthquake engineering community. Inthe present study, the numerical evaluations on the element andRUAUMOKO 2D program were conducted to validate the finite ele-ment models used in the analyses. Two 40 mm � 40 mm � 3 mmsquare HSS braces tested by Nip et al. [11] and one101.6 mm � 101.6 mm � 6.4 mm square HSS brace tested by Fellet al. [12] were chosen for the evaluation. Fig. 4A(1) shows the40 mm � 40 mm � 3 mm square HSS brace and cyclic loading his-tory. Two brace lengths, L = 2050 mm and 1250 mm, respectively,were used in the specimens to have slenderness ratio, KL/r = 70and 42, respectively. The braces were modeled by RUAUMOKO2D. The results are compared in Fig. 4A(2) and (3) for the braceswith KL/r = 70, 42, respectively. A single Steel Brace element inRUAUMOKO 2D produces a good simulation reflecting the inelasticdeformation behavior of a ductile brace: tension yielding; com-pression buckling; post-buckling deterioration of compressiveloading capacity. Fig. 4B(1) shows cyclic loading history for101.6 mm � 101.6 mm � 6.4 mm square HSS brace. The resultsfrom the test and simulation by RUAUMOKO 2D are comparedwell, as shown in Fig. 4B(2).

Columns were modeled by the steel beam–column element inRUAUMOKO 2D. The axial force-bending moment interactivecurves stipulated in AISC 360 [13] were employed. Two differentbeam elements were selected to model various beam types shownin Fig. 3. The beams intersected by braces, such as Types a, c, and d,are subjected to combined axial force and bending moment, and abeam–column element was used to simulate strong interaction

s in braced bay Gravity columns Gravitybeams

A Type Bframe

Type Cframe

Interior Exterior Corner

� 44 W33 � 221 W10 � 39 W10 � 33 W10 � 33 W21 � 44� 221 W21 � 44� 44 W33 � 291 W10 � 68 W10 � 39 W10 � 33� 291 W21 � 44� 44 W33 � 354 W10 � 100 W10 � 49 W10 � 33� 354 W21 � 44

gth as close to the required strength as possible; and (2) highly ductile members areed by braces.

Tabl

e2

Mem

ber

size

sof

the

12-s

tory

brac

edfr

ames

.

Leve

lB

race

sC

olu

mn

sin

brac

edba

yB

eam

sin

brac

edba

yG

ravi

tyco

lum

ns

Gra

vity

beam

s

Fram

eA

Fram

eB

Fram

eC

Inte

rior

Exte

rior

12H

SS7.

500�

0.50

0(K

L/r

=96

,D/t

=16

.1)

W14�

53W

21�

44W

33�

201

W12�

40W

12�

40W

21�

4411

W33�

201

W21�

4410

HSS

10.0

00�

0.50

0(K

L/r

=70

,D/t

=21

.5)

W14�

132

W21�

44W

33�

263

W12�

65W

12�

409

W33�

263

W21�

448

HSS

10.0

00�

0.62

5(K

L/r

=71

,D/t

=17

.2)

W14�

193

W21�

44W

33�

318

W12�

87W

12�

537

W33�

318

W21�

446

HSS

9�

9�

5/8

(KL/

r=

70,b

/t=

12.5

,h/t

=12

.5)

W14�

283

W21�

44W

36�

361

W12�

120

W12�

655

W36�

361

W21�

444

HSS

14.0

00�

0.62

5(K

L/r

=50

,D/t

=24

.1)

W14�

398

W21�

44W

36�

395

W12�

152

W12�

793

W36�

395

W21�

442

HSS

14.0

00�

0.62

5(K

L/r

=50

,D/t

=24

.1)

W14�

500

W21�

44W

36�

395

W12�

170

W12�

871

W36�

395

W21�

44

Not

es:

(1)

Rou

nd

and

rect

angl

ebr

ace

shap

eh

ave

been

use

dto

keep

the

brac

ede

sign

stre

ngt

has

clos

eto

the

requ

ired

stre

ngt

has

poss

ible

;an

d(2

)h

igh

lydu

ctil

em

embe

rsar

eu

sed

for

brac

esan

dco

lum

ns,

and

mod

erat

ely

duct

ile

mem

bers

for

the

beam

sin

terc

epte

dby

brac

es.

J. Shen et al. / Engineering Structures 76 (2014) 295–312 299

between axial force and bending moment. Type c beams are pri-marily subjected to axial force, and simple beam/column elementwas used for this type of beams.

All the beam-to-column connections were modeled as ‘‘simple’’connections. P–D effect was considered by introducing gravity col-umns linked to the main braced frame. The building masses wereassigned at each beam/column joints. The gravity loads transferredto the braced frame were applied at these joints as well. The grav-ity loads were defined by the combination of 1.05 dead and 0.25live loads.

Fracture in braces, in their connections, or in columns has beenreported in the literature, but was not included in the analyticalmodels. The objective of this study is to address an issue concern-ing a typical structural design using AISC 341-10: how to properlydesign brace-intersected beams so that braces are well supportedto dissipate input energy through the inelastic deformation capa-bility of adequately designed and fabricated braces and their con-nections. If fracture occurs in braces or connections, eitherprematurely or under extensive inelastic deformation beyond theexpected design inelastic deformation, the collapse of the entireCBF system, not the strength of intersected beams, is of main con-cern, which is beyond the scope of this study.

Time step size appears to influence results of time-history anal-ysis of the braced frames due to the complex cyclic behavior ofbraces. An extremely small time step size of 0.0001 s was neededto capture satisfactory analytical results.

2.3. Ground motions

The site selected in this study is Site Class D in Los Angles area.Three seismic parameters for design spectrum are SDS = 1.333 (g),SD1 = 1.000 (g) and TL = 12.0 s. 10 pairs of ground motion recordswith small mean squared error were selected from PEER StrongGround Motion Database [14] and no more than two of the groundmotions were taken from one earthquake to avoid event bias. Eachpair of ground motion records has one FN (Fault Normal) compo-nent and one FP (Fault Parallel) component. Fig. 5 summarizesthe elastic response spectra of the ground motions and Table 3 liststhe detailed information of these ground motions.

3. Characteristics of seismic demand on beams in CBFs subjectto one typical ground motion

Literature survey indicates that little is known about inelasticbehavior of brace-intersected beams and how such behavior wouldaffect seismic response of a CBF structural system. The ignorance ofinelastic behavior of beams in CBF might be mainly due to the lackof interest in it because common perception is that beams wouldremain elastic in the CBFs, which might not be the case in thetwo-story X-braced frames where brace-intersected beams wouldbe light, not necessarily remaining elastic during the design earth-quake. In order to reveal fundamental characteristics of seismicresponse of a CBF with possible inelastic beams, this sectionfocuses on the seismic response of braced frames under one typicalground motion (GM1). The braced frames were studied under GM1with ever-increasing scale factors times the ground motion accel-eration time history, driving the frames from elastic performancelevel to reach large inelastic deformation beyond the expecteddesign level. The global frame response was first presented interms of story drift ratio, followed by detailed investigation onthe seismic behavior of brace-intersected beams. The followingissues are to be addressed first in this section:

(1) Effects of design strength of the beam on overall seismicresponse of CBFs.

Axial Displacement (mm) Axial Displacement (mm)

Axial Displacement (mm)

(a) (b)

(c)

(b)

(c)

(a)

Fig. 4A. Experimental and simulation results of HSS 40 mm � 40 mm � 3 mm braces.

300 J. Shen et al. / Engineering Structures 76 (2014) 295–312

Fig. 4B. Experimental and simulation results of HSS 101.6 mm � 101.6 mm � 6.4 mm brace.

J. Shen et al. / Engineering Structures 76 (2014) 295–312 301

(2) Whether or not the seismic demand on brace-intersectedbeams is substantially lower in the two-story X-bracedframes than that in inverted V- or V-braced frames.

If it is evident that brace-intersected beams might reach theirdesign strength, the following issues are to be addressed:

(3) The impacts of inelastic deformation in brace-intersectedbeams on seismic performance of CBFs.

(4) Validity of using the story drift (ratio) as sole primaryresponse index in a CBF where inelastic deformation in mid-dle of beam spans occurs.

3.1. Structural properties and loading sequence

Fig. 6a shows the ground motion time history record of GM1and its corresponding response spectrum. The sequential numberin PEER Strong Ground Motion Database (PEER) for this record is1085. The Peak Ground Acceleration of this record is 0.979g. TheTarget Spectrum shown in Fig. 6b was developed following theASCE 7 design response spectrum, where spectral accelerations,values of Sa, for fundamental periods of 6-story, 12 story framesare identified. Note that fundamental periods of in 6-story, or in

12-story frames with different brace configurations are practicallythe same, respectively, as summarized in Table 4.

The Incremental Dynamic Analysis (IDA) approach wasemployed to investigate seismic response in terms of story driftindex (SDI) by subjecting the braced frames to ever-increasingintensities of the GM1 with altering scale factors. Structuralresponse at each scaled GM1 level (represented by the spectralacceleration at fundamental period) was evaluated. Since the dif-ference in fundamental periods between the 6-story and 12-storyframes is substantial, different scale factor increments were used,with 0.10g, 0.05g spectral acceleration increments for 6-story,12-story frames, respectively. The scale factor (SF) was deter-mined in such a way that the ground motion intensity with ascale factor of SF would have a spectral acceleration, Sa, equalto (SF) g. For example, a scale factor of 1.00 means that the scaledground motion has a 1.00g spectral acceleration at the fundamen-tal period.

3.2. Seismic response of structure system in terms of story drift ratio

The peak drift ratios of the braced frames were recorded atevery spectral acceleration increment. Fig. 7 plots the curvesrelating peak drift ratio in the frames to the ground motion inten-sity, Sa. Each data point in Fig. 7 represents the peak story drift

Fig. 5. Response spectra of the ground motions used in this study.

Table 3Ground motions used in this study.

ID no. NGA# Component Scale factor Event Year Mag Duration (s) PGA (g) PGV (in./s)

GM1 1085 FN 1.1675 Northridge 1994 6.69 40 0.979 5.35GM2 FP 0.578 3.60GM3 1489 FN 2.8835 Chi-Chi – Taiwan 1999 7.62 90 0.810 5.08GM4 FP 0.718 6.50GM5 1515 FN 2.5841 Chi-Chi – Taiwan 1999 7.62 90 0.643 5.71GM6 FP 0.513 5.02GM7 1009 FN 3.8019 Northridge 1994 6.69 55.33 1.041 4.84GM8 FP 0.985 3.68GM9 726 FN 6.5733 Superstition Hills 1987 6.54 21.89 0.817 2.03GM10 FP 1.059 4.61GM11 179 FN 1.9573 Imperial Valley 1979 6.53 39 0.699 6.00GM12 FP 0.929 3.09GM13 802 FN 2.3023 Loma Prieta 1989 6.93 39.955 0.835 5.03GM14 FP 0.866 3.92GM15 779 FN 1.0816 Loma Prieta 1989 6.93 25.005 1.021 4.13GM16 FP 0.581 3.07GM17 722 FN 4.8465 Superstition Hills 1987 6.54 21.98 0.512 2.72GM18 FP 0.669 6.31GM19 1148 FN 7.2093 Kocaeli – Turkey 1999 7.51 30 1.566 5.72GM20 FP 1.098 10.94

Note: NGA # – sequential number in PEER Strong Ground Motion Database.

302 J. Shen et al. / Engineering Structures 76 (2014) 295–312

value in the frame when subject to the factored ground motionGM1 with the spectral acceleration Sa. The following can beobserved from Fig. 7:

(1) It seems that there is no noticeable difference in peak storydrift response among the 6-story frames with three differentdesigns, two-story X-braced frame with strong beam (TypeA), two-story X-braced frame with weak beam (Type B),and inverted V-braced frame with strong beam (Type C),up to 6% story drift ratio response.

(2) The 6-story, 12-story frames reach their 2% design drift ratioapproximately at spectral accelerations, Sa, of 1.5g, 0.75g,respectively. It seems that peak drift ratios in all framesapparently increase faster than ground motion intensitydoes after 2% drift ratio.

(3) There are some differences in story drift ratio responseamong the 12-story frames with Types A, B and C designs.But, no clear trend for us to differentiate which frame per-forms better than others before 3.5% story drift ratio, afterwhich Type B frame shows a sign of losing its stability.

(4) It appears that peak story drift ratio, which has been usedextensively as a primary measurement of seismic responseof any structures, might not be an effective index to evaluateseismic performance of the frames under consideration,where vertical inelastic deformation of beams and its impacton structural performance are not reflected in story driftresponse. Other independent response items, such as beamdeflection and brace deformation, need to be included toaccurately evaluate seismic response of the frames with pos-sible inelastic beam deformation.

Fig. 8 plots the distributions of peak drift ratios along buildingheight for the 6- and 12-story frames at specific ground motionintensity levels, with Sa = 1.90g for the 6-story frames (Fig. 8a),and Sa = 1.00g for the 12-story frames (Fig. 8b). The following canbe observed from Fig. 8:

(1) There is a marginal difference in peak drift ratio responsebetween Type A and Type B frames in most floors. Note thatType A frame has much higher strength in its brace-intersected

6 StoryT1 = 0.72 s, Sa = 1.51g

12 StoryT1 = 1.30 s, Sa = 0.62g

Fig. 6. GM1 record and response spectrum.

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beams than that in Type B frame. This observation indicatesthat significant change in the beam strength will not havemuch impact on the peak drift ratio response. This observationmight result in two different conclusions, either that the X-configuration braces in the two-story X-braced frames is soefficient that a weak-beam (Type B) frame would work as wellas a strong-beam frame, or that story drift ratio response failsto reveal the difference in overall seismic response betweenthese two types of frames.

(2) Inverted V-braced frames show higher tendency of havingsignificantly larger story drift ratio than that of its counter-parts with two-story X-braced frames at certain floors.

3.3. Seismic response of braces

Braces are the most critical components in ductile concentri-cally braced frames since they are the only group of members des-ignated to provide inelastic deformation. Seismic performance ofbraces has been traditionally implicitly evaluated based on storydrift ratio. Such evaluation is only valid when the brace-intersectedbeams remain elastic. It is unknown whether or not any significantvertical deflection in the beam would adversely affect seismic per-formance of the braces. Fig. 9 plots the peak ductility demand onbraces under GM1 at increasing ground motion intensities. Theductility demand of a brace is the actual axial deformation, in ten-sion or compression, divided by the yielding or buckling deforma-tion of the brace. As a reference, the ductility demands on all bracesat the 2% story drift ratio in the 6- and 12-story frames are between6.0 and 8.0, assuming the beams intersected by braces remain elas-tic. The following can be observed from Fig. 9:

(1) Ductility demand in the braces is significantly differentbetween the frames with strong beams (Types A and C)and weak beams (Type B) in both 6- and 12-story frames.

(2) Brace ductility demand in the 6-story Type B frame (with theweak intersected beams) starts increasing substantially fas-ter than that in other two types after Sa = 1.0g groundmotion intensity (when some of beams yield under bendingat Sa = 1.0g, as shown later in the paper). The peak brace

Table 4Fundamental period (T1) of 6 story and 12 story frames (s).

Frame Frame A Frame B Frame C

6-Story 0.721 0.724 0.70112-Story 1.304 1.306 1.261

ductility demand reaches as high as 20 at Sa = 1.7g groundmotion intensity. Note that the frame has a peak story driftratio of 2% at Sa = 1.5g. Fig. 9a indicates that the peak braceductility demand has reached three times the inelasticdeformation design limit when the frame has just reachedits inelastic design drift ratio limit. Brace ductility demandresponse in the 12-story Type B frame follows the sametrends as observed in the 6-story Type B frame.

(3) Story drift ratio appears to be a poor measurement for seis-mic performance of braces in the two-story X-braced framewhen the brace-intersected beam has substantial inelasticdeformation at its middle span.

3.4. Seismic response of brace-intersected beams

The observed responses of the peak story drift ratio and braceductility demand in previous sections might be better understoodby revealing seismic response of the beams intersected by braces.The combined strength ratios of brace-intersected beams and thevertical deflections were summarized in the following subsections.

3.4.1. Combined strength ratio at intersected beamsFigs. 10 and 11 plot the combined effect on the beam strength

from axial force and bending moment for 6-story and 12-storyframes subject to various ground motion intensities. The combinedstrength ratio, P/Pc + M/Mc, was chosen to represent such combinedeffect on the beam strength, where P and M are the peak values ofaxial force and bending moment induced by the ground motion,respectively; and Pc and Mc are the axial load (either tension orcompression) and bending moment capacities, respectively. Thefollowing can be observed from Figs. 10 and 11:

(1) All brace-intersected beams in Type C braced frames remainelastic at least up to peak story drift ratio of about 6%, withpeak (P/Pc + M/Mc) ratio less than 0.70 in both 6- and12-story frames. Note that Type C frames are typicalinverted V-braced frames, required by the current seismicdesign specification to have strong beams. Such requirementis intended to keep beams elastic during design earthquakeground motion, and the beam response in Type C framesappears to demonstrate that this design intention is realized.

(2) The peak (P/Pc + M/Mc) ratio in brace-intersected beams isless than 0.50 in both 6- and 12-story Type A frames. Recallthat Type A has the same sizes of beams as Type C, but hasan X-type brace configuration over two stories. It appearsthat with the same strong beams as in the inverted V-braced

Fig. 7. Peak drift ratio development of frames subject to GM1.

Fig. 9. Normalized brace deformation (ductility demand) development under GM1.

Fig. 8. Drift ratio distribution along building height.

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frame, the two-story X-braced frames have reduced beamstrength demand to certain degree, from a peak (P/Pc + M/Mc) ratio around 0.70 in inverted V-braced frames to 0.50in two-story X frames.

(3) The strength demand on the braced-intersected beams inType B frames is dramatically different from those ofTypes A and C. The beams in Type B frames were designed

based on a popular assumption that the sum of all braceforces acting on the beam was very small, if not equalto zero, resulting in small size (weak) beams. All brace-intersected beams yield under combined axial force andbending moment (P/Pc + M/Mc = 1.0) in both 6- and12-story Type B frames when the frames have only 1.5%peak drift ratio.

Fig. 10. Peak combined strength ratio in brace-intercepted beams of 6-storyframes.

Fig. 11. Peak combined strength ratio in brace-intercepted beams of 12-storyframes.

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3.4.2. Vertical deflection of brace-intersected beamsFigs. 12 and 13 plot the peak vertical deflection of the beam at

intersecting point in 6- and 12-story frames at various groundmotion intensities. The peak deflections are normalized by theyielding deflection, Dy, the maximum vertical elastic deflectionunder a concentrated force at the brace intercepting point, whereDy = (FyZx)L2/(12EIx), Fy = yield strength of steel, Zx = plastic sectionmodulus of the beam, L is the beam span length, and Ix is momentof inertia of the beam. The positive Dy is for the downward deflec-tion, as shown in Fig. 14, where the vertical maximum deflectionsof the brace-intersected beams are indicated in the deformedshapes of the frames when peak ductility demands on these beamsoccur. The following can be observed from Figs. 12–14:

(1) Peak ductility demand on the brace-intersected beams is allunder 1.0 in Types A and C frames of the 6- and 12-storyframes.

(2) Ductility demand reaches 4.0 in the 6-story Type B frame,and 8.0 in the 12-story Type B frame.

(3) It appears that substantial inelastic deflection of brace-inter-sected beams in Type B frames is the main reason for exces-sive brace ductility demand observed previously in Fig. 9. Asdemonstrated in Fig. 14b, the middle span of the first floorbeam shifts from point A to point A0 due to combined verti-cal and lateral displacements of the same order during theearthquake ground motion GM1.

Fig. 12. Ductility demand, Dy, of brace-intercepted beams in the 6-story frames.Fig. 13. Ductility demand, Dy, of brace-intercepted beams in the 12-story frames.

306 J. Shen et al. / Engineering Structures 76 (2014) 295–312

(4) The significant inelastic deformation in the brace-inter-sected beams might impose additional strength and defor-mation demands on connections between braces andbeams, and beams and columns that are not considered incurrent design provisions.

3.5. Impacts of inelastic deformation of brace-intersected beam onoverall structural response

It appears that the unbalanced forces developed on brace-inter-sected beams for Type B frames might cause significant inelasticdeformation, as discussed in Section 3.4. This section focuses onthe potential adverse impacts of such inelastic deformation onoverall structural response of the two-story X-braced frames.

The seismic responses of the 6-story Type B frame underSa = 1.90g were studied as a typical case to show the possible fail-ure modes associated with this type frame. In case of the 12-storyframes, Type B braced frames had the similar seismic behaviorsunder high ground motion intensity.

3.5.1. Observed inelastic behavior of the brace-intersected beamsThe combined strength ratio response, as shown in Figs. 10b

and 11b, reveal that the probability for brace-intersected beamsto show inelastic deformation appears to be reasonably high. Someof these brace-intersected beams reached their full strength capac-ities under combined axial forces and bending moments at theground motion intensity of Sa = 1.0g, when the frames experiencestory drift ratios on the order of 0.015 that is well within expecteddrift ratio under the design earthquake (ASCE 7, 2010), after which

Fig. 14. Instant deformed shapes of Type B frames at peak ductility demand on brace-intercepted beams.

(a) Axial force and bending moment interaction at the beam middle span

Bending Moment (kip-inch) (b) Combined strength ratio time history

(c) Time history of ductility demand (normalized vertical deflection) at beam middle span

Fig. 15. Seismic response of the 1st floor brace-intersected beam in the 6-story Type B frame.

J. Shen et al. / Engineering Structures 76 (2014) 295–312 307

the beam went through significant inelastic deformation. Fig. 15shows a typical response of the 1st floor level brace-intersectedbeam from the 6-story Type B frames under the ground motionwith Sa = 1.90g. The axial force and bending moment interactioncurve, as shown in Fig. 15a, demonstrates that the beam yieldedunder various combinations of axial force and bending moment.

The beam had its initial yielding at the 3rd second (Fig. 15c), andwas subject to high cyclic strength demands for the rest of theground motion excitation, as shown in Fig. 15b. Fig. 15c plots thetime history of vertical deflection at the brace intersecting point.This time history indicates that the beam intersected by V-typebraces above and inverted V-type braces below experienced

7.8 in. downward1.8 in. downward

DR2 = 1.1 %

DR1 = 2.1 %

(a) At rest (un-deformed shape)

(b) Deformed shape when the first beam yielding occurred (with Sa = 0.45g)

(c) Deformed shape when peak vertical deflection occurred (with Sa

= 1.90g)

Fig. 16. Deformed shapes of the 1st floor beam in the 6-story Type B frame subject to GM1 earthquake ground motion. (DR1 = the drift ratio in the first story; DR2 = the driftratio in the second story).

“Pinch” phenomena after the inelastic deflection in girders.

(a) Type A (b) Type B

(c) Type C

Fig. 17. Normalized base shear versus the 1st level drift ratio for the 6-story frames subject to GM1 with Sa = 1.90g.

308 J. Shen et al. / Engineering Structures 76 (2014) 295–312

accumulative inelastic deformation as soon as its initial yieldingoccurred at the 3rd second into the ground motion excitation.

3.5.2. Impact on beam–column connectionsThe simple beam connections to the supporting columns are

traditionally considered capable of tolerating much larger storydrift than the frame as whole, and have not been an issue in seis-mic design process. However, this tradition needs to be scrutinizedwhen a significant vertical displacement occurs within the beamspan. Fig. 16 presents deformation shapes when the 6-story framewas subjected to GM1 earthquake ground motion with Sa = 0.45g,1.90g, respectively. The first yielding in the brace-intersectedbeams occurred at the 1st floor beam at Sa = 0.45g, as shown inFig. 16b, and this beam went on to reach a vertical displacementof 7.8 in. when the story drift ratio was 0.021 at Sa = 1.90g, as

shown in Fig. 16c. The vertical displacement of 7.8 in. imposedan additional 0.043 radian rotational demand on the beam-to-col-umn connection, more than twice as much as the story drift did(with assumption that inelastic connection rotation is approxi-mately equal to the story drift ratio). As a result, the shear connec-tion between the beam and column suffered more than 0.06 radianof rotation.

3.5.3. Effect on hysteresis and energy dissipating patternsInelastic deformation in the middle of beam span also alters the

hysteresis and energy dissipation patterns in the studied bracedframes. Fig. 17 plots the story shear force versus drift ratio of thefirst floor in the 6-story frames with three different bracing config-urations subjected to GM1 ground motion with Sa = 1.90g. Type Aframe and Type C frame have the full hysteresis loops as expected.

Fig. 18. Peak drift ratio of the braced frames subject to the set of ground motions (GMs).

J. Shen et al. / Engineering Structures 76 (2014) 295–312 309

Type B frame demonstrated ‘‘pinch’’ phenomena in its hysteresisloops due to additional inelastic deformation in the beam middlespan.

4. Seismic response of the concentrically braced frames subjectto 20 earthquake ground motions

The study on the seismic response of the CBFs to the singleground motion was extended to the response to a collection of20 earthquake ground motions. Based on the characteristicsobserved in the previous section, the extended study was decidedto focus on the response of critical members, such as ductilitydemands on braces and beams, together with traditional responseindex of story drift ratio in the 6- and 12-story frames subjected tothe group of 20 ground motions.

4.1. Global seismic response in terms of story drift ratio

Fig. 18 plots the peak story drift ratio (SDR) for the 6- and 12-story frames subjected to the 20 ground motions, which demon-strates that

(1) The SDR response varies substantially over the 20 groundmotions, from 1.5% to over 6.0% in the six-story frames,and 1.5% to 5.0% in the 12-story frames.

(2) The SDR response does not present a clear trend to indicatethe differences in seismic performance among the Types A, Band C frames.

It appears that the SDR, as an overall response index, is able toidentify severity levels of seismic response in the frames to individ-ual ground motions, based on which inelastic behavior of beamsand braces can be evaluated. For the convenience of subsequentdiscussions, we divide ground motion intensity levels into threegroups based on the SDR response. They are as follows:

(a) Group I ground motions (SDR 6 0.02): 6 ground motions(GMs) (30%) out of the 20 ground motions for the 6-storyframes, and 8 (40%) for the 12-story frames.

(b) Group II ground motions (0.02 < SDR 6 0.04): 6 groundmotions (30%) out of the 20 ground motions for the 6-storyframes, and 10 (50%) for the 12-story frames.

(c) Group III ground motions (SDR > 0.04): 8 ground motions(40%) out of the 20 ground motions for the 6-story frames,and 2 (10%) for the 12-story frames.

4.2. Ductility demand on braces

Fig. 19 plots the peak ductility demand on braces in the 6- and12-story frames subjected to the set of 20 ground motions. Theductility demand is the axial deformation divided by the initialyielding deformation in tension or initial buckling deformationin compression of braces. The following can be observed fromFig. 19:

(1) Ductility demand on the brace generally tends to be higherin Type B frames than that in other two types of frames.

Fig. 19. Peak brace ductility demand in the braced frames subject to the set of GMs.

310 J. Shen et al. / Engineering Structures 76 (2014) 295–312

(2) In the structures responding to Group I GMs (SDR < 0.02),the difference in the brace ductility among Types A, B andC seems to be insignificant or negligible;

(3) In the structures responding to Group II GMs(0.02 < SDR < 0.04), the ductility demand on the brace inType B frames is substantially higher than, in some casestwice as much as, that in Types A and C.

(4) When the response in the 6-story structures reachesSDR > 0.04 subjected to Group III GMs, the ductility demandon braces is substantial in all frames regardless of thedifference in design strength of brace-intersected beams,mainly due to inelastic deformation either in the beams ofType B frames or in columns of Types A and C frames.

(5) When the response in the 12-story structures reachesSDR > 0.04 subjected to two strong (Group III) GMs, the duc-tility demand on braces in Type B frames is about 2.2 times,and 1.5 times that in Types A, and C frames, respectively.

4.3. Seismic responses of brace-intersected beams

Seismic responses of brace-intersected beams were summarizedin terms of the combined strength ratio (P/Pc + M/Mc) in Fig. 20. Note

that P/Pc + M/Mc equal to 1.0 in Fig. 20 indicates that the brace-inter-sected beams yielded at least once during the given ground motionexcitation. The following can be observed from Fig. 20:

(1) The peak combined strength ratio in the brace-intersectedbeams appears to be relatively steady over various groundmotions within each type of frames.

(2) The beams in Type C frames (with inverted V type bracesintersecting strong beams) have the most steady strengthdemands in most (19 out of 20) ground motions in both 6-and 12-story frames, with the combined strength ratioaround 0.70.

(3) The beams in Type A frames (with X-type braces intersect-ing strong beams) have median strength ratio of 0.40 inthe most of 20 ground motions in both 6- and 12-storyframes, indicating that the X-type braces have impact onreducing strength demand on the beams that are strongenough to remain elastic even in Inverted V-bracedframes.

(4) The beams in Type B frames (with X-type braces intersectingweak beams) have reached P/Pc + M/Mc = 1.0 in the most of20 ground motions.

Fig. 20. Peak combined strength ratio of braced frames subject to the set of GMs.

J. Shen et al. / Engineering Structures 76 (2014) 295–312 311

5. Conclusions

Typical 6- and 12-story buildings using two-story X-bracedframes with strong and weak braced-intersected beams were sub-jected to a set of 20 earthquake ground motions, and resulting seis-mic responses were discussed in terms of seismic strength anddeformation demands on beams and the impact of inelastic deforma-tion in weak beams on critical components in two-story X-bracedframes. The main concern is whether or not the beam is likely tobecome inelastic during the design earthquake ground motion, andif so, how such inelastic behavior affects the seismic behavior ofthe frames as a whole. Major conclusions are drawn as follows:

(1) Brace-intersected beams in two-story X-braced framesdesigned with the minimum possible required strengthpermitted by the current design provisions would undergosignificant vertical inelastic deformation when the framesexperience expected 0.02–0.04 story drift ratio response.

(2) Inelastic deformation in the middle spans of brace-inter-sected beams substantially increases ductility demandson braces and beam-to-column connections. The rotationaldemand on beam-to-column connection is more than 0.06radians at the 0.02 story drift ratio response if the brace-intersected beam yields.

(3) The ductility demand on braces increases from less thaneight (8) in a CBF with strong brace-intersected beams toover 20 with weak brace-intersected beams at the 0.02story drift ratio.

(4) Use of story drift ratio as sole deformation response indexfails to reveal actual seismic response of critical compo-nents (braces, brace-intersected beams, and beam-to-col-umn connections) when beams experience inelasticdeformation within their own spans. A rational seismic per-formance evaluation of braced frames with intersectedbeams must include both lateral story drift and vertical dis-placement within beam spans.

(5) The required seismic strength demand on the brace-inter-sected beams in two-story X-braced frames is generallylower than that in inverted-V-braced frames when theintersected beams remain elastic (strong beam design).

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