Influence of Connection Design Parameters on the Seismic Performance Of

Journal of Constructional Steel Research 64 (2008) 607–623www.elsevier.com/locate/jcsr

Influence of connection design parameters on the seismic performance ofbraced frames

Jung-Han Yoo∗, Dawn E. Lehman, Charles W. Roeder

Department of Civil Engineering, University of Washington, Seattle, WA 98195-2700, United States

Received 5 September 2007; accepted 17 November 2007

Abstract

Special concentrically braced frames (SCBFs) are commonly used lateral-load resisting systems in seismic design. In SCBFs, the braces areconnected to the beams and columns by gusset plate connections, and inelastic deformation is developed through tensile yielding and inelasticpost-buckling deformation of the brace. Recent experimental research has indicated that the seismic performance of SCBFs can be improved bydesigning the SCBF gusset plate connections with direct consideration of the seismic deformation demands and by permitting yielding in thegusset plate at select performance levels.

Experimental research provides important information needed to improve SCBF behavior, but the high cost of experiments limits this benefit.To extend and better understand the experimental work, a companion analytical study was conducted. In an earlier paper, the inelastic finiteelement model and analysis procedure were developed and verified through detailed comparison to experimental results. In this paper, the modeland analytical procedure extend the experimental results. A parametric study was conducted to examine the influence of the gusset plate andframing elements on the seismic performance of SCBFs and to calibrate and develop improved design models. The impact of the frame details,including the beam-to-column connections, the brace angles, and their inelastic deformation demands, was also explored. The results suggest thatproper detailing of the connections can result in a large improvement in the frame performance.c© 2007 Elsevier Ltd. All rights reserved.

Keywords: Braced frames; Connections; Seismic design; Finite element method; Inelastic response

1. Introduction

Special concentrically braced steel frames (SCBFs) arestrong and stiff, providing the structural characteristics neededfor seismic design. The inelastic lateral response of SCBFsis dominated by tensile yielding and inelastic post-bucklingdeformation of the braces, and the corresponding designrequirements focus on the brace [1]. For example, limitsare placed on the local and global slenderness of the braceto permit plastic deformation of the brace in its buckledconfiguration. To ensure brace yielding, the current seismicdesign provisions [10] require that the axial capacity ofgusset plate connections exceed the expected axial (tensile andcompressive) capacities of the brace, since premature failureor fracture of the connection results in poor performance ofthe system. These expressions lead engineers to interpret thata stronger connection is inherently better.

∗ Corresponding author. Tel.: +1 206 543 1075.E-mail address: [email protected] (J.-H. Yoo).

0143-974X/$ - see front matter c© 2007 Elsevier Ltd. All rights reserved.doi:10.1016/j.jcsr.2007.11.005

The braces are connected to the beams and columns of theframe through gusset plate connections, which are designed byvariations in the uniform force method (UFM) [3]. The gussetplate connections must accommodate the cyclic end rotationexpected in a buckled brace while supporting the expectedtensile and compressive capacities of the brace. As a result,current design practice recommends a “2tp” linear geometricoffset be used, as illustrated in Fig. 1(a), where tp is the platethickness, to achieve this end rotation resulting from out-of-plane brace buckling. Use of the linear-offset rule results inrelatively large gusset plates, and the resulting connection maybe uneconomical and reduce the constructability of the frame.

Recent research has shown that SCBF frames withconnections designed to meet current practice may exhibitbehavior that is very different from that envisioned inthe original design and may have relatively poor seismicperformance [11,7]. To improve the seismic response of theseframes, an improved design concept has been proposed withan emphasis on identifying a primary yield mechanism(s)

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608 J.-H. Yoo et al. / Journal of Constructional Steel Research 64 (2008) 607–623

Fig. 1. Current and proposed clearance requirements; (a) AISC 2tp clearance,and (b) proposed elliptical clearance.

(e.g., tensile yielding or buckling of the brace) and balancingmultiple secondary yield mechanisms (e.g., yielding of thegusset plate) with the primary yield mechanism to enhance theoverall drift capacity of the system [9]. In particular, increasedflexibility and yielding in the connections at larger driftdemands have been shown to improve the seismic performanceof the frame and permit the use of HSS braces [7]. An initialexperimental study was conducted to develop and explorethis design premise. A companion analytical study resultedin an inelastic finite element model capable of accuratelysimulating the experimentally measured response and observedyield mechanisms [13].

Although this experimental and analytical research supportsthe development of the proposed balanced design concepts, thenumber of experimental specimens was limited by the high cost

of the tests. Therefore, the experimentally validated model wasused to conduct a parameter study to extend the experimentalfindings. This paper summarizes the parameter study, focusingon key issues affecting gusset plate connection performance,and presents proposals for improved gusset plate connectiondesigns to meet specific performance objectives.

2. Experimental study and companion analytical model

A comprehensive series of elastic and inelastic analyses wasperformed with ANSYS [4] structural analysis software to sim-ulate the response of the SCBFs and their gusset plate connec-tions. Detailed comparisons between the analytically predictedand observed experimental behavior were made to assure theaccuracy and reliability of the inelastic predictions, and a moredetailed description of the model and the comparison to exper-imental results are provided elsewhere [13,7].

The experimental program at the University of Washingtonwas developed to provide a comprehensive understanding ofthe global SCBF system, and local brace and gusset platebehaviors [7]. Fig. 2(a) and (b) illustrate the test specimen andsetup. The frames were full-scale simulations of a single bracedbay in the bottom story of a low-rise building or an upperstory braced bay of a taller structure. The sub-assemblagesincluded a brace, beams above and below the brace, gusset plateconnections at each end of the brace, and columns to completethe single bay frame assembly, as shown in the figure. Thebraces were HSS 5 × 5 × 3/8 inch tubes, and most beamscolumns were W16 × 45 and W12 × 72 sections of A992 steel,respectively. The gusset plate connections were varied from

(a) Test setup. (b) Test specimen. (c) FE model.

(d) Drift history.

Fig. 2. Braced frame specimen.

J.-H. Yoo et al. / Journal of Constructional Steel Research 64 (2008) 607–623 609

specimen to specimen to evaluate:

• current AISC and UFM design procedures,• weld requirements between the gusset plate and the beam

and column,• the linear and alternate elliptical clearance requirements,• the thickness and geometry of the gusset plate,• the relative stiffness of the brace, gusset plate, and framing

members, and• the relative performance of tapered and rectangular gusset

plates.

The sub-assemblages were subjected to a cyclic inelastic de-formation history based upon the ATC-24 testing protocol [5].This protocol requires a number of elastic cycles to establishstiffness and initial yield resistance, and repeated cycles ofinelastic deformation with increasing amplitude to investigatecyclic inelastic performance.

The experiments provided an improved understanding ofSCBF frame behavior and gusset plate design requirements.The work clearly showed the following.

• The gusset plate connections are not pinned connections andthey induce significant plastic deformations into the beamsand columns of the SCBF system.

• Welds joining the gusset plate to the beam and column mustbe designed to achieve the plastic capacity of the gusset platerather than the plastic capacity of the brace.

• The alternate elliptical clearance model provided perfor-mance equal to or better than that achieved with the 2tp lin-ear clearance while permitting a smaller and more compactgusset plate.

• Improved system performance was obtained when limitedyielding occurred in the gusset plate.

• With HSS tube braces, the most ductile ultimate failure wasachieved by initiation of cracking and ultimate fracture atmid-span of the buckled brace after localization of inelasticdeformation. The frame deformation associated with thislocalization of damage depends upon the details of theconnection.

• The strength and stiffness of the gusset plate connectionmust be large enough to develop the full capacity of thebrace, but should not be excessively large, because anoverly stiff or strong connection concentrates the inelasticdeformation into a short length at the center of the brace andcauses early brace fracture.

• Tapered gusset plates provide good end rotational capacityfor the brace, but they may result in increased inelasticdemands on the gusset plate and the welds.

In response to these experimental results, an improveddesign method was proposed, and a comprehensive nonlinear,inelastic finite element (FE) analysis study was initiatedto extend the understanding of the connection and systemperformance and to further calibrate improved design models.All members were modeled with the four-node quadrilateralshell elements (Shell 181), which has six degrees of freedom ateach node. The element displacement field includes membrane,flexural and transverse shear deformations. The element isappropriate for modeling thin and moderately thick plate and

shell elements [4]. Large-displacement element formulationswere used to simulate buckling, and a bilinear kinematichardening plastic material model was employed to simulatecyclic inelastic behavior. The material properties used in theanalyses were based upon measured stress–strain relationshipsobtained from the experimental research [7].

Fig. 2(c) shows a typical FE model. Boundary conditionssimulated the test restraints, including translational degrees offreedom of the bottom flange of the lower beam, roller supportsat the bottom of the columns, and restraint of out-of-planemovement at the top of the columns. Additional out-of-planerestraints were applied at the lateral support locations usedin the experiments. Nonlinear spring elements (COMBIN39)were used to model the bolts at beam–column shear-plateconnections. The nonlinear force–deflection behavior of thesprings was based on past experimental research on shear-plateconnections [8]. Rigid rotational and translational restraintswere imposed to simulate all welded joints. A mesh size ofapproximately 25 mm by 25 mm was used in the centerof the brace and at the beam–column and the gusset plateconnections to capture nonlinearity in regions where large localdeformations were expected. A coarser mesh was used whereonly limited inelastic deformation occurred. Greater detail onthe model, computation procedures, and verification of themodels are provided elsewhere [12,13].

Comparison with experimental results shows that the FEmodel accurately predicted the cyclic inelastic response of thetest specimens at both the global (e.g., total frame) and local(e.g., gusset plate connection) levels, as illustrated in Fig. 3.The global response, including the frame stiffness and resis-tance, was closely approximated at the global level, as shownin Fig. 3(a), with relatively small (less than 7%) variation in theobserved and predicted resistances for all test specimens. Theinelastic FE analysis also correlated well with local behavior,because it consistently predicted the location, initiation and ex-tent of this local yielding, as illustrated in Fig. 3 [13]. In partic-ular, both the experiments and analysis showed the following.

• Significant local yielding and ultimate fracture at the centerof the brace was due to localization of damage causedby large out-of-plane brace deflections during buckling asshown by comparison of the predicted brace deformationwith a photograph of the test specimen at the same framedeformation in Fig. 3(b).

• Significant local yielding in the gusset plate and limitedtearing adjacent to gusset plate welds was due to large platedeformations and local yielding caused by end rotation ofthe brace during buckling. This response is shown for theanalyses and experiments in Fig. 3(c).

• Significant local yielding of the beam and column adjacentto the gusset plate connections was a result of frame actioninduced by the size and rigidity of the gusset plates and theboundary conditions of the test specimen.The inelastic analysis model predicts the yielding, buckling

and inelastic deformation modes, but it cannot directly predictthe initiation of cracking, ductile tearing or fracture of the steel.Instead, the equivalent plastic strain, ε

pleqv, resulting from the


Fig. 3. Comparison of inelastic analysis and theoretical predictions [13]; (a) theoretical and measured force–deflection behavior of specimen HSS5, (b) typicalbrace buckling deformation, and (c) typical yielding of gusset plate.

inelastic analysis is used as an indicator of initial cracking andfracture of the steel and weld by calibrating the computed valueof ε

pleqv to the observed initiation of cracking and tearing in the

experiments [13]. In the analysis, εpleqv was based on the plastic

strain components using the general von Mises equation:

εpleqv =

1√

2(1 + υ ′)

[(ε

plx − ε

ply

)2+

(ε

ply − ε

plz

)2

+

(ε

plz − ε

plx

)2+

23

(γ

pl2xy + γ

pl2yz + γ

pl2zx

)] 12

(1)

where εplx , ε

ply , γ

plxy , etc., are the appropriate components of

plastic strain and υ ′ is the effective Poisson’s ratio. The work

showed that crack initiation could be predicted with reasonableaccuracy by defining a threshold value for ε

pleqv [13] for the

given stress–strain state. The threshold value of εpleqv varies

for different FE mesh size, crack locations and conditions, butcalibrated threshold values provide a reasonable mechanismto predict the initiation and development of cracking. Thesethreshold values were verified and confirmed by comparisonwith the experimental observations. It must be noted that theε

pleqv considered in this evaluation is the total plastic strain

developed during a compressive brace cycle of loading. Thisload cycle causes severe local deformations in the buckledregion at the center of the brace and out-of-plane rotation of thegusset plate. This ε

pleqv concept is expected to be applicable to


Fig. 4. Typical brace gusset plate connection and parameters: (a) elliptical clearance, (b) tapered gusset plate, (c) alternative beam-to-column connections, (d) gussetplate thickness, (e) beam and column size, (f) brace angle, and (g) brace-to-gusset plate weld length.

Table 1Material properties

Specimen Yield and ultimate strengths (MPa)HSS-5 (Reference) Beam (A992) Column (A992) Brace (A500) Gusset (A572)

395 501 409 522 505 549 447 602

other geometries and structural conditions, but the calculatedε

pleqv and the corresponding threshold limits depend on the

finite element type and mesh size. Thus, although the givenprocedure may be applicable to other geometries and systems,specific calibration is required for these other applications.More detailed development and verification of this procedureis provided elsewhere [13].

3. Overview of analytical parameter study

In this study, the previously described FE analysisprocedures were used to extend the prior studies to examine arange of parameters that were not evaluated in the experimentalresearch program. The results aid in extending and calibratingthe proposed design method to a braced frame system with abroader range of geometries and design details. The studieddesign parameters include the geometry of the gusset plate,the clearance model used for brace end rotation, sizes ofthe framing elements, the beam–column connection, and theconnection details (e.g. weld size, weld length, etc.). Theseparameters are evaluated in analysis groups as depicted inFig. 4. The purpose of this study was twofold: (1) to focusthe experimental research and provide direction for futureexperiments while providing the maximum benefit from eachrelatively expensive test, and (2) to develop and verify thedesign methodology and corresponding design expressions.

The parameter study investigated both system and connec-tion response and behavior. Comparisons are made in referenceto a frame which was tested as part of the experimental studyand used to calibrate the analytical model. The reference frame

geometry and member sizes simulated the HSS5 test specimen,which had

• W16 × 45 beams and W12 × 72 columns of A992 steel,• a 45◦-diagonal HSS 125×125×9.5 mm (5×5×3/8) brace

of A500 Type B/C steel,• a 9.5 mm gusset plate of A572 steel,• gusset plates designed using an elliptical offset of 8 times the

plate thickness (8tp) and a brace-to-gusset plate weld lengthof 375 mm, and

• beam-to-column connections fabricated with complete jointpenetration (CJP) welds joining the beam flanges and web tothe column flange.

The experimental results indicate a favorable response ofthis specimen, as shown in Fig. 3(a), and this analysis is identi-fied as GPT9.5 to indicate a Gusset Plate Thickness of 9.5 mm.Individual member sizes and connection details were variedfrom this baseline case to study the parameters illustrated inFig. 4 (and discussed previously) to study the effect of vari-ation in each parameter on the system and connection behav-ior. In general, the grouped analyses study variation in a singleparameter to provide clear comparisons between analytical re-sults; however, some parameters are inherently interrelated.

The computed behaviors included local yielding in the brace,beams, columns, and the gusset-plate and beam-to-columnconnections. The potential for crack initiation and fractureat the midspan of the brace and gusset plate welds werethe primary computed results, because these initiated localand global failure modes in the experiments. The material


Table 2Parametric study: Member descriptions

Category Modeldesignation

Clearancerequirement

Gusset platesize (mm)

Beam-to-columnconnection

Gusset platethickness (mm)

Frame size(Beam)(Column)

Braceangle

Splice length(mm)

ReferenceGPT9.5(HSS 5)

8tp 635 × 533 Fully welded 9.5W16 × 45

45◦ 375W12 × 72

Linearclearance

LC2t Linear 2tp 864 × 762 Fully welded 9.5W16 × 45

45◦ 375W12 × 72

Ellipticalclearance

EC3t 3tp 597 × 495 Fully welded 9.5W16 × 45

45◦ 375W12 × 72

EC12t 12tp 711 × 610 Fully welded 9.5W16 × 45

45◦ 375W12 × 72

TaperedT15 8tp Taper of 15◦ Fully welded 9.5

W16 × 4545◦ 375

W12 × 72

T25 8tp Taper of 25◦ Fully welded 11.1W16 × 45

45◦ 375W12 × 72


SPW 8tp 635 × 533 Shear plate welded 9.5W16 × 45

45◦ 375W12 × 72

SPB 8tp 635 × 533 Shear plate bolted 9.5W16 × 45

45◦ 375W12 × 72

Plate thickness GPT22.2 8tp 724 × 622 Fully welded 22.2W16 × 45

45◦ 375W12 × 72

Plate thicknessand tapered

GPT22.2T15 8tp Taper of 15◦ Fully welded 22.2W16 × 45

45◦ 375W12 × 72

Category Parameter Clearancerequirement

Gusset platesize (mm)


Gusset platethickness (mm)

Frame size(Beam)(Column)

Braceangle

Splice length(mm)

Frame size(9.5 mm plate)

GPT9.5LB 8tp 635 × 533 Fully welded 9.53*W16 × 45

45◦ 375W12 × 72

GPT9.5LC 8tp 635 × 533 Fully welded 9.5W16 × 45

45◦ 3753*W12 × 72

GPT9.5LBLC 8tp 635 × 533 Fully welded 9.53*W16 × 45

45◦ 3753*W12 × 72


GPT22.2LB 8tp 724 × 622 Fully welded 22.23*W16 × 45

45◦ 375W12 × 72

GPT22.2LC 8tp 724 × 622 Fully welded 22.2W16 × 45

45◦ 3753*W12 × 72

GPT22.2LBLC 8tp 724 × 622 Fully welded 22.23*W16 × 45

45◦ 3753*W12 × 72

Brace angle

BA30 8tp 853 × 427 Fully welded 11.1W16 × 45

30◦ 375W12 × 72


37.5◦ 375W12 × 72


52.5◦ 375W12 × 72


60◦ 375W12 × 72

Brace-to-gussetplate weldlength

WL.75 8tp 533 × 432 Fully welded 11.1W16 × 45

45◦ 281W12 × 72

WL.50 8tp 473 × 372 Fully welded 15.9W16 × 45

45◦ 187W12 × 72

properties used in the FE analysis were based on measuredmaterial properties obtained from the experimental program forSpecimen HSS-5 (Table 1). All specimens were subjected to thesame cyclic deformation history, as indicated in Fig. 2(d).

The parameter groupings and specific values for individualspecimens that were analyzed within each group are identifiedin Table 2 (shaded cells indicate the varied parameter relativeto the reference model). The simulated braced frame specimens

used analytical models that modified the reference simulationmodel GPT9.5. The designation of each simulation modelindicates the studied parameter and its value. As listed inTable 2 and illustrated in Fig. 4, the simulation modelsincluded:

• Model LC2t, which studied Linear Clearances of 2tp;• Models EC3t and EC12t, which studied Elliptical Clearances

of 3 and 12tp;


Table 3Parametric study: Resistance and drift ratio comparisons

Parameter Modeldesignation

Relativetensileresistance (toGPT9.5)

Relativecompressiveresistance (toGPT9.5)

EPS for initialweld tearing

Absolute driftratio for initialweld tearing

EPS for bracefracture

Absolute driftratio for bracefracture

Expectedbracefracture?

Reference GPT9.5(HSS 5)

1567 KN 671 KN 0.054 1.8% 0.285 3.2% Yes

Linear clearance LC2t 104% 101% Not predicted Not predicted 0.311 2.2% YesEllipticalclearance

EC3t 101% 101% 0.055 1.4% 0.279 3.2%

EC12t 106% 104% 0.059 3.2% 0.295 2.7% Yes

TaperedT15 95% 97% 0.059 1.4% 0.278 3.2%T25 94% 96% 0.054 1.4% 0.275 3.2%


SPW 92% 97% 0.055 1.8% 0.285 3.2% YesSPB 90% 96% 0.055 1.9% 0.287 3.4% Yes

Plate thickness GPT22.2 113% 123% 0.056 2.6% 0.290 2.2% YesPlate thicknessand tapered

GPT22.2T15 110% 119% Not predicted Not predicted 0.291 2.2% Yes

Parameter Modeldesignation

Relativetensileresistance (toGPT9.5)

Relativecompressiveresistance (toGPT9.5)

EPS for initialweld tearing

Absolute driftratio for initialweld tearing

EPS for bracefracture

Absolute driftratio for bracefracture

Expectedbracefracture?


GPT9.5LB 98% 99% 0.058 1.7% 0.284 3.1% YesGPT9.5LC 117% 125% Not predicted Not predicted 0.284 3.1% YesGPT9.5LBLC 115% 128% Not predicted Not predicted 0.282 3.1% Yes


GPT22.2LB113% 139%

0.061 2.6% 0.279 1.7% Yes100%* 113%*

GPT22.2LC124% 147%

Not predicted Not predicted 0.278 1.8% Yes110%* 120%*

GPT22.2LBLC126% 150%

Not predicted Not predicted 0.278 1.7% Yes112%* 122%*

Brace angle

BA30 119% 85% Not predicted Not predicted Not predicted Not predictedBA38 112% 93% Not predicted Not predicted Not predicted Not predictedBA53 92% 109% 0.065 1.0% 0.289 2.2%BA60 77% 110% 0.057 1.4% 0.290 1.7%

Brace-to-gussetplate weld length

WL.75 102% 103% 0.056 1.7% Not predicted Not predictedWL.50 103% 106% 0.055 2.6% Not predicted Not predicted

Note: Resistance values with * mark are relative to the resistances of Model GPT22.2.

• Models T15 and T25, which used Tapered plates with 15◦

and 25◦ taper angles;• Models SPW and SPB, which used Shear-Plate Welded and

Shear-Plate Bolted beam–column connections at the gussetplate;

• Model GPT9.5 and GPT22.2, which examined the GussetPlate Thickness, in which the number indicates the gussetplate thickness;

• Models LB, LC, LBLC, which used Large Beams only,Large Columns only, or both;

• Models BA30, BA38, BA53, and BA60, which used BraceAngles of 30, 37.5, 52.5, and 60 degrees, respectively; and

• Models WL.75 and WL.50, which used brace-to-gusset plateWeld Lengths equal to 75% and 50% of the reference length,respectively.

4. Results

The simulated resistance values (columns 3 and 4) andthe drifts (columns 6 and 8) corresponding to the providedlimiting equivalent plastic strain values (columns 5 and 7)for each model in the parametric study are provided in the

named columns of Table 3. Fig. 5(a)–(h) shows the simulatednormalized shear-drift envelopes for each parameter group,for which the shear force was normalized by the horizontalcomponent of the expected yield resistance of the brace.Expected maximum resistance values, inelastic deformationcapacities, and failure mode were used to investigate andcompare the simulated global behavior of each model.

Peak resistance values were normalized to the referencemodel (GPT9.5) for cases of the brace in tension and com-pression. Since the computer model does not directly esti-mate cracking fracture or failure, the resistance estimates in-clude yielding and strain hardening but do not include predictedcracking, failure and fracture. Comparing the differences in thecomputed tension and compression resistance values shows thatthe design of the framing elements and gusset plate can result inmoderate resistance increases; however, as indicated in Fig. 5,the elastic stiffness values of the frames are not greatly influ-enced by any of the connection parameters. Larger and thickergusset plates, heavier beam and column sections, and steeperbrace angles increase the lateral resistance of the frame withthe brace in compression, because the parameter reduces the


(a) Elliptical clearance. (b) Taper.

(c) Beam-to-column connection. (d) Plate thickness.

(e) Framing member size for thin (9.5 mm) plate. (f) Framing member for thick (22 mm) plate.

(g) Brace angle. (h) Brace-to-gusset weld length.

Fig. 5. Force–displacement response for parameter groups.


Fig. 6. Equivalent plastic stress distribution in and adjacent to gusset plate.

slenderness ratio of the brace. The expected resistance withthe brace in tension is increased by thicker gussets and heav-ier beam and column sections, because the parameter changesreduce yielding in the gusset plate and increase the strain hard-ening of the brace. The angle of inclination of the brace impactsthe resistance of the frame, but this effect is less apparent inFig. 5(g) because of the normalization used in plotting the re-sistance envelopes. Additional discussion of the impact of thesedesign parameters can be found in the following subsections.

While global comparisons are important, local behaviorincluding yielding, cracking, and fracture in the framingmembers and the connections has a dominate role in the seismicperformance. Further, a single numerical value is often notan ideal indicator of local behavior and failure, since failuredepends upon the extent and distribution of the local effects aswell as the local magnitude. As a result, comparisons of theequivalent plastic stress distribution are provided in Fig. 6 forselected analyses to show the distribution of yielding and areasof stress concentration with specific connection parameters.

The equivalent stress is defined as

σeqv =

(12

[(σx − σy

)2+

(σy − σz

)2+ (σz − σx )

2

+ 6(σ 2

xy + σ 2yz + σ 2

zx

)] ) 12

(2)

and σx , σy , etc., are the appropriate component stresses. Theequivalent stress results are displayed using stress contourplots. The contour shading becomes darker as the equivalentstress increases. Using the measured material properties [7],yielding of the gusset plate corresponds to an equivalent stressof approximately 450 MPa, yielding of the frame memberscorresponds to an equivalent stress of approximately 400 MPa,and yielding of the brace corresponds to an equivalent stressof approximately 500 MPa. These graphical stress distributionsare surface stresses, which may vary through the thicknessof the steel, and comparisons are made for the surface thatdemonstrates the greatest magnitude of the local stress state.


For the gusset plate, the bottom surface of the plate (i.e. thelower surface in the test configuration) is presented, since thebrace is configured to buckle upward and therefore the largeststresses occur on this surface during buckling. These resultsare used to study the impact of the design parameters on thedistribution of yielding in the gusset plate and adjacent beamand column within a specific parameter group.

Increased resistance does not correlate to increased expectedinelastic deformation capacity and or an improvement onor delay in the failure mode. As a result, the expectedinelastic deformation capacity and failure mode were estimatedusing experimentally equivalent plastic strain limits that weredeveloped in another paper and described earlier [13]. Specificplots of maximum ε

pleqv as a function of frame story drift are

provided in Figs. 7 and 8 to illustrate the relative potential forcrack development for variations in the design parameters forSCBFs. Earlier work showed the following.

• Crack initiation at the gusset plate-to-column developedwhen the maximum ε

pleqv at the crack location was in the

range 0.054–0.065.• Fracture in the center of the buckled brace occurred when the

maximum εpleqv in the locally deformed area of the buckled

brace was in the range between 0.271 and 0.306.

The drift ratios corresponding to the εpleqv values within

this range limit were computed for the onset of initial weldtearing and brace fracture, and are provided in Table 3 andFigs. 7 and 8. Experimental research shows that brace fractureis the primary failure mode for SCBF frames with HSS tubularbraces. Therefore, the analysis curves of Figs. 5, 7 and 8 aretruncated at the story drift where brace fracture is expectedby the ε

pleqv procedure. This truncation permits study of the

variations in the simulated connection deformation capacity andthe relationship between initiation of gusset weld cracking andultimate brace fracture.

4.1. Elliptical clearance requirement

Current seismic design practice employs a linear 2tp clear-ance, such as depicted in Fig. 1(a), to develop the brace end ro-tation required for out-of-plane buckling. This clearance modelcan lead to relatively large gusset plates and the connectionrigidity introduced by these large plates concentrates the cyclicstrain demand in the center of the brace, thereby reducing theinelastic deformation capacity of the system. An elliptical clear-ance model was proposed to provide the required rotational ca-pacity with a smaller, more flexible and compact gusset plate,as depicted in Fig. 1(b) [7]. This model follows the observedyield patterns in gusset plates after brace buckling in both ex-periments and inelastic FE analysis [6,13]. The model employsone quadrant of an ellipse with an orthogonal offset clearancethat is N times the plate thickness, tp, at both re-entrant cornersof the gusset plate, as shown in the figure.

The linear 2tp clearance model was developed and analyzedto compare to the elliptical clearance model. The linear 2tpclearance model had a small effect on the ultimate resistancewith an increase of 1% to 4% relative to the reference model

(GPT9.5), as shown in Fig. 5(a) and Table 3. The primarydifferences are revealed by considering the equivalent plasticstress distribution, as shown in Fig. 6(a) and (b), and theequivalent plastic strains, which were used to estimate initialweld tearing and brace fracture presented in Figs. 7(a) and8(a) [13]. When a linear 2tp clearance was used, significantyielding was predicted over a majority of the linear band ofthe gusset plate, as shown in Fig. 6(b), which delayed theweld cracking, as shown in Fig. 7(a). However, the story driftcorresponding to brace fracture decreased from 3.2% (ellipticaloffset model GPT9.5) to 2.2% (linear offset model LC2t), asshown in Fig. 8(a). This prediction of earlier brace fractureresults from the use of relatively large, stiff gusset plates thatresults in the localized large strain concentration at the middleof the brace, as discussed previously, and precipitates earlybrace fracture.

A series of analyses was also conducted to determine thebest offset value for the elliptical clearance, i.e., N in the Ntpexpression. Clearance values of 3, 8 and 12tp were evaluated,which resulted in relatively small variations in expected frameresistance, as indicated in Table 3. The ultimate tension loadand compression loads for the model with a 3tp ellipticalclearance model were about 1% larger than those of the 8tpelliptical clearance model. When the clearance was increasedto 12tp, the increase in ultimate resistance was approximately6% larger than in the reference model, GTP9.5. Comparing themodels with elliptical clearances of 8tp and 3tp (Fig. 6(a) and(c), respectively) indicates that a decrease in offset clearanceresults in a smaller yielded area with a higher equivalent stressand strain at the corners of the gusset plate. This indicatesthat the smaller clearance limit is likely to sustain weld crackinitiation and tearing at smaller story drifts, as indicated inTable 3 and shown in Fig. 7(a). In contrast, when a largerclearance of 12tp was used, significant yielding was predictedover a majority of the elliptical band of the gusset plate, whichdelayed the onset of weld cracking (Fig. 7(a)).

Similar comparisons can be made for the three variationsby considering the ε

pleqv in the center of the brace, as shown

in Fig. 8(a). Larger values of N result in smaller driftscorresponding to the limiting ε

pleqv in the center of the brace.

Similar to the linear offset model, the larger offset clearanceresults in a larger gusset (and sometimes thicker due to gussetplate buckling requirements), and this large plate creates greaterconnection stiffness, which induces earlier brace fracture [13].Combining these observations, it is clear that the ellipticalclearance model results in performance equal to or better thanthe current 2tp linear clearance model, and an intermediateelliptical clearance limit of approximately 6tp to 8tp offered thebest compromise for good frame performance when the samegusset plate thickness was used. Smaller clearances lead toearlier cracking of the gusset plate welds, while larger clearanceleads to earlier brace fracture.

4.2. Taper of gusset plate

In current design, using tapered gusset plates reduces theplate size while still meeting the linear offset expression.Relative to rectangular plates, tapered plates provide a more






Fig. 7. εpleqv at re-entrant corner of column on North East gusset plate (see Fig. 2(a) for direction notation).

compact connection and reduced stiffness of the zones at the

end of the brace, and therefore the behavior may better mimic a

pin connection, which is assumed in design. Simultaneously, a

tapered gusset plate receives less support and restraint from the






Fig. 8. εpleqv at the middle of brace.

beam and column, and so the gusset plate may be more likelyto yield and buckle. In structural engineering practice, bothrectangular and tapered gusset plates are used, and so tapered

plates, such as shown in Fig. 4(b), were studied to examine itseffect. The tapered angles studied included 0◦ (reference modelwith rectangular plate), 15◦, and 25◦.


In general, the simulated resistance values found for theframes with tapered gusset plates were slightly less thanthose predicted for frames with rectangular gusset plates. Theultimate tension load and compression loads for the framewith a 15◦ tapered plate were about 5% and 3% smaller,respectively, than those of a comparable rectangular plate, asshown Fig. 5(b). When the gusset plate taper was increasedto 25◦, the decreases in ultimate loads were 6% and 4%,respectively (see Fig. 5(b)). Note that a 25◦ tapered modelused 11.1 mm thick gusset plate to meet the Whitmore widthrequirements in the design of the gusset plate.

The equivalent plastic stress distribution plots show thatincreasing the degree of taper results in increase stresses andstrains and more widely distributed yielding in the gusset plate(see Fig. 6(d)). In particular, stress and strain concentrationsincreased at the re-entrant corners of the gusset where crackinitiation develops, because tapering the plate reduces theeffective area of the plate in tension and compression. As aresult, weld crack initiation is expected at smaller story driftsfor the tapered plate than noted for the rectangular plate withelliptical clearance, as indicated in Fig. 6(b) and Table 3.CJP welds joining the gusset to the beam and column maydelay this cracking somewhat, because the experimental studyshows that high quality CJP welds have greater resistance tocrack initiation than fillet welds, but this difference was notdramatic [7]. In addition, Fig. 6(d) shows high stresses in thebeam–column panel zone area and at the frame-to-gusset plateintersection for the 25◦ tapered plate model. Increased panelzone yielding may place increased strain demands on the gussetplate welds and contribute to the early crack initiation, butthe consequences of this observation are not completely clear.Fig. 8(b) shows that brace fracture for the tapered gusset platesoccurred at the same drift ratio compared to the rectangulargusset with the 8tp elliptical clearance.

4.3. Different beam-to-column connections

The models and past experiments in the prior descriptionshave used fully welded beam-to-column connections at thegusset plate, that is, CJP welds join the beam flanges and webto the column flange. Many engineers regard this connectionas the best option for braced frame gusset plate connections,because the axial forces expected in the beams must betransferred through this joint. However, welded connections arerelatively expensive, and some regard this fully welded jointas unnecessary and overly expensive. Instead, some engineersuse a simple shear-plate beam–column connection such asdepicted in Fig. 4(c). To examine the impact of using a shear-plate beam–column connection at the gusset plate (Fig. 4(c)),two variations of this alternate Shear-Plate connection wereanalyzed: (a) an SPW case in which the beam web was joinedto the column through a Welded shear-plate connection and(b) an SPB case in which only the beam web was joined tothe column through a Bolted shear-plate connection. The beamflanges were not attached to the column flange in either case.

Fig. 5(c) and Table 3 show that the ultimate tension loadand compression loads for the frame with a welded shear-plate connection were about 8% and 3% smaller, respectively,

than for the reference model with a fully welded connection.When a bolted shear-plate connection was used, the decreasein expected frame resistance was 10% and 4%. The stressand strain distributions in the gusset plate of the weldedshear-plate connection model were not significantly differentthan those obtained for the reference model, as shown bycomparing Fig. 6(a) and (e). However, the equivalent plasticstress distribution plots in Fig. 6(f) show that the bolted shear-plate connection results in increased stresses and strains inthe gusset plate and the elliptical yield line. These increasedstress and strain concentrations occurred because of the reducedrestraint on the beam which reduced the stresses in the beamand permitted the beam to twist.

Figs. 7(c) and 8(c) and Table 3 show that weld crackinitiation and brace fracture for the shear-plate connectionsare expected at similar story drifts for the reference model.Subsequent experimental results show that weld crackingdoes initiate at similar levels, but brace fracture occurssomewhat earlier with the shear-plate connections because ofthe increased beam twist noted as cracking progresses. Becausethe FE element model does not simulate crack development, itdoes not model the reduction in the restraint as weld crackingoccurs and therefore does not capture this full twisting effect.

4.4. Gusset plate thickness

Although current design seismic design provisions for gussetplate connections imply that a thicker gusset plate is better,previous analyses have shown that thicker and larger gussetplates increase the connection stiffness, increase prematureyielding in the beams and columns of the framing system,and cause earlier brace fracture [13]. As a result, furtherstudy of the influence of gusset plate thickness on SCBFperformance was made. For this study, a 22.2 mm thick platewas analyzed and compared with the thinner, 9.5 mm gussetplates recommended by this research for both rectangularand tapered gusset plates. The reference specimen for therectangular gusset plate comparison was the usual referencemodel (GTP9.5), but the reference for the tapered gusset plateanalysis was Model T15.

The expected maximum compressive and tensile resistancesof the thick, rectangular gusset plate were approximately 23%and 13% greater than for the reference frame, as shown inFig. 5(d) and Table 3. For the tapered gussets, the maximumexpected resistances were approximately 22% and 16% largerthan noted for the tapered reference model T15. The increasedrotational end restraint of the brace provided by the thickergusset plate decreased the effective length coefficient of thebrace and increased the compressive buckling capacity. Thereduced yielding in the thicker gusset plates resulted in greaterstrain hardening of the brace in tension.

Equivalent plastic stress distributions for the reference andthicker plate models are provided in Fig. 9(a) and (b). Theresults show that the thicker plate decreases the stress demandswithin the gusset plate but significantly increases the inelasticaction, including local buckling and inelastic deformationdemands, in the column adjacent to the gusset plate. Comparing


Fig. 9. Equivalent plastic stress distribution in and adjacent to the gusset plate.

the stress distribution for the thin and thick tapered plates,Figs. 6(d) and 9(c) respectively, shows similar results for thetapered gusset plates.

The thickness of the gusset plate had a significant effecton crack and fracture potential, as shown in Figs. 7(d) and8(d). Increasing the thickness of the gusset plate resulted in anincrease in the drift ratio corresponding to the expected weldcrack initiation limit from 1.8% to 2.6% for the rectangulargusset plates. This is largely a result of the lower stresses inthe plate. Fig. 7(d) and Table 3 suggest that using a thick,tapered gusset plate may prevent weld cracking. However, asshown in Fig. 8(d) and Table 3, brace fracture is predicted tooccur at smaller story drift ratios. The drift at expected bracefracture decreases from 3.2% to 2.2% for both the tapered andrectangular gusset plates. The stiffer and stronger gusset plateconcentrates yielding over a shorter length in the middle of thebrace, thereby leading to larger local strains in the brace andearlier brace fracture. This is an important observation becausethe ultimate reason for failure of SCBF frames is tearing at this

brace location, and the analytical results suggest that using athicker, and thereby stiffer and stronger, gusset plate reduces theductility and inelastic deformation capacity of SCBF frames.

4.5. Beam and column sizes

The braces, beams and columns of braced frames wereinitially sized to resist the required seismic design loads [2].Hence the member sizes for the beam and columns may berelated to the brace size, but beams and column sizes clearly areinfluenced by other factors (such as gravity loads), which arenot correlated to the brace or the gusset plate connection. Sincethe gusset plate connections do not act as pins, the stiffnessand strength of these framing members can impact the globalresponse of the frame. To study the effect of beam and columnsizes, three alternative framing systems were considered:

(1) Large beam (LB) systems, in which the web and flangethicknesses of the beam were increased by a factor of threeand all other frame properties unchanged,


(2) Large column (LC) systems, with thicknesses increased bya factor of three, and

(3) Large beam and large column (LBLC) systems.

Models with both thin (9.5 mm) and thick (22.2 mm) gussetplates were analyzed. Hence, a total of six models weredeveloped and analyzed. This variation provides a broadperspective of the potential effect of member size variation onsystem performance.

Increased beam size had a small effect (less than 2%) on theexpected maximum resistance relative to the reference model(GPT9.5). However, increasing the column size had a greaterimpact, since it increased the expected lateral load capacityby approximately 17% in tension and 25% in compression.Similar results are noted for the LBLC models. Analyses andexperiments show that plastic hinges form in the columns dueto frame action at large lateral story drifts, and the increasedexpected resistance is largely due to the increased columnshears caused by the larger plastic moment capacity of thecolumns.

Larger columns cause increased inelastic stress and straindemands on the beam and reduced inelastic stress and straindemands on the column. Larger columns also have the potentialto increase the story drift associated with weld crack initiation,as shown in Table 3 and Fig. 7(e) and (f). Larger beams increasethe inelastic stress and strain demands on the column and thegusset plate, as shown in Fig. 9(d). Larger beam size increasedthe ε

pleqv at the re-entrant corners of the gusset plate, as shown

in Fig. 7(e) and (f). Experiments suggest that the gusset weldswhich initiated cracking at smaller story drifts also sustaingreater crack length growth during testing. However, duringthe experiments, ultimate fracture of gusset plate welds wasavoided by sizing the welds to achieve the plastic capacity of thegusset plate and by using demand critical weld electrodes [7,2].

Larger frame member sizes increase the εpleqv in the brace

and decrease the story drift associated with brace fracture(Fig. 8(f)). In particular, this is noted for Model GPT22 LB,which uses a large beam and thicker gusset plate. Thiscombination leads to a significant increase in the ε

pleqv at the

middle of the brace and a dramatic reduction in the SCBF storydrift at brace fracture from 3.2% (for reference model GPT9.5)to 1.7%. This was initially observed in the analytical study, andit was later confirmed in the experimental research [7].

4.6. Brace angle

The brace angle of inclination was investigated to determineits effects on system and connection performance. The braceangle was varied as shown in Fig. 3(f) and included values of30◦, 37.5◦, 45◦ (angle in reference model), 52.5◦, and 60◦. Thecolumn spacing was adjusted to accommodate the brace angleusing a fixed column height of 3.66 m. Note that 30◦ and 60◦

brace angle models used 11.1 mm thick gusset plate becausethicker gussets were required to satisfy the Whitmore widthdesign expression.

The results indicate that the angle impacts the systemresistance, as expected. For example, the steepest brace angledecreased the expected tensile resistance by 23% and increased

the resistance in compression by 10%. This effect is rationalbecause steeper brace angles lead to a shorter brace length,which increases the compressive resistance of the brace. Theyield capacity of the brace is independent of the angle, butsteeper braces have a smaller horizontal component of force.The opposite trend is noted for shallow brace angles.

The brace angle increases the equivalent plastic strains atthe re-entrant corners of the gusset plate, which may indicatea lower drift ratio corresponding to weld crack initiation, asindicated in Fig. 7(g) and Table 3. The drift ratio correspondingto the weld crack initiation limit decreases from 1.8% (forreference model GPT9.5 with an angle of 45◦) to 1.0% (formodel BA53 with a brace angle of 53◦). The drift ratioincreased when the 60◦ brace angle model was used, but athicker plate was needed and this resulted in smaller stressand strain demands within the gusset plate (which is consistentwith the trend noted previously). Weld crack initiation datain Fig. 7 and Table 3 are for the region adjacent to thecolumn, since this is the most common area for crack initiation.Steeper brace angles place large out-of-plane post-bucklingdeformation demands on the middle of the brace, and Fig. 8(g)shows that this is expected to brace fracture at smaller storydrifts (1.7% as compared to 3.2% for the reference model).The flatter brace angle affects the strain in the gusset plateat different locations and is not apparent in the figure. Flatterangles initiate cracking adjacent to the beam, while the steeperbrace angles initiate cracking adjacent to the column. This canbe seen by the stress distribution in Fig. 9(e).

4.7. Brace-to-gusset plate weld length

The weld length required to join the brace to the gusset plateis largely controlled by the size of the weld, the Whitmore widthdesign expression and satisfying the block shear requirement ofthe gusset. The variation in the weld length for the experimentswas limited, and this limited change did not exhibit significantblock shear yielding or failure. Therefore, a series of analyseswas performed to explore the impact of the weld length on theconnection and system performance. Weld lengths that were3/4 and 1/2 of the length required by the AISC block sheardesign equation were evaluated and compared to the weldlength of 37.5 mm that was used for the reference model.

Fig. 5(h) shows that the expected maximum frame resistanceincreased slightly with the shorter weld lengths. However,Table 2 shows that somewhat thicker gusset plates wererequired with these shorter weld lengths to satisfy the Whitmorewidth design expression. As a consequence, the increase inresistance is not viewed as a significant difference.

Shorter weld lengths result in smaller gusset plates, and theelliptical clearance converges toward the 2tp linear clearancewith these smaller plates. As a result, the yield pattern shown inFig. 9(f) approaches the linear case. In addition, high inelasticdemands local buckling and inelastic deformation resulted inthe column adjacent to the gusset plate and in the gusset plateadjacent to the beam. Fig. 7(h) shows that as the weld lengthdecreased, the drift ratio corresponding to the predicted weldcrack initiation for the gusset plate adjacent to the columnincreased from 1.8% (reference) to 2.6% (half weld length).


Weld crack initiation at the re-entrant corner of beam wasevaluated, because Fig. 9(f) shows significant yielding in thisarea, but crack initiation potential is not increased at thislocation. This can be explained by noting that the thicker (butmore compact) gusset plate distributed the high stresses tothe portion of the gusset plate that is adjacent to the brace,rather than concentrating within the elliptical yield line. Inconjunction with this observation, Fig. 8(h) shows that thelikelihood of brace fracture has diminished, thereby suggestingthat the drift capacity of the specimen may be increased. Theseobservations make this design concept an attractive candidatefor experimental research, and they suggest that the detrimentaleffects of the thicker (and stiffer) gusset plate on the bracebuckling capacity may be overcome by using a small andcompact gusset plate. Experiments have not yet been performedon this configuration.

5. Summary and conclusions

A numerical investigation and parameter study of thebehavior of brace frames and gusset plate connections wasconducted using a validated model with the finite elementprogram ANSYS. The inelastic FE model was validated usingmeasured data and observed damage state from a seriesof experiments conducted on full-scale one-story, one-bayspecimens. The validated model was capable of accuratelysimulating the cyclic nonlinear behavior of SCBF frames andgusset plate connections. This previous study also showedthat the equivalent plastic strain computed by this modelprovides an accurate estimate of weld crack initiation and bracefracture, when the equivalent plastic strains are calibrated toexperimental results and the mesh size of the computer model.

Using this validated inelastic FE analysis model and theequivalent plastic strain approach, a series of simulationswas used to investigate the impact of different gusset plateconnection design parameters on connection and systemperformance. The parametric study included evaluation of thefollowing.

• The current linear 2tp clearance requirement and a proposedelliptical clearance model.

• Tapered and rectangular gusset plates.• Welded flange and shear-plate beam-to-column connections.• Gusset plate thickness.• Variations in the size of beams and columns at the gusset

plate connection.• Weld length joining the brace to the gusset plate connection.• Frame geometry and brace angle of inclination.

The results from the parameter study have been partiallyconfirmed through observation of experimental results [7]. Theconclusions from this parameter study include the following.

1. The performance of specimens and models designed usingthe proposed elliptical model was an improvement over thedesign of comparable specimens/models using the current2tp linear clearance model if the elliptical offset clearancewas in the range 6–8tp. This elliptical model resulted insmaller more compact gusset plates with smaller localyielding in the beams and columns. If the elliptical clearance

was decreased below 6tp, weld crack initiation was predictedand observed at smaller frame story drifts. If the ellipticalclearance was increased, brace fracture was predicted atsmaller frame story drift.

2. Tapered gusset plates resulted in predictions of bracefracture at story drifts similar to those noted for modelswith well designed rectangular gusset plates. These taperedgussets resulted in decreased local yielding in the beamand column adjacent to the gusset, but tapered gusset plateshad earlier predicted weld cracking than the rectangularalternatives.

3. Analyses suggested that bolted shear-plate connectionsmay have only slight reductions in system deformationcapacity and resistance. This observation is disputed byexperimental results, because experiments show that twistwithin the connection causes reduced system ductility afterweld cracking initiates. The FE model does not simulatethe effect of crack growth and, therefore, cannot capture theexperimentally observed behavior.

4. Thick gusset plates significantly increase the stiffness of thegusset plate connection. The reduced stress in the plate canresult in earlier and increased local yielding of the beamand column adjacent to the plate, and reduces the storydrift corresponding to brace fracture. However, the lowerstress levels associated with the thicker gusset plate reducesyielding in the gusset plate and the potential for weld crackinitiation.

5. The sizes of the framing members may be much largerthan required to resist earthquake forces because of gravityloads and other effects. Analyses show that increasedbeam and column sizes have a significant effect onsystem performance. The effect is significantly greaterwhen increased beam size is combined with thicker gussetplates. Increased beam and column sizes increase the lateralresistance of the frame, but they do this by differentmechanisms. Increasing the beam size primarily reduces theeffective length of the brace; increasing the column sizeincreases the resistance if plastic hinging in the columnis present. Increased beam size results in earlier predictedinitiation of weld cracking; however, increased column sizehas the potential to reduce the likelihood of weld crackinitiation. Finally, increased beam size cause a significantreduction in the story drift associated with brace fractureparticularly when combined with a thicker gusset plate.

6. Different angles of inclination of the brace affect the braceand connection performance. Steeper brace angles resultin the potential for earlier brace fracture and weld crackinitiation.

7. The weld length used to join the brace to the gusset plateaffects the block shear action and the Whitmore width usedin the gusset plate connection design. Shorter weld lengthsresult in more compact gusset plates. The more compactgusset plates decrease the connection stiffness and increasethe story drift needed to cause brace fracture. However,shorter weld lengths decrease the effective Whitmore widthin the design, and somewhat thicker gussets are required.The analyses clearly show that controlled yielding of the


steel in the gusset plate at larger frame story drifts isbeneficial to the seismic performance of the SCBF system.As a result, the block shear yield condition may not warrantgreat conservatism in the seismic design. The combinedbenefits of the more compact (but slightly thicker) gussetachieved and shorter weld length appears to have someattractive benefits. Nevertheless, block shear fracture is notcaptured in the FE model, and experimental research isneeded to verify this observation.

Acknowledgements

The research is funded by the National Science Foundationthrough Grant CMS-0301792, Performance-Based Seismic De-sign of Concentrically Braced Frames. Dr. Steven L. McCabewas the Program Manager for this research. This financial sup-port is gratefully acknowledged. The authors also want to thankMr. Tom Schlafly of American Institute of Steel Construction,Ms. Cheryl Burwell of Magnusson and Klemencic, Mr. TimFraser of CANRON Fabricators, Mr. Walterio Lopez of Ruther-ford and Chekene, and Mr. Rafael Sabelli of DASSE Design fortheir advice on the design and fabrication of braced frames andgusset plate connections. Finally, special thanks are given to thegraduate and undergraduate students who were involved in theexperimental work.

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3rd ed. Chicago (IL): American Institute of Steel Construction; 2001.[2] AISC. Seismic provisions for structural steel buildings. Chicago (IL):

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[7] Lehman DE, Roeder CW, Herman D, Johnson S, Kotulka B. Improvedseismic performance of gusset plate connections, ASCE Journal ofStructural Engineering (2007) [in press].

[8] Liu J, Astaneh-Asl A. Cyclic testing of simple connections, includingeffects of the slab. Journal of Structural Engineering 2000;126(1):32–39.

[9] Roeder C, Lehman D, Yoo JH. Improved design of steel frameconnections. International Journal of Steel Structures 2005;141–53.

[10] Thornton WA. On the analysis and design of bracing connections.In: Proceedings of national steel construction conference. Chicago (IL):AISC; 1991. p. 1–33. Section 26.

[11] Uriz P, Mahin S. Seismic performance of concentrically braced steelframe buildings, in: Proceedings, 13th world congress on earthquakeengineering. 2004. Paper ID 1639.

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Documents

Influence of Connection Design Parameters on the Seismic Performance Of