cyclic behavior of the connection assembly with various

Cyclic behavior of the connection assemblywith various deep columns

N. Sutchiewcha.rn &J. ShenDepartment of Civil and Architectural En@zeering, lllinois Institute ofTechnology, USA

Abstract

This paper presents a study on the cyclic behavior of beam-to-columnconnections with deep column sections ranging from W 14 to W33. A compactbeam section was used for most of parametric studies, considering the fact thatalmost all available wide flange sections are compact. For comparison, a non-compact section beam was also included. Detailed nonlinear finite elementanalyses were conducted to address the issues that influence the cyclicperformance and design consideration of one of most commonly used connectionpre-qualified by FEMA 350 (namely RBS connection) when the columnbecomes deeper and deeper. Based on the observed performance of the beam-to-column connection assembly, no considerable reason was found to prevent theuse of deep column sections when designed in accordance with the currentseismic design provisions including lateral bracing and compact sectionrequirements. The cyclic behavior is similar to a conventional connectionconsisting of W 14 columns. It should be commended that the systemperformance of a steel moment fmrne with deep columns might be different fromthat of a steel frame consisting exclusively of W 14 columns.

1 Introduction

After 1994 Northridge earthquake, extensive studies have been conducted toimprove the performance of the steel moment-resisting frame when subjected tostrong ground motions. Since then, the Reduced Beam Section (RBS), whichremoved a potion of the beam flanges in order to force the plastic hinge in thebeam away from the column face, was proposed. Researchers have studied thebehavior of the RBS when connected to the conventional W14 columns, and

© 2002 WIT Press, Ashurst Lodge, Southampton, SO40 7AA, UK. All rights reserved.Web: www.witpress.com Email [email protected] from: Structures Under Shock and Impact VII, N Jones, CA Brebbia and AM Rajendran (Editors).ISBN 1-85312-911-9

324 .$trl[crzlre,~ L“tlder Shock and lmpuct I “II

found that the connections with RBS have an extended ductility from the sameconnections without RBS. This type of beam-to-column connection assemblyhas been pre-qualified by FEMA-350 [1 ] for seismic design of moment-resistingframes. In recent years, it has been recognized that there is a strong economicincentive for the design engineer to use deep columns to satisfy increasinglymore stringent drift limitation. Using W 14 for such drift limitation often resultsin unnecessarily heavy columns. Structural engineers have, from time to time,used deeper columns for some steel building projects, when they have resourcesto carry out physical tests of project-based comections. The deep columns wouldhave been more extensively used for moderate-rise to high-rise buildings if thetime consuming and costly physical test could be avoided. So far, limitedresearch has been done regarding the behavior and design of a beam-to-columnconnection with deep column. A recent test on a connection with W27 columnby Gilton et al. [2] demonstrated potential lateral torsional buckling of the beamwith the column being twisted. This is a failure mode that has not been observedin W 14 column cases. A systematic study on steel moment frames with variouscolumn sections is desirable. Such study would includes: (1) detailed nonlinearfinite element analyses of beam-to-column sub-assemblages; (2) seismic designcomparisons of steel moment frames with only W 14 columns and the frameswith various column sizes; (3) seismic response analyses of such steel momentframes. The ultimate goal of the systematic study is to provide the engineer witha solid understanding of seismic behavior of steel frames with various columnsizes and practical design procedure consistent with FEMA-350 [1] for seismicdesign of steel moment-resisting frames. This paper presents the work focusedon detailed nonlinear finite element analyses, investigating the behavior of thesteel RBS moment connection with the deep column sections when subjected tocyclic and monotonic loadings. The analyses began with building the model of abeam-to-column sub-assemblage that was physically tested [2]. After the testedspecimen was well simulated by the finite element model, a group of morerealistic beam-to-column sub-assemblages were analyzed, and the results wereevaluated.

2 Simulation of cyclic behavior of tested specimen usingnonlinear finite element method

A tested steel beam-to-column assembly with RBS was simulated by nonlinearfinite element method in order to compare the analytical capability in predictionphysical test results, and build a sound knowledge base for parametric studiesusing exclusively analysis.

A computer model simulating a test specimen, DC-2 [2], was constructedwith the nonlinear finite element program, ABAQUS [3]. The specimen was astandard beam-to-column assembly consisting of a W27X 194 column andW36X 150 beam, both specified as A572 Gr.50 steel. A reduced beam section(RBS) was introduced to make the connection pre-qualified by FEMA 350 [1].The details of the RBS, the column stiffeners and web shear tab plate aredescribed in Figure 1. The test setup of the beam-to-column assembly is shownin Figure 2.


Structures L’nder Shock and impact Lll 325

-L-Jd

Figure 1: Reduced Beam Section (RBS) and Comection detailswith W27X194 column and W36X150 beam.

Figure 2: Test setup for DC-2.

The computer model, named as ABQ-DEEP used fully integrated six-node andeight-node three-dimensional solid elements (Element types C3D6 and C3D8 inABAQUS). A finer mesh was used in the RBS area, panel zone and shear tabplate. The rigid links were used to connect the beam tip to the actual loadingpoint (reference node), which was also restrained to prevent out-of-planetranslation. The material properties of the steel, yield strength and ultimatestrength, were specified from the mill certified coupon test of the Specimen DC-2. The linear kinematic hardening was used to take into account of theBauschinger effect on the reduction in yield stress upon load reversals. Thecyclic loading pattern in the test, controlled by the displacement at the tip of the

beam (i5tiP),was of a standard small-to-large displacement type with two cycles ateach displacement level. Conventionally, beam tip displacement is converted tothe story drift ratio, which is conventionally defined, in a building frame, as thedifference between the lateral displacements of two adjacent floors divided bythe story height. In this test, the story drift ratio is equivalent to &,JL (Figure 2).The specimen remained virtually elastic before 1% drift cycles, when some


326 Strllcnlws ( underShock and Impact [“[l

yielding was observed. Though such elastic deformation cycles might bedesirable for physical testing, a finite element analysis does not record any effectof elastic cyclic loading on the assembly. Thus, in the simulation analysis, thecyclic loading history for the analysis started from the cycles immediately beforeany yielding was observed. The number of inelastic cycles appeam to have asignificant influence on the post-buckling behavior in terms of strengthdegradation. This can be observed in Figure 3, the test result of the cyclicresponse of specimen DC-2. The strength was reduced considerable y when theinelastic cycle was repeated. Such cycle-related strength reduction became moresignificant when a larger inelastic cycle was repeated, apparently due to theBauschinger effect and low-cycle fatigue phenomenon. The kinematic hardeningoption, built in ABAQUS, is capable of considering the Bauschinger effect toaccount for a portion of the reduction when each inelastic deformation level wasapplied twice, The modifkd Riks method was employed in order to simulate thepost buckling behavior.

Stow Drit3 Ratio (%)

-6 -4 -2 0 2 4 6

200

~ 100

.EJ

~ o3

d -1oo

-200

Bean fip Displacement (in)

F@re 3: Load-displacement curve of specimen DC-2.

Stow Drift Ratio (’%)

-6-4 -2. oi’46

4-4—>44+”+-:---- - -+-i

I 1 I

-5 ~

Beam TIp Displacement (in)

Figure 4: Load-displacement curve of ABQ-DEEP.


Sti-uctuwx Lnder Shock (uld Impact 1’11 3?7

Figure 4 shows the load-displacement curves from ABAQUS model ABQ-DEEP. The overall cyclic responses from the analysis and test match reasonablywell. There are some noticeable discrepancies in unloading and reloadingregions, particularly at large inelastic deformation levels. The unloading curveof the tested specimen was highly nonlinear, significantly different from thelinear unloading curve conventionrdly used as analytical hysteresis. Thereloadlng in an opposite direction after a full inelastic unloading made thespecimen further soft. The softening in unloading and reloading was responsiblefor an accelerated strength reduction from its peak value after each cycle with thesame or higher level of displacement. The kinematic hardening built inABAQUS captured a portion of such reduction.

The deformed shapes from ABAQUS model ABQ-DEEP at 5% drift levelare presented in Figures 5 and 6, showing an isometric view of the bucklingshape near the beam-to-column joint and the deformed shape viewed above thetop flange. The deformed shape is similar to the final buckling shape observedfrom the test [2], especially in the RBS region. The maximum principrd stressand maximum principal strain occurred obviously in the RBS region causing theforming of plastic hinges as expected in a moment resisting frame with RBS.

Figure 5: Isometric view of the buckling shape of ABQ-DEEP at 5% storydrift ratio.

I

: —-” ~_—- —’ ---

!WZ==i ..”.. —

L-:I

Figure 6: Top view of deformed shape of ABQ-DEEP at 5% story driftratio.

3 Parametric study of cyclic behavior of the connection withvarious column depths

Having successfully simulated the tested specimen, the ABAQUS model ABQ-DEEP, as the prototype, was extended to model the connection assembly with


various columns sizes. In the seismic design of steel moment-resisting framesbased on improved connection details summarized in the recent FEMApublication [I], there are some concerns related to the connection strengthreduction after its peak strength is reached. Slower reduction might indicate amore stable comection performance, and vice versa. It is simple to define suchreduction based on monotonic loading. It has been observed that strengthreduction after the peak strength is reached heavily depends on the number ofinelastic cycles. The main goals of the parametic study include: (I) toinvestigate whether or not there are any significant characteristics in aconnection with deep column sections that are not considered in current designpractice; (2) to compare and correlate strength degradation rates of theconnection assembly subject to cyclic and monotonic loadings. The maximumdisplacement was increased to 6% story drifi ratio due to the expected increasedstrength and ductility capacity from lateral restrains as explained subsequently.With two beams section, five column sections, as listed in Table 1, were selectedto construct the connection assemblies within a practical range. These column

sections were selected based on their plastic section modulus (ZJ, elastic sectionmodulus (Ix and IY) so that the comparison can be made with respect to lateraltorsional buckling with different combinations of Zx, 1,, and IY. In addition, theeffect of lateral bracing on the connection assembly performance was alsoinvestigated by introducing actual lateral supports from transverse beams and theconcrete with metal deck floor in any steel framed building. In some analyticalcases, the beam was laterally braced along the beam top flange outside the RBS.Three different boundary conditions are: (1) no any lateral restraints; (2) laterall yrestrained in panel zone and top flange except in the REM region; and (3)laterally restrained in the panel zone with continuous lateral supports along thetop flange of the beam. To distinguish the results from various studied cases interms of lateral bracing conditions, N, R and FR are assigned to the resultsassociated with the boundary condition (1), (2), and (3), respectively.

Table 1. The section properties of the studied column and beam sections.. .

.495.:::8-I%?13aW14X426 W27X194 W30X191 W33X169 W33X201

Area (it) 125 57 56.1

Depth (in) 18.67 28.11 30.68 33.82

tw (in) 1.875 0.7s 0.71 0.67 0.715

bf (in) 16.695 14.035 15.04 11.5 15.745

tf (in) 3.035 1.34 1.185 1,22 1.15 M

w“Noncoqact wCIIOn


%wtuws [/I’IL&i’Shock and Impact [‘II 329

3.1 Cyclic versus monotonic loading

The responses of ABQ-DEEP with W27X194 column to cyclic and monotonicloadings are plotted in Figure 7. Under the cyclic loading, the strengthdegradation occurred upon the load reversal in both positive and negativedeformation regions in each cycle after the plastic hinge formed in the RBSregion. The overall strength was the same under both loading histories before itspeak value. The difference in strength after the peak value is mainly due to low-cycle fatigue and Bauschinger effect. The strength degradation started after themaximum (peak) load at about 3% story drift ratio.

storyOrift Ratio (*A)-6-4-20246

200

~ 100~3 0$A-1oo

-2W

-5 5Beam Ttp Oisplacancnr (in)

Figure 7: Load-displacement curve of ABQ-DEEP subjected to cyclic andmonotonic loads.

Stmy Ihifi Ratio(?’0)--6 -4 -2 0246

DC.] $ i

,-- ;T~ ‘

M

200

I ! ~~’

~ 100 -- —-- < —.—~–—_

~~:

go

g 1’-100 –-–—–—–- –— ~ .+.—

l!

-200 —-11 .—. .L—---- . ..-. ——

-5 5Beam ~p Dis@IccmcrIt(in)

Figure 8: The envelopes of cyclic responses of specimen DC2, model ABQ-DEEP subjected to monotonic, one-cycle, and two-cycle per drifilevel.

The strength reduction rate (the ratio of the current strength over the peakstrength) from the analyses subject to the one-cycle displacement loading historywas much less than that subject to the two-cycle disp~dcement loading history,which in turn was slightly less than the test result. Figure 8 plots the envelopes ofcyclic responses from the physical test, analyses with one-cycle and two-cycledisplacement loading histories, together with monotonic loading result. Littlestrength reduction is observed from the monotonic loading up to 6% drift ratio,but such reductions are noticeable in the results from cyclic loading cases. At 4~o


330 ,Strucruws (.’nder Shock and [Inpoct 1’11

drift level, the strength reduction rate is about 5%, 18%, and 22Y0, from the one-cycle loading history analysis, two-cycle loading history analysis, and testedresult, respectively. At 5’%0drift level, the strength reduction rate is about 11Yo,28%, and 30%, from the one-cycle loading history analysis, two-cycle loadinghistory analysis, and tested result, respectively. It is obvious that the strengthdegradation is much more severe under cyclic inelastic deformation than undermonotonic pushover.

3.2 Effect of Lateral bracing

The lateral supports to the beam flange under compression significantlyimproved the inelastic behavior. In particular, the post-buckling strengthdegradation was reduced considerably by increased lateral supports, as shown inFigure 9. The fully restrained assembly (FR), with a continuous lateral suppottsto the beam, avoided lateral torsional buckling mode, and had almost twice asmuch deformation before the smength started reducing. The local buckling of theflanges and web was mainly responsible to a slow degradation in strength at alater deformation stage. With less lateral supports, the overall performance fromthe assembly model R, with lateral supports along the upper flange of the beamoutside the RBS region, is very similar to that of FR models, indicating that localbuckling was dominant factor in both cases. It also indicates that there is noapparent benefit to add lateral bracing within RBS region. However, the lateralbracing from the floor had almost obviously no effect on the assembly when thebeam top flange was in tension, and extra lateral supports are necessary to ensurea stable inelastic cyclic behavior. Note that all cases involved a compact beamsection, W36X150 with F~50 ksi, which represents most practical application. If

any non-compact beam section is used, the strength degradation would have beenmuch more significant.

Stmy Dnfi Ratio (“A)

Rem-nTip Displacemeti (in)

Figure 9: Comparison of load-displacement curves of W33X201 columnwith various boundary conditions.

As shown in Figure 10, with the same lateral support conditions, the resultsfrom the assemblies with different column depths but similar ZX show aconsistent trend in post-buckling behavior.


.Mwcture.s [wier Shock Lmd impmt i 71 331

3.3 Effect of column sizcddepth

Figures 11 and 12 present the deformation patterns of various columns at a 6%story drift ratio level. No lateral bracing was provided to reveal the effect of thecolumn size on the lateral stability of the beam.

Story Drift MO (Y,)-6-4-20246

.?,?xr,\.F\

NoI -=%-

/w BX16+R

,,

~ 100 i-;.

a ::~ !

-d 0 ~ Iz I4 !’ !,

-100 !;~,1, i

f-m -.~

,!,.

-5 5BeamTipDisplacement(in)

Figure 10: Comparison of load-displacement curves of various columns withlateral bracings along the beam outside the RBS.

I

:_ 1!

(a) (b)

Figure 11: Lateral torsional buckling shape of W27X194-N at 6% story driftratio: (a) Axial view from the beam to column; (b) Top flangeview.

IL ‘- L I

(a) (b)

Figure 12: Lateral torsional buckling shape of W33X1 69-N at 6% story driftratio: (a) Axial view from the beam to column; (b) Top flangeview.


332 .Sm{ctuw.s(under Shock atrd Im,mcr f ’11

It is apparent that such lateral stability is closely related to the torsionalproperties of the columns. It seems that the deep columns were flexible in torsionand weak-axis bending, providing the beam with weak constraints to prevent oralleviate the lateral torsional buckling of the beam. If a W 14 column is selectedfor the same beam, a much heavier section is needed, and much higher torsionalstiffness and weak-axis flexural stiffness will have significant impact on thelateral stability of the beam. Referring to the results from Khjasateanphun [4],ABQ-el was consisted of W 14x426 column and W36X150 column. Aspresented in FQure 13, the lateral torsional buckling of the same beam, when thecolumn was changed to W14X426, was reduced significantly. The dramaticdifferences in torsional stiffness and weak-axis flexural stiffness between a W 14and deeper sections with a comparable strong-axis bending strength are mainlyresponsible for the effect of the column size on the lateral stability of the beam.

(a)H I

(b)

Figure 13: Buckling shape of W 14x426 ABQ-el at positive 5 in.: (a) Axialview from the beam to column; (b) Top flange view.

3.4 Effect of beam section compactness

It is vital to use a compact beam section in the earthquake-resistant momentframe to ensure a stable cyclic performance during a strong earthquake. The limit

for a compact flange, & is equal to 52/(FY)l’2. In practice, most of wide flangesections are compact sections. In this study, all previous discussions have been

based on a compact beam section, W36X150 (&= b#2/t~ = 6.4; ~~=0.87; and(L~-LP)/(L,-~)=7 %). In this section, a non-compact section, W30X90 b~2/t~ =

8.5; k&= 1.16), was selected to compare the behavior of the deep-columnconnection assembly with compact and non-compact beam sections. Figure 14shows the cyclic response of the assembly with W30X90 beam((Lb-LP)/(L,-LJ= 19%) and W27X194 column. The strength reduction rates aress~o and 50% at 470 and 57o story drift levels, respectively, which are twice asmuch as those observed from previous analyses based on W36X 150 beam. Anearly local buckling of flange as well as the lateral torsional buckling might beresponsible for such accelerated strength degradation. It is apparent that thebuckling of the flange is much more extensive with a non-compact flange thanthat with a compact one. With a beam of non-compact flange and weak lateral


.ftructures L“mlerSiIock and lnqmct I’11 333

torsional resistance, the W27X194 column has shown no appreciable torsionaldeformation even when the beam suffered a large lateral torsional buckling.

~-’=-~

—-———=.1: ~+~

—,

(a) (b)

Figure 14: Buckling shape of the assembly with W30X90 beam andW27X 194 column: (a) Isometric view from the beam to column;(b) Top flange view.

4 Conclusions

The analytical models of the RBS moment connections were established andsimulated the tested specimen, almost in the same way as the physical test did,by using the non-linetu finite element approach. The cyclic behavior of thesimulated model was investigated. With the modified models, the performance ofthe beam-to-column moment connections with column sections of various depthswas investigated. The following conclusions can be drawn based on the study.

1.

2.

3.

4,

5.

The cyclic behavior of the simulated model matches very well with theresults from the physical test. The non-linear finite element program can beused as an eftlcient tool to simulate and analyze the model together withlimited physical tests to reduce the physical test cost and more importantlyto extend models supported by the limited test for further parametric studiesand simulation.The strength degradation rate heavily relies on the number of inelasticcycles, and is significantly higher than that evaluated based on monotonicloading analysis (pushover). Nevertheless, the monotonic loading can be aneffective alternative to cyclic loading for the investigation of failure modes.The lateml torsional buckling is more likely to occur in a deeper columnsection if no lateral bracing is provided. However, such tendency isinsignificant when lateral supports are provided.The lateral bracing at lower flange appears to be necessary to ensure anormal performance of the connection with deep column section,From the local performance of the comection assembly viewpoint, there isno reason to prevent the use of deep column sections.


References

[1] FEMA-350 Recommended Seismic Design Criteria for New Steel Momettt-Fram.e Buildings, Federal Emergency Management Agency, MD, 2000.

[2] Ciilton, C.. Chi, B. and Uang, C. M. Cyclic Response of RBS MomentConnections: Weak-Axis Configuration and Deep Column Effects, ReportNo. SSRP-2000/03, Structural Systems Research Projec6 Department ofStructural Engineering, University of California, San Diego La Jo1lA CA.,2000.

[3] ABAQUS User Manual I, II and III, Version 6.2, Hibbitt, Karlsson &Sorensen, Inc., Providence, RI, 2001.

[4] Khja.sateanphun T. Seismic performances of Reduced Beam Section Frames,Ph.D. Thesis, Civil and Architectural Engineering, Illinois Institute ofTechnology, Chicago, IL, 2001.


cyclic behavior of the connection assembly with various

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