Amin Mohebkhah Et Al_2014_Elsevier_Overstrength and Rotation Capacity for EBF Links

Overstrength and rotation capacity for EBF links madeof European IPE sections

Amin Mohebkhah a,n, Behrouz Chegeni b

a Structural Engineering Division, Faculty of Civil and Architectural Engineering, University of Malayer, Malayer, Iranb Young Researchers Club, Khorramabad Branch, Islamic Azad University, Khorramabad, Iran

a r t i c l e i n f o

Article history:Received 2 June 2012Received in revised form4 October 2013Accepted 16 October 2013

Keywords:OverstrengthInelastic rotation capacityEccentrically braced frameLink beamIPE section

a b s t r a c t

Overstrength factor and inelastic rotation capacity are the key parameters in eccentrically braced frames(EBFs) design which may affect signicantly the design economy or safety. The overstrength factor givenin the 2005 AISC Seismic Provisions is based on the previous tests on wide-ange link beams commonlyused in the united states. Despite the extensive research conducted on EBFs link beams, it is not knownwhether the overstrength factor given by the Provisions can be used for the design of EBFs having IPE linkbeams. In this paper a three dimensional nite-element model using ABAQUS is developed for theinelastic nonlinear analysis of IPE link beams. The model is used to investigate the applicability of theoverstrength factor and inelastic rotation capacity given by the Provisions to design of EBFs with IPE linkbeams. It was found that the strain hardening overstrength factor of short link beams made of EuropeanIPE sections with closely spaced stiffeners is greater than the Provisions' factor. Therefore, using theProvisions' overstrength factor may lead to unconservatie design of EBFs having such links. However, theoverstrength factor given by the Provisions can be used conservatively to design EBFs with intermediateand long IPE links. Also, it was shown that links made of IPE sections can sustain much larger rotationsthan the rotations required by the Provisions.

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1. Introduction

The concept of eccentrically braced frame (EBF) was proposed inthe late 1970s and developed later by Popov and his co-workers ([16]among the others) at the University of California, Berkeley (UCB). Tohave a ductile EBF, plastic hinges must be formed in the specicallydesigned ductile link beams while the other adjoining members (i.e.braces, columns and beam outside of the link) remain in elastic range.In other words, the links in an EBF must act as structural fuses anddissipate earthquake-induced energy in a stable manner. To achievethis, based on the capacity design concept the adjacent members which are presumed to be brittle and elastic must be designed tohave strength in excess of the maximum shear capacity of the linkbeams. The main reason of considering this excessive shear capacity isto account for the normal uncertainties of material strength andstrain-hardening effects at high strains [7]. Under-prediction of themaximum link shear capacity can lead to the premature failure of theadjoining members intended to remain elastic under severe earth-quake loads. Therefore, according to the 2005 AISC Seismic Provisions[8] and also the fact that link beams develop larger shear strength than

nominal shear strength (Vn) (due to strain hardening and materialuncertainties), the maximum shear capacity of link beams (Vu) can beestimated as follows:

Vu ORyVn 1in which, is the overstrength due to strain hardening. Values of 1.25and 1.1 have been given for in the Seismic Privisions [8] for thedesign of brace and beam outside link (also for columns), respectively.Ry factor (material overstrength) adjusts the nominal plastic shearcapacity (Vn) to the actual capacity which is the ratio of expected yieldstrength to the minimum specied yield strength. Vn is computed as thelesser of Vp or 2Mp/e as per the AISC Seismic Provisions [8]. Theproposed value of in the Seismic Privisions for brace design istraditionally based on the experiments conducted at the UCB in the1980s on rolled wide-ange Links. However, it is less than the factor of1.5 proposed by Popov and Engelhardt [9] for a number of reasonsincluding [8]: (1) the use of Ry in the link but not in the brace, and(2) the use of resistance factors when computing the strength ofthe brace.

Arce [10] conducted a test program to investigate the cyclicbehavior of wide-ange links constructed of A992 steel in seismicresistant EBFs using the old-AISC loading protocol specied in the2002 AISC Seismic Provisions [11]. The results of these tests showedthat, the average strain hardening overstrength () of the sectionswas 1.28 with a variation from 1.17 to 1.44 [10]. The experiments

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n Corresponding author. Tel.: 98 851 2232346; fax: 98 851 2221977.E-mail addresses: [email protected], [email protected]

(A. Mohebkhah), [email protected] (B. Chegeni).

Thin-Walled Structures 74 (2014) 255260

performed by Itani et al. [12] indicated that higher strain hard-ening overstrength factor of about 2.1 may be observed for built-up shear links with heavy anges. However, Richards [13] arguedthat overstrength factor much beyond the ratio Fu/Fy does notseem to be merely due to strain hardening and it may also beattributed to the anges shear resistance and existing axial forces inthe link beams because of boundary conditions applied to the testspecimens.

Richards and Uang [14] developed and veried a nite elementmodel to investigate the inuence of the ange width-to-thicknessratio on the rotation capacity of wide-ange links in EBFs. Theyfound that under the 2002 AISC Seismic Provisions [11] cyclicloading protocol, many of the intermediate link beams do notachieve the design inelastic rotation capacity predicted by theprovisions.

Knowing the signicant effects of loading protocol on linkbeams behavior, Okazaki et al. [15] conducted an experimentalinvestigation to reevaluate overstrength factors for EBF rolledwide-ange links constructed of A992 steel using a revisedprotocol developed and proposed by Richards and Uang [16].The results of these tests showed that, the assumed overstrengthof 1.5 in the 2002 AISC Seismic Provisions is reasonable, andperhaps somewhat conservative for longer links. Barecchia et al.[17] investigated the overstrength of European hot-rolled steelproles (including IPE, HE series) with no web stiffeners using anumerical nite element modeling. They found that for short andintermediate IPE links with axial restraints, the overstrength factorunder monotonic loading is equal to 1.6 and 2.0 for sheardeformation angles of 0.1 and 0.2 rad, respectively. Della Corteet al. [18] investigated the plastic shear strength of stiffened andunstiffened short links with axial restraints using nonlinear FEanalysis. The results showed that, unstiffened shear links made ofEuropean hot-rolled shapes may be subjected to strength andstiffness degradation under cyclic loading even in the case ofaxially restrained boundary conditions [18]. They also concludedthat the axial force effect on the link response is considerablewhen the link is subjected to large rotation demand. Della Corteet al. [19,20] also studied the effects of tensile axial forces inducedby the presence of axial restraints (boundary conditions) andgeometric nonlinearity on the plastic overstrength of short linksmade of European shapes using nonlinear FE analysis. They foundthat for stiffened links made of European IPE shapes with orwithout axial restraint, the hysteresis loops are stable in the rangeof inelastic rotation of 70.08 rad and hence, their ultimate shearcapacity can be estimated by monotonic analysis [20]. They alsoassuming an elastic-perfectly plastic model for steel, proposed asimple analytical equation based on the FE analyses to estimatethe plastic overstrength of short links at inelastic rotation of0.08 rad.

Daneshmand and Hosseini Hashemi [21] studied the generalbehavior of intermediate and long links made of European IPE andbuilt-up sections using nonlinear FE analysis. The main purpose ofthe paper was to investigate the impact of parameters such asstiffener spacing and geometric properties of the link beams on

the their inelastic rotation capacity. They found that the links inthe controversial region (i.e. links with 1:8oo2:2) may notsatisfy the provisons on inelastic rotation capacity unless someadditional requirements mentioned in the paper are utilized [21].

Based on the abovementioned literature review, it can beconcluded that the link overstrength factor depends on thefollowing factors:

(1) Flange-web area ratio [12,1820] or shear resistance ofanges [13].

(2) link beam length ratio [15,18].(3) loading protocol [15,22,16], and(4) presence of axial forces due to boundary axial restraints

[13,1820].

Despite the aforementioned studies, the overstrength factors(, Ry) of EBF links made of European hot-rolled IPE sections withdifferent lengths has not been investigated. On the other hand,most of the design rules given in the AISC Seismic Provisions for EBFlinks are based on the results of tests performed on Americanwide-ange link beams by Popov and his students at the UCB.Therefore, the applicability of current seismic provisions should beexamined and validated to be used for IPE link beams.

The purpose of this paper is to investigate the overstrengthfactors and inelastic rotation capacity of EBF links made of hot-rolled IPE sections which are commonly used in Iran for low-riseEBFs. For this purpose a nite-element model based on thecommercial software package ABAQUS [23] is developed for thenonlinear analysis of IPE link beams with a wide variety of span-length (i.e. short, intermediate and long links). Then, it is used toinvestigate the applicability of the 2005 AISC Seismic Provisions [8]to design of EBFs having IPE link beams.

2. Nonlinear nite-element model

To investigate the inelastic behavior of IPE link beams, anonlinear inelastic nite-element model is developed based onthe specications and assumptions given in the following sections.

2.1. Mesh and material properties

The nonlinear computations were performed using the com-mercial nite element software package ABAQUS [23]. ABAQUS[23] has the ability to consider both geometric and materialnonlinearities in a given model. Large displacement effects wereaccounted for by utilizing the nonlinear geometry option inABAQUS. A 4-node doubly curved shell element with reducedintegration S4R [23] from the ABAQUS element library were usedto model the web, anges and the intermediate stiffeners.

The S4R element is suitable for complex plastic bucklingbehavior and has six degrees of freedom per node and providesaccurate solutions to most relevant applications. Flanges were

Nomenclature

Aw link section web areae link beam lengthFy yield stress of steelFu ultimate stress of steelMp section plastic moment capacityFyZRy material overstrength factor

Vn section nominal shear capacityVp0.6 FyAwVu section maximum shear capacity link rotation angle (ratio of the relative displacement

of the ends of the link to the length of the link)p link inelastic rotation capacitye link elastic rotation capacity strain hardening overstrength factor length ratio

A. Mohebkhah, B. Chegeni / Thin-Walled Structures 74 (2014) 255260256

modeled with 6 elements across the width and 10 elements wereused throughout the web height.

The steel is modeled as a J2 material with nonlinear kine-matic hardening and a trilinear stress-strain curve as given in Gioncuand Mazzolani [24] is assumed. In the stressstrain curve, a typicalvalue for the modulus of elasticity (E204,000 MPa) is considered.Nominal yield stress (Fy) and ultimate stress (Fu) values of steel S235are specied as of 235 and 360 MPa, respectively. It should be notedthat the effects of residual stresses and low-cycle fatigue (brittlefailure mode) were not considered in this work.

2.2. Boundary conditions, cyclic loading and solution procedure

Since in this study the behavior of isolated link beams isinvestigated, boundary conditions are the same as proposed byRichard and Uang [14]. As can be seen in Fig. 1, nodes on the leftend were restrained against all degrees of freedom except hor-izontal translation. However, nodes on the right end wererestrained against all degrees of freedom except vertical transla-tion. Loads were applied as displacement-controlled on the rightend nodes.

Full cyclic analysis is necessary in this study to consider theeffects of local buckling and associated strength degradation.The link loading protocol in Appendix S of the 2005 AISC SeismicProvisions [8] was used for the study. Link rotation was denedas the imposed transverse displacement divided by the linklength.

3. Validation of the modeling technique

In this part, the accuracy of the nite element model of the linkbeams was investigated. The model was developed to predict theperformance of two links tested at the Univ. of California, Berkeley(UCB) by Hjelmstad and Popov [4] and two A992 rolled shape linksrecently tested at the Univ. of Texas, Austin (UTA) by Arce [10].Boundary conditions, loading, material properties and otherdetails on modeling were the same as experimental conditions.Table 1 shows a comparison between maximum shear capacityobtained from the tests and the nite element analysis for all thespecimens. It can be seen that, the agreement between experi-mental and numerical results is satisfactory with a maximum errorof 5% for specimen UCB14. Fig. 2 compares the deformed geometryand hysteresis of the experimental specimen and the modelfor UTA 9.

4. Parametric study

After validating the nite element model, a nonlinear analysiswas performed looking at the strain hardening overstrength androtation capacity of IPE link beams. Owing to the fact that theoverstrength factor for IPE series sections is constant for a targetshear deformation angle [17] (i.e. it does not depend on thecross-section depth of the section), only IPE270 section which iscommonly used in low-rise EBFs links in Iran is taken into accountin the present study. The link beam lengths were chosen torepresent a wide spectrum of behavioral zones. This section looksat overstrength due to strain hardening and inelastic rotationcapacity for IPE links.

According to the AISC 341-05 Seismic Provisions [8] (Sec. 15.3.a), links of lengths 1.6Mp/Vp or less (short links) shall be providedwith intermediate web stiffeners spaced at intervals not exceeding(30twd/5) for a link rotation angle of 0.08 rad or (52twd/5)for link rotation angles of 0.02 rad or less. Intermediate linksshould also meet these stiffeners requirements correspondingto the upper-bound and lower bound rotation angles. However,these are not required for long links. Therefore, in order to investi-gate the effect of web stiffeners' spacing on the strain harden-ing overstrength factor and rotation capacity of IPE links,36 links were modeled and analyzed under the 2005 AISC SeismicProvisions [8] cyclic loading protocol in two categories:

(1) A number of 21 short, intermediate and long IPE links withclosely spaced stiffeners required to reach the target rotationangle of 0.08 rad. (as per Table 2) and

(2) a number of 15 Short and intermediate IPE links with sparselyspaced stiffeners required to reach the target rotation angle of0.02 rad (as per Table 3).

Tables 2 and 3 list key characteristics, calculated strain hard-ening overstrength () and inelastic rotation capacity for each ofthe links analyzed in this study. Inelastic rotation capacity of thelinks is calculated as follows:

p uein which u and e are the ultimate and elastic rotation capacities,respectively. The ultimate inelastic rotation capacity was denedas the point where the hysteresis curve reduced below 80% of theultimate shear capacity as proposed in Richards and Uang [14].

5. Discussion of the results

5.1. Overstrength factor for IPE links with closely spaced stiffeners

As can be seen in Table 2, the strain hardening overstrengthfactor () calculated from nite element analyses is in a range ofabout 1.531.77 (average 1.60) for short links, about 1.291.46(average 1.37) for intermediate and 1.391.41 (average 1.40) forlong links. As it was pointed out earlier in Section 1, the over-strength factors given in the 2005 AISC Seismic Provisions [8] are

Fig. 1. FEM model boundary conditions applied to the links: (a) initial congura-tion and (b) deformed conguration (as per Ref. [14]).

Table 1Comparison of experimental and nite element analysis maximum shearcapacities.

Specimen Section e (in) e=Mp=Vp VuEXP(kip) VuFEM(kip) Difference%

UCB 4 W1840 28 1.16 207 208 0UCB 14 W1835 36 1.91 184 193 5UTA 7 W1033 73 3.4 73 72 1UTA 9 W1636 48 2 173 172 0

A. Mohebkhah, B. Chegeni / Thin-Walled Structures 74 (2014) 255260 257

based on an assumed overstrength factor of 1.5 obtained in theprevious experiments. Therefore, the obtained overstrength factorsusing FEA in this study indicate that the assumed overstrength in

the Provisions is unconservative for short IPE links with closelyspaced stiffeners and may lead to unsafe design of EBFs. However,the AISC assumed overstrength factor is conservative for intermedi-ate and long IPE links' design. The observed high strain hardeningoverstrength for short IPE links in relation to wide-ange links maybe attributed to the high compactness of their constituent plates(anges and web plates with low local slenderness). In fact,European hot-rolled IPE beams are seismically compact sectionsand there would be no severe plastic local web or ange bucklingprior to the achievement of fully plastic shear capacity at relativelyhigh rotation angles. Also, it can be seen that, the overstrength factordecreases as the length ratio increases for short and intermediatelinks and then increases a little for long links again. Similar over-strength variation reported previously by other researchers [10] forwide-ange links. The lower value obtained for intermediate linkshas been attributed to shearmoment interaction [25]. Therefore,it seems that the overstrength factor for link beams should bemodied as a function of length ratio.

-250-200-150-100-50

050

100150200250

-0.1 -0.075 -0.05 -0.025 0 0.025 0.05 0.075 0.1

Lin

k Sh

ear

(Kip

s)gp(rad)

Fig. 2. Deformed geometry and hysteresis curve foe specimen UTA9: (a) test [10] and (b) FEM analysis.

Table 2Overstrength and rotation capacity of the analyzed link beam models withintermediate web stiffeners spaced at intervals (30tWd/5).

ModelNo.

Linklength e(mm)

Length ratio e=Mp=Vp

Intermediatestiffeners

Vu/Vn

p(rad)

Short 1 270 0.58 1@ 135 mm 1.6 0.192 326 0.7 2@ 109 mm 1.77 0.173 373 0.8 2@ 124 mm 1.59 0.174 419 0.9 2@ 140 mm 1.55 0.175 500 1.07 3@ 125 mm 1.65 0.176 559 1.2 3@ 140 mm 1.53 0.177 652 1.4 4@ 130 mm 1.59 0.158 745 1.6 5@ 124 mm 1.55 0.15

Intermediate 9 792 1.7 5@ 132 mm 1.46 0.1310 838 1.8 5@ 140 mm 1.41 0.1311 885 1.9 6@ 126 mm 1.41 0.1312 932 2 6@ 133 mm 1.29 0.1313 1000 2.15 6@ 143 mm 1.32 0.1314 1071 2.3 7@ 134 mm 1.35 0.1315 1118 2.4 7@ 140 mm 1.36 0.11

Long 16 1258 2.7 203 mmfrom eachend

1.39 0.09

17 1365 2.93 203 mmfrom eachend

1.4 0.09


1.41 0.09


1.41 0.09


1.4 0.05


1.41 0.04

Table 3Overstrength and rotation capacity of the analyzed link beam models withintermediate web stiffeners spaced at intervals (52tWd/5).

Modelno.

Linklength e(mm)

Length ratio e=Mp=Vp

Intermediatestiffeners

Vu=Vn p(rad)

Short 1 270 0.58 1.31 0.192 326 0.7 1@ 163 mm 1.48 0.173 373 0.8 1@ 186 mm 1.4 0.174 419 0.9 1@ 210 mm 1.37 0.175 500 1.07 1@ 250 mm 1.33 0.176 559 1.2 1@ 280 mm 1.32 0.177 652 1.4 2@ 217 mm 1.34 0.158 745 1.6 2@ 248 mm 1.31 0.15

Intermediate 9 792 1.7 2@ 264 mm 1.3 0.1310 838 1.8 2@ 280 mm 1.3 0.1311 885 1.9 3@ 221 mm 1.3 0.1312 932 2 3@ 233 mm 1.27 0.1313 1000 2.15 3@ 250 mm 1.32 0.1314 1071 2.3 3@ 268 mm 1.34 0.1315 1118 2.4 3@ 280 mm 1.34 0.11


5.2. Overstrength factor for IPE links with sparsely spaced stiffeners

According to Table 3, it is observed that increasing intermediatestiffeners' spacing to achieve the target rotation angle of 0.02 rad,signicantly affects the overstrength factor. The overstrengthfactor for these models is in a range of about 1.311.48 (average1.39) for short links and 1.271.34 (average 1.30) for intermediatelinks. Therefore, it can be concluded that the assumed over-strength in the Provisions is conservative for IPE links with sparselyspaced stiffeners and leads to a safe design. These ndings showthat, the overstrength factor is a function of not only length ratiobut also web stiffeners' spacing. Variation of the inelastic rotationangle versus shear hysteresis loops for the model No. 5 in Table 3 isshown in Fig. 3. As can be seen, this link which has even oneintermediate stiffener experiences plastic local web buckling atinelastic rotation of 0.02 rad degrading to some extent the linkshear strength. Therefore, even if the IPE link sections areseismically compact; they are prone to minor shear strengthdegradation due to plastic local buckling.

5.3. Inelastic rotation capacity

According to Tables 2 and 3, it can be seen that all of theanalyzed link models can achieve well inelastic rotation capacitiesmuch larger than the rotations required by the Provisions. This wellbehavior can also be attributed to the high compactness of thesection that prevents severe plastic local web buckling. However, itshould be mentioned that these rotations may not be consideredas the actual rotation capacity of IPE link beams. This is because,the nite element models do not predict material failures andfracture such as high-cycle fatigue which generally occur inlaboratory tests and result in loss of strength and consequentlylow rotation capacity. Therefore, these obtained rotation capacitiesshould be validated through some experimental tests on IPE links.

It can also be seen that, even the links with the least inter-mediate stiffeners (Table 3) and relatively low overstrength factorscan sustain much larger rotations than the rotations required by theProvisions. Hence, it appears that stiffeners requirements can berelaxed for IPE links. In other words, it seems that providing IPE

links with the least stiffeners required by the Provisions exhibitinglow overstrength factor may lead to economic design of EBFs.Therefore, more numerical and experimental studies are needed tohave a reliable conclusion on the relaxation of stiffeners require-ments for IPE links. This is the subject of an ongoing research atMalayer University by the authors.

6. Overstrength factors proposal

As it was observed in the previous section, starin hardeningoverstrength factor () of IPE link beams depends on their lengthand stiffeners spacing. The overstrength factor tends to be max-imum for short links. To propose a reliable strain hardeningoverstrength factor for IPE links in different behavioral zones (i.e.for short, intermediate and long links), more comprehensiveresearch has to be conducted. Furthermore, a proposal of anoverstrength factor should take into account the inuence of theadjoining members (beam, brace, slab effect etc.) as per the SeismicProvisions [8] and hence, link beam should not be treated as anisolated element. Although it is possible to provide differentstrain-hardening factors for short, intermediate and long IPE links,however, due to the limited number of link beams studied herein,just a strain hardening overstrength factor is proposed for suchlinks with different length.

According to the obtained results in this paper, the strainhardening overstrength factors given in the Provisions (i.e. 1.25for brace and 1.1 for other adjoining members) are suggested to beused conservatively for IPE links except the short links with closelyspaced stiffeners (i.e. required stiffeners to achieve the targetrotation angle of 0.08 rad as per the Provisions). For the shortlinks with closely spaced stiffeners, it is suggested to increase theoverstrength factors given in the Seismic Provisions [8] by 10% tohave a safe design.

As described earlier, the material overstrength factor (Ry) is theother factor needed to estimate the maximum expected shearcapacity of link beams. This factor is determined by testing con-ducted in accordance with the requirements for the specied gradeof steel [8]. However, the factor should be monitored periodicallybecause it depends on the quality of steel production practice ineach country. Although, the steel S235 is widely used in Iran,however, there are no comprehensive material tests on its mechan-ical characteristics. To have a rough data on the statistical character-istics of the steel S235, the comprehensive material tests datapresented by Melcher et al. [26] on the steels S235 and S355produced in the Czech Republic can be used herein. Based on the562 observations, the mean value and standard deviation of thesteel S235 yield strength have been reported [26] as 297.3 and16.8 MPa, respectively. Therefore, it seems that a material over-strength factor of 1.3 is reasonable for the steel S235. However,separate material tests must be conducted in each country to reach areliable material overstrength factor.

7. Conclusions

The nonlinear analysis of EBFs links made of hot-rolled IPEsections with a wide spectrum of length ratio were studied bymeans of the nite element method. The main aim was toinvestigate the effect of link beam section type on the overstrengthand inelastic rotation capacity of EBFs links. It was found that, thestrain hardening overstrength factor given by the 2005 AISC SeismicProvisions is unconservative for the design of EBFs having short IPElinks with closely spaced stiffeners and it should be increasedby about 10% to have s safe design. However, the Provisionsoverstrength factor can be used conservatively for other IPE links.

-350

-250

-150

-50

50

150

250

350

-0.16 -0.12 -0.08 -0.04 0.00 0.04 0.08 0.12 0.16

Fig. 3. (a) Deformed geometry and (b) variation of shear capacity versus inelasticrotation angle for the model No. 5 in Table 3.

A. Mohebkhah, B. Chegeni / Thin-Walled Structures 74 (2014) 255260 259

Furthermore, it was observed that IPE link beams can achieveinelastic rotation capacities much larger than the rotations requiredby the Provisions. However, owing to ignoring the effect of materialfailures (e.g. low-cycle fatigue) in nite element modeling, theobserved high rotation capacities are not yet conclusive and furtherexperimental studies must be carried out to validate the results.

Acknowledgments

The authors are grateful to enormous help of Professor M.D.Engelhardt in providing documents regarding this research.Reviewers provided helpful suggestions that signicantlyimproved the paper. Their contribution is appreciated by theauthors.

References

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[10] Arce G. Impact of higher strength steels on local buckling and overstrength oflinks in eccentrically braced frames. [Masters thesis]. Austin, Texas: Univ.Texas; 2002.

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[12] A Itani, BM Douglas S El-Fass. Cyclic behavior of shear links in retrottedRichmond-San Rafael Bridge towers. In: Proceedings of the 1st world congresson structural engineering, San Francisco. Paper No. T155-3, New York: Else-vier; 1998.

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Overstrength and rotation capacity for EBF links made of European IPE sectionsIntroductionNonlinear finite-element modelMesh and material propertiesBoundary conditions, cyclic loading and solution procedure

Validation of the modeling techniqueParametric studyDiscussion of the resultsOverstrength factor for IPE links with closely spaced stiffenersOverstrength factor for IPE links with sparsely spaced stiffenersInelastic rotation capacity

Overstrength factors proposalConclusionsAcknowledgmentsReferences

Documents

Amin Mohebkhah Et Al_2014_Elsevier_Overstrength and Rotation Capacity for EBF Links