Journal of Constructional Steel Research 98 (2014) 1–11

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Journal of Constructional Steel Research

Earthquake resistance frames with combination of rigid andsemi-rigid connections

Mohammad Razavi, Ali Abolmaali ⁎Center for Structural Engineering Research and Simulation (CSER), Department of Civil Engineering, The University of Texas at Arlington, Arlington, TX 76019, United States

⁎ Corresponding author at: 425NeddermanHall, 416Ya76019, USA.

http://dx.doi.org/10.1016/j.jcsr.2014.02.0060143-974X/Published by Elsevier Ltd.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 14 November 2013Accepted 22 February 2014Available online 18 March 2014

Keywords:Hybrid steel framesSemi-rigid connectionsEarthquake engineeringSAC framesReliability analysisPerformance based design

The concept of the hybrid steel frame system, as it pertains tomixtures of fully-rigid and semi-rigid steel connec-tions used in 20-story SAC frames, is presented herein. Several different patterns and locations of semi-rigidconnection replacements within the frame were examined in order to identify hybrid frames with the bestseismic performance. The effective connection stiffness was identified by performing a parametric study on theinitial stiffness of the semi-rigid connections. Then, the cyclic behavior of the connectionswith themost effectivestiffnesswas obtained, using nonlinear finite element analysis. Inelastic dynamic analyseswere conducted on theproposed selected frames by subjecting them to Los Angeles earthquake records characterized as those with 2%and 10%probabilities of exceedance infifty years. Themaximum story drift for the hybrid frameswas determinedand comparedwith the “life safety” and “collapse prevention” performance limits, as recommended by FEMA356[12]. The story drift andmember forces for the proposed hybrid frameswere comparedwith those of convention-al SAC frames without semi-rigid connections. Finally, a reliability analysis, utilizing the collapse margin ratiopresented in FEMA P695, was performed to quantify and compare the collapse performance of the proposedhybrid frames and conventional rigid frames.

Published by Elsevier Ltd.

1. Introduction

Seismic performance of structural systems has been at theforefront of research for many years. Occurrences of more than 18severe earthquakes, with magnitudes of more than 5.8 Richter inthe state of California in the 15-year period between 1979 and1994, have been reported. The premature brittle failures of weldedconnections after the Northridge earthquake of 1994 particularlymotivated researchers to look beyond the conventional designphilosophies

In the past few decades, several researchers have introduced newdesign concepts and approaches to improve the seismic perfor-mance of steel structures. These include, but are not limited to, theintroduction of more ductile connections and new lateral resistantsystems, including energy dissipating technologies such as baseisolators, frictional or visco-elastic dampers, and active controlelements.

An innovative seismic design method is the Performance BasedPlastic Design (PBPD) that was introduced and developed by ProfessorGoel and his associates at the University of Michigan [14,17]. Thedevelopment of thismethodwas in response to shortages in the current

tes St., Box 19308, Arlington, TX

seismic design codes on satisfying a performance objective in a directmanner. In PBPD, the base shear is calculated by equating the workdone bypushing the structure to a predefined target driftmonotonicallyto thework done by an equivalent elastic-perfectly plastic single degreeof freedom system. The idealized inelastic response spectra by [19] areused in this study.

Development of the seismic eccentric braced frames (EBF), intro-duced by Popov and Englehardt in 1988, was another attempt toenhance the seismic behavior of steel frames. Well-designed EBFs,constructed with shear links, provide high elastic stiffness andstrength under low to moderate ground motions, combined withhigh ductility and energy dissipation capabilities in severe groundmotions.

Recently, Abolmaali et al. [4] introduced a new lateral resistant steelmoment frame referred to as a “Hybrid Steel Frame.” This system,whichwas the foundation of the research leading to thework that is being pre-sented in thismanuscript, is based on the concept of introducing energydissipating mechanisms in the structural frame systems by targetingand replacing selected rigid connectionswithmore ductile energy dissi-pating semi-rigid connections.

The proposed structural system enhances the seismic behavior ofthe steel frames by taking advantage of the inelastic energy dissipativesemi-rigid connections, along with stiffer and higher strength rigidconnections. In the case of low intensity earthquakes, while rigid

Fig. 1. Beam compound with stiff end zone and plastic hinges.

2 M. Razavi, A. Abolmaali / Journal of Constructional Steel Research 98 (2014) 1–11

connections remain elastic, the semi-rigid connections absorb seismic en-ergy and assist the system in damping out the basemotion acceleration ata faster rate. On the other hand, in the case of higher intensity earth-quakes, this study shows that hybrid frames reduce the risk of collapsewhen compared with its corresponding SMFs.

Current design codes have almost eliminated the partially restrainedconnections in high seismic zones. However, there are several studiesthat show high energy dissipating characteristics of the semi-rigid con-nections with high stiffness and strength, as reported by Ackroyd andGerstle [5], Bjorhovde et al. [10], Astaneh et al. [6], Astaneh-Asl et al.[8], Astaneh-Asl [7], Kukreti and Abolmaali [16], Abolmaali et al. [1],Abolmaali et al. [2], and Abolmaali et al. [3].

Seismic behavior of SMFs with semi-rigid connections has beeninvestigated in several studies, both theoretically and experimentally[18]. Excessive inter-story drift was a major concern for using semi-rigid connections in steel frames. These studies showed that whenconnection stiffness increases, base shear increases; however, inter-story drift does not decrease proportionally.

Astaneh et al. [6] and Abolmaali et al. [3] studied the energy dissipa-tion characteristics of different types of semi-rigid connections andshowed that they are capable of undergoing large inelastic rotation(in excess of 0.05 rad), given that the connection is designed so thatthe angle or plate yielding governs the behavior. In other words, if theplate or angle thickness is relatively small compared to the bolt diame-ter, bolt yielding and fractures are prevented, and plate yielding resultsin a ductile connection behavior by undergoing large inelastic rotation.

In this research, The Los Angeles 20-story SAC frame is used as acase study. SAC frame dimensions are presented in [15]. Selectedrigid connections were replaced by ductile semi-rigid connections.A suit of 20 accelerograms [22], which was developed as a part ofthe SAC project for the Los Angeles site, with different frequencieswas applied during inelastic dynamic analyses, and the results

Fig. 2. Beam compound with semi-rigid connections and plastic hinges.

Fig. 3. Parameters of the monotonic backbone curAfter ATC72-10.

were compared with the corresponding responses of the fully rigidSAC frames.

A reliability-based analysis utilizing the Collapse Margin Ratio(CMR), proposed in FEMAp695,was performed to quantify the collapseperformance of the Los Angeles SAC 20-story rigid frames and theircorresponding hybrid frames.

1.1. Nonlinear modeling

The concentrated plastic hinge model was adopted to introducenonlinear behavior in beams with rigid connections, beams with semirigid connections, and columns of structures. Beams with rigid connec-tions and columns, as shown in Fig. 1, were modeled as compoundelements consisting of an elastic Bernoulli beam element at the middleand confined by two plastic hinges and two end-zones that connect themember to the rigid connections. The assumption of the formation ofplastic hinges at the two ends of beams and columns was adoptedbased on the hypothesis that the failure mechanism is governed bythe seismic loading.

The semi-rigid beamcompounds, as shown in Fig. 2, were defined byreplacing the two stiff end zones with two non-linear moment-rotationsemi-rigid hinges in the rigid beam compounds. In this configuration,plastic hinges and semi-rigid connections are both sources of nonlinear-ity. However, since the plastic moment of semi-rigid connections isusually much smaller than the plastic moment of beam sections, thebehavior of the beam compound is governed by the behavior of thesemi rigid connections. In fact, the moment demand in beams cannotexceed the plastic moment of the semi-rigid connections; therefore, itwill not reach the plastic moment of the beam section.

The nonlinear behavior of plastic hinges is commonly expressed bypresenting their moment-rotation backbone-curves. In this study, thebackbone curve for different beam and column members were con-structed based on the beam deterioration modeling guideline providedin ATC-72 [9] as shown in Fig. 3.

The plastic hinge parameters for the beams used in this study aresummarized in Table 1.

Parameters used for modeling of semi-rigid connections will bepresented after the effective connection parameters are identified.

2. Selection of hybrid frame patterns

For a reasonable placement of semi-rigid connections in a hybridframe, it is necessary to investigate the local and global effects of addingsemi-rigid connections to the moment resistance frames' performance.These effects were investigated as follows.

2.1. Moment redistribution/act as a fuse

Semi-rigid connections act as rotational springs; consequently, theychange the distribution of moments between beams and columns.Moreover, the plastic moment of semi-rigid connections is generally

Pre-capping plastic rotation (θp)Post-capping rotation range (θpc)Ultimate rotation (θu)Effective yield strength and rotation (My and θy)Capping strength and rotation, (Mc and θc)Residual strength, Mr

Effective elastic stiffness, Ke

Post yield tangent stiffness, Kp

Effective post capping tangent stiffness, Kpc

Deterioration parameter (Λ)

ve of the modified Ibarra–Krawinkler model.

Table 1Parameters used for modeling plastic hinges in beams.

Section name θy θp θpc My Mu Mr Λ

W21X50 0.001272 0.031515 0.144247 6050 6655 2420 0.911012W24X62 0.001123 0.027519 0.141778 8415 9256.5 3366 0.925926W27X84 0.000974 0.022837 0.106695 13,420 14,762 5368 0.725497W27X94 0.000967 0.022909 0.124601 15,290 16,819 6116 0.864289W30X108 0.000881 0.021128 0.117753 19,030 20,933 7612 0.840001W30X99 0.00089 0.020455 0.103769 17,160 18,876 6864 0.731785

3M. Razavi, A. Abolmaali / Journal of Constructional Steel Research 98 (2014) 1–11

less than the plastic moment in their adjacent frame members (beams/columns); thus, the moment cannot exceed the plastic moment of theconnection, and formation of plastic hinges in the adjacent structuralmembers is avoided.

A pushover analysis was performed on SAC 3-story rigid and hybridframes to investigate the effects of semi-rigid connections on momentredistribution. Moment demands of the fully rigid 3-story frame andits corresponding hybrid frame at roof drift of 3% are illustrated in Fig.4-a and -b, respectively. In this study, a hybrid frame with a diagonalpattern of semi-rigid connections was selected. Semi-rigid connectionsare shown as rotational springs in Fig. 4-b. Moment demands of the

a) Moment in Ful

b) Moment in H

-1836425358

6994

-3008325069

20028-25042

-8374

16737-23450

-773323239

15505

166910826

12431

-29983-23901

1662

1669 -1605

Fig. 4. Bending moment dema

beams and columns adjacent to the semi-rigid connections in the hybridframeare noticeably less than themomentdemands on the correspond-ing rigid frame members, as shown in Fig. 4.

2.2. Base shear reduction

In general, the stiffness of semi-rigid connections is smaller than therigid connections. Thus, implementing semi-rigid connections in a steelframe reduces the overall stiffness of the frame and increases theframe's fundamental period of the structure. Considering the shape ofthe design spectra, as shown in Fig. 5, the softer frame experienced a

ly rigid Frame (kip-in)

ybrid Frame (kip-in)

-19342

7729-25468

-5522

-3840.7-1681

-12333

10882-23215

10817-10817

-1250323441

12598

1072421456

-10732

-30138 -24063

1602

-1659

nds at global drift of 3%.

Spec

tral

Res

pons

eA

ccel

erat

ion,

Sa

(g)

Period, T(sec)

SDS

t1 t2

Sa(t1)

Sa(t2)

Fig. 5. Schematic presentation of the Design Response Spectrum (ASCE 7–10).

4 M. Razavi, A. Abolmaali / Journal of Constructional Steel Research 98 (2014) 1–11

reduced amount of acceleration. Fig. 5 shows that increasing the periodof the structures from t1 to t2 decreases the acceleration from Sa (t1) toSa (t2). However, since using semi-rigid connections will reduce thesystem's stiffness, the stiffness of semi-rigid connections should bedetermined to find the minimum base shear, which still satisfies theinter-story drift limit criteria. On the other hand, semi-rigid connections

a) Rigid Frame b) Simplified Model c) First

Fig. 6. The simplified mo

a) Hybrid Frame b) Simplified Model

Fig. 7. The simplified mod

may be used to shift the natural frequency of structure and avoidresonance.

2.3. Shifting structures' period and changing their mode shapes

As explained in the previous section, implementing semi-rigid con-nections in a SMRF reduces the stiffness of the frame; thus, the naturalperiods of hybrid frames are higher than the natural period of corre-sponding rigid frames. The natural mode-shapes of hybrid frames willconsequently differ from the fundamental mode-shapes of the corre-sponding SMRF. The idea of the hybrid frame began with a simple as-sumption that if a high-rise building is seen as a single cantileverbeam, theoretically, an indefinite number of mode shapes is consideredfor this system. The idealized simple model of rigid frame and its first,second, and third mode shapes are shown in Fig. 6.

Replacing rigid connections with flexible semi-rigid connections atcertain story levels simulates spring development within the beam, asshown in Fig. 7. These simplified models explain why the two cases ofrigid andhybrid frames have a significant difference in seismic behavior,where the newly formed springs may help to reduce the frame's modeshapes into two mode shapes, as shown in Fig. 7.

Mode d) Second Mode e) Third Mode

del of a rigid frame.

c) First Mode d) Second Mode

el of a hybrid frame.

Fig. 8. Energy dissipated in plastic hinges of the SAC20 frame under LA35.

5M. Razavi, A. Abolmaali / Journal of Constructional Steel Research 98 (2014) 1–11

2.4. Increase energy dissipation

Introducing semi-rigid connections in SMRFs helps to reduce theseismic demands in structures by dissipating seismic energy. In hybridframes, seismic energy dissipates in plastic hinges formed in framemembers (Beams/Columns) and in the semi-rigid connections. Theamount of the energy dissipated in each plastic hinge or semi-rigidconnection is found by calculating the area confined by the outer loop

Rotational SpringApproach

Energy DissipationApproach

a) HSAC20-1 b) HSAC20-2 c) HSAC

Fig. 9. Hybrid models based on t

of the moment-rotation hysteresis loop. Fig. 8 shows the locations ofplastic hinge formations, in SAC 20 story frame's members subjectedto LA35 ground motion, by filled circles.

2.5. Hybrid frame pattern selection

Based on the aforementioned effects of the semi-rigid connectionson the response of steel moment frames, three different approacheswere adopted for placement of semi-rigid connections in the 20-storyhybrid frame. Frames are designated as HSAC20, where the letter “H”stands for Hybrid and “SAC20” represents the 20 story SAC framedesigned for Los Angeles site.

The first approach was based on introducing a rotational spring atfive middle stories of the frame. This approach was implemented by re-placing rigid connections with flexible semi-rigid connections in stories9 to 13 of the SAC 20 story rigid frame, as shown in Fig. 9(a). The newlyformed springs decoupled the earthquake acceleration into two modeshapes, as is shown in Fig. 7. Although the performance of this systemwas tested with initial linear models in Abolmaali et al. [4], in thisstudy, the pattern was evaluated using a comprehensive nonlinearmodel analysis.

The second approach was based on utilizing the semi-rigid connec-tions as an energy dissipative tool. As shown in Fig. 8, for a SAC 20-story frame subjected to LA35 ground motion, plastic hinges formed inbeams and columns located in stories 1 through 5. On the other hand,structural members of stories 6 through 20 remained elastic for themost part and did not contribute to the inelastic energy dissipation.The analysis result of the 20-story frame, under other maximum credi-ble earthquake (MCE) groundmotions scaled for the Los Angles site, hascommonly followed the same pattern of plastic hinge propagation overthe height of frame. These results are presented in Razavi [20]. In thesecond approach, semi-rigid connections were placed in the beams,

Stability Approach

20-3 d) HSAC20-4 e) HSAC20-5

hree proposed approaches.

0

5

10

15

20

1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0% 5.5% 6.0%

Stor

y

Maximum interstory drift ratio, θmax

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%Col

laps

e P

reve

ntio

n L

imit

The percentages refer to thestiffness of the beam with semirigid connection with respect tothe stiffness of the beam withrigid connection

Fig. 12. Average story drift diagrams for HSAC20-4 with various connection stiffnesssubjected to LA MCE records.

0

2

4

6

8

10

12

14

16

18

20

0.0% 1.0% 2.0% 3.0% 4.0% 5.0%

Stor

y

Drift

HSAC20-1HSAC20-2HSAC20-3HSAC20-4HSAC20-5RIGID

Lif

e Sa

fety

Lim

it

Fig. 10. Average of story drift diagrams for various models of 20-story structure subjectedto L.A. DBE records.

6 M. Razavi, A. Abolmaali / Journal of Constructional Steel Research 98 (2014) 1–11

which remained elastic. Thus, these connections contributed to the en-ergy dissipation of the frame. This approach resulted in two patterns ofHSAC20-2 and HSAC20-3, as shown in Fig. 9(b) and (c), respectively.The former pattern had more energy dissipative members; however,the system was softer. Nevertheless, the HSAC20-2 frame experiencedless acceleration since it was softer and consequently had a largerperiod.

The last approachwas based onmaintaining stability of the structureunder strong groundmotions. Collapse occurs when plastic hinges formin all columns of two different stories. Semi-rigid connections, as men-tioned before, might be used as a fuse to protect their adjacent columns.This approach aims to protect at least one column in each story level.Using this approach, two patterns of HSAC20-4 and HSAC20-5, asshown in Fig. 9(d) and (e), were proposed.

2.6. Evaluation of proposed patterns based on inter-story drift angle

Inter-story drift angle, which is expressed as inter-story drift (δ), di-vided by the height of the story (h) is known as one of the best measuresof seismic performance at the story level of steelmoment resistant frames(SMF). The story drift is a global parameter since it is related to the globaldrift angle (roof drift angle), which is defined as the roof displacementdivided by the height of the roof and consequently to the spectraldisplacement demand. It is also a local parameter since it provides agood estimation of member forces and deformation demands [15].

Amajor concernwith using semi-rigid connections in steel frames isthat it may cause the inter-story drifts to increase beyond acceptable

0

2

4

6

8

10

12

14

16

18

20

0.0% 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% 14.0% 16.0% 18.0% 20.0%

Stor

y

Drift

HSAC20-1HSAC20-2HSAC20-3HSAC20-4HSAC20-5RIGID

Col

laps

e P

reve

ntio

n L

imit

Fig. 11. Average of story drift diagrams for various models of 20-story structure subjectedto L.A. MCE records.

limits. Although the use of hybrid frames causes a decrease in the initialstiffness, the ground motions do not act similarly to static lateral loadson frames. Groundmotions exert forces to frames by introducing accel-eration to stories'mass in story levels. Since semi-rigid connections shiftthe period of structures, the amount of acceleration will reduce. On theother hand, although the initial stiffness of a SMRF is more than the ini-tial stiffness of its corresponding hybrid frame, the system stiffness ofthe frame changes during an earthquake due to yielding in structuralmembers and nonlinear moment-rotation behavior of semi-rigid con-nections. Consequently, the stiffness of the hybrid frame can be higherthan the stiffness of the corresponding moment frame during a groundmotion excitation. Thus, all frames are evaluated using an inelastic timehistory analysis.

In order to determine the most effective pattern, the five proposedhybrid frames were modeled using a comprehensive nonlinear modeland were subjected to the SAC ground motions at the Los Angeles site.SAC ground motions are categorized into two levels: Design BasedEarthquakes (DBE) and Maximum Credible Earthquakes (MCE), basedon their return period. The models were first subjected to the set of 20DBE records, LA01 to LA21, to be evaluated for the first performanceobjective, which was to satisfy the Life Safety (LS) performance underthe DBE hazard level. The acceptance criterion for this performanceobjective is to maintain an average inter-story drift of less than 2.5%.The models were then subjected to the set of 20 MCE records, LA21 toLA40, to be evaluated for the second performance objective, which isto satisfy the Collapse Prevention (CP) performance under MCE hazardlevel. The acceptance criterion for this performance objective is tomain-tain an average inter-story drift of less than 5%.

0

5

10

15

20

1.0% 2.0% 3.0% 4.0% 5.0% 6.0%

Stor

y

Maximum interstory drift ratio, θmax

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Col

laps

e P

reve

ntio

n L

imit

The percentages refer to the stiffness of the beam with semi rigid connection with respect tothe stiffness of the beam with rigid connection

Fig. 13. Average story drift diagrams for HSAC20-5 with various connection stiffnesssubjected to LA MCE records.

Column Beam

2

Top Angle Bolted

Seat Angle Bolted

15.6

3/4

d

4

Column

2

1/4

4

4

Weld

4

8.3 1/4

3/4

4

3/4

21/4

15

3Web Angle

Fig. 14. Typical sketch of top- and seat-angle with double web angle connections.

7M. Razavi, A. Abolmaali / Journal of Constructional Steel Research 98 (2014) 1–11

Figs. 10 and 11 show the average of all drift results for the five pro-posed hybrid frames and the original SAC rigid frame subjected to DBEandMCE records, respectively. In these graphs, each line shows an aver-age of story drift ratios, which resulted from the dynamic inelastic timehistory analysis of a frame subjected to 20 earthquake records. Thus,each graph summarizes 120 nonlinear analysis drift results. Fig. 10shows that all proposed models met the LS drift criteria, except theHSAC20-1 model. However, HSAC20-4 and HSAC20-5 models havethe minimum amount of drift demand.

Similarly, drift results of the proposed hybrid frames subjected to theMCE records confirmed the effectiveness of the semi-rigid connectionlocation pattern of HSAC20-4 and HSAC20-5 frames.

These observations led to selecting patterns used in HSAC20-4 andHSAC20-5 models as the most effective patterns.

3. Sensitivity study on semi-rigid connections initial stiffness

To determine the effective connection properties, a parametric studywas performed on the initial stiffness of semi-rigid connections used in

Rigid End-Cap

Fig. 15. Top- and seat-angle with double web angl

the selected hybrid frames. These frames were subjected to the LosAngeles MCE level records, and the average of results is presented foreach frame in Figs. 12 and 13.

As shown in Fig. 3, the beam model consisted of an elastic beam–

column model, two plastic hinges, and two semi-rigid connections.The flexural rigidity of a beam is a function of the flexural rigidity ofits components. The elastic beam–column member and the semi-rigidconnection can be considered as two rotational springs. Thecompound's stiffness for this system of series springs is obtained by:

Kcompound ¼ 11

KBeamþ 1KConnection

¼ KBeam � KConnection

KBeam þ KConnection: ð1Þ

Therefore, for connection stiffness equal to infinity, the stiffness ofthe compound is equal to the stiffness of the beam. On the other limit,for a connection stiffness equal to zero, the compound's flexural stiff-ness equals to zero. Based on Eq. (1), the connections' initial stiffnessis back calculated for a total component stiffness of 10% to 100% of the

Cyclic Load

Connection

e finite element model, and mesh properties.

-226

-169.5

-113

-56.5

0

56.5

113

169.5

226

-2000

-1500

-1000

-500

0

500

1000

1500

2000

-6% -5% -4% -3% -2% -1% 0% 1% 2% 3% 4% 5% 6%

Mom

ent

(kip

.in)

Drift (%)

(kN

.m)

Fig. 16. FEMhysteresis loops for top- and seat-anglewith doubleweb anglewithW21X50.

8 M. Razavi, A. Abolmaali / Journal of Constructional Steel Research 98 (2014) 1–11

stiffness of the beam. For an elastic beam–column member subjectedto double curvature bending, the initial stiffness of the beam equals to6EI/L, where “E” is the modulus of elasticity of steel material, “I” is themoment of inertia of the beam's cross section, and “L” is the length ofthe beam. For the purpose of parametric study, the compound stiffnessis varied between 10 and 100% of the beams' stiffness. Then, the framesare subjected to theMCE groundmotions. Finally, the drift demands arecompared for selection of the best connections' initial stiffness.

Average drift diagrams for HSAC20-4 and HSAC20-5 frames withvarious connection stiffness values subjected to LA MCE records areillustrated in Figs. 12 and 13, respectively. These two graphs show thatin both semi-rigid patterns used for the 20-story frame, there is aninverse relationship between connection stiffness and the maximumdrift. Further study on the frame drift demands subjected to singleearthquake records indicated that for ground motions with smaller ac-celeration intensity, such as LA21, the greater connection stiffnesscorresponded to the less drift demands. However, when frames weresubjected to a high intensity earthquake records, such as LA30, thegreater connection stiffness caused more drift demands. Story driftratio plots for individual ground motions are presented in Razavi [20].

Based on the presented study, a connection with stiffness of 30% to50% of the stiffness of the beam was selected for implementation inhybrid frames. Average story drift results support the hypothesis that

Table 2Semi-rigid connections properties.

Beam Size Θy My (kip-in) Θu Mu (kip-in) Ke Kp

W21X50 0.003 1032 0.05 1750 344,000 15,277W24X62 0.003 1203 0.05 2000 401,000 16,957W27X84 0.003 1411 0.05 2250 470,333 17,851W30X99 0.003 1584 0.05 2450 528,000 18,426W33X141 0.003 1920 0.05 2900 640,000 20,851W36X150 0.003 2080 0.05 3300 693,333 25,957

0

5

10

15

20

0 0.2 0.4 0.6 0.8 1Rat

Fig. 17. The ratios of the moment in beams for th

using connections with stiffness in this range reduces the probabilityof collapse in MCE excitations; on the other hand, in the case of DBEexcitations, the system is stiff enough to meet the life safety criterion.

4. Semi-rigid connections

In general, bolted–bolted or welded–bolted connections with slipcritical bolts, which are pre-tensioned to 70% of their minimum tensilestrength, are known as semi-rigid connections. Static and dynamic char-acteristics of semi-rigid connections are categorized by their momentrotation (M-θ) curves and hysteresis loops, respectively.

For the purpose of selection of the type of semi-rigid connection, re-sults of several experiments conducted by Abolmaali et al. [3] and Chenand Kishi [11] were studied. Based on the effective initial stiffness andductility of the semi-rigid connections, top-and seat-angle with doubleweb angle connectionswere found to be the bestmatch for the purposeof this study. The hysteresis behavior of beam–column steel connectionswas predicted by means of a 3D non-linear finite element analysis(FEA). Incremental nonlinear analysis takes into account material,geometry, and contact nonlinearities in predicting moment-rotationhysteresis loops. The results obtained from the finite element analyseswere validated by a series of full-scale structural tests performed byAbolmaali et al. [3]. Modeling details are discussed in detail in Razaviet al. [21] and Razavi [20]. Finally, semi-rigid connections used in thisstudy for different beam sizes were simulated. A bilinear curve wasfitted to the moment-rotation hysteresis loop of each connection.These curves were then used in global modeling of the hybrid frames.

A typical sketch of the top-and seat-angle with double web angleconnections selected for this study is shown in Fig. 14. A 3-D finiteelement model of the top-and seat-angle with double web angle ispresented in Fig. 15. Fig. 16 shows the hysteresis loops for top-andseat-angle with double web angle with W21X50 and the bilinear fittedcurve.

The connections properties are also summarized in Table 2. Nota-tions are explained in Fig. 3.

5. Force demands

To compare the shear and bendingmoments of the HSAC versus theoriginal rigid SAC frames, the ratios of the absolute value of maximumforces for the HSAC were normalized with respect to the forces of theSAC frame. Thus, a ratio of unity indicates that the HSAC forces areequal to the rigid SAC forces, and the ratio of less than unity implies areduction in a given force for the hybrid frame (lower demand).

As an example, the beam's and column's moment ratios for the H-SAC20-5 to the 20-story rigid frames subjected to two sets of groundmotions are plotted in Figs. 17 to 18. Each point in these graphs corre-sponds to a normalized demand value, and the solid line shows the

1.2 1.4 1.6 1.8 2io

LA21 LA22LA23 LA24LA25 LA26LA27 LA28LA29 LA30LA31 LA32LA33 LA34LA35 LA36LA37 LA38LA39 LA40

e 20-Story HSAC20-5/SAC subjected to MCE.

0

5

10

15

20

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Stor

y

Ratio

LA21 LA22

LA23 LA24

LA25 LA26

LA27 LA28

LA29 LA30

LA31 LA32

LA33 LA34

LA35 LA36

LA37 LA38

LA39 LA40

Fig. 18. The ratios of the moment in columns for the 20-Story HSAC20-5/SAC subjected to MCE.

9M. Razavi, A. Abolmaali / Journal of Constructional Steel Research 98 (2014) 1–11

average in each story level. In addition, the average values of the mem-bers' moment and shear ratios are tabulated in Table 3. On average, themember forces are reduced between 6 and 16%.

6. Reliability analysis

This section focuses on evaluating and quantifying the collapseperformance of the Los Angeles SAC 20-story rigid frame and the pro-posed hybrid frames by application of the FEMA P695 reliability analysismethodology. An Incremental Dynamic Analysis (IDA) was performedon the comprehensive nonlinear models of the rigid frame and its twocorresponding hybrid frames. The IDA was performed by applying the20 records of the set of MCE, 2% probability of exceedance in 50 years,ground motions. Finally, the collapse performance of the frames wasquantified and compared by computing the Collapse Margin Ratio(CMR) value.

Incremental Dynamic Analysis (IDA), also known as Dynamic PushOver (DPO), is an analysis method developed by Vamvatsikos andCornell [23]which aims at determining the global capacity of structures.In this method, structures are subjected to one or more ground mo-tion(s), each scaled to multiple levels of intensity Measure (IM). An IMis a non-negative parameter, such as Peak Ground Acceleration (PGA)or Spectral Acceleration (Sa), which represents the ground motion'sintensity. Then, the structure is analyzed under each scaled groundmo-tion, utilizing a nonlinear dynamic analysis, and the Damage Measure(DM) of interest is recorded. A DM is a measurable response of a struc-ture such as ductility, global drift, or inter-story drift that is an output ofthe nonlinear dynamic analysis under the prescribed seismic loading.The smallest scale factor is selected to ensure an elastic response ofthe structure, then the scale factor increases until the collapse limitstate is reached. The scale factor increment should be small enough tocapture the collapse point. Finally, a graph of DMs versus IMs is plottedwhich also called IDA curve. In this study, the 5% damped first modespectral acceleration (Sa (T1, 5%)) and the inter-story drift angle(θmax) were selected as the IM and DM parameters, respectively.

Table 3Average hybrid/SAC demands response ratio.

Number of stories Model name Under DBE records Under MCE records

Beams' moment HSAC20-4 0.88 0.88HSAC20-5 0.84 0.85

Beams' shear HSAC20-4 0.87 0.88HSAC20-5 0.84 0.85

Columns' moment HSAC20-4 0.92 0.94HSAC20-5 0.86 0.91

Columns' shear HSAC20-4 0.90 0.92HSAC20-5 0.85 0.89

A fragility function for collapse limit-state expresses the probabilityof exceeding the limit state under a given groundmotion with a certainlevel of intensity. The fragility function is produced by using collapsedata from IDA results through a cumulative distribution function(CDF) that expresses the probability of collapse as a function of groundmotion intensity (Ibarra et al., 2002). For this purpose, a lognormal dis-tribution is fitted to the collapse data obtained from IDA results. Whilefor a structure, the IDA is performed and the fragility curve is developed,the median collapse intensity, SCT, should be identified. The lowestintensity at which one-half of the records cause collapse is the mediancollapse intensity, SCT [13]. In turn, this value is the spectral accelerationcorresponding to the 50% probability of collapse in the fragility curve.The SCT value is a representative of the capacity of the structure. Onthe other hand, the MCE intensity, SMT, which is defined as the median5%-damped spectral acceleration of the MCE ground motions at thefundamental period of the structure, is a representative of the plausibledemands applied to a structure.

To quantify the collapse performance of steel frames, FEMA P695introduced the collapse margin ratio, CMR, which is the ratio of theSCT to the SMT, as shown in Eq. (2).

Collapse Margin Ratio CMR ¼ SCTSMT

ð2Þ

Indeed a bigger CMR corresponds to a less probability of collapse.The collapse point of a frame for a particular ground motion is

defined as the lowest value of the following criteria: a) the pointwhere the slope of the IDA curve falls below 20% of the initial slope ofthe curve, and b) the upper-bond inter-story drifts capacity of 10%.

The IDA curves and their corresponding fragility curves for different20-story frames are shown in Fig. 19. Hollow circles in the IDA curvescorrespond to the collapse points in structure. Moreover, each blackdot in the fragility curve corresponds to a cumulative probability ofcollapse obtained from the IDA curves. The collapse margin ratio fordifferent SAC rigid frames and the proposed hybrid frames are shownin Table 4. A larger CMR corresponds to a better performance.

Fig. 20(a) and (b) shows the final deformed shape of SAC-20 storyrigid and the H-SAC20-5 frames subjected to LA36 ground motion, re-spectively. The zigzag line in Fig. 20(b) was obtained by connectingthe locations of semi-rigid connections. As previously shown in Fig. 8,formation of plastic hinges in stories 1 through 5 of the rigid framecaused collapse in the original SAC frame. Although, the H-SAC20-5has also shown excessive deformation, this structure did not collapsewhen subjected to the identical earthquake record.

7. Conclusion

In this study, a new lateral resistant system called hybrid frame,which is a combination of semi-rigid and fully rigid connections in

10 M. Razavi, A. Abolmaali / Journal of Constructional Steel Research 98 (2014) 1–11

steel frames, was introduced to improve the performance of momentresistant steel frames subjected to seismic excitations. The 20-storySAC frame for the Los Angeles site was used as benchmark in thisstudy. Hybrid frames were designed by replacing selected fully-

a) IDA Curves for Model SAC Rigid 20-Story

c) IDA Curves for Model HSAC20-4

e) IDA Curves for Model HSAC20-5

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0% 5% 10% 15%

Sa(T

1, 5

%)

/ g

Maximum interstory drift ratio, θmax

Maximum interstory drift ratio, θmax

Maximum interstory drift ratio, θmax

0

0.2

0.4

0.6

0.8

1

1.2

0% 5% 10% 15%

Sa(T

1, 5

%)

/ g

0

0.2

0.4

0.6

0.8

1

1.2

0% 5% 10% 15%

Sa(T

1, 5

%)

/ g

Fig. 19. IDA and fragility curves fo

rigid connections with more flexible semi-rigid connections in theSAC frame.

The effective semi-rigid connection patterns and the effectiveconnection stiffness were identified. Performance of the 20-story SAC

b) Fragility Curve for Model SAC Rigid 20-Story

d) Fragility Curve for Model HSAC20-4

f) Fragility Curve for Model HSAC20-5

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Prob

abili

ty o

f C

olla

pse

Sa(T1, 5%) / g

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Prob

abili

ty o

f C

olla

pse

Sa(T1, 5%) / g

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Prob

abili

ty o

f C

olla

pse

Sa(T1, 5%) / g

r different 20-story models.

Table 4Collapse margin ratio for different frame models.

Structure type CMR

Rigid 1.48HSAC20-4 1.80HSAC20-5 1.99

11M. Razavi, A. Abolmaali / Journal of Constructional Steel Research 98 (2014) 1–11

rigid and its corresponding hybrid frames were evaluated using thereliability analysis presented in FEMA P695.

Comparison of performance of the 20-story SAC rigid frameswith itscorresponding hybrid frames showed a superior performance for thehybrid frame. Collapse Margin Ratio of the investigated hybrid frameswas between 20 and 33% better than the performance of the corre-sponding rigid frame. This, in turn, reduced the probability of collapsewhen the frame was subjected to severe ground motions.

The force demands in the beams and columns of the proposed 20-story hybrid frames were reduced up to 16%. Considering the fact thatthe structural members' (beams and columns) sections in the hybridframes were the same as those of the corresponding rigid frames, theproposed frame system performed superior to conventional SMFswhen subjected to earthquake excitation.

a) Rigid SAC 20- Story b) H-SAC20-5

Fig. 20. The final deformed shapes of the SAC20-story and HSAC20-5 frames subjected toLA36 ground motion.

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