Seismic behavior of steel beams and CFT column...

Journal of Constructional Steel Research 63 (2007) 1479–1493www.elsevier.com/locate/jcsr

Seismic behavior of steel beams and CFT column moment-resistingconnections with floor slabs

Chin-Tung Chenga,∗, Chen-Fu Chana, Lap-Loi Chungb

a Department of Construction Engineering, National Kaohsiung First University of Science and Technology, Taiwanb National Center for Research on Earthquake Engineering, Taiwan

Received 14 September 2006; accepted 31 January 2007

Abstract

This research investigates the seismic performance of four steel beams to concrete filled steel tube (CFT) column connections with floor slabs,including two interior and two exterior joints. The objective of this research is to evaluate firstly the composite effect of the steel beam and floorslab commonly used in Taiwan in practice. Secondly, the seismic behavior of new connection details such as the taper flange or larger shear tab inthe beam-end is investigated to prevent complete joint penetration welds (CJP) of the girder flanges from the unexpected brittle failure found inthe latter after the Northridge earthquake. In addition to the experimental investigation, the development and validation of analytical models forthe assessment of the force–deformation behavior of the joint components are also conducted. The slab effect on the shear transfer in the panelzone is investigated as well.c© 2007 Elsevier Ltd. All rights reserved.

Keywords: Concrete filled steel tube; Composite structures; Beam–column connections; Panel zone; Shear distortions; Testing

1. Introduction

Research by Leon et al. [1] showed that composite beamsexceeded the plastic moment strength of their bare steel beams,thus indicating the potential of having an unexpected strong-beam–weak-column framing system instead of the desirableopposite, if the composite effect was neglected in the design.The composite effect may vary with the distribution of shearstuds, the floor thickness, and the amount of reinforcing steelin the slab. In general, the shallow beam depth used in thelow-to-midrise building will have larger composite effects.Yu et al. [2] showed that the presence of a concrete slab incomposite beams eliminated the lateral–torsional buckling ofthe beams, but local buckling in the beam flange did develop,resulting in significant strength degradation. Besides, Liu andAstaneh-Asl [3] conducted tests of twelve steel beam to columnconnections with floor slabs (20% of full composite). Testresults showed that the composite action was lost at a rotationof 0.04 rad. Cheng and Chen [4] also tested six compositesteel beam and reinforced concrete column connections. Test

∗ Corresponding author. Tel.: +886 7 6011000x2118; fax: +886 7 6011017.E-mail address: [email protected] (C.-T. Cheng).

0143-974X/$ - see front matter c© 2007 Elsevier Ltd. All rights reserved.doi:10.1016/j.jcsr.2007.01.014

results indicated that the initial stiffness and ultimate strength of49% of partially composite beams were significantly increased.Therefore, the objective of this paper is firstly to evaluate thecomposite effect of the steel beams and floor slabs commonlyused in practice in Taiwan.

After the 1994 Northridge earthquake, a large numberof unexpected brittle fractures in the region of the bottombeam flanges of welded steel moment-resisting frame (SMRF)connections were reported. Many of the failures wereconcentrated near the complete joint penetration welds (CJP)of the girder flanges and in the heat affected zone (Youssefet al. [5]). The reasons causing this premature failure maybe due to the welds’ discontinuities, arising from both thepresence of access holes and difficulties in executing the welds,especially when sitting on the top flange of a deep girder. Inaddition, the presence of the floor slab had played a majorrole in the local behavior of the connection. When compositebeams were subjected to a sagging moment, the compressivestrength contributed by the floor slab raised the strain demandon the bottom flanges. To improve the seismic performance ofwelded SMRF connections, many details have been proposed,such as strengthening the interface of the beam to columnflange or reducing the beam section in the potential plastic

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1480 C.-T. Cheng et al. / Journal of Constructional Steel Research 63 (2007) 1479–1493

Notation

Ac effective area of the floor slab;Ag gross area of the column section;Amain area of the primary concrete strut in the panel

zone;As area of bare steel beam;Asc area of shear studs;Astr total area of the concrete strut in the panel zone;Asub area of the secondary concrete strut in the panel

zone;a depth of neutral axis in composite beams;ac depth of the compression zone in columns;b effective width in the composite beam;bc column width in the loading direction;C compressive force of internal moment couple in

the composite beam;D axial force in the primary concrete strut;db center distance between upper and lower beam

flanges;dc column diameter;Es Young’s modulus of the steel tube;fc theoretical strength of the strut concrete;fcc confined strength of the strut concrete;f ′c measured concrete strength;

fl confining stress to the strut concrete in the panelzone;

Fh horizontal shear resistance by the concrete strut;L beam length with respect to the column face;Lc distance from the center of the actuator at the top

of column to the floor slab;L t taper length in the beam-ends;lzw distance between the point’s z and w in the panel

zone;lqw distance between the point’s q and w in the panel

zone;lqz distance between the point’s q and z in the panel

zone;lmw distance between the point’s m and w in the panel

zone;ME moment capacity of beam at the column face;Mp plastic moment of the beam;P axial load at the top of the column;Qn force transfer by each shear stud at the top of

beams;s reduction rate of the strength in the tube wall due

to biaxial stress state;V shear resistance in the panel zone;Vc shear resistance of the concrete strut;Vc1 horizontal shear force transmitted by the primary

concrete strut;Vc2 horizontal shear force transmitted by the sec-

ondary concrete strut;V ′

h shear transfer of a partial composite beam;V jh shear force in the panel zone;Vsy shear force of the steel tube at the yield point;

Vsr shear force of the steel tube at the stiffnessdegradation point;

Vsu shear force of the steel tube at the ultimatestrength point;

α normalized tube diameter and thickness ratio;∆b deflection of the beam tip due to the beam flexure;εcc confined strain of the strut concrete;εsT strain corresponding to the σsT ;εt tensile strain of the strut concrete;εsy yield strain of the tube wall;γh distribution factor of the shear force in the

secondary strut;γh1 modified distribution factor of the shear force in

the secondary strut;ϕb curvature of the beam;ϕc curvature of the column;ζ soften factor of the strut concrete due to

orthogonal tensile stress;σsy yield strength of the steel;σsT post-yield stability strength of the steel tube;σsu ultimate strength of the steel;θ angle of primary concrete strut with respect to the

horizontal for connection without the floor slab;θ1 angle of primary concrete strut with respect to the

horizontal for connection with the floor slab;θ2 angle of secondary concrete strut with respect to

the horizontal after modification;θ3 angle of secondary concrete strut with respect to

the horizontal before modification;θb rotation due to the beam flexure;θc rotation due to the column flexure.

hinge region, in an effort to move the beam plastic hingesaway from the column face for protecting the CJP and the heataffected zone of the girder flanges. Wu et al. [6] have testedseveral bolted steel beam to CFT column connections where ataper flange was found to be effective in stiffening the beam-end. In this paper, the seismic behavior of similar connectiondetails that can suppress the brittle fracture in the CJP ofbeam flanges reported after the 1994 Northridge earthquake isinvestigated.

The third objective of this paper is to propose analyticalmodels that can simulate the force–deformation behavior of thejoint components, especially the shear distortion behavior of thepanel zone. To simulate the shear transfer in the panel zone ofsquare CFT connections, Fukumoto and Morita [7] proposeda tri-linear load deformation model for both the concreteinfill and steel tube based on experimental results. Cheng andChung [8] improved the concrete model by accounting for theaxial load effect for circular CFT connections. Although thesemodels are found to be suitable for the simulation of the sheartransfer in the panel zone of the connections, the effect of thefloor slab for the force transfer in the panel zone is unknown.Therefore, a new model for the steel beam and CFT columnconnections with floor slabs is proposed herein.

C.-T. Cheng et al. / Journal of Constructional Steel Research 63 (2007) 1479–1493 1481

Fig. 1. Schematic drawing showing the deformation of connections in real structures.

Fig. 2. The shape of our specimens.

2. Specimens and test procedures

In order to investigate the seismic behavior of the proposedconnection details, four CFT connections with floor slabs wereconstructed under the assumption that the mid-span of thecomposite beams and mid-height of the CFT columns are allhinges based on the deformation shape, as shown in Fig. 1.In real structures, columns drift laterally under seismic loads,but these were held still to avoid the interfering of the P–deltaeffect in the subassembly tests. Therefore, the story drift can berepresented in the form of beam tip rotations instead of columnrotations in this research.

Among the four CFT beam–column subassemblies, twospecimens represent interior column joints in cruciform shape;the other two represent exterior column joints in a tee shape,as shown in Fig. 2. Except for the different connection detailsapplied in each specimen, the steel beams, slabs, and columnsfor the four specimens are all identical. Concrete-filled steeltube columns 350 × 350 × 9 mm in size were made of two9 mm thick steel plates cold-formed into channel shape andvertically seamed by a full penetration weld. After the filletweld of interior diaphragms to the tube wall as shown in Fig. 2,the top and bottom column tubes were horizontally spliced inthe middle of the panel zone by a full penetration weld. Then,the tube wall was slot cut, inserted in a continuous shear tabpassing through the panel zone and fillet welded. Two triangularplates were groove welded to the beam flange to form the taperflange at the beam-end as shown in Fig. 3. In practice, all thewelding up to this step can be performed in the factory to ensure

Fig. 3. Relations between the taper flange and beam moments.

its quality. Then, the beam flanges connect to the column tubewall by a full penetration weld on site. Composite beams consistof a steel beam H450 × 200 × 9 × 14 mm and a two meterwide 150 mm thick slab with 75 mm concrete topping on themetal deck. Construction details of the concrete slab are shownin Fig. 4. To avoid welds in the potential plastic hinge of thebeams, shear studs for the composite beam are prohibited in theregion of 500 mm from the column face. The concrete strengthfor the columns and for the floor slab are 24.5 and 15 MParespectively.

Table 1 shows the investigated parameters and connectiondetails for the specimens. In the specimen numbering, the firstcharacter, C, represents an interior joint in cruciform shape;while T denotes an exterior joint in tee shape. The second andthird characters WT (web through) represent the continuous


Table 1Investigated parameters and connection details

Specimens Tapered beam flange Beam web Connection between the web and shear tabsTop Bottom In panel zone Shear tab Lap length (mm)

C-WT2 None None Web through Single 235C-WT3 None Yes Web through Single 160T-WT2 Yes Yes Web through Single 235T-DS Yes Yes Shear studs Double 235

Fig. 4. Details of the composite beam with floor slab.

shear tab (beam web) passing through the panel zone of theconnection; while DS is for the applied shear studs in the innertube wall and two shear-tabs in the outer tube wall to sandwichthe beam web, trying to stiffen the beam-ends near the columnface as shown in Fig. 5. In practice, one of the shear tabs canbe welded to the tube wall in the factory, while the other onehas to be fabricated in the field for the erection of steel beams.The last character 2 or 3 represents the lap length of the shear

Table 2Steel properties

Components σsy (MPa) σsu (MPa)

Steel tubes 9 mm 462 641Beam web 9 mm 405 500Beam flange 14 mm 391 500Shear tab 15 mm 423 560

tab and beam web to be half or one-third of the beam depth,respectively. In addition to the bolts used to connect the beamweb and shear tab, fillet welds all around the shear tab wereapplied for all specimens, as shown in Fig. 5. Material strengthsfor the steel are summarized in Table 2.

The design of the tapered beam flange is schematicallyshown in Fig. 3, where MP represents the plastic strength of thebare steel beam. Based on the geometry, the required tapered-beam strength at the column face ME can be expressed as

ME =L

L − L tMP (1)

Fig. 5. Connection details in the panel zone.


Fig. 6. Test setup.

Fig. 7. Loading protocol.

where L = the beam length up to the column face and L t isthe taper length, which was arbitrarily set as half of the beamdepth. This length represents the distance of the beam plastichinges moving away from the column face and should be longenough to smoothly transfer the beam stress. Based on the re-quired moment capacity ME of the tapered beams calculatedby Eq. (1), the width of the triangular plates at the column face,bs , can be estimated. The objective of the tapered flanges is toprotect the CJP welds of beam flanges to the tube wall. Taperedbeam flanges were applied for all specimens except specimenC-WT2 as shown in Table 1. Tests of Leon et al. [1] showedthat the composite effects raised the strain demand of the bot-tom flange. Therefore, only the bottom flange was tapered in thespecimen C-WT3. And all backing bars for the groove weld inthe bottom flange of the four specimens were removed and re-placed by a reinforcing fillet weld as suggested by Yu et al. [2].

Fig. 6 shows the test setup. Before each test, a 1500 kNconstant axial load was applied by the oil jack at the topof the column, representing 0.14 of the column squash load,which is calculated as the summation of the ultimate axialcapacities of both the steel tube and concrete infill. Then the

Fig. 8. Measurements in the panel zone.

hydraulic actuator at each beam tip applied the cyclic loadwith displacement control in the form of triangular waves asshown in Fig. 7, which is modified from FEMA suggestions [9].The displacement rate for all cycles was set to be constant as1.875 mm/s. As shown in Fig. 8, two diagonal displacementgauges in π shape measured the shear distortion in the panelzone and two clinometers for the measurement of the columnrotations. Consequently, beam flexural deformations can beestimated by subtracting the deformations due to the sheardistortion in the panel zone and the column rotation from thetotal deformations measured at the beam tip.

3. Test results

Due to the strong-column—weak-beam design, all speci-mens were made in a ductile manner with plastic hinges form-ing at the beam-ends. The column and panel zones experiencedminor yielding in the tests of interior column specimens, whilethey remained elastic at all times in the tests of exterior columnspecimens. In the slab, a wide flexural crack near the columnface formed under the hogging moment and splitting cracks


(a) T-DS. (b) C-WT2.

Fig. 9. Yielding of the bottom beam flange for specimens T-DS and C-WT2.

Fig. 10. Photos showing the tear of the tube wall in the west beam during 5% drift and the fracture of the beam flange and web in the east beam during 4% drift forspecimen C-WT2.

along the stud lines occured under the sagging moment in theloading cycle of 0.375% drift for all specimens. In the loadingcycle of 4% drift, the floor concrete crushed and spalled at thecolumn face under the sagging moment. With the lateral supportof the floor slab, the top beam flanges in exterior column speci-mens buckled in the loading cycle of 5% drift, while it was 4%for bottom flanges. In the tapered steel beam, the bottom flangesyielded during the loading cycle of 3% drift, while it was 2%for beams without taper. The taper effect can be seen in Fig. 9,where the tapered bottom flange of specimen T-DS yielded at200 mm from the column face, compared with 15 mm in thebare steel beam of specimen C-WT2. It is evident that the ta-per flange in the specimen T-DS moved the beam plastic hingeaway from the column face.

Without a taper flange, specimen C-WT2 failed by thefracture of the bottom flange and the web at the east beam inthe loading cycle of 4% drift, and the torn column tube wallat the west beam in the loading cycle of 5% drift as shownin Fig. 10, due to the slab effect that largely increased thestrain demand on the bottom flange. With the tapered bottomflange, specimen C-WT3 failed due to the fracture of the weldedinterface at the top flange in the loading cycle of 6% driftas shown in Fig. 11. With tapered top and bottom flanges,both exterior column connections exhibited excellent ductileperformance and concluded the tests in the loading cycle of

Fig. 11. Photo showing the fracture of the top flange at the conclusion of thetest (6%) for specimen C-WT3.

7% drift. Specimen T-DS failed due to the fracture in the heataffected zone of the top flange as shown in Fig. 12, while inthe bottom flange of specimen T-WT2 failure was due to localbuckling. Fig. 13 shows the hysteretic loops recorded at theeast beam for all specimens. On the basis of these figures,envelopes of force–displacement relation for four specimenscan be illustrated in Fig. 14. Therefore, the ultimate strengthsand initial stiffnesses for each specimen are summarized inTable 3. It is found that exterior joints with tapered beam flanges


Table 3Test results

Specimens Ultimate flexural moment (kN m) Initial stiffness (kN m/rad)

Sagging Hogging S/H Sagging Hogging S/H

C-WT2 E 1005 820 1.23 61 208 42 282 1.44W 981 862 1.14 60 773 45 123 1.35

C-WT3 E 948 825 1.15 51 242 42 306 1.21W 907 820 1.10 47 858 42 895 1.12

T-WT2 1083 694 1.56 64 418 44 419 1.45T-DS 1018 725 1.40 65 852 44 724 1.47

Fig. 12. Photo showing the beam local buckling at the conclusion of the test(7%) for specimen T-DS.

performed much better in terms of the strength and ductilitythan the interior joints.

Test results also show that the strength of the compositebeam is increased 10%–56% from the sagging to the hoggingmoment. When subjected to the sagging moment, the floorslabs of composite beams increase in flexural strength througha direct bearing action against the column tube wall, while thestrength under the hogging moment is only slightly increaseddue to the tension in the slab. If the beam strength is fullydeveloped by suppressing premature failure, either in the beamflange, tube wall, or welded interface through the installation ofa taper flange in a place such as the exterior joints, the initialstiffness and ultimate strength of composite beams under thesagging moment can be increased by 46% and 48% on average,respectively, when compared with those under the hoggingmoment.

By using instruments installed in the panel zone (Fig. 8),deformations measured at the beam tip can be decomposedinto three components, attributed to the flexural rotations of thebeam and column, and the shear distortions in the panel zone.Fig. 15 shows the typical decomposition results for specimenC-WT3. It can be found that deformations of the connectionmostly resulted from the beam flexure, while it was partlycontributed by the slightly nonlinear deformation in the columnand panel zone. Evidence can also be found in Fig. 16, wheretube walls in the panel zone were opened up after tests. It isnoted that interior joints framed with a cross beam have morecracks than the exterior joints framed with only one beam.

4. Simulations of force–deformation behavior

Since deformations of connections measured at thebeam tip can be decomposed into three components, theforce–deformation behavior of each component is sequentiallysimulated. Cheng and Chung [8] have proposed a theoreticalmodel to simulate the force–deformation behavior of CFTbeam–column connections without floor slabs; however, therole of the floor slabs in the shear transfer of the panel zoneis unknown and is investigated in what follows.

4.1. Panel zone

Fig. 17 shows the CFT connection without the floor slabsubjected to seismic moments. Due to the panel distortion,a concrete strut may be formed to transfer the seismic forceacross the joint. Therefore, the shear strength in the panelzone is the superposition of the strength from the steel tubewall and concrete strut. To evaluate the shear distortion ofthe tube wall in the panel zone, a tri-linear force–deformationmodel proposed by Fukumoto and Morita [7] is applied asshown Fig. 18, where Vsy , Vsr , and Vsu are the shear forcesin the tube wall to reach the yielding, stiffness degradation, andultimate strength points. Details of the relationship can be foundin the research of Cheng and Chung [8]. The shear strengthin the strut concrete is evaluated by firstly defining the strutarea, estimated through the depth of the column compressionzone. In the research of Paulay and Priestley [10], the depthof the compression zone in the column was originally derivedfor reinforced concrete columns. For the CFT column, it ismodified by accounting for the confinement of the tube wallto the concrete infill and expressed as

ac =

(0.25 + 0.85

PAg fcc

)dc (2)

where P = axial load of the column, Ag the gross area of thecolumn, dc the column depth in the loading direction, and fccconfined concrete strength on the basis of Mander et al. [11] tobe

fcc = f ′c

(−1.254 + 2.254

√1 +

7.94 fl

f ′c

− 2fl

f ′c

)(3)

in which fl is confining stress provided to the concrete infill.To simulate the shear distortion of the strut concrete, the

compatibility conditions in the panel zone are shown in Fig. 19,


Fig. 13. Hysteretic curve at the east beam end for all specimens.

Fig. 14. Envelope of the force–displacement relationship for all specimens.

where the shortening diagonal strut is axially compressedand simultaneously tensioned in the orthogonal direction.Therefore, the compressive behavior of the strut concrete maybe softened due to the tension in the orthogonal direction.Resulting from the shear distortion, γ , in the panel zone, thecompressive strain in the diagonal strut, εc, can be calculated as

εc =

√(lqw − lmqγ

)2+ l2

mq − lmw

lmw

(4)

and the tensile strain in the perpendicular direction, εt , isexpressed as

εt =

√(lzwγ + lqw

)2+ l2

zw − lqz

lqz(5)

where lzw =l2qz

lmq, lqw, lqz , lmw represent the distance between

points in the panel zone as shown in Fig. 19, respectively.To simulate the compressive behavior in the strut concrete, aconfined stress–strain model proposed by Mander et al. [11] isapplied, and modified by adding the softening effect due to theorthogonal tension as shown in Fig. 20, where the compressivestrength of the concrete is expressed as

fc =ζ fccxr

r − 1 + xr (6)

where x =εc

ζεcc, ζ is the softening coefficient due to the

orthogonal tension and r the parameter to define the descendingbranch in the stress–strain relationship of the strut concrete.Details of the model can be found in the research of Cheng andChung [8].

Without the floor slabs in connection as shown in Fig. 17,the angle of the diagonal concrete strut is defined as

θ = tan−1(

db

dc

)(7)


Fig. 15. Decomposition of the beam tip displacements for specimen C-WT3.

Fig. 16. Photos showing the cracking in the panel zone after open-up for all specimens.

where db = the center distance between the upper and lowerbeam flanges and dc the column depth in the loading direction.Therefore, the panel shear resisted by the concrete strut forconnections without floor slabs can be expressed as

Vc = fcacbc cot θ (8)

where bc is the column width in the loading direction.

With the floor slabs in the connections shown in Fig. 21, asecondary path (from points A, D, B, to C) may be formulatedto transfer the panel shear through the concrete strut and tensileresistance of the interior diaphragm at the top beam flange level.It is believed that the ultimate shear strength in joints may notbe dramatically changed due to the similar strut area at point Afor connections with or without the secondary strut. However,


Fig. 17. Concrete strut in the panel zone of the connection without a floor slab.

Fig. 18. Tri-linear shear force vs. strain model for the tube wall.

Fig. 19. Schematic graph showing shear distortion in the panel zone.

the secondary strut may call for a larger area of panel concreteto participate in the shear transfer. The distribution factor ofthe horizontal shear force in the primary concrete strut, γh ,estimated by Schafer model [12] can be expressed as Fig. 22(a)

γh =2 tan θ1 − 1

3(9)

where θ1 is the primary strut angle corresponding to thehorizontal. Due to the position of the interior diaphragm, thedistribution factor of the horizontal shear force in the secondaryconcrete strut may be modified as Fig. 22(b)

γh1 =2 tan θ1 − 1

3·

cos θ2

cos θ3(10)

Fig. 20. Stress–strain relationship of the concrete strut.

Fig. 21. Strut and tie in the panel zone of the connection with the floor slab.

where θ3 and θ2 are the secondary strut angles correspondingto the horizontal before and after the modifications. Therefore,the horizontal force resisted by the secondary concrete strut iscalculated as

Fh = γ h1V jh (11)

where V jh is the total shear force transmitted into the panelzone. Relatively, the axial force in the primary concrete strutcan be calculated as

D =(1 − γh1)

cos θ1V jh (12)

then the ratio of the axial force in the primary and secondarystruts is

(1 − γh1)

cos θ1:

γh1

cos θ2cos (θ1 − θ2) . (13)

Therefore, the area in the primary concrete strut out of thetotal strut area may be calculated as

Amain =

(1−γh1)cos θ1

(1−γh1)cos θ1

+γh1

cos θ2cos (θ1 − θ2)

· Astr (14)


(a) Original Schafer model. (b) Modified Schafer model.

Fig. 22. Modification of the Schafer model.

(a) Primary strut. (b) Secondary strut.

Fig. 23. Force transfer in the concrete strut.

where Astr = bc · ac is the total strut area. The strut area in thesecondary strut is

Asub = Astr − Amain. (15)

As shown in Fig. 23, the total shear force resisted by theconcrete strut is

Vc = Vc1 + Vc2 (16a)Vc1 = fc Amain cot θ1 (16b)Vc2 = min {Vct , Vcb} (16c)Vct = fc Asub cot θt (16d)Vcb = fc Asub cot θ2 (16e)

where Vc1 is the horizontal shear force transmitted by theprimary concrete strut and Vc2 the shear force in the secondaryconcrete strut. For exterior connections subjected to a hoggingmoment, the tensile capacity of the floor slab may be ignored,and only the primary concrete strut is accounted for in the sheartransfer.

On the basis of the above theory, the relationships of shearforce vs. shear strain in the panel zone of interior connectionsare simulated and shown in Fig. 24, where two analytical curvescalculate the shear resistance of connections with or withoutthe contribution gained from passing through a shear tab (beam

web), respectively. As shown in Fig. 5, the tube wall in thepanel zone was slot cut and inserted to pass through a sheartab that connected the beam web. Comparison shows that thetest results are close to the analytical results without the sheartab. This may be attributed to the open space required betweenthe interior diaphragms and the shear tab for the access holes atthe beam-ends. Therefore, the contribution of the shear transferby passing through the shear tab is ignored in the successivesimulations. The vertical dashed line in Fig. 24 indicates thatthe panel zone of the interior column specimens yielded beforethe loading cycle of 3% drift.

A typical simulation of shear distortions in the panel zone ofspecimen C-WT2 is illustrated in Fig. 25. It is found that boththe analytical predictions slightly underestimate the tested shearstrength, and the difference of two analytical curves with orwithout the floor slab is marginal. The addition of a secondarystrut in the theoretical model of the connection with the slabmay call for a larger area of panel concrete to participate in theshear transfer, but is compensated for by the less inclined angleof the primary concrete strut in the connection without the floorslab, such as points B to C in Fig. 21. In addition, the jointstrength for both cases is constrained by the same total strutarea in the panel zone. It is concluded that the slab’s effect onthe shear transfer of the panel zone may be neglected.


Fig. 24. Simulation of shear force vs. strain in the panel zone of the interiorcolumn specimens.

Fig. 25. Typical comparison of the shear force vs. strain in the panel zone ofspecimen C-WT2.

4.2. Composite beam

When composite beams are subjected to a sagging moment,the floor slab is compressed and contributes to the strength,while it may be ignored under a hogging moment due to theminimum amount of reinforcement provided in the slab. Sincebeams and the floor slab may be fully or partial compositedepending on the force transfer by the shear studs on thetop flange, the shear transfer in the composite beams can becalculated on the basis of AISC-LRFD [13] as

V ′

h = min{

0.85 f ′c Ac, Asσsy,

∑Qn

}(17)

where

Qn = 0.5Asc√

f ′c Ec (ksi) ≤ Ascσsu (18)

in which Qn = the force transfer by each shear stud, Ac isthe effective area of the floor slab, As and Asc are the cross-sectional area of the bare steel beam and the shear stud, σsy andσsu (ksi) are the yield strength of the steel beam and the tensilestrength of the shear stud, and f ′

c and Ec are the compressivestrength and modulus of the concrete for the floor slab (ksi),respectively.

Due to insufficient shear studs provided for the beams, allspecimens are 71% partially composite. Based on the forceequilibrium, the ultimate strength of the composite beams can

Table 4Comparison of the analytical and experimental strengths in composite beams

Specimens Experimentalmoment (kN m)

Analyticalmoment (kN m)

Exp/Analytical

S H S H S H

C-WT2 E 1005 820

1007 656

1.00 1.25W 981 862 0.97 1.31

C-WT3 E 948 825 0.94 1.26W 907 820 0.90 1.25

T-WT2 1083 694 1.08 1.06T-DS 1018 725 1.01 1.11

be obtained by calculating the neutral axis from the followingequation

a =C

0.85 f ′cb

=

∑Qn

0.85 f ′cb

(19)

where b is the effective width of the composite beam to be1.5 m based on the ACI definition [14], and a the neutraldepth of the composite beam under the sagging moment,and C the corresponding compressive force due to thissagging moment. By applying force equilibrium, compatibilityconditions, and stress–strain relations, the moment–curvaturerelations of the composite beam section may be established.Then, the deflection of the beam-tip can be calculated as

∆b =

∫ L

0ϕbxdx (20)

where ϕb is the curvature along the beam length. Therefore, therotation due to the beam flexure can be expressed as

θb =∆b

L. (21)

Fig. 26 shows the simulation of the beam flexure forall specimens and Table 4 summarizes the experimental andanalytical strengths of beams. It is found that the analyticalstrengths of composite beams under a sagging momentevaluated by the insufficient shear studs and the perfectly elasticplastic steel strength in the steel are in good agreement withthe test results with over-strength in the beam flange. If theanalysis accounts for the over-strength in the beam flange, thecomposite strength should be higher so that the analysis usingthe ACI effective width overestimates the composite beamstrength. Instead of the effective width used in the case of thecontinuous floor slab, the column width contacted with 2 mwide slab concrete in specimens through a bearing action isapplied to calculate the composite beam strength of 793 kN m.This strength is significantly lower than the test results andanalysis, as shown in Table 4. Therefore, the width of thecomposite beam in the analysis should be less than the ACIeffective width but larger than the column width. In addition,this evaluation is unable to model the strength degradation dueto the beam’s buckling.

4.3. Column

The procedure to simulate the flexural behavior of CFTbeam–column connections is the same as in the research of


Fig. 26. Simulations of the beam flexure for all specimens.

Fig. 27. Stress–strain curve for the column tube wall.

Cheng and Chung [8], where a nonlinear fiber element analysiswas proposed. The cross section of the column is firstly dividedinto many fiber elements. Based on their compatibility, eachelement consists of the concrete or steel tube materials ina nonlinear stress–strain relationship. Due to the combinedaction of the axial load and the bending moment, the tube wallmay experience multi-axial stresses. The stress–strain modelused for the tube wall is illustrated in Fig. 27, where σsT =

(1.19 − 0.207√

α)σsy represents the post-yield stability stress,and εsT = 4.59·s·εsy is the compressive strain corresponding tothe applied σsT . σsy and εsy are respectively the yielding stressand strain; while σsu and εsu the ultimate stress and strain of thesteel tube under uni-axial loads, respectively. And the reductionrate of the strength of the tube wall under axial compression andcircumferential tension stresses may be estimated as

s =1.0

0.698 + 0.128α ×4.0

6.97

(22)

where α = d2c σsy/(t2 Es) is the normalized ratio of the

tube depth dc and thickness t . In contrast, a 10% increaseof the yield strength for the tube wall under both axialand circumferential tension may be applied. To simulate thestress–strain behavior of the concrete infill, a confined modelproposed by Mander et al. [11] is adopted. Based on the forceequilibrium with a constant axial load on top of the columns, themoment–curvature relation for the CFT column section may beestablished. Similar to the beam flexure, the moment–rotationbehavior of the column can be calculated by the integration ofthe moment–curvature along the column height and expressedas

θc =23

∫ Lc

0ϕcdx (23)

where ϕc is the curvature of the column, Lc the column heightfrom the top of the column to the slab, and the ratio of 2

3accounts for the column moment applied to one hinge end of asimply supported column. The simulations for all specimens areshown in Fig. 28. Where the test strength of the interior columnsalmost reaches the predicted yield point, it validates the factthat all columns remain elastic as shown in the tests. Table 5summarizes the maximum bending moments of columns undera,1500 kN axial load on the basis of this nonlinear analysis aswell as the AISC-LRFD regulations.

4.4. Entire sub-assemblage

Combining the force deformation relations derived for eachstructural component, the force–deformation behavior of theentire sub-assemblage can be simulated by firstly assuming asimilar rotation in each beam end. Then, the corresponding


Fig. 28. Simulations of the column flexure for all specimens.

Table 5Ultimate strength of beams and columns

MB LRFD (kN m) Mc (kN m)∑

Mc/∑

MBSagging (1) Hogging (2) LRFD (3) Nonlinear analysis (4) W/O slab With slab

(3)(2)

(4)(2)

2×(3)(1)+(2)

2×(4)(1)+(2)

1007 656 819 1039 1.25 1.58 0.98 1.25

beam-end moments with sagging in one end and hogging in theother can be obtained on the basis of the elastic beam theory.Based on these beam-end moments, the column moment andthe panel shear can be calculated. Deformed by the columnflexure and panel zone distortions, beam tip rotations can beestimated from the previously derived theory. Therefore, totalrotations at the beam tip corresponding to beam-end momentsare the superposition of rotations due to panel distortions,and beam and column flexure. This procedure is repeated byassuming a new rotation in each beam end. Finally, the envelopeof the force–deformation for the entire sub-assemblage canbe obtained and compared with hysteretic loops, as shown inFig. 29. Note that the tendency of this simulation looks similarto the simulation of the beam flexure as shown in Fig. 26, butmay have a slight improvement in the stiffness simulation asthe underestimated panel zone stiffness may compensate theoverestimated beam stiffness.

To validate the strong-column–weak-beam performance ofthe connections, Table 5 shows the analytical strengths of thecolumns, along with the composite and the bare steel beamsfor comparison. It is found that the composite effect of floorslabs is indeed significant. On the basis of the AISC- LRFDregulations, the moment ratio of the column to bare steel beamsis 1.25, but this is reduced to 0.98 if one considers the strength

of the composite beams, violating the code requirement of1.2. However, the moment ratio of the column to compositebeam can be raised up to 1.25 based on the more rigorousnonlinear analysis of the column strength. In tests, the ratio ofthe column moment (assumed 1039 kN m) to the sagging andhogging beam moments, on an average as shown in Table 3,is slightly lowered to 1.17, indicating the strong-column–weak-beam performance of connections.

5. Conclusions

On the basis of experimental and analytical investigation, thefollowing conclusions can be drawn:

(1) The composite effect of the floor slab and the steel beamis significant under the sagging moment, as the flexuralstrength is increased by a direct bearing action betweenthe column tube wall and the concrete slab. In contrast,the flexural strength of composite beams under the hoggingmoment is slightly increased due to the minimum amountof reinforcement provided in the slab when compared withthe strength of the bare steel beam.

(2) The test results show that the tapered beam flanges andlengthened shear tabs stiffened at the beam-ends andeffectively moved the plastic hinges away from the column


Fig. 29. Simulations of force–deformation relations for all specimens.

face to prevent premature brittle failure of the CJP welds inthe beam flange, resulting in the ductile performance of theconnections.

(3) The test performance shows that the shear tab passingthrough the panel zone has only a marginal effect on theshear transfer in the panel zone due to the open spacebetween the shear tab and the interior diaphragm requiredfor the access hole at the beam-ends.

(4) Analytical models validate the strong-column–weak-beamperformance of the connections in the tests. And theslab effect on the shear transfer in the panel zone maybe neglected. In addition, the proposed model simulatesthe envelope of force–deformation behavior for the entireconnection, including flexural deformation in the beamsand columns as well as shear distortions in the panel zone.

Acknowledgements

Financial supports from the National Science Council inTaiwan through grant No. NSC92-2625-Z-327-001 is greatlyappreciated. In addition, technical help from the NCREE Lab isalso acknowledged.

References

[1] Leon RT, Hajjar JF, Gustafson MA. Seismic response of compositemoment-resisting connections I: Performance. Journal of StructuralEngineering ASCE 1998;124(8):868–76.

[2] Yu QS, Noel S, Uang C-M. Composite slab effects on strengthand stability of moment connections with RBS or welded haunch

modification. In: Proc. of 6th ASCCS conference. 2000. p. 705–12.[3] Liu J, Astaneh-Asl A. Cyclic behavior of shear connections with floor

slab. In: Proc. of 6th ASCCS conference. 2000. p. 745–52.[4] Cheng C-T, Chen C-C. Seismic behavior of steel beam and reinforced

concrete column connections. Journal of Constructional Steel Research2005;65(5):587–606.

[5] Youssef NFG, Bonowitz D, Gross JL. A survey of steel moment-resistingframe buildings affected by the 1994 Northridge earthquake. Rep. noNISTIR 5625. Gaithersburg (Md): National Institute of Standards andTechnology; 1995.

[6] Wu L-Y, Chung L-L, Tsai S-F, Shen T-J, Huang G-L. Seismic behavior ofbolted beam-to-column connections for concrete filled steel tube. Journalof Constructional Steel Research 2005;61(10):1387–410.

[7] Fukumoto T, Morita K. Elasto-plastic behavior of steel beam to squareconcrete filled steel tube (CFT) column connections. In: Proceedings of6th ASCCS conference. 2000. p. 565–80.

[8] Cheng C-T, Chung L-L. Seismic performance of steel beams to concrete-filled steel tubular connections. Journal of Constructional Steel Research2003;59(3):405–26.

[9] FEMA. Recommended seismic design criteria for new steel moment-frame buildings. FEMA-350; 2000. p. 3–75.

[10] Paulay T, Priestley MJN. Seismic design of reinforced concrete andmasonry buildings. John Wiley& Sons; 1992. p. 274.

[11] Mander JB, Priestley MJN, Park R. Theoretical stress–strain model forconfined concrete. Journal of Structural Division, ASCE 1988;114(8):1804–26.

[12] Schafer K. Strut-and-tie models for the design of structural concrete.In: Notes of workshop. Tainan (Taiwan): Department of CivilEngineering, National Cheng Kung University; 1996. p. 140.

[13] American Institute of Steel Construction. Manual of steel constructionload and resistance factor design. 2nd ed. Chicago: AISC; 1994.

[14] American Concrete Institute Committee 318. Building code requirementsfor structural concrete and commentary. Mich.: American ConcreteInstitute; 2005.

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