application of steel channels as stiffeners

Journal of Constructional Steel Research 61 (2005) 1650–1671

www.elsevier.com/locate/jcsr

Application of steel channels as stiffeners in boltedmoment connections

H. Tagawaa,∗, S. Gurelb

aDepartment of Environmental Engineering and Architecture, Nagoya University, Furo-cho, Nagoya 464-8603,Japan

bDepartment of Civil Engineering, Nagoya University, Furo-cho, Nagoya 464-8603, Japan

Received 17 August 2004; accepted 29 April 2005

Abstract

This paper proposes a stiffening method to meet some architectural needs. This method usesbolted channels as alternatives to both continuity and doubler plates in bolted moment-resistantbeam-to-column connections. The present study investigates the performance of channels asstiffeners to: increase yield load in the tension zone of connection, gradually increase overall momentcapacity of connection, and avert shear failure of the column web panel zone. We conductedexperiments to examine the tension region of the connection loaded from T-stubs. The momentcapacity of full connection was predicted by considering T-stub idealization and shear effects onthe column web panel. T-stub tensile behavior and overall connection behavior were also monitoredusing three-dimensional finite element simulations in ANSYS simulation software because thisproblem is three-dimensional in nature. Effects of geometrical and material non-linearities oninteraction among connecting members should be clarified. This study showed marked strengthimprovement in connection by use of channels. The performance of channel stiffeners was examinedthrough comparison of results.© 2005 Elsevier Ltd. All rights reserved.

Keywords: Beam-to-column joint; Bolted moment connection;Stiffener; Channel; Yield mechanism; Testing;Finite element modeling

∗ Corresponding author. Tel.: +81 52 789 3766; fax: +81 52 789 3837.E-mail address:[email protected] (H. Tagawa).

0143-974X/$ - see front matter © 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.jcsr.2005.04.004

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H. Tagawa, S. Gurel / Journal of Constructional Steel Research 61 (2005) 1650–1671 1651

Fig. 1. A typical bolted connection with traditional stiffeners.

1. Introduction

Damage to several steel moment-resisting frames involving brittle failure of weldedbeam-to-column connections, such as that which occurred in the 1994 Northridge and1995 Kobe earthquakes, has emphasized some drawbacks related to welding. Recently,bolted connections have become an important alternative in consideration of their goodperformance in past earthquakes. In particular, bolted beam-to-column connections are thecommon forms of moment-resisting frame joints. Nevertheless, a limiting factor hinderstheir design: deformation of the column flange in the tension region makes it difficultto satisfy strength and stiffness criteria without using stiffeners. The traditional methodof reducing this deformation includes theuse of welded transverse stiffeners (Fig. 1). Ifrequired, doubler plates are also used to prevent panel zone shear failure.

Some previous studies, such as Moore and Sims [1], have addressed the stiffeningof the tension zone in end-plate beam-to-column connections using backing plates asan alternative. Grogan and Surtees [2] also monitored the stiffening with bolted backingangles in their studies.

Recently, requests from the architectural sectorrelated to industrial building details haveprompted us to investigate other alternatives to achieve design flexibility for installation ofoperating equipment. We intended to eliminate transverse stiffeners to allow ducting insideof the joint and prevent misuse or neglect of transverse stiffeners such as that observedin some industrial buildings. This paper presents a new option for stiffening of boltedmoment connections. It could provide sufficient strength against all of the aforementionedeffects using the same element (Fig. 2). Channel members are installed between column

1652 H. Tagawa, S. Gurel / Journal of Constructional Steel Research 61 (2005) 1650–1671

Fig. 2. Proposed stiffening with channels.

flanges on both sides instead of doubler plates and transverse stiffeners. The beam endsconnect to the column flanges by extended end-plates or T-stubs and bolts shared withthe channel connection. Because the use of welds is minimized in this configuration, themethod of stiffening with channels is also helpful for eliminating drawbacks related towelding.

This study specifically addresses investigation of the elasto-plastic behavior of thechannel stiffened bolted beam-to-column moment connections using test results and theirthree-dimensional finite element method (3D-FEM) simulations. This paper also includessome information gainedfrom the previous studies [3,4].

2. Local tensile strength

2.1. T-stub failure mechanisms

In most bolted moment connections, connection failure is governed by yielding andexcessive deformations of the tension zone. For that reason, we began with inspection ofstrength in that tension part to examine connection moment resistance. Individual T-stubswere monitored instead of full connections. The tension part of connection was subjectedto an axial load based on the expected beam flange forces in actual connections.Fig. 3(a)and (b) show the application of this concept.

Previous researchers, such as Packer and Morris [5], have addressed T-stub behaviorunder tension load. Three different failure mechanisms, depending on the relative stiffnessof components and bolts, are possible in either the T-stub flange or the column flange:


Fig. 3. (a) Extended end-plate connection, (b) its T-stub idealization.

Fig. 4. Failuremechanism A.

yielding of the bolts, simultaneous yielding of the flange and bolts, or yielding of theflange alone. Failure by bolt fracture is ignored in our study. To clarify column flangeyielding behavior and the effects of channel stiffeners, failure by simultaneous flange andbolt yielding is also averted by choosing the T-stub flange and bolts as extremely stiff inrelation to the column flange and channels. Therefore, tension zone studies described inthis paper address only failure by yielding of the column and channel flanges. Some yieldline patterns based on the yield line theory developed by Johansen [6] are applied to explainplastic behavior of the column flange and channel flanges.

Figs. 4and5 show the proposed failure mechanisms produced by taking note of priorstudies [5,7]. Regarding the contact between the channel flange and column flange surfaces,


Fig. 5. Failuremechanism B.

we assumed that compatible yield line patterns are developed in both of them. Two differentyield patterns are applied for the column flange and channel stiffener flange. Tension yieldload Fy-t is evaluated using the equation of internal energy and the work done by theexternalload for failure mechanism A (Fig. 4) as

(Fy-t/2)δ = {2mpcn(δ/m) + 2mpcδπ + mpcC(δ/m) + 2mpc(n − 0.5D′)(δ/m)

+ mpc(C − D′)(δ/m)} + {2mpchδ2π + mpchC(δ/m)

+ mpch(C − D′)2(δ/m)},wherempc = t2

fcσyc/4 andmpch = t2fchσych/4 perunit length, and

Fy-t = t2fcσyc{π + (2n + C − D′)/m} + t2

fchσych{2π + (1.5C − D′)/m}. (1)

Variablesmpc and mpch used in these equations are the respective plastic momentcapacities per unit length of yield lines in the column flange and channel flange. Respectiveyield stresses in the column and channel areσyc and σych. Thicknesses of the columnflange and channel flange aretfc andtfch, respectively;C is the vertical bolt pitch betweenupper and lower rows of tension bolts. The bolt-hole diameter is represented asD′;m is the distance from the bolt centerline to the edge of the root fillet. The distancefrom the bolt centerline to the side of the column flange isn, whereasδ represents asmall unit displacement.Fig. 5shows another yield pattern comprising two circular hinge


Fig. 6. Details of the test specimen without stiffeners (T-N).

fields around the bolt-holes for the channel stiffener. Tensile yield loadFy-t is evaluatedusing the equation of internal energy and the work done by external load for failuremechanism B as

(Fy-t/2)δ = {2mpcn(δ/m) + 2mpcδπ + mpcC(δ/m)

+ 2mpc(n − 0.5D′)(δ/m) + mpc(C − D′)(δ/m)} + {2mpchδ4π},wherempc = t2

fcσyc/4 andmpch = t2fchσych/4 perunit length, and

Fy-t = t2fcσyc{π + (2n + C − D′)/m} + t2

fchσych{4π}. (2)

Comparisonof Eqs. (1) and (2) shows thatthe failure behaviors of the column flange areidentical in the two mechanisms. Therefore,m, n, C, and D′ can be assigned easily interms of bolt size and location on the column flange. According to the provisions of ourdesign, channels are inserted such that thechannel flange edges coincide with the edge ofthe root fillet of the column flange. This condition should be provided to observe failuremechanisms for channel flanges that were explained previously. In practice, if it is difficultto provide an appropriate channel section in the case of stiffening with hot-rolled channels,then the contribution of circular hinge fields in the channel flange to the overall failuremechanism should be reduced while the column flange failure mechanism andm parameterin the formulae remain unchanged.


Fig. 7. Details of the specimen with 6 mm and 9 mm thick cold-formed channel stiffeners (T-6 and T-9).

2.2. Physical tests

Four tests were performed to determine the effects of channel stiffeners on the columnflange yield mechanism and common connection failure. The specimen group compriseda simple connection in which a T-stub was connected to a short length of column usingno stiffener (specimen T-N) and three T-stub to column connections stiffened with the hot-rolled (specimen T-C) and 6 mm thick (specimen T-6) and 9 mm thick (specimen T-9)cold-formed channels. T-stubs were manufactured using a 22 mm thick plate.Figs. 6–8show the test specimen dimensions.Fig. 8shows that a 4.5 mm thick filler plate is used forinstallation of the hot-rolled channel stiffener on one side and tapered plates are insertedbetween its inner surface and bolts to provide a sufficient contact. All specimens have22 mm diameter bolt-holes. The external radii of corners are 13 and 18 mm for the 6 mmplate and 9 mm plate cold-formed channels, respectively.

The actual dimensions of every test specimen were checked before tests. Ourmeasurements showed that variations from nominal thicknesses were permissible forcolumn and channel members. Actual lengths and widths were also nearly exact becausethe fabrication process used skilled workmanship and proper techniques. On the otherhand, we observed some cross-sectional variations that had occurred during installationof channels and tightening of the bolts in the test specimen with cold-formed channels.Even though these cross-sectional variations are small and limited to within the length ofcolumn along the connection, they can induce some internal stresses and secondary effects.


Fig. 8. Details ofthe specimen with hot-rolled channel stiffeners (T-C).

Variations in cold-formed channel cross-sections can also affect their support to the columnweb against compression loads in addition to the load transfer to them. Therefore, it isdeduced that filler plates should be used in stiffening, not only with hot-rolled, but also withcold-formed channels to provide a proper channel installation between column flanges. Ifappropriate filler plates of identical thickness are applied on both sides of every channelsymmetrically on both sidesof the column, such a configuration is expected to reducecross-sectional variations and prevent non-symmetrical effects. Use of similar detail alsosimplifies the erection process.

Table 1listsmaterial properties of components and results of some pilot standard tensiletests done to inspect material characteristics of channels and the column using couponsfrom components. Four grade-F10T M20 bolts pretensioned by 182 kN force were usedfor connection. The ultimate tensile load of a bolt is 245 kN.

For every testspecimen, yield loads were predicted using Eqs. (1) and (2) respectivelywith regard to failure mechanisms A and B. They are shown inTable 2. In calculation ofthe yield load for hot-rolled channels, the 8 mm thickness of the mid-point of the flangeleg isaccounted for astfch.

After each specimen was placed in a 2 MN capacity tensile testing machine, tensionloads were applied incrementally via T-stub webs. Only failure by yielding of the columnand channel flanges is considered to clarify the yielding behavior of the column flangeand the effects of channel stiffeners. For that reason, the tests were ended when plasticdeformations occurred in bolts; loading was continued until bolt extensions were observed.


Table 1Material properties

Component Material Yield stress Ultimate stress Elongation (%)(N/mm2) (N/mm2)

Column(H-150× 150× 7 × 10) SN400B 288 427 30.5Hot-rolled channel(C-125× 65× 6 × 8) SS400 328 451 27.0Plate: 6 mm SN400B 339 460 26.0Plate: 9 mm SN400B 305 446 29.5Plate: 22 mm SN490B 352 538 26.5

Table 2Predicted tensile yield loads

Test Stiffener Fy-t (kN) Fy-t (kN)for mechanism A for mechanism B

T-N – 259 259T-6 Plate: 6 mm 396 418T-9 Plate: 9 mm 528 570T-C C-125 488 523

Fig. 9. LVDT locations.

Relative displacements between two points on T-stub plates 70 mm away from the T-stubflange surface were measured using linearvariable displacement transformers (Fig. 9).The average of the measurements from these two transformers was taken into accountin drawing Ft –∆ diagrams. Some wire strain gauges were also used to check the straindistribution of the column web, channel webs, and T-stub webs.

Fig. 10 shows the load–displacement curves recordedin tests and the predicted yieldloads for each specimen using Eq. (1) for the failure mechanism A. It also depictsthe load–displacement curves for specimens T-N and T-9, which resulted from partialfinite element analysis (FEA), which is explained in the following section. Loading,displacement measurement andcollecting strain data using strain gauges from webs in theplastic range were continued after gradual yielding of the joint initiated in the column andchannel flanges. Although increasing loads were utilized, we intended to present gradual


Fig. 10. Load–displacement relationships for test specimens.

yielding instead of defining an exact yield point or an exact ultimate load accompanyingfailure of excessive deformations, cracking, orfracture, because plastic deformations thatoccur in the column or connections themselves are avoided in overall frame design as apractical matter.

Residual deformations were examined after separation of the tested connectionelements. Failure mechanism A and its combinations with mechanism B with increasingloads were observed in all tests.

2.3. Partial finite element analysis of the tension zone

Studies on beam-to-column end-plate connections have increasingly used finite elementsimulations because of the three-dimensional nature of the problem and the complexityof geometrical and material non-linearity. That complexity makes their numerical analysisquite onerous. Moreover, not all behavior characteristics of connection are readily availablefrom experiments. Therefore, using finite element simulations provides supplementary datafor elucidating the stress and the strain distributions. It also provides another alternative forchecking our experimental results.

Relevant papers of Bahaari and Sherbourne [8–10], Bursi and Jaspart [11,12], Yanget al. [13], and Harada et al. [14] were reviewed to establish an appropriate approachfor finite element simulation of connection. Here, partial 3D finite element models of thetension zone will also be adopted for non-linear structural FEA of T-N and T-9 specimensusing a simulation software package (ANSYS, Version 7.0) [15].

2.3.1. Modeling and element typesThe finite element mesh for the connection tension part of 1/8 is shown inFig. 11.

This part is assigned by considering the symmetries around all global axes to reduce thenumber of nodes. It is possible to use some higher order elements with mid-nodes forsome curved connection parts (like column fillet, channel curved corner, bolt head andshank, washer, and nut), but a 3D eight-node structural solid element named SOLID185in ANSYS was used to model all components. Higher solution accuracy was achieved bymesh refinements in predicted critical strain zones because the first order solid elementsare more suitable for plasticity type problems with discontinuities at the element edges.


Fig. 11. Finite element mesh of the tension zone.

Bolt, washer, and nut were modeled as one integrated component; threads were neglected.Considering the fact that they stay in close contact with their connecting plates throughall load steps, the continuity of mesh nodes was achieved using the Boolean operator— “glue”. Bolt and bolt-hole diameters were assumed as equal for node continuity, butinteraction between bolt and hole surfaceswas ignored. In the contact surfaces betweenend-plate, column flange and channel flange, contact conditions were defined accordingto the penalty technique using the elastic Coulomb friction coefficient (µ) of “0.45” andCONTA174 elements. Special pretensionelements, named PRETS179 in ANSYS, wereused to define a strain surface in the bolt shank.

2.3.2. Material propertiesElasto-plastic material models as regards coupon test results given inTable 1 were

defined for components. We used the modulus of elasticity of 205 000 MPa and Poisson’s


Fig. 12. Tension deformations in the channel flange.

ratio of 0.3. The tangential stiffness after the yield point was taken as 0.1% of the elasticitymodulus for plasticity based on the Von Mises–Hill yield criterion, the associative flowrule, and the rate-independent bilinear isotropic (work) hardening rule. Tangential stiffnessof the bolt material whose yield stress is 900 N/mm2 was defined as10% of the elasticitymodulus.

2.3.3. Loads and resultsBoundary conditions along the symmetry axis were defined as displacement values of

zero in three orthogonal planes. A uniformly distributed tension load was applied to thenodes on the end surface of the plate that represented the beam flange. In the first step ofthe solution, a pretension load of 182 kN was applied to the pretension surface in the boltshank by fixing the associated bolt nodes in space and using PRETS179 elements. Then, anon-linear large displacement static analysiswas performed for present load conditionsin the Newton–Raphson option with 100 loading steps. Load–displacement curves forspecimens T-N and T-9 generated from FEA are shown inFig. 10. Their agreementwith the physical test results demonstrates the efficiency of FEA in simulating actualT-stub behavior. Predicted yield loads derived from failure mechanism A are alsocompatible with the FEA results.Figs. 12 and 13 show the deformation contoursdetermined by nodal displacements on theY-axis for channel and column flanges at theend of loading. In these figures, deformations are magnified to 20 times their actual values.It is possible to clearly view proposed failure mechanisms for flanges.

3. Compression behavior

In a bolted beam-to-column connection, yielding is generally governed by the onset ofyielding in the tension zone. For that reason, attention was given to stiffening the tensionzone of connection. Nevertheless, to assume the tension yield strength as the limit for


Fig. 13. Tension deformations in the column flange.

the moment capacity of the connection, it should be proved that the yield load of thecompression zone is larger than that of the tension zone. The compression zone shouldhave sufficient strength to prevent member instability; in addition, distortions that inhibitthe rotation capacity should remain small.

Our studies and tests on compression zone behavior continue to examine local webbuckling and crippling as well as compression yielding. We anticipate a contribution ofchannel webs to resistance of the column web against compression forces. Nevertheless,until sufficient knowledge of individual compression components is obtained, channels’contributions can be ignored for conservative estimates and the compression yield strengthcan be predicted using some conventional formulas, such as LRFDs [16]:

Fy-c = (6k + N + 2tp)σywtwc (3)

wherek is the distance from the outer face of the flange to the web toe of the fillet,N is thebeam flange delivering the concentrated force plus two leg sizes of fillet welds or grooveweld reinforcement, andtp is the end-plate thickness. The yield stress and thickness of thecolumn web are respectively represented asσyw andtwc.

Nevertheless, in columns without transverse stiffeners, the compression component istransferred to the column web by a bearing at the bottom of the connection in relation togeometrical conditions, whereas the tension group of bolts carries the tension componentof the beam moment. Knowledge of the pressure distribution between the end-plate andcolumn flange is fundamental to connection design. This point will also be incorporatedinto the theoretical estimation of the connection yield moment.

4. Panel zone shear behavior

Panel zones of moment-resisting beam-to-column connections are subjected to mo-ments, axial forces and large shear forces, which can induce significant shear distortions.


Fig. 14. Panel zone of a moment connection with channel stiffeners.

This study applies a conventional model of web panel deformation with rectilinear edgesdepending on constant shear stress distribution to thecase with channel stiffeners. Thereby,we also examine channel web panel deformation. As shown inFig. 14, the panel zonebreadth of a channel,Bch-pa, is longer than the column’s,hc, if the open form of channelsis considered. This difference between breadths implies that the contribution of a chan-nel’s shear resistance to the column panelzone shear strength decreases because the ratiobetween panel zone shear strains of channels and column is inversely proportional to theratio between their breadths (Fig. 15). When the shear-yieldinglimit of joint is reached, thecolumn web panel starts yielding while the channel web panels remain elastic. Therefore,the panel zone shear strength of the connection is formulated as

Tpanel=(

twchc + 2hc

Bch-patwchBeff

ch-pa

)τyc (4)

where thevalue of( hcBch-pa

τyc) is smaller thanτych. The respective shear yield stresses ofthe column and channels areτyc andτych. The thickness of the channel web istwch.

An effective breadth,Beffch-pa, is defined for the channel web plane and the contribution

of channel flanges is ignored because the shear stresses along the channel flanges act inopposite directions. Furthermore, secondary effects depending on the eccentricity of thechannel cross-section also induce some loss of shear force transferred to channels from thecolumn.


Fig. 15. Panel zone shear behavior models.

Here, we assumed that bolts are sufficientlyreliable to provide shear transfer betweenthe column and channel flange surfaces. We further assumed that using the requiredwidth–thickness ratios for web plates prevents local buckling of channel webs.

5. Overall connection strength

This section is intended to show a derivation of theoverall connection strength usingsome simplifiedanalytical evaluations for beam-to-column connection samples with andwithout stiffeners, which will also be analyzed by FEM later (Fig. 16).

Although compression zone studies are still in progress to inspect instabilitycharacteristics, we performed some strength evaluations for beam-to-column connectionswithout stiffeners and with 9 mm thick cold-formed channel stiffeners as depending on thetension yield load, compressionyield load, and critical shear load. We combined themto assess the overall moment behavior of the connection. Thereby, we produced somepredictions regarding strength that are useful for comparing FEA results.

5.1. Theoretical yield moment of connection

Most studies of end-plate connections have assumed that a couple whose forces actat beam flange level can replace the beam moment. Two simple T-stubs are adopted tosimulate the connection tension and compression zones. Using the minimum yield load,Fy, observed from tension or compression zone strength evaluations, the theoretical yieldmoment of the beam-to-column connection,My, can be estimated as

My = Fyd, (5)

whered is distance between the couple forces. This distance varies from the distancebetween centroids of the top and bottom beam flanges,df , as shown inFig. 3(a), to thedistance from the outer row of tension bolts to the compression edge of the end-plate,as related to the pressure distribution. When we consider our overall connection samples,which will be presented later, it is possible to assume that the rigid end-plate remains planarwhile it rotates. Thus,d is evaluated by considering a triangular stress distribution in thecompression zone and bolts’ tensile forces using Bernoulli–Navier assumptions.


Fig. 16. Beam-to-column connection stiffened with channels.

Connection yield moment values derived from Eq. (5) according to the tension(My-t ) and compression(My-c), and the shear yield (My-sh) moment are marked inFig. 17. Here it should be reiterated that the contributions of channel stiffeners to thecompression strength are ignored in evaluations because of the lack of informationabout the compression zone. In other words,My-c in Fig. 17 uses only the compressionstrength of the column web. Therefore, it is very small compared to the yield momentobserved in FEA of the channel-stiffened specimen. The increase of the yield momentin the stif fened specimen case indicates that channel stiffeners support the column webin the compression zone of the connection. If further strength improvements are needed,doubler plates can also be provided for compression zones in cooperation with channelstiffeners.

5.2. Finite element modeling of the overall connection

A simple frame joint like that shown inFig. 16 was examined to elucidate the overallbehavior of the beam-to-column connection stif fened with channels. A 1500 mm longcantilever beam connects to a 1800 mm long simple supported column at its mid-span. TheP vertical load acts at the beam end. A sample of a connection with 9 mmthick cold-formed channel stiffeners and an unstiffened connection were examined for


Fig. 17. Moment–rotation relationships and theoretical moment capacities.

Fig. 18. Moment–shear strain relationships.

comparison. The beam and end-plate were defined as rigid rectangular prismatic solids tosuppress their plastic deformations and to reveal channel utility by focusing on the columnresponse.

5.2.1. Modeling, element types and material propertiesConsidering a symmetry plane,Y–Z, only half of the frame was modeled. Here it is

notable that this modeling restrains occurrences of instability, such as web crippling and


Fig. 19. Web shear strains of an unstiffened column at state A.

buckling, to the compression zone of connection. It also leads to increased deformationcapacity of this zone. The total number of nodes was 30 478, although only half of theframe was modeled. As in partial modeling, a 3D eight-node structural solid elementnamed SOLID185 in ANSYS was used to model all components. A coarser mesh wasgenerated for parts other than critical zones such as distant column parts. The materialproperties were identical to the material properties that were used for partial FEA of thetension zone.

5.2.2. Loads and resultsNon-linear large displacement static analysiswas performed for the system preloaded

with bolt pretensions. TheP load was applied in 50 loading steps. Post-processing basedon the nodal output generated the relationships between the beam end moment and end-plate rotation for stiffened and unstiffened models. For comparison, those relationshipsare given inFig. 17 along with theoretical moment capacities. Theoretical yield momentsreferring to tension and panel zone shear indicate good agreement with relationshipcurves.

Fig. 18 shows moment–shear strain diagramsfor unstiffened and stiffened jointsamples. It shows the comparison of columnand channel panel zone shear behaviors asregards shear strains measured from the centers of panel zones. Inspection of these curvesreveals that the contribution of channel webs to panel zone shear behavior of the connectionremainslimited. This situation is explained as a result of the force losses depending


Fig. 20. Web shear strains in a column with a channel: 9 mm stiffeners at state B.

on the channel shape properties and localization of channels in the whole cross-sectionlayout.

Figs. 19–21show distributions of shear strains in the column web panel for the states A,B, and Cas indicated in the diagrams. Deformations in these figuresare magnified to tentimes their actual value. Channel web elements are not shown inFigs. 20and21 to allowa view of the strain distributions on the column web. Inspection of the figures shows thatthe useof channel stiffeners reduces the shear strains in the column web. As regards nodaldisplacements in theY-axis, overall joint deformations at the end of loading are shown inFig. 22 for the bolted end-plate connection stiffened with a 9 mm channel. In this figure,the rigid end-plate and beam are made invisible again to check the column flange behavior.Deformations in the column stiffened with channels remain considerably smaller for higherload values in comparison to the unstiffened case.

6. Conclusions

This study utilized finite element simulations to examine the strength of steel beam-to-column connections stiffened with bolted channels.

By assuming T-stub idealization, yield tensile loads evaluated from the proposed failuremechanisms were compared toload–displacement curves that were generated from test and


Fig. 21. Web shear strains in a column with a channel: 9 mm stiffeners at state C.

FEA results. Failure mechanism A, based on the yield line theory, gives good, reasonable,and conservative estimates of the yield load for all tests. Tensile yield loads predicted andobtained from tests indicate that stiffening with channels improves the yield strength ofthe specimen without stiffeners by 53%–104% as related to the channel stiffener thickness.Similarities of FEA load–displacement curves to experimental curves emphasize the abilityof three-dimensional non-linear FEA to simulate actual physical conditions for bolted end-plate connections.

The overall connection was simulated to investigate beam-to-column connectionbehavior because not all connection behavior characteristics are readily availablefrom experimentation. Yield moments estimated by simplified theoretical methods thatincorporate column flange tension yielding failure and column web shear failures arecompatible with yield moments observed from moment–rotation curves of the FEA.Inspection of them shows that, if the column is unstiffened, prior occurrence of the columnweb shear mechanism prevents column flanges from exhibiting their actual strength. Forthat reason, stiffeners are also required to prevent panel zone failures. This inferenceemphasizes the importance of the contribution of channel webs to column web shearstrength.

Although the present study excludes instability characteristics in the compressionzone, the method of stiffening with channels is found to be satisfactory for simultaneous


Fig. 22. Joint deformations of a column with a channel: 9 mm stiffeners at state C.

strengthening of the column web against shear forces and flanges against tension forces.The contribution of channels to the compression zone requires further study, which willprovide complete information regarding the connection design with channel stiffeners.

Acknowledgement

This study was partly supported by a Grant-in-Aid for Scientific Research (No.16760450) from The Ministry of Education, Culture, Sports, Science and Technology ofJapan.

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application of steel channels as stiffeners

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