Engineering Structures 91 (2015) 182–196

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Engineering Structures

journal homepage: www.elsevier .com/locate /engstruct

Numerical simulation for seismic performance evaluation of fibrereinforced concrete beam–column sub-assemblages

http://dx.doi.org/10.1016/j.engstruct.2015.02.0150141-0296/� 2015 Elsevier Ltd. All rights reserved.

⇑ Corresponding authors at: Institute for Lightweight Structures and ConceptualDesign, Universitaet Stuttgart, Pfaffenwaldring 7, 70569 Stuttgart, Germany. Tel.:+49 711 6856 6227; fax: +49 711 6856 6968 (C. Roehm).

E-mail addresses: constanze.roehm@gmx.de (C. Roehm), sasmalsap@gmail.com(S. Sasmal).

Constanze Roehm a,⇑, Saptarshi Sasmal b,⇑, Balthasar Novák a, Ramanjaneyulu Karusala b

a ILEK, Universitaet Stuttgart, Germanyb CSIR-Structural Engineering Research Centre, CSIR Campus, Taramani, Chennai 600113, India

a r t i c l e i n f o a b s t r a c t

Article history:Received 20 March 2014Revised 11 February 2015Accepted 12 February 2015Available online 21 March 2015

Keywords:Beam–column sub-assemblageSteel fibre reinforced concreteCyclic loadingMaterial modelingNumerical analysisJoint shear strength

In the present study, performance of exterior beam–column sub-assemblages designed using normalconcrete (NC) and steel fibre reinforced concrete (SFRC) is investigated. Nonlinear finite element methodis adopted to analyse the sub-assemblages under reverse cyclic loading. To suit the material models forSFRC, available concrete model is judiciously modified. Cyclic behaviour of reinforcement, concrete (bothnormal and fibre reinforced) modeling based on fracture energy, bond–slip relations between concreteand steel reinforcement have been incorporated. The study also includes numerical investigation of crackand failure patterns, ultimate load carrying capacity, strain comparisons and formation of plastic hinges,load displacement hysteresis, energy dissipation and ductility. Experimentally validated numericalmodels are used to study the influence of various parameters on the performance of the beam–columnsub-assemblage. Results obtained from experimental investigation were used for numerical validation.The influence of several parameters such as concrete strength, number of stirrups in the joint and amountof steel fibres on joint shear behaviour and strength of beam–column sub-assemblages are investigated. Itis found that the failure mode cannot be favourably changed by adding fibres, if the compressive strengthof the matrix is too low. It is also observed that the influence of fibre contribution to improve the residualtensile strength and fracture energy is significant and inter-dependent. Further, increase in residual ten-sile strength of FRC is found to be linear with increase in joint shear strength. In the present study,relationship for strength degradation depending on joint shear deformation for FRC has been established.

� 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Till recently, numerous earthquakes have caused severe damageor have led to collapse of many structures. Seismic performance ofthe old structures is extremely alarming. As a consequence, designprovisions of different standards are stipulated to use large amountof reinforcement in disturbed regions (D-regions) of newly builtstructures to attain the required level of ductility insure requiredstructural performance against earthquakes. For instance, beam–column sub-assemblages which are treated as one of the most cru-cial structural components during earthquake, are required to havevery high stirrup reinforcement ratio in the joint region to provideadequate confinement and ductility. On one hand, congestion ofreinforcement in joint region brings the difficulty in concrete

compaction at site and on the other hand, large diameter and higherpercentage of reinforcement bars in beams are difficult to be ade-quately anchored within slender column widths. Therefore, theapplication of steel fibre reinforced concrete (SFRC) could be oneof the promising alternatives to avoid reinforcement congestion injoint region for confinement and therefore, has the potential tofacilitate smooth construction and desired performance under cyc-lic loading. Further, joint strength, energy dissipation and jointintegrity could be improved by taking advantage of confining effectand enhanced mechanical properties provided by fibres. Hence, it isutmost important to evaluate the performance of the beam–columnsub-assemblages constructed using normal concrete (NC) and steelfibre reinforced concrete (SFRC), and to find out realistic models(geometric- and material-models, bond–slip, etc. along with othercomputational issues) for further studies.

Few investigations were carried out for evaluating the perfor-mance of beam–column subassemblages using FRC. Henageret al. [1] conducted experimental investigations on concrete jointusing fibre reinforced concrete and it was aimed to minimizeunwanted steel congestion common to seismic-resistant building

Nomenclature

cts tension-stiffening factorf c concrete compressive strength (cylinder)f ct axial tensile strengthf ct;fl flexural tensile strength

f fct0;u axial residual tensile strength according to DAfSt Rich-

tlinie Stahlfaserbetonf f

cflk;L2 flexural residual tensile strength according to DAfStRichtlinie Stahlfaserbeton

f fctR;u axial residual tensile strength according to DAfSt Rich-

tlinie Stahlfaserbeton (design value)ft,res residual tensile strength according to Gebekken et al.f yh yield strength of stirrupsGf fracture energyle theoretical bond length of the fibre

lf fibre lengthVf fibre contentw crack openingbu empirical factor according to DAfSt Richtlinie Stahlfa-

serbeton to consider application of FRC in combinationwith reinforcement bars

gVol steel fibre volumeghl fibre orientation factor.

k fF fibre orientation factor

j fG geometry factor

qw;qsw volumetric stirrup ratiorðWÞ crack opening lawrs fibre stress at bond failure

C. Roehm et al. / Engineering Structures 91 (2015) 182–196 183

joints. It was reported that the modified joints were more damagetolerant and crack resistant than the conventional joints. Filiatraultet al. [2] brought out the potential usage of fibre reinforced con-crete for providing more cost-effective ductile beam–column jointssubjected to seismic loading. It was found that by reducing theamount of confinement reinforcement in the joint regions and bycompensating for the required shear strength by steel fiber rein-forced concrete, better performance can be achieved. Bayasi andGebman [3] pointed out that application of FRC in joint regionwould lead to increase in hoop spacings within the joint regionand reduction in lateral reinforcement in beams and columns,without negatively affecting the performance of the joints undercyclic loading. Parra-Montesinos et al. [4] developed a procedurefor damage tolerant beam column joints using high performanceFRC composites (HPFRCC). It was emphasized that HPFRCCbeam–column joints perform satisfactorily under large shearreversals and the joints were able to sustain a drift of 5.0% withbeam rotation capacities of about 0.04 rad. An experimentalinvestigation was carried out by Ganesan et al. [5] to study theeffect of hybrid fibres on the seismic performance of beam columnjoints. Crimped steel fibres and polypropylene fibres were used inhybrid form and high performance concrete was designed for thebeam column joints. It was observed that addition of fibres inhybrid form improved many of the engineering properties suchas the first crack load, ultimate load, energy dissipation, less stiff-ness degradation and ductility factor of the composite. Further,efficacy of HPFRCC on improvement of deficient low strength rein-forced concrete exterior beam–column joints under reverse cyclicloading was examined by Bedirhanoglu et al. [6]. Maya et al. [7]attempted to develop a methodology for providing connection ofprecast elements using ultra high performance fibre reinforcedconcretes (UHPFRC). It was aimed to avoid the typical complexreinforcing details and inefficient construction processes. It wasclaimed that the proposed configurations using UHPFRC avoidsthe interference between longitudinal and transversal reinforce-ment and provides an efficient construction process. An exclusiveexperimental program was conducted by Caballero-Morrisonet al. [8] to study the behaviour of columns subjected to combina-tions of constant axial and lateral cyclic loads and to assess the roleof slenderness, axial load level, transverse reinforcement ratio, andvolumetric steel-fibre ratio on the maximum load and deformationcapacity of the columns.

The behavior of beam–column sub-assemblages is influencedby several parameters. Further, usage of nonconventional materialssuch as FRC in beam column joint significantly increases the num-ber of key parameters. Hence, the investigations on the influence ofvarious parameters on the behaviour of beam–column sub-

assemblages under cyclic loading cannot be fully studied throughexperimental investigations. Therefore, validated numerical mod-els are required to study the behaviour of beam–column sub-assemblage with different variables which would pave the wayfor achieving the better and optimally designed structures.

Lee and Liang [9] proposed a computational model to predictthe effective mechanical behavior and damage evolution in fiberreinforced cellular concrete (FRCC). The effective moduli of theFRCC are estimated using micromechanics proposed by Eshelby.Damage mechanics based constitutive model was implementedinto a finite element code to predict the performance of typicalfiber reinforced concrete. Numerical investigations on the influ-ence of column axial load on the joint shear strength of the exteriorbeam–column joints were carried out by Haach et al. [10]. It waspointed out that the column axial load made the joint more stiff.It was further observed that a more uniform stress distributionin the joint region was obtained when the stirrup ratio wasincreased. Shannag et al. [11] formulated a nonlinear static proce-dure to model the behavior of interior beam–column joints underlateral cyclic loading. It was concluded that the nonlinear staticanalysis (termed as pushover analysis) seemed to be an efficienttool to predict the structural behavior parameters such as load–de-flection and moment–curvature responses of beam–column joints.Papanikolaou and Kappos [12] developed computational frame-work of three-dimensional nonlinear finite element analysis ofreinforced concrete bridge pier sections for providing convenienttransverse reinforcement arrangements to enhance both thestrength and ductility. An emphasis was given for modelling ofconstitutive laws for materials and confinement effects. To simu-late the structural responses of the reinforced concrete specimenswith severe geometric and material nonlinearity, Yu and Tan [13]proposed a component-based joint model. Macro model-basedfinite element analysis with fiber elements was adopted andbond–slip behavior under large tension was simulated using seriesof springs. Masi et al. [14] numerically analysed the beam columnjoints. Numerical simulations were used to evaluate the stress dis-tribution in the joint panel as a function of the axial load and toquantify the beam rebar deformations. Collapse mode due to thefailure of beam longitudinal rebars was investigated. Numericalinvestigations on behaviour of steel fibre reinforced concretebeam–column joints were carried out by Abbas et al. [15]. Thejoints were subjected to reverse cyclic loading and constant axialforce was applied on the column. Further, parametric studies werecarried out to evaluate the efficacy of introduction of steel fibres tocompensate for requirement of conventional transverse reinforce-ment. Seismic performance of reinforced concrete rectangular hol-low piers made of steel fiber reinforced concrete was investigated

Table 1Specimens details.

Specimens Fibre reinforced concrete(FRC) properties

Geometrical andmaterial details

SP-6 – Column: Length 3800 mm,section 300 � 300 mmBeam: Length 1700 mm,section 300 � 400 mmConcrete: C30/3 7Steel: S500

SP-6-2 Lf/df = 30/0.38, 1 vol.%Lf/fd = 13/0.175, 0.5 vol.%

SP-6-3 Lf/df = 30/0.38, 1 vol.%,Lf/fd = 13/0.175, 0.5 vol.%

184 C. Roehm et al. / Engineering Structures 91 (2015) 182–196

by Zhang et al. [16] through experimental investigations andnumerical simulations. For numerical simulations, OpenSees, wereemployed. Seismic behavior of the specimens in terms of failuremode, hysteretic characteristics, ductility, stiffness degradationand energy dissipation capacity were investigated and an improve-ment in seismic performance of structural elements with steelfibers was observed. To exploit the improved tensile properties ofsteel fiber reinforced concrete (SFRC) for applying as repair materi-als, numerical simulation of the mechanical behavior of a series ofreinforced concrete beams repaired with high performance selfcompacting SFRC under shear was carried out by Ruano et al.[17]. It was brought out the validated numerical models can beused to improve the design technique for repair or retrofittmentusing such composites.

Though few research works addressed the issues of numericalmodelling of normal and fiber reinforced concrete [9–17], detaileddiscussion on methodology for numerical simulations of the per-formance of the critical reinforced concrete components such asbeam–column joints using materials like FRC, under reverse cyclicloading, is very scanty and inadequate. Further, though importanceof development and usage of new materials for construction activi-ties have been increased dramatically, the research on materialproperties required for effective evaluation of cyclic response ofthe structural components made of fiber reinforced concrete isscarce. Further, as a disturbed zone, beam column joint is one ofthe most important structural components under seismic typeloading. The effect of the parameters like strength of concrete,quantity of FRC and stirrups in joint region on energy dissipation,strength deterioration, joint shear degradation received extremelyminimal attention. This paper aims to address these issues. First,the available and modified concrete models to accommodate thenonlinear behaviour of normal- and fiber reinforced-concreteunder cyclic loading are presented, followed by the brief descrip-tion of experimental investigations carried out on beam–columnsub-assemblages. Efficient numerical models are proposed in thepresent study to simulate the behaviour of fibre reinforced con-crete in combination with conventional reinforcement. The nonlin-ear finite element (FE) software ATENA, which was developedexclusively for reinforced concrete structures, has been used inthe present study. Further, the beam–column sub-assemblagesare numerically simulated and results obtained from numericalinvestigations are compared with those obtained from experimen-tal investigations. Finally, to identify the potential usage of fibrereinforced concrete in structures subjected to earthquake loading,validated numerical models are used for carrying out studies ondevelopment of shear strength in joint region where concreteproperties, steel reinforcement ratio, fibre reinforced concretecharacteristics etc. are the parameters.

2. Experimental investigations

In the present study, three beam–column sub-assemblageshave been experimentally investigated by the authors and theresults obtained from the experimental investigations are consid-ered as reference for the numerical work. One of the specimensnamed as SP-6 is designed and detailed according to Eurocode 2[18] and Eurocode 8 [19] incorporating the provisions of detailing(medium ductility) according to Eurocode. The other two speci-mens (SP-6-2 and SP-6-3) are the modifications of the first onewith reduced number of stirrups in the joint but using steel fibrereinforced concrete and increased concrete strength in the jointregion. All the beam–column sub-assemblages have the same gen-eral and cross-sectional dimensions as given in Table 1. Thegeometry (top and bottom segments of column- and beam- fromjoint face) is chosen to match the bending moment distribution

at the joint for which it was designed. The reinforcement detailsof the specimens are presented in Fig. 1.

The test set-up was arranged on the test floor so that thebeam–column joint is tested horizontally by applying cyclic loadin the plane of the test floor. Vertical arrangement was avoidedto make the testing arrangement simplified and to apply a prede-fined axial load in column through a hydraulic jack resting on testfloor. The schematic and actual test set up are shown in Fig. 2a.The fatigue rated 25 T capacity actuator was used for controlledreverse cyclic loading. A new fabrication had been adopted fortransfer of force from actuator to the beam tip where a hingewas made to maintain the verticality of applied load from actua-tor. To simulate the axial load in the column of a building, initiallya level of 300 kN was applied through the jack positioned betweenone end of the column and the reaction block and proper transferof axial force through the column was checked from load cellplaced between the column and bulk head and aimed to applyconstant axial load. It is to be mentioned that during the processof the test the level of axial loads slightly dropped. At the end ofthe test, the axial load on column was found to be in the rangeof 270–290 kN in various tests performed by the authors. It isimportant to mention here that application and transfer of axialforce through the column is not so straight forward. For instance,it was found several times that the load applied by the hydraulicjack and the load measured from load cell placed on other end ofthe column were not same. The main reason for mismatch was thepresence of many bolts in fabricated test set up and the arrange-ment of the specimen on test floor. On each occasion, rollersplaced between the specimen and test floor were inspected andthe holding bolts in the top and bottom bracket of the columnswere loosened to ensure effective transfer of applied axial loadthrough the column.

The lateral load was applied on the beam tip using displace-ment control as per the load history shown in Fig. 2b. Reverse cyc-lic load is applied in terms of drift ratio (%) of the componentwhere the drift is calculated as the ratio of the applied displace-ment at the beam tip to the length of the beam segment from col-umn face to the application point of the displacement.

The amplitudes of the peaks in the displacement history weremultiples of the yield displacement, whereas the yield displace-ment was defined as the tip displacement corresponding to yield-ing of the beam main reinforcement at the column face. Threecomplete cycles were performed at each displacement ductilitylevel. The lateral displacement increments have been applied in aquasi-static reverse cyclic manner. Although in the case of seismicaction the loading rates are higher than the rates corresponding tostatic conditions, it is advantageous since the quasi-static cyclictesting allows a careful monitoring of the specimen behaviour dur-ing the test. Since, the focus of the present paper is on numericalinvestigations, further details on the instrumentation, test proce-dure, loads, etc. have not been presented here and can be foundelsewhere ([20,21]). However, various response parameters suchas load–deflection hysteresis, crack pattern, and joint shear defor-mation, obtained from the experimental investigations are

SP-6 SP-6-2

SP-6-3

Fig. 1. Reinforcement details of the specimens (sectional details are given in Table 1).

C. Roehm et al. / Engineering Structures 91 (2015) 182–196 185

presented together with the numerical results for better readabil-ity and clarity.

3. Modelling of the specimens for numerical analyses

3.1. Geometric modelling

Geometry of the specimens is modelled by using differentmacro-elements for representing the B- and D-regions (Bernoulli

region and Disturbed region, respectively) of the specimen as wellas steel plates at load/reaction zones. For concrete, three-dimen-sional quadratic ‘‘brick’’-elements and for steel support plates, ‘‘te-trahedal’’-solid elements are used. Reinforcements are modeledusing discrete truss elements embedded in concrete, whereas thehook anchorage is modelled by an additional diagonal truss con-necting the bent part with the main reinforcement. The propertiesof this truss element are same as that assigned for main reinforce-ment bars. Since, these numerical analyses were computational

(a)

(b)

Fig. 2. (a) Test setup and (b) loading history.

186 C. Roehm et al. / Engineering Structures 91 (2015) 182–196

intensive due to cyclic loading, two different sizes of FE mesh wereused. In the joint zone, three adjacent macro-elements weremeshed with 50 mm size and the rest part of the model wasmeshed with 100 mm size elements. The connection between thedifferent zones was assigned as ‘‘fully rigid’’ which ensures thestrain compatibility between two adjacent macro elements.

During experiment, specimens were provided with hingesusing steel plates and rollers at column top and bottom. Thesesteel plates with rollers were inserted in between specimen andsteel channels (shown in Fig. 2a). It is obvious that during loadingat beam tip, there was a movement at column top and bottomdepending on the stiffness of the steel channel which held thehinging arrangement and the specimen. To simulate this beha-viour, springs were modelled on outer and inner faces at topand bottom ends of the column, which would provide a certaindegree of flexibility at the support locations. Geometrical modeland finite element mesh including reinforcements are shown inFig. 3.

Fig. 3. Macro-elements, reinforcem

3.2. Material modelling

Modelling of the material properties has a great influence onthe quality and accuracy of results obtained from numerical analy-ses. Therefore, it is very important to understand the assumptionsand simplifications incorporated in the material models in ATENA[22]. Concrete model in ATENA is based on the plane stress con-stitutive model. A smeared approach is used to model the crackproperties so that the material properties defined for a materialpoint are valid within a certain material volume. Material modelfor concrete includes the following effects of the concrete beha-viour: (i) non-linear behaviour of concrete in compression includ-ing hardening and softening, (ii) fracture of concrete in tensionbased on non-linear fracture mechanics, (iii) biaxial strength fail-ure criterion, (iv) reduction of compressive strength after cracking,(v) tension stiffening effect, (vi) reduction in shear stiffness aftercracking (variable shear retention), and (vii) fixed and rotatingcrack model based on crack direction.

ent and finite element mesh.

Fig. 5. Exponential crack opening law.

C. Roehm et al. / Engineering Structures 91 (2015) 182–196 187

3.2.1. Concrete modellingFor concrete, complete equivalent uniaxial stress–strain diagram

is shown in Fig. 4. From the curve it is clear that, unloading isassumed to be a straight line and with subsequent reloading, linearunloading path is followed until the last loading point U is reachedand beyond that the loading function is resumed. Change in theincrement in the sign of strain implies change from loading tounloading and vice versa. The loading history affects the relationbetween rc

efand eceq, hence it is not unique. The equivalent uniaxial

stress also relates with biaxial stress state peak values of stress incompression ft

0ef and tension ft0ef are also reflected in biaxial stress

state. The effective stress rcef and the equivalent uniaxial strain ec

eq

are used to describe non-linear behavior of concrete in the biaxialstress state. Here, equivalent uniaxial strain is introduced in orderto eliminate the Poisson’s effect in the plane stress states, as:

eeqc ¼

rxi

Exið1Þ

The strain produced by the stress rxi in a uniaxial test withmodulus Exi is called equivalent uniaxial strain. Exi associates withthe direction i. The behavior of concrete in tension without cracksis assumed to be linear elastic and the modulus of concrete in ten-sion Eci is the initial elastic modulus of concrete in compression. Afictitious crack model based on a crack-opening law and fractureenergy is used for tension after cracking. It is used in combinationwith the crack band. The exponential crack opening law is appliedas shown in Fig. 5.

The stress–strain behavior shown in Fig. 6 demonstrates thecompressive stress–strain relationship for concrete adopted inthe software. For the ascending branch of concrete stress–strainbehaviour, CEB–FIP [23] recommendation and for descending partlinear variation are adopted. The slope of softening law is definedby means of a softening modulus Ed and it is defined by two strainlimits, i.e., strain corresponding to compressive strength of con-crete ec and a limiting compressive strain ed. The later part of strainis calculated from plastic displacement wd and band size duringfailure in compression Lc. The behavior of concrete in tension with-out cracks is assumed to be linear elastic. The plastic displacementwd defines the end point of the softening curve in case of compres-sion. The softening displacement diagram indirectly reflects theenergy required for generating a unit area of the failure plane.The descending branch of the compressive stress–strain behaviourof concrete is defined by wdmax. It is the maximum possible postpeak displacement of defined concrete and the value of wdmax =5 mm was proposed in the present study. The basic definition offracture energy used in the present study is shown in Fig. 7.Concrete material model ‘‘CC3DNonLinCimentitious2’’, the same

Fig. 4. Uniaxial constitutive law for concrete.

profile of fracture energy is used. Remmel [24] presented anapproach in calculating fracture energy as given in Eq. (2), wherecompressive strength of concrete and particle size were theparameters for calculation.

GF ¼ GF0 � ln 1þ f c

10

� �½N=mm� ð2Þ

where

GF0 = 0.065 N/mm for concrete with river gravel aggregate.GF0 = 0.106 N/mm for concrete with crashed basalt aggregate.

Eq. (2) provides the best fit for the experimental data obtainedby Remmel [24]. Fracture energy calculated from the above equa-tion as proposed by Remmel is used in material modelling.However, it needs to be mentioned that the proposed fracturemodel for concrete is not valid for very low strength concretes.

In concrete elements, cracks cannot fully develop through theconcrete section if reinforcement is present, and further concretecontributes to the steel stiffness. This behavior, called tension stif-fening, is incorporated in concrete model‘‘CC3DNonLinCementitious2’’ by specifying a tension stiffening fac-tor cts. This factor cts represents the relative limiting value of tensilestrength in the tension stiffening as shown in Fig. 7. In the presentstudy, value of cts is considered as 0.4.

3.2.2. Steel reinforcementThe steel reinforcements are modeled as discrete reinforcing

bars in the form of truss elements. The same is adopted for bothtransverse and longitudinal reinforcement. Bauschinger’s effectfor reinforcement under cyclic loading is incorporated by usingMenegotto–Pinto model [25]. The reinforcement bars used in theexperiments were tested for their stress–strain behaviour andcorresponding values are incorporated. The reinforcements areassumed to follow the bilinear law, i.e. elastic–plastic behaviourwith strain hardening. The behaviour of different diameters ofreinforcements showed a variation in stress–strain relationsthough the elastic part was quite similar. Hence, in the numericalmodels post-yield behaviors for reinforcement bars with differentdiameters are incorporated accordingly. The stress–strain relation-ship is considered as:

r� ¼ be� þ ð1� bÞe�

ð1þ e�RÞ1=R ½MPa� ð3Þ

where r� ¼ e�ereo�er

and r� ¼ r�rrro�rr

.A curved transition from a straight line asymptote with slope Eo

to another asymptote with slope E1 can be seen from Fig. 8. In the

Fig. 6. Stress–strain diagram in compression.

Fig. 7. Tensile softening and tension stiffening.

Fig. 9. Bond–slip model according to CEB–FIP model code 1990 [23].

188 C. Roehm et al. / Engineering Structures 91 (2015) 182–196

figure, r0 and e0 are stress and strain at the point where twoasymptotes meet; rr , er are stress and strain at the point wherethe last strain reversal with equal stress takes place. After eachstrain reversal, stress–strain sets (r0 and e0) and (rr and er) areupdated. R is a parameter which influences the shape of the transi-tion curve and allows a good representation of the Bauschinger’seffect. Further, strain hardening ratio (b) is calculated as ratiobetween slope E1 and E0. CEB–FIB model code [23] proposes abond–slip relationship for reinforcement bars and the same isadopted as shown in Fig. 9. Quality of construction is assumed tobe poor with confinement less concrete is considered. Bondstrength at different level of slips can be calculated from the setsof equations given below:

s ¼ smaxs

s1

� �a0 6 s 6 s1

s ¼ smax s1 6 s 6 s2

s ¼ smax � ðsmax � sf Þ s�s2s3�s2

� �s2 6 s 6 s3

s ¼ sf s3 < s

9>>>>>=>>>>>;

ð4Þ

The parameters described for bond–slip relationship, as pro-posed by CEB–FIB model code [23], are described in Table 2 wherethe values corresponding to confined concrete can be used for

Fig. 8. Cycling reinforcement model based on Menegotto–Pinto [25].

structural components with concrete cover P5/, clear spacingbetween bars 610/ or with suitable confining reinforcement, andfor all other cases where the above mentioned criteria is not satis-fied, it can be assumed as unconfined. In the present study, bond–slip relation corresponding to unconfined concrete has beenadopted. Bond–slip characteristics to the flexural rebars asdescribed above are incorporated in the numerical model whereasperfect bond between concrete and stirrup reinforcements is con-sidered. Further, it is to mention that no special cyclic bond–slip

Table 2Values for the prediction equation according to CEB-FIP90 [23] for good bondcondition.

Parameters Confined concrete Unconfined concrete

s1 1.0 mm 0.6 mms2 3.0 mm 0.6 mms3 Distance between ribs 1.0 mma 0.4 0.4s1 2.5

ffiffiffiffiffif c

p2.0

ffiffiffiffiffif c

ps2 0.4 s1 0.15 s1

Fig. 10. Crack opening laws for FRC (average lf = 24.3 mm).

C. Roehm et al. / Engineering Structures 91 (2015) 182–196 189

has been used. It has been found from the reported studies that byusing sufficiently small elements and cycling model for thereinforcement, role of bond model under cyclic loading can be min-imised and the analysis can be able to capture by the cracking ofsurrounding concrete elements efficiently [26]. Further discussionon the numerical modelling and analysis parameters are discussedelsewhere [27,28].

3.2.3. Modelling of fiber reinforced concrete (FRC)For modelling of FRC, ATENA offers two possibilities, (i) material

model ‘CC3DNonLinearCementitious2’ for normal concrete can beadjusted to the behaviour of FRC by modifying the parameters likefracture energy and tension stiffening, and (ii) the model‘CC3DNonLinearCementitious2User’, which is based on the pre-vious one, but requires the definition of complete stress–straincurves (constitutive models) for tensile and compressive behaviouras well as shear retention for shear stiffness degradation and ten-sile strength degradation due to lateral stress. Since, in the presentcase, FRC is of strain-softening type and is always used in combina-tion with conventional steel reinforcement, the use of‘CC3DNonLinearCementitious2’ allows for simulation of directchange from 0 vol.% of fibres to arbitrarily amount of fibres withoutthe effects of different material models.

The crack opening law of FRC allows for wider maximum crackopening and less tensile strength degradation as compared to NC.Force transfer in NC can occur only through aggregate interlockand crack friction, whereas in FRC, fibres contribute for bridgingthe cracks. Therefore, to adjust the NC crack-opening law, suitablevalues for fracture energy and tension stiffening factor need to bederived from available models in literature. For determining thefracture energy for FRC, Pfyl [29] proposed a parabolic crack open-ing law as described in Eq. (5).

rðwÞ ¼ ð1� 2w=lf Þ2f ct ð5Þ

Assuming that the maximum crack width is half of the fibrelength (wc ¼ lf =2), the fracture energy can be calculated as:

Gf ¼Z wc

0rðwÞdw ¼ f ct � lf

6ð6Þ

In this model, total fracture energy depends only on the tensilestrength and the fibre length. Hence, it is clear that the role ofamount of fiber is considered in terms of tensile strength of fiberreinforced concrete. Further, it is important to state that influenceof other fibre properties such as end hook, and surface roughnessare not considered for calculating fracture energy.

However, Kützing [30] developed a simplified tri-linear soften-ing function. In the study, concrete is assumed to transfer stressesacross the crack till the crack width reaches 0.5 mm. Further, con-crete and fibres act together and finally only the fibres transfer theload. The pullout-energy in the following section is neglected andthe stress at the crack width w1 = 50 lm is calculated (Eq. (7))based on the proportion of steel fibres and the linear part of soft-ening as proposed by Remmel:

r1 ¼ f t2 1� 0:05w2

� �þ gVol � gh � rs 1� 0:05

le

� �ð7Þ

where ft2 is the tensile stress proportion according to Remmel, w2 isthe maximum crack width for plain concrete (depending on aggre-gate and strength between 160 and 250 lm), gVol is the steel fibrevolume, ghl is the fibre orientation factor, rs is the fibre stress atbond failure and le is the theoretical bond length of the fibre.When the crack width reaches w2, only the crack bridging effectof the fibres is active:

r2 ¼ gVol � gh � rs 1�w2

le

� �ð8Þ

Since, it is unrealistic to assume that the crack propagatesexactly through half of the fibre length, the maximum crack widthis assumed to be lf =4 as suggested by Kützing. To consider differentfibre lengths with different volumes required for the hybrid FRCused in this study, the characteristic points of Kützing’s approachare estimated separately and incorporated in the numerical model.Hence, for different fibre lengths, different characteristic points arecreated at lf =4 of the shorter fibre when this one has been pulledout (as shown in Fig. 10).

Further, the exponential function of Hordijk [31], which isincorporated is used for calculating fracture energies proposed in[24–25]. For Kützing [30], the softening in the beginning is similarto the test, whereas the degradation in the test is decreased after-wards and ends up in a smaller maximum crack width. Thestrength degradation in the Hordijk–Pfyl curve is much lowerand therefore is on the unsafe side. Since the material under studyis used in combination with reinforcement, tension stiffening fac-tor cts s suitably modified in material model. Fibers require a cer-tain crack width to be activated. The first part of the post-peakbehaviour is therefore in general similar to NC and CEB FIPModel code 2010 [23] and is characterized by a steep load drop.The load drop in the first branch of the post-peak behaviour isimportant for the overall behaviour of the specimens and hence,the Hordijk-curve has been used in the present study by calculat-ing the fracture energy according to Kützing for a systematic cal-culation of fracture energy for different percentages of fibres.

3.2.4. Fracture energy and residual tensile strengthFor determining the fracture energy and residual tensile

strength of FRC to correctly simulate the behaviour of the beam–column sub-assemblages considered in the present study, severalfour-point-flexural tests were performed in this study followingthe guidelines of Richtlinie Stahlfaserbeton [32]. According tothose guidelines, the residual tensile strength can be calculatedby multiplying the corresponding flexural tensile strength at a dis-placement of 3.5 mm (Performance class 2) with the empirical fac-tor 0.37 when using FRC in combination with reinforcement barsand using a constant tensile stress block. The basic values for axialresidual tensile strength are obtained as:

f fct0;u ¼ f f

cflk;L2 � bu ¼ f fcflk;L2 � 0:37 ð9Þ

To obtain a design value, parameters like geometry factor andfibre orientation are also considered, as:

f fctR;u ¼ j f

F � jfG � f

fct0;u ð10Þ

where j fG is geometry factor and defined as j f

G ¼ 1:0þ Ac � 0:5 61:70, j f

F is fibre orientation factor and generally taken as 0.5.

0

2

4

6

8

10

12

14

0 0.5 1 1.5 2 2.5 3 3.5 4

Deflection [mm]

Flex

ural

Ten

sile

Str

ess

[N/m

m²]

Test 1 Test 2

Test 3 G2c025

G2c02 G2.5c025

G2.5c01 G3c025

G3c02 G4c025

G4c01 G5c025

G5c02

Fig. 11. Comparison of stress–deflection relationship from test and numericalsimulation for variation of fracture energy and residual tensile strength [parameterindex is Gxcy where G is fracture energy varying from 2 to 5 kN/m and c is tensionstiffening factor varying from 0.1 to 0.25].

190 C. Roehm et al. / Engineering Structures 91 (2015) 182–196

To examine the concept of simulating FRC by increasing fractureenergy and tension stiffening factor, several flexural prisms arenumerically investigated by varying the fracture energy (from 2to 5 kN/m) as well as the tension-stiffening factor cts, which corre-sponds to the residual tensile strength between 0.1 and 0.25.Fig. 11 shows the flexural tensile strength-displacement behaviourof various specimens obtained from numerical and experimentalstudies. In general, with increase in fracture energy, the maximumflexural tensile strength increases and the descending branchbecomes flatter. With increase in tension-stiffening factor, theresidual stress remains higher. The stress-crack-opening curve pro-posed by Hordijk shows that the descending branch is also forhigher fracture energy – steeper than from the test. The maximumtensile capacity as well as the residual tensile strength of the speci-mens can be simulated very well. The axial tensile strength of thetested specimen is calculated according to CEB FIP Model code2010 [23] as f ctm ¼ 0:6f ct;fl ¼ 6:8 MPa, as it is assumed that the ten-sile strength is not increasing in spite of presence of reasonableamount of fibres. Calculating the average residual tensile strengthfor the available prisms based on Richtlinie Stahlfaserbeton [32]leads to 0:37 � f ctm;L2 ¼ 1:75 MPa � 0:25f ctm, which corresponds toa tension-stiffening factor cts = 0.25 for FRC without additionalreinforcement bars.

For using the material model to simulate the response of thebeam column sub-assemblages under cyclic loading as obtainedfrom the test, further influencing parameters also need to be inves-tigated. First of all, distribution of fibres can be greatly influenceddue to the presence of the rebars or the fibres may not be fully acti-vated together with the rebars. Therefore, fibre orientation is consid-ered as prescribed in DAfStb Richtlinie Stahlfaserbeton [32] using afibre orientation factor of 0.5 for 3D-fibre distribution. Nevertheless,the cyclic loading may lead to further damage and therefore, itreduces residual tensile strength. Tschegg [33] has further shownthat fracture energy in case of biaxial stresses, as it occurs in thebeam–column joint, is significantly lower than under uniaxial stres-ses. To consider this aspect, fracture energy is calculated based onlow bond stresses of 1.5–2 N/mm2 (as shown in Fig. 10).

4. Comparison of results from FE analysis and experimentalinvestigations

4.1. Load–displacement hysteresis and crack pattern

In the numerical investigations, total axial load of 300 kN wasgradually applied on column in first few steps. Subsequently, the

displacement cycles were applied at beam tip. Axial loading phaseof the simulated model was solved by arc-length method and thenthe solver was changed to Newton–Raphson method during dis-placement cycles. For better numerical accuracy, displacementswere incorporated in small steps. Initially, a convergence studywas carried out with different displacement steps and finally, a dis-placement increment of 1 mm in each step was chosen by main-taining the accuracy of results and total number of stepsrequired to simulate the experimental investigations of the speci-mens subjected to cyclic loading. Several other methods are alsoavailable and readers may also refer to other reported works onnonlinear analysis of concrete components [13].

Fig. 12 shows the load–displacement hystereses of NC and FRCspecimens obtained from both experimental investigations andnumerical (using the ‘CC3DNonLinearCementitious’ model) analy-ses. The figures show that the results obtained from the numericalanalyses of the FRC specimens are in good agreement with theexperimental results. The negative strength (strength during nega-tive displacement cycles) is overestimated by maximum of 15%,whereas the positive strength is matching well. For SP-6-2,strength is overestimated in the numerical simulations as the weakinterface observed between NC and FRC in the experimental speci-men could not be replicated exactly in the numerical simulations.It is important to mention that in SP-6-2 the interface between NCand FRC in joint zone was weak due to construction process andfrom the experimental investigations, the cracks were found tobe along the interface itself. Since, the construction process wasnot simulated in the numerical investigation, the weak construc-tion joint region was not depicted from the numerical studies.Therefore, development of cracks observed from experimentalinvestigations differ from that obtained from numerical sim-ulations. Development of cracks observed from numerical studiesand experimental investigations are shown in Fig. 13. Final crackpatterns of SP-6 and SP-6-3 show that they are well corroboratedwith the experimental results. Crack patterns from the numericalanalysis confirmed that the final damage in FRC and NC specimenswas in the joint zone or at the face of the column. It is evident fromthe figures of crack pattern and load–displacement hysteresis thatthe numerical analysis had predicted the crack pattern and finaldamage scenario quite accurately.

4.2. Energy dissipation of NC and FRC specimens

During the experimental investigations, all the specimens weresubjected to three repeated cycles at each displacement level.Nevertheless, to restrict computational efforts in the numericalstudies, the specimens were subjected to one cycle only at eachdisplacement level. It is important to study the comparativeresponse of the specimens, in terms of energy dissipation, obtainedfrom experimental studies (repetitive cyclic loading) with numeri-cal analyses (mono cyclic loading). This will provide an avenue toestimate the actual energy dissipation of a structural componentwhen such an elaborate experimental investigation is not possibledue to time or cost restrictions. Fig. 14(a) shows the total energydissipation obtained from numerical analysis vs. ratio of experi-mental to numerical result. In the specimens with ultimate jointshear failure, the ratio of average energy dissipation from threecycles at each displacement level obtained from experiment, toenergy dissipation calculated from numerical analyses is in a rangeof 0.7–1.1. Hence, for joint with shear failure criteria, there is a ten-dency in numerical analysis to overestimate the average experi-mental value. Further, Fig. 14(b) shows the correlation betweenenergy dissipation obtained from experimental (only first cycle)– and numerical- studies to get an idea of the extrapolated energydissipation during real test. Overall, it can be mentioned that the

-200

-150

-100

-50

0

50

100

150

-150 0 50

Displacement (mm)

Load

(kN

)

SP-6 from test result

-200

-150

-100

-50

0

50

100

150

Displacement (mm)

Load

(kN

)

SP-6-2 from test result

SP-6-2 from numericalanalysis

-200

-150

-100

-50

0

50

100

150

Displacement (mm)

Load

(kN

)

SP-6-3 from test result

SP-6-3 from numericalanalysis

SP-6 from numerical analysis

-50-100 150100 -150 0 50-50-100 150100

-150 0 50-50-100 150100

Fig. 12. Experimental and numerical load–displacement hysteresis for NC and FRC specimens with joint failure.

SP-6 (NC)

SP-6-2 (FRC) SP-6-3 (FRC)

Fig. 13. Final crack pattern of specimens.

Fig. 14. Comparison of experimental and numerical energy dissipation (a) average experimental compared to numerical energy dissipation, and (b) experimental (first cycle)compared to numerical energy dissipation.

C. Roehm et al. / Engineering Structures 91 (2015) 182–196 191

192 C. Roehm et al. / Engineering Structures 91 (2015) 182–196

numerical results reflect the experimental results in a reasonablerealistic way.

4.3. Joint shear degradation of NC and FRC specimens

Apart from the change in strength due to individual parameters,the influence on joint shear deformation of the joint is also impor-tant. Generally, codal design rules for joints are based on forceswithout considering the corresponding deformations which arerequired to reach the maximum resistance. Previous researchers(Pantazopoulou and Bonacci [34], Parra-Montesinos et al. [35],Sasmal et al. [36]) have shown that joint deformation is of interestto evaluate the joint performance, though the relationship betweenjoint shear distortion and strength is still not clear.

Therefore, joint shear deformations obtained from the experi-ments and numerical analyses need to be investigated as well.From experiments, joint shear deformations could not be mea-sured for all specimens and further, the set up for measuring thejoint shear deformation (where two LVDTs were fixed diagonallyon the joint face) could not be retained till the end of the testdue to excessive damage on the surface of the joint.Unacceptable records obtained from the LVDTs during high dis-tress stages are shown in dotted lines in the diagram. Fig. 15 showsthe comparison of the shear deformations from numerical analyses(hysteresis) and tests (envelope) for SP-6-3. The measured and cal-culated shear deformations are in good agreement until dislodge-ment of the LVDTs from the joint face.

4.4. Parametric studies on joint shear strength of FRC specimens

To describe the joint shear behaviour and especially the influ-ence of steel fibres on joint shear strength, parametric studies are

-800

-600

-400

-200

0

200

400

600

800

-0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04

Joint shear deformation [rad]

Join

t she

ar s

tren

gth

[kN

] SP6-3-ATENASP6-3-Test

Fig. 15. Comparison of joint shear deformation for SP-6-3 (FRC).

Table 3Parameters for numerical study on joint shear strength.

Parameter Stirrupsinjoint (�)

Concrete quality(DIN 1045-1[38])

Performance class (DAfStb Richtlinie Stahlfaserbeton [32])

Fibre content(vol.%)

Fracture energy (10�4 MN/m)(according to Kützing [30])

Residual tensile strength fr (MPa)(according to DAfStb RichtlinieStahlfaserbeton [32])

Index P C – F c

C30/37,ft = 2.9 MPa

C50/60,ft = 4.1 MPa

cts (�) C30/37,ft = 2.9 MPa

C50/60,ft = 4.1 MPa

Range 01357

C16/20C30/37C50/60C70/80

0 0.725 1.025 0.35 0 00.5 8.09 8.56 0.5 0.435 0.6151 14.79 15.26 0.6 0.725 1.0252 28.20 28.67 0.8 1.015 1.4353 42.1 42.1

performed using validated numerical models. Table 3 representsthe parameters as well as their range which have been consideredin the present study. SP-6 is considered as the reference specimen.The indices to describe the specimen properties are also given inTable 3, e. g. a specimen referenced as SP6-P3-C30-F1-c035 is aparametric specimen based on SP6 with three stirrups in joint, con-crete quality C30/37, fracture energy determined based on a fibrecontent of 1.0 vol.% and residual tensile strength is 0.35fctm.

The behaviour of steel fibre reinforced concrete is describedusing the parameters such as fracture energy and residual tensilestrength, which are, amongst others, dependent on fibre content.For this reason, DAfStb Richtlinie Stahlfaserbeton [32] uses perfor-mance classes (‘‘Leistungsklassen’’) to classify the FRC. In numeri-cal analysis, certain amount of fibre content has been chosen tocalculate the corresponding fracture energy.

Gebekken et al. [37] related fibre content (Vf) and residual ten-sile strength (ft,res) as:

f t;resðVf Þ ¼ ð0:1115 � Vf Þ � f tðVf Þ ð11Þ

Based on this relationship, 0:1115 � Vf is the contributory part ofthe tension-stiffening factor (cts) due to fibre contribution. Table 4shows the tension-stiffening factors for different fibre quantities aswell as the factors corresponding to residual tensile strengthaccording to DAfStb Richtlinie Stahlfaserbeton [32]. Though forconcrete grade C30/37, the proposed equation shows a good agree-ment with the test results, for higher grades of concrete the con-tribution from higher volume-percentages of fibres would beoverestimated. In the parametric study, fracture energy has beencalculated depending on fibre content and the corresponding resid-ual tensile strength according to Richtlinie Stahlfaserbeton and hasbeen considered as shown in Table 4. Further, fracture energy andresidual tensile strength have been varied independently to iden-tify their individual influence. Slenderness of the beam–columnjoint has been kept constant, as no reference tests have been per-formed on size effects in joint.

4.4.1. Influence of concrete gradeFig. 16 shows the influence of concrete grade on the joint shear

strength. Concrete grade is varied based on DIN 1045-1 [38]. Meanvalues are chosen as input values and yield strength of beam andcolumn longitudinal reinforcement is increased up to 650 MPa toavoid yielding in the beam longitudinal reinforcement whichwould limit the ultimate load. It is found that the joint shearstrength increases significantly with improvement in concretestrength. Concrete compressive strength is used in most of thecodes as decisive parameter and sometimes it is treated as the solecontributor to joint shear strength. In strut-and-tie models, apartfrom dimensions of the compression zone, joint strength is solelydepending on concrete strength in struts and joints of the model.From the parametric study, it has been estimated that the joint

Table 4Linking of fibre content and residual tensile strength.

Gebekken et al.[37]

DAfStb Rili Stahlfaserbeton [32]

Vf

(vol.%)cts

(Fiber)L2 ff

ct0,s ffctR,u

a cts (C30/37,fctm = 2.9 MPa)

cts (C50/60,fctm = 4.1 MPa)

0.5 0.06 1.2 0.44 0.239 0.08 0.061 0.11 1.8 0.67 0.364 0.13 0.091.5 0.17 2.4 0.89 0.484 0.17 0.122 0.22 3 1.11 0.60 0.21 0.15

a f fctR;u ¼ j f

F � jfG � f

fct0;s ¼ 0:5 � 1:045 � 1:04 � f f

ct0;s where j fG is deformation beha-

viour according to DAfStb Richtlinie Stahlfaserbeton [32].

y = 128.64x0.4638

R2 = 0.9396

0

200

400

600

800

1000

1200

0 20 40 60 80 100

fcm [MPa]

V jh

[kN

]

Fig. 16. Influence of concrete grade on joint shear strength (under constantparameters as: fy = 650 MPa, 3 stirrups in joint, axial compression incolumn = 300 kN).

0

0.2

0.4

0.6

0.8

1

1.2

2 3 4 5 6 7 8

Drift [%]

norm

aliz

ed n

egat

ive

stre

ngth

de

grad

atio

n [-

]

SP6-P3-C16SP6-P3-fcm30SP6-P3-C30SP6-P3-C50SP6-P3-C70

Fig. 17. Influence of concrete grade on load–displacement behaviour.

0

0.2

0.4

0.6

0.8

1

1.2

0 0.01 0.02 0.03 0.04 0.05 0.06

Joint shear deformation γ [-]

norm

aliz

ed n

egat

ive

stre

ngth

de

grad

atio

n [-

]

SP6-P3-fcm30SP6-P3-C16SP6-P3-C30SP6-P3-C50SP6-P3-C70

Fig. 18. Influence of concrete grade on joint shear deformation.

y = -14.32x + 1.1687R2 = 0.9423

0

0.2

0.4

0.6

0.8

1

1.2

0 0.01 0.02 0.03 0.04 0.05 0.06

Joint shear deformation γ [-]

norm

aliz

ed n

egat

ive

stre

ngth

de

grad

atio

n [-

]

degradation

Linear(degradation)

Fig. 19. Strength degradation depending on joint shear deformation.

0.98

1

1.02

1.04

1.06

1.08

1.1

0 0.001 0.002 0.003 0.004 0.005 0.006

Gf [MN/m]

V jh,

i/Vjh

,0 [-

]

P3 P1

y = 1.1748x 0,017

R2 = 0.9921

y = 1.1993x 0,0197

R2 = 0.9514

Fig. 20. Influence of fracture energy on joint shear strength (under constantparameters as: fcm = 38 MPa, fy = 500 MPa, stirrups = 1 or 3, cts = 0.35, Axial com-pression in column = 300 kN).

C. Roehm et al. / Engineering Structures 91 (2015) 182–196 193

shear strength is dependent on the grade of concrete through itsmean compressive strength (Vjh1 (fcm)0.46]. In Eurocode 8 [19]and ACI 352R-02 [39,40] joint shear strength is calculated basedon (fc)0.5, whereas Eurocode 8 used (fck)2/3 and the New Zealandcode NZS 3101 [41] has implemented a linear relationship (fcm)1.An investigation by Hegger and Roeser [42] has shown that extrap-olation of

ffiffiffiffif c

pleads to overestimation of shear strength for high

strength concrete. The approach of Hegger und Roeser thereforecontains a linear correction parameter. Plotting the term and trans-ferring it into a potential function leads to the trend as (fcm)0.33 forstrengths between 20 and 100 MPa, which is lower than the trendobtained from numerical analysis for concrete strengths between24 and 78 MPa.

The influence of concrete grade on load-deformation behaviourof the beam column joints is shown in Fig. 17. It shows the normal-ized envelope (referring to maximum strength) for negative loadingonly (load creates negative bending moment at the face of the col-umn), as it provides higher joint shear force due to the longitudinalreinforcement detailing in the beam than for positive loading. Withthe increase in the grade of concrete, strength degradation of thebeam column joint is found to be less owing to the fact that withincrease in concrete strength, shear deformation of joint reduces(shown in Fig. 18). The elaborate discussion on the influence of con-crete strength on joint shear strength can be found in Vishnu et al.[43]. Thus, with the increase in the concrete strength, certainly uptoa certain limit, better load-deformation behaviour of beam–columnjoint is expected. The proportion of the joint shear deformation ofthe same overall displacement at the beam tip (drift level) is reducedwith increasing concrete grade and therefore the proportion of beambending compared to overall drift is increasing, which leads to areduction of strength degradation.

Strength degradation starts at a joint shear deformation ofapproximately 0.01, which is given as permissible value of joint

(a) (b) 0

0.2

0.4

0.6

0.8

1

1.2

2 3 4 5 6 7 8nega

tive

norm

aliz

ed s

tren

gth

degr

adat

ion

[-]

SP6-P1-C30F0-c035

SP6-P1-C30F1SP6-P1-C30F3

0

0.2

0.4

0.6

0.8

1

1.2

2 3 4 5 6 7 8

Drift [%]

nega

tive

norm

aliz

ed s

tren

gth

degr

adat

ion

[-]

SP6-P3-C30F1SP6-P3-C30F2SP6-P3-C30F3SP6-P3-C30F4

Drift [%]

SP6-P3-C30F0-c035

Fig. 21. Influence of fracture energy on load–displacement behaviour (a) specimens with 1 stirrup, and (b) specimens with 3 stirrups.

y = 0.0964x + 0.9997R2 = 0.9946

y = 0.0975x + 1.001R2 = 0.9861

0.98

1

1.02

1.04

1.06

1.08

1.1

1.12

1.14

0 0.2 0.4 0.6 0.8 1 1.2 1.4

fr [MPa]

V jh,

i/Vjh

,0 [-

]

P3 P1

Linear (P3) Linear (P1)

Fig. 22. Influence of residual tensile strength on joint shear strength (underconstant parameters as: fcm = 38 MPa, fy = 500 MPa, stirrups = 1 or 3, cts = 0.35, Axialcompression in column = 300 kN and Gf = 72.5 N/m).

Table 5Influence of confinement according to Tsonos [45] and numerical prediction.

No of stirrups P(�)

qsw,V

(�)K(�)

fc0.46

(�)fc

0.46/fcP30.46

(�)Vjh

(kN)Vjh/Vjh,0

(�)

0 0 1.00 5.33 0.95 702.7 0.9771 0.0031 1.04 5.43 0.97 708.5 0.9853 0.0094 1.12 5.61 1.0 719.4 1.05 0.0157 1.22 5.84 1.04 732.0 1.0177 0.022 1.29 5.99 1.07 739.5 1.027

fcm = 38 MPa, fyk = 500 MPa.

194 C. Roehm et al. / Engineering Structures 91 (2015) 182–196

shear deformation in non-conforming RC beam column joints inFEMA 273 [44]. Here, after reaching this limit, strength degrada-tion starts and is found to be approximately 14% at joint sheardeformation of 0.01 as can be seen from the linear regression curvein Fig. 19.

0

0.2

0.4

0.6

0.8

1

1.2

0 0.01 0.02 0.03 0.04 0.05 0.06

Joint shear deformation γ [-]

nega

tive

norm

aliz

ed s

tren

gth

degr

adat

ion

[-]

SP6-P1-C30-c035

SP6-P1-C30-c05

SP6-P1-C30-c06

SP6-P1-C30-c08

(a)

Fig. 23. Influence of joint shear deformation on joint shear strength where residual tenstirrups.

4.4.2. Influence of fracture energy and residual tensile strengthFracture energy determines the ductility of any material, i.e.

with decrease in fracture energy tensile strength of any materialreaches the remaining residual tensile strength faster. During theexperimental investigations and numerical studies, it is observedthat the first crack in the joint occurred before reaching the ulti-mate load. Therefore, fracture energy determines whether residualtensile strength is already critical for ultimate load or not. Fig. 20shows that the increase in joint shear strength due to increase infracture energy for beam column joints having one (P1) and three(P3) stirrups in the joint. The values are normalized based on theresult for NC. The diagram shows that the magnitude of incrementis not same for both the cases. This might be due to the fact thatless number of stirrups allows for higher strain in the joint andtherefore the remaining tensile strength is less or the residual ten-sile strength is active. Therefore fracture energy should not be con-sidered independently from stirrups. Fig. 21 shows that theenvelopes of the load–displacement diagrams (for negativemoment in beam) are closely placed. Therefore, due to higher frac-ture energy the remaining strength in higher drift levels is found tobe higher, although the proportional strength degradation isalmost same.

In higher deformations and with corresponding wider crackwidths, only the residual tensile strength can be activated for loadtransfer. In DAfStb Richtlinie Stahlfaserbeton [32], residual tensilestrength is stipulated to be used for design up to a calculated strainof 2.5%. Fig. 22 shows increase in the joint shear strength depend-ing on residual tensile strength for different degrees of stirrup con-finement (P1 = one stirrup, P3 = three stirrups) in the joint.Residual tensile strength increases the tension stiffening con-tribution from conventional reinforcement as described above(see Table 5) and fracture energy is not increased compared toNC. Compared to fracture energy, ultimate joint shear strengthincreases and therefore joint shear strength can be increased byan independent contribution from residual tensile strength. Inview of joint shear deformation and strength degradation anothertrend is also identified. At the same drift level, joint shear

(b)

0

0.2

0.4

0.6

0.8

1

1.2

0 0.01 0.02 0.03 0.04 0.05 0.06

Joint shear deformation γ [-]

nega

tive

norm

aliz

ed s

tren

gth

degr

adat

ion

[-]

SP6-P3-C30-c035

SP6-P3-C30-c05

SP6-P3-C30-c06

SP6-P3-C30-c08

sile strength is a parameter (a) specimens with 1 stirrup, and (b) specimens with 3

600

650

700

750

800

850

0 0.005 0.01 0.015 0.02

ρsw,V [-]

V jh [k

N]

stirrups

P1+fibres

P3+fibres

Fig. 24. Joint shear forces for increasing amount of stirrups in combination withcertain amount of fibre contents (under constant parameters as: fcm = 38 MPa,fy = 500 MPa, Axial compression in column = 300 kN and fiber content = 1 and3 vol.%).

C. Roehm et al. / Engineering Structures 91 (2015) 182–196 195

deformation is reduced for increased residual tensile strength, andjoint shear strength remains at a higher level as can be seen fromFig. 23.

4.4.3. Influence of fibres and stirrupsIn the previous sections, fibres are considered as parameter for

calculating the joint shear strength. Fig. 24 shows the maximumjoint shear strength for increasing amount of stirrups in the jointalong with different amount of fibres. It is clear from the figure thataddition of steel fibre increases the residual tensile strength whichleads to higher joint shear strength. Fig. 24 shows that the jointshear strength for both one stirrup (P1 case: qsw ¼ 0:003) and threestirrups (P3 case: qsw ¼ 0:016) together with FRC is higher than thecase with 5 stirrups (qsw ¼ 0:016)without any fibre in the joint. It issignificant to mention here that by adding fibres without any stir-rup in joint leads to an increase in joint shear strength; but in thiscase, after pull out of the fibres, the residual tensile strength is notactive any more. The same has been observed from experiment aswell and it was noted that strength degradation was faster forjoints with steel fiber alone. Therefore, combination of fibres andstirrups is more favourable for beam–column sub-assemblagesunder repetitive reverse cyclic loading.

5. Concluding remarks

In the present study, non-linear Finite Element (FE) programATENA has been used for analysing NC and FRC beam–columnsub-assemblages which were experimentally investigated as well.For mathematical model of FRC material, the model for NC availablein ATENA has been suitably modified to represent FRC in combina-tion with reinforcement bars. This was carried out by adjusting thetensile behaviour through higher values for fracture energy andresidual tensile strength using material tests carried out on FRC.

It is found from the results that the load–displacement hystere-ses and damage pattern, obtained from the numerical analyses arein close agreement with those obtained from the experimentalinvestigations. The results of the numerical study indicate that itis possible to predict the cyclic load response of NC and FRC speci-mens in terms of load–displacement hysteresis and damage pat-tern. It is attempted to correlate the energy dissipation obtainedfrom the numerical analyses with those obtained from experimen-tal investigations. This would give an idea of the actual energy dis-sipation in the real structure and pave the way for alternate/improved designs.

Finally, an elaborate parametric study is carried out to identifyand quantify the influencing parameters which play key role on

shear strength of joint, strength degradation, shear deformationetc. Based on the results obtained from the tested specimens, theinfluence of several parameters such as concrete strength, numberof stirrups in the joint and content of steel fibres on joint shearbehaviour and strength are investigated. It was confirmed thatconcrete strength is the main influencing parameter on joint shearstrength. Further, a relationship for strength degradation depend-ing on joint shear deformation is established. Stirrup contributionis found to be less effective than fibre contribution for the presentgeometry, though combination of stirrups and fibres seem to befavourable for shear strength enhancement. The effect of fibre con-tribution from residual tensile strength and fracture energy cannotbe considered independently, whereas using the residual tensilestrength only for design would lead to provide over conservativeresults. Fibre contribution in concrete can be incorporated in thenumerical models by changing the residual tensile strength whichhas more prominent effect than fracture energy. Increase in resid-ual tensile strength leads to a linear increase in joint shearstrength. It is also found that the failure mode cannot be changedby adding fibres only, if the compressive strength is too low. Thepresent study brings out the role and importance of individualcomponents and contributes to the understanding and improve-ment of cyclic load behaviour of beam–column sub-assemblageswhich are designed using conventional materials and materialswith improved engineering properties such as FRC.

Acknowledgements

The paper is being published with the kind permission of theDirector, CSIR-SERC. Some of the results reported here are part ofthe Indo-German collaborative research project entitled‘Development of methods for fatigue and seismic resistant designand management of concrete structures’ between CSIR-StructuralEngineering Research Centre (CSIR-SERC), India and Institute forLightweight Structures and Conceptual Design (ILEK), Universityof Stuttgart, Germany under CSIR-FzJ Cooperative ScienceProgramme sponsored by DLR-IB-BMBF and CSIR. The authors wishto express their gratitude and sincere appreciation to the Directorand officials of CSIR-Structural Engineering Research Centre (CSIR-SERC), Chennai, India for facilitating the experimental works.

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