snGArticle history:Received 30 August 2007Received in revised form27 August 2008Accepted 27 August 2008Available online 23 September 2008

Keywords:Steel joist girdersTrussed frameColumn base fixityIndustrial buildingsNonlinear dynamic behavior

As the trend towards developing performance-based design specifications for the seismic design ofstructures gains momentum, it is clear that very little is known about the performance of light industrialstructures under large lateral loads. Among the main outstanding issues related to the seismic design ofthese structures are (1) the determination of appropriate response modification factors (R, Cd and0),(2) the establishment of drift limits to avoid damage of structural and nonstructural components, and(3) clarification of the role that the roof diaphragm plays on the seismic behavior of light-weight roofstructures. This study attempts to elucidate some of those issues for a particular class of light-weightindustrial structures, those composed of one-story, weak columnstrong beam joist girder frames. Twotypes of analysis models were developed for the nonlinear dynamic analyses of these structures. The firstis a simplified 2-D analysis model, using SAP2000 and the second is a complex 3-D analysis model, usingABAQUS. Nonlinear time history analyses were performed for sites in Los Angeles (CA), Boston (MA), andMemphis (TN). The accuracy of the simplified 2-Dmodelwas verified by comparisonwith the results fromthe 3-D model. The results indicate that the behavior of these structures is almost always in the elasticrange, and that substantial roof bracing should be installed for this type of structure, to prevent excessivedrifts in the weak direction. When two horizontal components of excitations were applied concurrentlyto check the effect of torsion of the frame, it was found that torsional effects were negligible for structuresregular in plan, and that a 2-D model can provide reasonable analysis results. Column base fixity effectson the dynamic behavior were also investigated and it was determined that column base fixity should beconsidered, to obtain more accurate dynamic behavior of the steel joist girder structures.

Published by Elsevier Ltd

1. Introduction

Joist girder frame structures consist of repetitive, open, tall,one-story frames with or without additional bracing along theperimeter (Fig. 1). These structures are inherently very flexible,and in the past their design has controlled by drift criteriafor wind. Their performance during past earthquakes has beensatisfactory, with damage limited to brittle faade elements andpoorly detailed column bases [1]. This is in spite of the fact thatno specific seismic design guidelines exist for these structures,and that these structures are generally weak columnstrongbeam systems. With the advent of seismic performance-baseddesign (PBD), there is a need to evaluate the performance ofthese structures under a wide range of seismic loads, in orderto provide rational design guidelines. Among the main issuesto be addressed are the determination of response modificationcoefficient (R) and deflection amplification factor (Cd) for design,

Corresponding author. Tel.: +1 714 278 2805; fax: +1 714 278 3916.E-mail address: ukim@fullerton.edu (U. Kim).

and the determination of the drifts associated with different levelsof seismic excitations. For these flexible structures, two importantanalysis parameters are the degree of column base fixity and theamount of diaphragm action on the roof. Both of these have alarge effect on both the displacements and forces attracted to thejoist girders, as almost all of the seismic mass is concentrated onthe first sidesway mode [2]. To study the seismic behavior of joistgirder systems, a combined analytical and experimental programwas carried out under the auspices of the Steel Joist Institute (SJI)[3]. As far as the authors know, this is the only work available onthe seismic performance of moment frames with joist girders, andone of the few to address industrial structures of this type [4].There are typically four levels of structural analyses conducted

for seismic design: linear static, linear dynamic, nonlinear staticand nonlinear dynamic. Because of the regularity of the structuresand the insignificant influence of higher modes, linear static andnonlinear static (nonlinear pushover) analyses should be sufficientto design a typical steel joist girder structure [5]. Nevertheless,as part of these studies, the following tasks were performed tosimulate the actual behavior of the steel joist girder structuresunder large seismic excitations:Engineering Structure

Contents lists availa

Engineering

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3-D nonlinear dynamic behavior of steelUksun Kim a,, Roberto T. Leon b, Theodore V. Galamba Department of Civil and Environmental Engineering, California State University, Fullertob School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta,c Department of Civil Engineering, University of Minnesota, Minneapolis, MN 55455, USA

a r t i c l e i n f o a b s t r a c t0141-0296/$ see front matter. Published by Elsevier Ltddoi:10.1016/j.engstruct.2008.08.018s 31 (2009) 268274

ble at ScienceDirect

Structures

evier.com/locate/engstruct

joist girder structuresos c

, CA 92834, USAA 30332, USA

rU. Kim et al. / Engineering St

Fig. 1. Typical joist girder structure.

Develop a simplified, two-dimensional (2-D) analysis modeland verify its accuracy and robustness, through a comparisonbetween this 2-D analysis for a Los Angeles (CA) site on firmsoil (SD) and a 3-D nonlinear FE analysis results. Perform nonlinear time history analyses for Los Angels forpinned and partially restrained (PR) column base conditions, toassess the effect of base fixity. Perform linear and nonlinear dynamic analyses for other twolocations (Boston, MA and Memphis, TN) using the simplified2-D analysis model to determine the nonlinear effects on thistype of structures.

2. Input data for time history analyses

Several measured and simulated ground motions for threecities (Los Angeles, Boston and Memphis) were used to performa time history analyses. For Los Angeles and Boston, the simulatedground motions developed by one of the SAC joint project teamswere selected for time history analyses [6,7]. Ten pairs of groundmotions with a probability of exceedance of 10% in 50 yearswere used in this study as shown in Tables 1 and 2. Each pairof ground motions is comprised of two horizontal components,a fault-normal and a fault-parallel component. For Memphis, thesimulated ground motions used (Table 3) were developed bythe Mid-America Earthquake Center [8], also for a probability ofexceedance of 10% in 50 years for a representative soil site. Becausethese structures are assumed to be designed for a comparativelyshort life, ground motions with a probability of 10% in 50 yearsrather than 2% in 50 years were used. From these tables, theaverage maximum PGA values are 0.59g for Los Angeles, 0.20gfor Boston and 0.08g for Memphis, respectively. The average ofpseudo-acceleration values at the natural period of the prototypeframe in this study (T = 1.5 s) are 0.49g for Los Angeles, 0.059gfor Boston and 0.021g for Memphis, respectively.To perform time history analyses, the use of distributed masses

were deemed necessary for an accurate 2-D and 3-D dynamicanalysis, given the relatively small mass of the structure. The solidcircles on the top chord of the joist girder (Fig. 2) indicate thelocation of the lumped masses. The following parameters wereassumed for the mass calculations:(1) Lumpedmasses are comprised of 1.0 times dead loads plus 0.2times snow loads.

(2) A portion of column weight (37%) was incorporated [9].(3) Dead loads are comprised of built-up roof gravel surface(287.3 N/m2), roof deck (81.4 N/m2 for 22 gage deck),insulation (47.9 N/m2) and mechanical systems (239.4 N/m2).The total dead loads are 656.0 N/m2.

(4) Based on the above assumptions, the lumped masses for all

three cities are summarized in Table 4.uctures 31 (2009) 268274 269

Fig. 2. Elevation of 3-bay frame.

Fig. 3. Two-dimensional model for nonlinear dynamic analysis.

3. Development of the analysis model

Two kinds of analysis models were developed for the nonlineardynamic analyses. The first was a simplified 2-D analysis model,using SAP2000 [10]. It was used as a compromise between aSDOF system and a complex 3D FE model to reduce the analysistime cost, but yet achieve reasonable results. It was deemed tobe as complete as a designer may do as he/she attempts to gainconfidence in the performance of these structures. The second isa complex 3-D analysis model using ABAQUS [11] to determine3-D global behavior and local performance (local buckling, hingerotations, etc.). It was intended to provide as accurate analyticalresults as possible. The design of the structures and a comparisonbetween the experimental results and the 2-D model has beenpresented elsewhere [2]. Table 5 shows the main member sizesfor the structures analyzed herein. The structures had periods of1.56 (Los Angeles), 1.83 (Boston) and 1.64 (Memphis) seconds,respectively. Flexible metal siding with little stiffness and masswas assumed in the design.The basic assumption of the 2-D model (Fig. 3) is that the

joist girder members remain in the elastic range throughoutthe full range of the ground excitation, and that the plasticzones are concentrated on the column-to-joist connection. Theseassumptions are based on both observations during the full-scaletest and the results of previous analyses [3]. They are consideredreasonable, except for extremely severe ground excitation cases.The 2-D model was developed using SAP2000 with NLLINKelements used for the upper region of each column as shownin Fig. 3. One of the NLLINK elements restrictions is that thiselement can be used for a limited region of plastification only.Thus, in case of globally spreading plastification, the accuracyof the nonlinear analysis results cannot be guaranteed. Again,observations from the full-scale test indicate that plastificationwill localize over a small distance, probably less than twice thecolumn depth [3]. Thus the assumptions appear reasonable. Toverify the stability of frames, a careful consideration of globaland local imperfections should be required and recommendationvalues of imperfections are given in Eurocode 3 [12]. Exceptionally,sway imperfection may be disregarded where horizontal loads aregreater than 15% of vertical loads. In this study, imperfections arenot incorporated in the analysis according to this special condition,however, imperfections should be considered under routine designprocedures to insure that instability issues do not occur [1315].To consider global plastification and 3-D effects, a larger model

was developed, using ABAQUS (Fig. 4). The span in the transversedirection is 40 ft. The columnmembersweremodeled using B32OS

elements, a 3-D beam element that uses quadratic interpolationand accounts for warping effects. Each column was comprised

rBO16 Saguenay, 1988 0.01 2958 0.25 0.60 0.019BO17 Saguenay, 1988 0.01 3906 0.18 0.80 0.073BO18 Saguenay, 1988 0.01 3906 0.23 1.00 0.030BO19 Saguenay, 1988 0.01 3325 0.18 0.70 0.052BO20 Saguenay, 1988 0.01 3325 0.27 0.76 0.054Avg. 0.20 0.68 0.059

Shaded numbers represent maximum values in each column.

Table 3Summary of ground motions for Memphis

Record DT (s) No. of GM points Max. PGA (g) Max. pseudo-accel. (g) Pseudo-accel. at T = 1.5 s (g)ME01 Simulation, soil 0.01 3000 0.06 0.23 0.030ME02 Simulation, soil 0.01 3000 0.08 0.30 0.014ME03 Simulation, soil 0.01 3000 0.07 0.25 0.029ME04 Simulation, soil 0.01 3000 0.07 0.25 0.029ME05 Simulation, soil 0.005 3847 0.11 0.29 0.011

ME06 Simulation, soil 0.005 3847 0.05 0.23 0.065ME07 Simulation, soil 0.005 4068 0.07 0.25 0.018ME08 Simulation, soil 0.005 4068 0.09 0.33 0.003ME09 Simulation, soil 0.005 3752 0.09 0.26 0.002ME10 Simulation, soil 0.005 3752 0.06 0.22 0.013Avg. 0.08 0.26 0.021

Shaded numbers represent maximum values in each column.

of 9 segments 1016 mm long. The boundary conditions for the properties, linearized stressstrain relationships were used, basedLA16 Northridge, 1994 0.005 2990 0.58 1.69 0.673LA17 Northridge, 1994 0.02 3000 0.57 1.17 0.468LA18 Northridge, 1994 0.02 3000 0.82 2.79 0.794LA19 North Palm Springs, 1986 0.02 3000 1.02 3.35 0.294

LA20 North Palm Springs, 1986 0.02 3000 0.99 3.92 0.704Avg. 0.59 1.92 0.490

Shaded numbers represent maximum values in each column.

Table 2Summary of ground motions for Boston

Record DT (s) No. of GM points Max. PGA (g) Max. pseudo-accel. (g) Pseudo-accel. at T = 1.5 s (g)BO01 Simulation, hanging wall 0.01 3000 0.12 0.34 0.075BO02 Simulation, hanging wall 0.01 3000 0.07 0.73 0.216BO03 Simulation, foot wall 0.01 3000 0.14 0.55 0.063BO04 Simulation, foot wall 0.01 3000 0.11 0.35 0.094BO05 New Hampshire, 1982 0.005 3847 0.58 1.83 0.043BO06 New Hampshire, 1982 0.005 3847 0.32 1.01 0.031BO07 Nahanni, 1985 0.005 4068 0.09 0.24 0.031BO08 Nahanni, 1985 0.005 4068 0.08 0.16 0.042BO09 Nahanni, 1985 0.005 3752 0.06 0.15 0.041BO10 Nahanni, 1985 0.005 3752 0.07 0.21 0.046BO11 Nahanni, 1985 0.005 3804 0.13 0.59 0.060BO12 Nahanni, 1985 0.005 3804 0.14 0.53 0.057BO13 Saguenay, 1988 0.005 3548 0.20 0.69 0.035BO14 Saguenay, 1988 0.005 3548 0.29 0.90 0.033BO15 Saguenay, 1988 0.01 2958 0.52 1.55 0.077Summary of ground motions for Los Angeles

Record DT (s) No. of GM points Max. PGA (g) Max. pseudo-accel. (g) Pseudo-accel. at T = 1.5 s (g)LA01 Imperial Valley, 1940 0.02 2674 0.46 1.47 0.393LA02 Imperial Valley, 1940 0.02 2674 0.68 1.79 0.368LA03 Imperial Valley, 1979 0.01 3939 0.39 1.42 0.396LA04 Imperial Valley, 1979 0.01 3939 0.49 1.54 0.179LA05 Imperial Valley, 1979 0.01 3909 0.30 0.84 0.343LA06 Imperial Valley, 1979 0.01 3909 0.23 0.93 0.205LA07 Landers, 1992 0.02 4000 0.42 0.99 0.324LA08 Landers, 1992 0.02 4000 0.43 1.19 0.345LA09 Landers, 1992 0.02 4000 0.52 1.31 0.904LA10 Landers, 1992 0.02 4000 0.36 1.30 0.612LA11 Loma Prieta, 1989 0.02 2000 0.66 2.63 0.642LA12 Loma Prieta, 1989 0.02 2000 0.97 3.64 0.277LA13 Northridge, 1994 0.02 3000 0.68 2.64 0.605LA14 Northridge, 1994 0.02 3000 0.66 2.39 0.704LA15 Northridge, 1994 0.005 2990 0.53 1.46 0.562270 U. Kim et al. / Engineering St

Table 1columns included fixity for the three translational degrees offreedom and for the torsional degree of freedom. For materialuctures 31 (2009) 268274on the results of the coupon test from the full-scale test structure.Yield stresses were assumed as 417 MPa for the columns, and

rTable 6. From FEMA-369 [17], when 7 or more ground motionsare used, mean values of the response parameters may be usedfor design. Thus, at the bottom of Table 6 the average values andstandard deviations are provided, and these values were used forthe comparisons. In comparing the base shears shown in Table 6with the pushover analyses in Fig. 5, it is clear that for the 2-D model only the LA09 and LA14 ground motions resulted ininelastic behavior, while LA09, LA10, LA13, LA14, LA16 and LA18produced inelastic behavior for the 3-D case. When comparing

4. Nonlinear dynamic behavior along the strong-axis

For the simplified 2-D analysis model, linear and nonlinearanalyses were performed for all three sites (Los Angeles, Bostonand Memphis). Fig. 6 shows the behavior obtained from a lineartime history analysis, while Fig. 7 shows the hysteretic behaviorfrom the nonlinear time history analysis for the LA09 groundmotion. Fig. 8 shows the sequence of the plastic hinge formationand (b) nonlinear time history under the simulated Los Angelesground excitations. Fig. 5 shows the pushover curves for the 2-Dand 3-D models. The estimated capacity of the 3-bay joist girderframe is 298 kN from the 2-D analysis model and 320 kN from the3-D analysis model. The difference between 2-D and 3-D modelsis attributable to the stiffening effect of both the roof joists anddiagonal bracing incorporated in the 3-D modeling [16].The comparison of the nonlinear time history analysis results

between the 2-D and 3-D analysis models is summarized in

cases, the force and moment equilibrium could not be achievedwithin the desired tolerance of 0.5%, and therefore the results werenot deemed reliable and eliminated from consideration. From thecomparison of mode shapes, natural periods, pushover analyses,and nonlinear time history analyses, a simplified 2-D analysismodel exhibited good accuracy and considerable reduction ofmodeling and analysis time. The time required to carry out a 2-Dmodel analysis is about 2040 times shorter than the required forthe 3-D model when using a PC with limited memory.U. Kim et al. / Engineering St

Table 4Lumped masses for 3-bay frame

Parameter Los Angeles, CA

Snow loads 0 N/m2

Lumped mass 1 1.477 kN s2/mLumped mass 2 1.785 kN s2/mLumped mass 3 1.082 kN s2/m

Table 5Main structural member sizes

Location Joist Joist girder

Los Angeles, CA 24K4 40G8N8K(1016G8N36 kN

Boston, MA 26K7 40G8N11K(1016G8N49 kN

Memphis, TN 24K4 40G8N8K(1016G8N49 kN

Fig. 4. Three-dimensional model for nonlinear dynamic analysis.

352 MPa for the joists and joist girders. To consider the dampingeffect, a 5% damping ratio was used because this is a typical valuein design spectra. When interaction with non-structural elementsis considered, this value seems reasonable, albeit probably on thehigh side for the Boston and Memphis locations.The comparisons between the 2-D and 3-D models were used

to test the validity of two kinds of results: (a) pushover analysesdrifts, it is clear that only small inelastic deformations occurred.This argues for an elastic design (R = 2 or less) for this typeuctures 31 (2009) 268274 271

Boston, MA Memphis, TN

1676 N/m2 958 N/m2

2.188 kN s2/m 1.838 kN s2/m2.520 kN s2/m 2.153 kN s2/m1.498 kN s2/m 1.262 kN s2/m

Column in in. lb/ft (mm kg/m)Interior W 14 61 (W 360 91)

) Exterior W 14 53 (W 360 79)Interior W 14 68 (W 360 101)

) Exterior W 14 61 (W 360 91)Interior W 14 61 (W 360 91)

) Exterior W 14 53 (W 360 79)

Fig. 5. Pushover curves (2-D vs. 3-D).

of structure. The stiffness of the structures was governed by theH/100 limit assumed for wind, which also resulted in a substantialoverstrength (0 = 3.5 4, typically). Similarly, these results willargue for a low value of the amplification factor Cd. The overallresults make a strong case for the use of an R = Cd approach forthese flexible structures.The dashed lines in Table 6 for LA14 and LA20 represented a

failure to converge during the analysis, not collapses. For theseand Fig. 9 shows the plastic hinges at 3% roof drift level in thecolumn from the full-scale cyclic test. Table 7 gives a summary of

r272 U. Kim et al. / Engineering St

Table 6Comparison between 2-D vs. 3-D nonlinear model

2-D model (SAP 2000) 3-D model (ABAQUS)Roof drift (mm) Base shear (kN) Roof drift (mm) Base shear (kN)

LA01 212 169 221 183LA02 178 143 190 157LA03 194 153 180 149LA04 104 84 114 94LA05 184 148 192 159LA06 97 78 89 74LA07 162 128 161 133LA08 164 130 158 131LA09 461 333 424 318LA10 315 246 361 297LA11 333 252 315 260LA12 122 98 105 87LA13 332 258 410 314LA14 383 285 LA15 308 236 303 251LA16 351 264 456 321LA17 274 210 288 238LA18 366 277 359 296LA19 167 133 163 135LA20 339 258 Avg. 252 194 249 200Std. 106 76 117 87

Fig. 6. Hysteretic behavior under the applied ground motion (linear).

Fig. 7. Hysteretic behavior under the applied ground motion (nonlinear).

the average responses for comparison purposes among three cities.For Boston and Memphis, all responses remained in the elasticrange. Again, it appears that except for near-field ground motionsin regions of high seismicity, the design of these structures shouldbe carried out using linear techniques.Based on the comparison of results, a simplified 2-D analysis

model appears sufficiently accurate for obtaining reasonableresults along the strong-axis. However, one of the major concernswhen considering dynamic behavior of this type of structuresis the bowing effect due to excessive drift of unbraced frames.

To investigate and solve this problem, a 3-D analysis modelas shown in Fig. 4 was used with a detailed roof deck model.uctures 31 (2009) 268274

Fig. 8. Sequence of hinge formation.

Fig. 9. Plastic hinge in the column at the 3% drift level.

Table 7Summary of average responses

Linear time history Nonlinear time historyRoof drift(mm)

Base shear(kN)

Roof drift(mm)

Base shear(kN)

Los Angeles, CA 268 218 252 194Boston, MA 30 27 30 27Memphis, TN 16 13 16 13

The contribution of the roof deck was investigated by replacingthe roof deck with spring elements with equivalent roof deckstiffness (SPRINGA element in ABAQUS). The equivalent roof deckelement was calculated from the truss analogy for the roof deck asdescribed in the Steel Deck Institute Diaphragm Design Manual[18]. The equivalent stiffness (Ks) of the roof deck segment forthese structures is 263 N/m. Table 8 gives a comparison ofdynamic responses along the weak-axis among three differentroof details. With a roof deck, there is considerable reductionin the drift of the unbraced frame but this additional in-planestiffness is not sufficient to obtain rigid diaphragmaction. To obtainrigid diaphragm action, very stiff roof diagonal bracing should beinstalled for this type of structure in addition to the roof deck.To study the effect of two simultaneous horizontal components

of excitations, the fault-normal and fault-parallel componentswere applied concurrently to check the effect of horizontal torsionon the frame with roof deck and diagonal bracing. FEMA 356 [19]

defines the displacementmultiplier,, as the ratio of themaximumdisplacement on the roof diaphragm to the average displacement

rU. Kim et al. / Engineering St

Table 8Dynamic responses along the weak-axis (LA09)

Intermediate frames End framesRoofdrift (mm)

Baseshear (kN)

Roofdrift (mm)

Base shear (kN)

Joists only 762762 10.010.0 254254 44.544.5Roof deck 10276 6.76.7 5151 200.2164.6Roof deck &bracing

6464 5.85.8 5151 200.2182.4

Table 9Resultant responses under bi-directional excitations

Roof drift (mm) Along withfront joist girder

Along withrear joist girder

Average

LA01+ LA02 222 220 221.0 1.00LA03+ LA04 180 180 180.0 1.00LA05+ LA06 192 192 192.0 1.00LA07+ LA08 161 161 161.0 1.00LA09+ LA10 429 427 428.0 1.00LA11+ LA12 315 314 314.5 1.00LA13+ LA14 LA15+ LA16 306 303 304.5 1.00LA17+ LA18 LA19+ LA20 164 161 162.5 1.01

Fig. 10. Secant model for PR column base (exterior column).

(max/avg). This prestandard specifies that if the displacementmultiplier () exceeds 1.5, 2-D models should not be permittedand a 3-Dmodel should be used. Table 9 summarized the nonlineartime history analysis results under bi-directional excitations with values. From Table 9, it can be concluded that the effect ofhorizontal torsion for this frame is negligible, and 2-D model canprovide reasonable analysis results. The dashed line in the tablerepresented a failure to converge during the analysis.To asses the effect of base fixity, time history analyses were

performed for a site in Los Angeles on firm soil with a total of10 pairs of simulated ground motions. Table 10 shows roof driftand base shear results from the time history analyses and pseudo-acceleration values, according to the respective natural period forpinned and PR column base conditions. The PR column base modelfor the dynamic analysis is the linearized one, because there isno simple pinched hysteresis model available in SAP 2000. Thelinearized stiffnesses were taken as the secant stiffness from theorigin to the 0.02 rad rotation in the bilinear model as shown inFigs. 10 and 11. Reasonable results can be obtained in the range ofmajor interests using this linearization.From the comparison results, it can be seen that the maximum

roof drift of the PR frame was reduced by about 10%, even though

the induced base shear increased by about 22%. Therefore, whilethe reduction of the roof drift is the one of the advantages ofuctures 31 (2009) 268274 273

Fig. 11. Secant model for PR column base (interior column).

Fig. 12. Plot of base shear vs. displacement for different column bases.

the PR base connection, careful consideration must be taken toaccount for the large increase of base shear. This phenomenon canbe examined graphically from the Fig. 12, which shows a plot ofbase shear versus roof drift for different column bases. A majoradvantage of considering the PR column base, is that more realisticand accurate frame responses can be obtained, and the structuralengineer can design the frame properly based on these improveddata [20]. And, to apply the column base fixity effect practicallyin the design procedure, recommended K value (effective lengthfactor) of this type of buildings should be developed for the designpurpose.

5. Conclusions

Currently, there are no established seismic design guidelines forthe steel joist girder structures, because the dynamic character-istics of these structures have not been sufficiently investigated.Much experimental and analytical work is needed to determinereasonable R values for these structures. For the particular caseof industrial structures with moment frames incorporating joisttrusses, this study concludes that:

1. The results of the analyses argue for an elastic design, as fromthe results of the nonlinear analyses there is little or no inelasticbehavior under low or moderate seismic excitations.

2. There is some limited inelastic behavior under severe seismic

excitation, which will argue for allowing some inelasticity indesign, perhaps with R = Cd = 2.

reAcknowledgements

This work was conducted under the sponsorship of the SteelJoist Institute. The opinions presented are solely those of theauthors and not of SJI or any other organization.

References

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Table 10Nonlinear time history analysis result for different column fixities

Roof drift (mm) BasPinned PR Pinn

LA01 212 243 169LA02 178 219 143LA03 194 185 153LA04 104 112 84LA05 184 168 148LA06 97 77 18LA07 162 173 78LA08 164 156 130LA09 461 356 333LA10 315 256 246LA11 333 262 252LA12 122 84 98LA13 332 324 258LA14 383 355 285LA15 308 279 236LA16 351 330 264LA17 274 207 210LA18 366 301 277LA19 167 147 133LA20 339 319 258Avg. 252 228 189a Pseudo-accel. at 1st mode of nonlinear model (natural period for pinned: 1.390 s;

3. Column base fixities have a significant effect on the framebehavior, and special considerations should be required for thedesign of steel joist girder structures with PR column bases.Time history results show that the roof drift decreased and baseshear increased when considering column base fixity.

4. Pushover analyses show that a simplified 2-D analysis modelcan provide a reasonable approximation to the accurate framebehavior predicted by a sophisticated 3-D analysis model forstructures without plan and stiffness irregularities.

5. For the results for the Los Angeles frame, there was a littleincrease for roof drift, but there was some reduction of baseshear due to the nonlinear effects.

6. For weak-axis behavior, an apparent bowing behavior can beexpected if the roof deck and roof bracing are not detailed toobtain rigid diaphragm behavior.uctures 31 (2009) 268274

shear (kN) Pseudo-acceleration (g)a

ed PR Pinned PR

254 0.442 0.689230 0.368 0.621197 0.394 0.514121 0.214 0.312180 0.386 0.46883 0.200 0.210183 0.329 0.471165 0.340 0.424361 1.060 1.030266 0.746 0.707271 0.680 0.71190 0.252 0.227334 0.798 0.954362 0.808 1.040286 0.635 0.777341 0.846 0.974216 0.587 0.561310 0.805 0.835156 0.343 0.400325 0.738 0.880237 0.549 0.640

for PR: 1.204 s).

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[5] Federal Emergency Management Agency (FEMA). Recommended seismicdesign criteria for new steel moment-frame buildings, FEMA 350.Washington(DC): FEMA; 2000.

[6] SAC. Development of ground motion time histories for phase 2 of theFEMA/SAC steel project, SAC/BD-97/04. Sacramento (CA): SAC Joint Venture;1997.

[7] SAC. Suites of earthquake ground motions for analysis of steel moment framestructures, http://nisee.berkeley.edu/data/strong_motion/sacsteel/ground_motions.html. SAC Joint Venture; 1997.

[8] Wen YK, Wu CL. Generation of ground motions for Mid-America cities. Mid-America Earthquake center report. Urbana (IL): University of Illinois; 1999.

[9] Blevins RD. Formulas for natural frequency and model shape. New York (NY):Van Nostrand Reinhold; 1979.

[10] Computers and Structures, Inc (CSI). SAP2000 tutorial manuals. Berkeley (CA):CSI; 1998.

[11] Hibbit, Karlsson & Sorensen, Inc (HKS). ABAQUS theory and users manual.Pawtucket (RI): HKS; 1998.

[12] European Committee for Standardization (CEN). Eurocode 3: Design of steelstructures part 101: General rules and rules for buildings. CEN; 2005.

3-D nonlinear dynamic behavior of steel joist girder structuresIntroductionInput data for time history analysesDevelopment of the analysis modelNonlinear dynamic behavior along the strong-axisConclusionsAcknowledgementsReferences