Open Access A Simplified Procedure for the Seismic Design of Hybrid Connections in Precast Concrete Structures

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1 Send Oer for Rerint to The Oen Contrution and Building Tehnology Journal, 2013, 7, Oen Ae A Simlified Proedure for the Seimi Deign of Hybrid Connetion in Preat Conrete Struture F. Poro *, D. Raffaele and G. Uva Diartimento DICATECh, Politenio di Bari, Italy Abtrat: The orret ue of non-adherent retreing tehnique in beam-olumn onnetion an ignifiantly inreae the eimi erformane of reat onrete frame, making them a ometitive alternative to the traditional at-in-lae onrete truture. In thi ene, a fundamental fator of the node deign i rereented by the orret alibration of the ratio between the amount of mild teel and that of ot-tenioned reinforement, in oer to rovide the reribed flexional and rotational aaity to the beam-olumn interfae, and to guarantee at the ame time the required diiative and re-entering aaity. In thi aer, a imle algorithm for the otimal and quik re-dimenioning of the above mentioned arameter i rooed. It i baed on the knowledge of the material mehanial arameter and of the target tree and deformation orreonding to the required erformane level, whih an be omuted either through a Fore Baed Deign aroah or by a Dilaement Baed Deign aroah. In the ae of entered ot-tenion and in the reene of ymmetrial mild teel, the roedure an alo be effetively rereented in a grahial form, making it i eaily oible to determine the ot-tenioning tre that hould be alied to the able in oer to guarantee that they remain in the elati field after the eimi event, and to obtain the reentering of the ytem. Keywo: Preat onrete frame, hybrid beam-olumn onnetion, ot-tenion, elf-entering aaity, eimi deign. 1. INTRODUCTION Over the lat thirty year, the ientifi ommunity ha been extenively involved in reearh rogram aimed at invetigating the oibility of an organi aroah to the ue of reat omonent, in oer to overome the traditional idea that their deign hould emulate that of at-in-lae truture. Still today, in fat, the advantage of uing refabriated omonent alo in area of high eimiity are not yet fully exloited beaue of the retritive rerition ontained in many international tehnial ode [1, 2]. In thee ode, a a matter of fat, the ue of reat ytem in whih element are aembled by uing dutile dry onnetion i limited, and referably the ue of integrative at-in-lae onrete filling, wet onnetion, i uggeted, whih of oure inreae exeution time and related ot. The reent ACI tanda [3] ontain deign roviion for reat onrete truture exoed to high eimi rik. It i anyway ointed out that uh requirement are baed redominantly on field and laboratory exeriene with monolithi reinfored onrete building truture and reat onrete building truture deigned and detailed to behave monolithi. The extraolation of thee requirement to other tye of at-in-lae or reat onrete truture hould be baed on evidene rovided by field exeriene, tet, or analyi. *Addre orreondene to thi author at the Diartimento DICATECh, Politenio di Bari, via Orabona 4, Bari, Italy; Tel: ; Fax: ; f.oro@oliba.it In the lat few year, the ue of ot-tenioning tehnique for aembling reat element ha been onidered with great interet. Many exerimental tudie were devoted to thi iue, whih however howed ome drawbak: thee ytem have a very low energy diiation if omared to wet onnetion, and, beide, they exhibit a relevant tiffne redution beaue of the retenion loe uffered by the tendon. The iniration of introduing unbonded tendon in the onnetion among reat beam and olumn in oer to otimize the eimi erformane of the ytem wa rooed for the firt time by Prietley and Tao [4]. Later, Stone and other [5] drew on thi initial idea, while exerimental evidene were rovided by the PRESSS (PREat Seimi Strutural Sytem) reearh rogram, arried out at UCSD (California Univerity, San Diego) from 1990 to 1999 [6]. During thi rogram extenive exerimental tet were erformed over model of a 5 torey building (in a 2:3 ale) ubjeted to eimi load, roviding different tye of node among the reat element, both for moment frame and hear wall reiting ytem. By now, it ha been widely demontrated through both exerimental and theoretial tudie that the ue of unbonded retreing tendon a a onnetion ytem ignifiantly imrove the eimi erformane of reat frame, that an o be onveniently ued a a ometitive otion to at-inlae frame. It i imortant to emhaize that a wideread ue of reat ytem, with element made in the fatory, would avoid the dierion of the reitane value of the in itu onrete / Bentham Oen

2 64 The Oen Contrution and Building Tehnology Journal, 2013, Volume 7 Poro et al. that often adverely affet the trutural erformane [7-9]. In the aer the euliar feature of ytem baed on hybrid node will be extenively diued. The aim i that of deribing a method for the raid otimal reliminary deign of the main arameter: ottenione able area, initial value of the retenion and mild teel area. With thi roedure it i oible to attain the required flexural rotational and diiative aaity a well a the elf-entering aaity, that i the ability of the truture to return towa it initial onfiguration uon unloading. 2. SEISMIC PERFORMANCE OF DUCTILE CON- NECTIONS 2.1. Traditional Pretreed Connetion Preat frame aembled uing traditional retreing tehnique, i.e. adherene i obtained by grouting the able after ot-tenion, have generally hown a good level of dutility, whih i omarable to that of traditional at-in-lae frame. Neverthele, even for low damage level, thee frame exhibit an exeive and dangerou tiffne redution [10, 11], whih will determine a dro of the original retenion level when the initial train onfiguration i reovered after the eimi event. The higher the exurion beyond the roortionality threhold during the earthquake, the more evere the lo of the retre i. For examle, in the ae of the onnetion hown in (Fig. 1a), thi henomenon would oniderably redue the tiffne of the ytem, onequently reduing the aaity to uort vertial load, and inreaing the amount of hear reinforement required to guarantee the roer flexional aaity for the beam and for the node [12]. The henomenon i deribed in the diagram of (Fig. 1b), howing the tretrain diagram of the retreing able (σ -ε ). If σ 1 i the ervie tre in the able, urged of the initial loe of tenion, under a mall variation around oint 1 the able remain within the elati field, and no tre dro i rodued. Under higher eimi load, intead, the truture enter in the lati field. Let uoe that the able reahe the tre-train tate rereented by the oint 2 in (Fig. 1b), belonging to the lati branh of the ontitutive urve. It an be immediately oberved that the unloading ath to the initial deformation ε 0 i haraterized by the retenion lo (σ 1 -σ 2 ) A. It ould be alo haen, for higher dutility level (oint 3 in Fig. 1b), that the whole initial retenion fore i lot. In onluion, a mot eriou rik i that the lo of retenion indued by the yielding of the retreing able an make the ytem unable to utain even the only gravity load Pretreed Connetion Realized with Pot- Tenioned Unbonded Tendon The ue of unbonded able reent a number of advantage, whih were highlighted alo by exerimental reearh rogram, among whih it i worth mentioning the work arried out by Prietley and Tao in 1993 [4] on node rototye like the one hown in (Fig. 2a), where the aembly of reat beam-olumn element wa obtained by uing unbonded able deigned in oer to maintain an elati behavior throughout the load yle. Among the feature haraterizing the eimi erformane of thi tye of node, the following aet an be ointed out: a) Sine the behavior of the able i urely elati even under the maximum dilaement demand, eimi ation will not indue any lo of retre, and therefore the fritional hear reitane of the interfae etion and the related reitane to vertial load will not be ermanently affeted at the end of the horizontal load yle. b) Thi tye of onnetion able are aommodated into ot-tenioning dut without any grouting, and thi ha the non-negligible advantage of dramatially reduing the eimi damage level - whih i tyially onentrated at the interfae etion - wherea in other node tye, beaue of the adherene, it i uually read all over the trutural omonent. In other wo, thi involve a ignifiant redution of reair and maintenane ot and, more in general, a mitigation of the one- Fig. (1). (a) Beam-olumn onnetion realized with adherent able; (b) Stre-train diagram for the retreing able.

3 A Simlified Proedure for the Seimi Deign of Hybrid The Oen Contrution and Building Tehnology Journal, 2013, Volume 7 65 quene related to the oible interrution of ue and lo of ervieability. ) The overall ytem trutural reone i baially elati, even if non-linear. When onidering the eimi erformane, thi behavior ha the advantage of allowing the ytem to reover the initial undeformed onfiguration, with no areiable reidual deformation after the earthquake. On the other hand, thi mean alo that there i a almot no energy diiation aaity (Fig. 2b), and that the trength demand will onequently be high. Fig. (2b) deribe the tyial fore dilaement relationhi (F-Δ) for the onnetion tye hown in (Fig. 2a), realized through ot-tenioned unbonded able. In the diagram, F and Δ reetively are the fore alied and the horizontal dilaement of the harateriti oint hoen for monitoring the ytem. The beam-olumn interfae etion i fully omreed and the overall reone of the node i linearly elati until oint 1, orreonding to the firt raking of the onrete. With a good aroximation, a linear elati behavior an be aumed until the rak i limited to half the height of the beam (oint 2 in the diagram of Fig. 2b). Beyond thi oint, the fore-dilaement relationhi i a highly non-linear elati one, and finally, at oint 3 the able tre reahe the yielding limit Hybrid Connetion The main diadvantage of the ot-tenioned able onnetion deribed in the reviou aragrah i rereented by the non-linear elati reone of the ytem, that i virtually aoiated with a zero additional daming. Conequently, a very low diiation aability an be attained and a higher demand of trutural trength i required. The eimi behavior of retreed onnetion with unbonded able an be oniderably imroved by the imlementation of the o-alled hybrid onnetion, obtained by ombining the ue of unbonded tendon with the imultaneou ue of mild reinforement [5]. A well a the laial retreed node, uh a onnetion (Fig. 3) i oneived in oer to lum the damage ditribution at the interfae etion, thank to the oening/loing effet, but allow at the ame time a ignifiant energy diiation related to the yielding of the oinary reinforement. Alo in thi ae, the able kee an elati behavior during the eimi event, and oible loe of retre are revented. Conequently, the fritional hear reitane at the interfae i ket at the maximum level, and a ignifiant elfentering aaity i guaranteed, minimizing oible reidual deformation. The harateriti Fore-Dilaement urve of a hybrid onnetion i ubtantially different from that of onventional retreed node. Fig. (4a) how, in a imlified bi-linear form, the tyial non-linear elati reone of a onnetion oniting only of unbonded ot-tenioned able, obtained by lotting the bending moment M alied at the node againt the rotation θ, a defined in (Fig. 2). The hyothei of elatiity mean that, during the loading and unloading yle, the ame initial ath i alway followed, and that no energy i diiated. On the other hand, (Fig. 4b) how the ideal hytereti yle of an elati-lati ytem endowed with energy diiation. When load are removed, thi ytem an reent a onitent reidual dilaement, uually omarable to the maximum hift attained during the loading yle. Obviouly, hybrid ytem are harateried by a ombination of the reviouly deribed behavior. A artiularly effetive olution i hown in (Fig. 4) (flag hae hyterei loo): the diiative aaity tyial of mild reinforement i ombined with the elf-entering roertie of unbonded able in uh a way that the ytem ha no reidual dilaement when the load i removed [4]. A a limit ae, in the reene only of the unbonded ot-tenioned able, the ontitutive behavior would be the non-linear elati one hown in (Fig. 4a), whih guarantee the omlete elf-entering of the ytem. If the unbonded Fig. (2). (a) Beam-olumn onnetion realized with unbonded able; (b) Non-linear elati reone of the ytem.

4 66 The Oen Contrution and Building Tehnology Journal, 2013, Volume 7 Poro et al. Fig. (3). Shematization of a Hybrid beam-olumn onnetion [13]. Fig. (4). Tyial bending moment-rotation urve: a) for a bi-linear elati ytem; b) for a hytereti diiative ytem; ) for a hybrid ytem. tendon are miing, intead, the behavior i haraterized by the hytereti yle hown in (Fig. 4b), whih allow the maximum available energeti diiation, but require a well a great reidual lati deformation. It an be oberved that if the ontribution of the ot-tenioned able (M rt ) i inreaed, a lower diiative aaity reult, but the ytem an rovide a higher dilaement demand, thank to a greater elf-entering aaity.

5 A Simlified Proedure for the Seimi Deign of Hybrid The Oen Contrution and Building Tehnology Journal, 2013, Volume 7 67 On the other hand, by reduing the amount of ottenioned teel, the diiative aaity grow, wherea reidual dilaement beome relevant, with a onequent inreae of both damage and related ot for the otearthquake retrofitting. The otimal balane between M rt and M t i uually dedued from the required erformane level, that i to ay by ontrolling the maximum dilaement exeted under the deign earthquake and the aetable damage, exreed by a roer limitation of reidual deformation. Thene, one the final flexural aaity M of the node i fixed, the flexural ontribution M rt of the ot-tenioned able and the ontribution M r of the yielded mild teel an be roerly ombined and ued a the main deign arameter. The reliminary deign of hybrid onnetion will then rovide, firt of all the a-riori hoie of the arameter Γ: M rt = (1) M Aoing to the reviou onideration. Then, aoing to the heme of (Fig. 5), a reliable value of the equivalent daming of the ytem (ξ eq ) an be determined, or, alternatively, a roer behavior fator q. The firt arameter i the bai for the definition the eant tiffne of the equivalent ytem, if a Dilaement Baed Deign aroah i to be ued, wherea the eond one i ueful for a laial Fore Baed Deign. The diagram how that by inreaing the ontribution related to the ot-tenion, the diiative aaity i redued, wherea the ytem i till able to atify the eak dilaement demand, thank to the higher elf-entering aaity. On the other hand, by reduing the amount of ottenioned reinforement, the diiative aaity i inreaed but the reidual drift beome non-negligible, with a oniderable growth of the eimi damage level and of the onequent reair and maintenane ot after the earthquake. For thee trutural tye, a orret deign hould therefore require the a-riori definition of the ontribution to the overall flexural node reitane reetively aigned to the yielded mild teel (M r ) and to the retreing able (M rt ). In artiular, the reliminary knowledge of Γ ratio will allow to define a reliable value of the equivalent daming ratio ξ eq, whih i the eential element to be ued either in the evaluation of the eant tiffne of the "relaement ytem" within a Diret Dilaement Baed Deign (DDBD, [11]), or in the determination of the adequate behavior fator q, aoing to the laial Fore Baed Deign aroah FBD (ee Fig. 5). The deign of the reinforement, aoing to the hoie made about Γ=M rt /M will then follow from thee arameter, and it will be alo oible to hek if during the loading roe the tre level of the retreing able remain within the elati limit and if the onnetion kee an adequate elf-entering aaity. If the eleted ratio Γ doe not atify the deign erformane level, it will be neeary to realibrate it. Thi will require the identifiation of a new value of equivalent viou daming and the reiteration of the related DDBD roe, or alternatively the redefinition of the trutural fator q, reliminary to a new FBD analyi. Fig. (5). Diagram howing the variation of the drift θ of the node (to), equivalent daming and trutural fator (bottom) with the arameter = M rt / M. 3. A SIMPLIFIED PROCEDURE FOR THE DESIGN OF HYBRID CONNECTIONS 3.1. Parameter and Equation Governing the Deign Preat onrete frame are often introdued in building with the ole uroe of oerating a a braing element, whereby the effet of gravity load beome negligible if omared to eimi tre, and the adotion of ymmetrial mild reinforement together with a entered ot-tenion reult artiularly rational. In thi ae, the deign of the beam-olumn interfae etion of a hybrid onnetion an be onveniently erformed by mean of the imle aroah that i baed on the ue of few dimenionle arameter whih exre the main variable involved in the analyi (Fig. 6) [14]. The following ymbol and non-dimenional arameter are now introdued: b = deth of etion d = effetive height of etion = x / d = normalied neutral axi deth = / d = normalized onrete over deth = d = mild reinforement ratio; A / = f / f y f = onrete omreive trength f y = nominal yield trength of teel;

6 68 The Oen Contrution and Building Tehnology Journal, 2013, Volume 7 Poro et al. Fig. (6). The Beam-olumn interfae etion: geometry; definition and ymbol; tre ditribution. When the mild teel i yielded, the reitant moment M of the etion an be exreed in dimenionle term by the following equation: M * 1' m = = '& %$ $ 2 " 2 + ' ( + (2) bd f, 2 ) 2 Similarly, the dimenionle exreion of the axial fore N (whih in thi ae i given by the ot-tenion in the able) i: N n = = " (3) bdf The value of the ontant and, whih define the reultant of the omreive tree over the etion and the oition of the neutral axi deend on the ontitutive law adoted for the onrete. In (Fig. 7), θ and M reetively are the deformation meaure and the internal ation of a tyial node obtained after a DDBD/ FBD analyi of the overall truture, in whih it ha been aigned in advane the value of Γ=M rt /M, flexural aaity rovided by the ot-tenion able over total flexural aaity of the beam-olumn interfae at the target deformation. From the analyi of equation (2), it an be notied that the firt term at the right member rereent the ontribution of the able tre to the non-dimenional reitant moment m rt, wherea the eond term define the quota m r took over by the mild teel, whih i uoed to be yielded in orreondene of the atual limit deformation. It i worth oberving that the target drift lay a fundamental role in defining the amount of ot-tenion reinforement whoe behavior mut remain within the roortionality limit under thi deformation, if we wih to avoid dangerou loe of retre. Thene, it i fundamental to identify firt of all the relationhi that link the flexional aaity m rt ulied by the able to the rotation θ at the beam-olumn interfae. With the notation in (Fig. 7), if the able i uoed to be unbonded along the entire length L na, it i oible to exre the able elongation a a funtion of the rotation θ or equivalently a a funtion of the train variation Δε of the able a follow: ( ht % " L = 2 + & ) x = "* Lna (4) ' 2 $ that, if we all τ na the length of the unbonded tendon belonging to eah beam-olumn interfae (in the ae of the figure: τ na =L na /2), beome: + h * 2 t $ ), x& = %" $ ( ' na By introduing the arameter χ t = τ na /h t, rereenting the ratio between the ortion of the able reviouly defined and the overall height of the etion h t (ee Fig. 7), and the non-dimenional meaure of the arameter hown in (Fig. 6), the additional eifi elongation Δε of the able an alo be written a: (-, & * = $ 0.5 ' + % 1+ ) " t From eq. (5) and (6), the relationhi between the interfae rotation θ and the able elongation at the limit train i finally obtained: $ % = & 0.5 ' 1+ " t For the deign uroe, it i uoed that the able ha jut been reahed, with no further exurion, the limit elati deformation, and thene the orreonding tre value f y. Conequently the train variation of the able i: " = f y E f i where f i i the initial tre alied to ut the able under tenion (net of the initial lo). (5) (6) (7)

7 A Simlified Proedure for the Seimi Deign of Hybrid The Oen Contrution and Building Tehnology Journal, 2013, Volume 7 69 Fig. (7). Deformation at the beam-olumn interfae in orreondene of the target drift. After introduing the non-dimenional quantitie: f y y =, f f i i =, f E E = f and defining: &) y ') i + = * ( $ t (8) % ) E " Eq. (7) an alo be written a: $ = " 0.5 % 1+ Uing the reviou reult, and after ome algebrai maniulation of eq. (2), the following exreion for m rt an be dedued: (9) & 2 ) m = ' + $ *) ' ( 1+ () " (10) rt % 2 Solving eq. (9) for ξ, and relaing it in (10), it i finally oible to obtain the funtion exreing the ontribution m rt of the able, that uoed to work at the elati roortionality limit, and the rotation, whih i aumed a the main erformane deign arameter: 2 & 2" m = &%( 1 + $ ) [ ( & 1) & 2" ] (11) rt 2 4 In (Fig. 8a) it i hown the diagram of the funtion m rt (θ), aoing to eq. (11), wherea in (Fig. 8b) the variation of m rt and θ with the oition of the neutral axi i hown. All the diagram are reented for a et of value of the fator β, whih deend on the onrete la and the teel tye, obtaining a et of urve. Beide, the diagram were lotted auming the arabola-retangle ontitutive law rovided by the tehnial tanda for onrete lae with f k 50 MPa [1, 2], auming the value κ=0.809; η= Some Remark With referene to the diagram of (Fig. 8), when a oule (m rt = Γm ; θ) orreonding to the erformane required to the node i aigned, it i immediately ingled out the value, and, onequently, the maximum ot-tenion value for whih the able remain within the elati field during the eimi event. In fat, remembering the exreion of β, we obtain: * ( ) i ' % & max = y $ E " t (12) When the limit reitane of the etion i attained, the maximum omreive fore in the onrete mut be equal to the maximum fore exerted by the tendon at the elati limit, ine the mild reinfored have been uoed to be ymmetrial and are both yielded. Thi imlie: f bd " = A f (13) from whih, alled ρ =A /bd, we obtain: y " y $ = (14) Thi relationhi rovide the amount of teel required for the ot-tenioning a a funtion of the oition reahed by the neutral axi at the yielding limit of the ot-tenioned reinforement. It hould be noted that the deign of the retreing reinforement i indeendent both from the mild teel amount and from the initial value of the retenion fore, whoe maximum value i governed by eq. (11). A reviouly remarked, the 2 nd addendum at the right member of eq. (2) rereent the ontribution m r to the total flexural aaity of the etion rovided by the yielded mild

8 70 The Oen Contrution and Building Tehnology Journal, 2013, Volume 7 Poro et al. Fig. (8). (a) m rt - ϑ diagram for different value of β. (b) Plot of the funtion m rt (ξ) and ϑ( ξ) for different value of β. teel. Remembering that Γ=M rt /M, thi an be alo written a: 1 " m r = % $ ( 1 " ) = m (15) rt Another fundamental aet in the deign of hybrid node i rereented by the monitoring of the elf-entering aaity of the onnetion. It hould be noted that, when the external ation eae, all the mild teel will be omreed and, therefore, in oer to enure the elf-entering of the etion it will be uffiient that the retreing able rovide a tenile ation greater then the omreion reultant of the oinary reinforement. In formula, thi mean that it hould reult: f " 2 f (16) i y whih, with the uual non-dimenional notation, an be written a: 1 i " " (17) 2 At lat, it hould be ointed out that if the ondition exreed by eq. (17) i not atified, it i neeary to retart the deign of the etion, by inreaing the arameter. Thi obviouly mean that the new equilibrium ondition for the reitant moment at the node alo hange the individual value of the bai deign arameter, the equivalent viou daming ratio ξ eq in a DDBD or the behavior fator q in an FDB, and the entire analyi mut be retarted by uing new value of the arameter An Iterative Simlified Proedure for the Preliminary Deign Baed on a 4-Way Abau The obervation reented in the reviou aragrah are an ueful bai for the deign of an hybrid onnetion, and allow to addre the roedure to a artiularly onvenient and imle iterative aroah, ummaried in the flow hart hown in (Fig. 9) and briefly exlained below: a. Firt of all, a trial value i et for the arameter ξ (defining the oition of the neutral axi) and f i, (whih rereent the initial tenile fore alied to the tendon, after deduing the initial loe). b. From eq. (6), the value of the additional eifi elongation of the able i omuted a a funtion of the deign rotation θ of the onnetion, and the overall fore i thene known: f = f + " E. i. A hek i arried out to ee whether the able ha reahed the yielding oint and, if o, the initial retenion fore i redued, returning to te 1. d. Aoing to the value hoen for the neutral axi oition and for the arameter, on whih the analyi i baed, the two ontribution m and rt m r of the reitant moment of the interfae etion are alulated, together with the orreonding teel ratio: = m r /( 1$ ") and $ = " /. e. It i heked if the reultant flexural aaity M d atifie the ondition m d mrt + mr, and if it doen t, the oition ξ of the neutral axi i hanged, oming bak to the te 2 of the roedure and retarting the dimenioning of the reinforement. f. At the end, after a oitive feedbak about the reviou oint, the exitene of an adequate elf-entering aa- " $ 2 " /, other- ity of the etion i heked ( ) i wie the arameter i reonidered, by inreaing the ontribution m rt of the able and retarting from te 1. After omleting the above deribed roedure, it i highly adviable to ae the omatibility of the maximum train attained in the mild reinforement by onidering the

9 A Simlified Proedure for the Seimi Deign of Hybrid The Oen Contrution and Building Tehnology Journal, 2013, Volume 7 71 Fig. (9). Flow hart of the roedure for the deign of hybrid onnetion. atual mehanial arameter of the teel, above all with reet to a oible fatigue behavior. An aet that ould affet the deribed roedure i obviouly rereented by the orret evaluation of the limit elati reitane of the mild teel, onidering the oibility that it may aume different value in tenion and omreion. Keeing in mind thee warning, the abau hown in (Fig. 10) i artiularly effetive for the raid reliminary deign of the mild and retreing teel ratio, a well a for the immediate aement of the elf-entering aaity of the onnetion. The abau ontain the fundamental arameter involved in the deign of the hybrid onnetion, a later exlained, and wa obtained in the imlifying aumtion of an elati-erfetly lati ontitutive model, with equal over-trength fator both in tenion and in omreion, for the mild reinforement In the firt quadrant of the abau, the funtion m rt = f rovided by eq. (10) i lotted, after dividing it ( ) by the arameter = f / f for an eaier grahial rereentation. y The eond quadrant ontain intead the lot of the funtion ξ=ξ(ρ ) exreed by eq. (14), whih define the minimum quantity of ot-tenioned reinforement aable to guarantee the required flexural aaity m rt when the oition reahed by the neutral axi varie, and the teel remain within the roortionality limit.

10 72 The Oen Contrution and Building Tehnology Journal, 2013, Volume 7 Poro et al. Fig. (10). The abau for the deign of the reinforement and for the verifiation of the elf-entering aaity hybrid beam-olumn onnetion. In the thi quadrant, the amount of mild reinforement that, after the yielding oint, i able to guarantee the flexural aaity m r a well a the diiation demand i lotted a a funtion of the arameter Γ, aoing to eq. (15). i Finally, the thi quadrant of the abau how the lot of the linear equation = 0.5 f / f, whih divide the quadrant into two half-ae and, realling eq. (17), allow the immediate araial of the ytem elf-entering aaity. It hould be alo aid attention to hek that the maximum value of the ratio f / = / atifie eq. (12), o that i f the able remain within the elati field. i The abau reented in (Fig. 10) an be a very ueful ratial tool for the dimenioning beam-olumn hybrid node, by following the roedure reented in (Fig. 11), through a ratial examle of the aliation. It i uoed that the material and their harateriti mehanial arameter are reliminarily aigned for the onnetion (onrete la, teel tye). Thene, in eah quadrant a ingle urve i extrated from the familie ontained in the general abau of (Fig. 10). One the deign arameter,,, and are y i E aigned, together with the deign reitant moment oinate of oint A, given by rt m, the m / = " m / i immediately identified. Starting from oint A, the ath ABCD i followed until the roer urve " ( ) i intereted (the eletion of the urve, a reviouly remarked, i governed by the material roertie), and thi determine the area of the ot-tenion reinforement A = " bd whih, at the limit of roortionality, rovide the moment m = " m together with the treed onrete under limit ondition. rt Alway tarting from oint A, but roeeding in vertial along the ath AEF, the interetion found with the horizontal axi ρ orreond to the mild reinforement ratio whih, at the yielding, enure the ontribution m r = ( 1 ") m, i.e. it i oible to dimenion the oinary reinforement A = A ' = " bd. The aement of the elf-entering aaity of the ytem i erformed by heking if the oint G(, ) lying in the 3 quadrant fall within the area haded in (Fig. 11), that i harateried by the ondition exreed by eq. (16): " 1/ 2 " ( i / ) max. The ratio ( i / ) an be eaily alulated from eq. (12), after analytially obtaining max from eq. (11), or, in a quiker way, grahially determining it from the abau in (Fig. 8). Fig. (11). Examle of the ue of the deign 4-way abau of Figure 10.

11 A Simlified Proedure for the Seimi Deign of Hybrid The Oen Contrution and Building Tehnology Journal, 2013, Volume CONCLUSION The aim of the rooed roedure i to rovide a imle tool for the reliminary deign of the main arameter governing the reitane of an hybrid onnetion, under ome imlifying but reaonable aumtion: retangular etion with ymmetrial mild reinforement and entered ot-tenion. In artiular, a non-dimenional 4-way abau ha been lotted, whih allow, through an immediate grahial aroah, the alulation of the following arameter: - teel ratio both for the mild reinforement teel and for the ot-tenioned able; - tenile fore to be alied to the unbonded tendon in oer to guarantee an elati behavior. Even if the abau wa built under the aumtion that the mild teel i yielded, wherea the ot-tenioned able train do not exeed the limit of roortionality, the ue of non dimenional arameter in the abau eaily enable to hange the above mentioned hyothee. For intane, in oer to take into aount the reene of haening in the ontitutive behavior ondition the oinary reinforement, or to limit the maximum train in the able, uitable redued value of the normalized fator = f y / f and y = f y / f an be introdued in the abau. CONFLICT OF INTEREST The author() onfirm that thi artile ontent ha no onflit of interet. ACKNOWLEDGEMENT The reearh reented in thi artile wa artially funded by the Italian Deartment of Civil Protetion, Projet Re- LUIS-DPC REFERENCES [1] CEN. Euroode 8: Deign roviion for earthquake reitane of truture Part 1: General rule, eimi ation and rule for building. Euroean Committee for Standaiation EN1998-1, Bruel, Belgium, [2] DM 14/01/08 Norme tenihe er le otruzioni NTC2008, G.U. n. 29., 4th February 2008; Roma; Italy (in italian) [3] ACI Committee Strutural Building Code: Building ode requirement for trutural onrete (ACI 318m-08) and Commentary. ACI, June [4] M.J.N. Prietley, and J.T. Tao, "Seimi Reone of Preat Conrete Frame with Partially Debonded Tendon", PCI Journal, vol. 38, no. 1, , [5] W.C. Stone, G.S. Cheok, and J.F. Stanton, A Hybrid Reinfored Preat Frame for Seimi Region, PCI Journal, vol. 42, no. 2, , [6] M.J.N. Prietley, S. Srithara, J.R. Conley, and S. Pamanin, Preliminary Reult and Conluion from the PRESSS Five-Story Preat Conrete Tet Building, PCI Journal, vol. 44, no. 6, , [7] G. Uva, F. Poro, A. Fiore, and M. Mezzina, Prooal of a methodology of in-itu onrete tet and imroving the etimate of the omreive trength, Contrution and Building Material, vol. 38, no. 1, , [8] A. Fiore, F. Poro, G. Uva, and M. Mezzina, On the dierion of data olleted by in itu diagnoti of the exiting onrete, Contrution and Building Material, vol. 47, , [9] F. Poro, and G. Uva, Aement of the reliability of Strutural Conrete During Exeution Phae, In: M. Paadrakaki, V. Paadooulo, V. Plevri, Ed. COMPDYN th ECCOMAS Themati Conferene on Comutational Method in Strutural Dynami and Earthquake Engineering, Ko Iland: Greee, June 12 14; [10] M.J.N. Prietley, G.M. Calvi, and M.J. Kowalky, Dilaementbaed eimi deign of truture, IUSS Pre: Pavia, Italy, [11] M.J.N. Prietley, Diret Dilaement-Baed Deign of Preat/Pretreed Conrete Building, PCI Journal, vol. 47, no. 6, , [12] M.J.N. Prietley, Myth and Fallaie in Earthquake Engineering, IUSS Pre: Pavia Italy, [13] Federation internationale du beton, fib Bulletin n. 27 Seimi deign of reat onrete building truture, ISBN , January [14] M. Mezzina, D. Raffaele, and A. Vitone, Ed. Teoria e Pratia delle otruzioni in emento armato - Vol. I Dalla onezione trutturale alle verifihe agli tati limite, DeAgotini Suola S..A., 2007 (in italian). Reeived: May 20, 2013 Revied: July 31, 2013 Aeted: Augut 03, 2013 Poro et al.; Lienee Bentham Oen. Thi i an oen ae artile liened under the term of the Creative Common Attribution Non-Commerial Liene (htt://reativeommon.org/- liene/by-n/3.0/) whih ermit unretrited, non-ommerial ue, ditribution and rerodution in any medium, rovided the work i roerly ited.