41 ГОДИНА ГРАЂЕВИНСКОГ ФАКУЛТЕТА СУБОТИЦА

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1 4 ГОДИНА ГРАЂЕВИНСКОГ ФАКУЛТЕТА СУБОТИЦА Савремена достигнућа у грађевинарству 4 април 05 Суботица СРБИЈА EXPERIENCES ON THE SHEAR MODEL OF fib MODEL CODE 00 Imre Ková УДК: 607:66698 DOI:0445/konferenijaGFS 0508 Rezime: International Organization fib ha introdued a ne tandard (Model Code 00) for hear reinfored onrete and pretreed onrete The equation that deribe the model ue to parameter: angle of the rak that i reated under the influene of hearing fore k v oeffiient of onrete ontribution Standard (MC00) deribe three level ith an approximate deteration of thee parameter The firt and third level relie on the theory of modified tre field hile the eond level of the theory of modified field of plati deformation The paper preent and deribe the method applied in the oure of a large number of pratial meaurement of hear performed in the laboratory for teting of truture and material The aim of the experiment a to ompare the Hungarian reult of the meaurement obtained on onrete that ere reinfored ith polypropylene and teel fiber Keyord: pomična čvrtoća razina približavanja INTRODUCTION The fib Model Code 00 omprie a mehanial baed et of hear deign proe that i intended to offer for the engineer flexibility in eleting a balane beteen omplexity and auray for ne trutural deign and for evaluation or verifiation of exiting truture a ell [][] The ne ode proviion ontain four Level of Approximation (LoA) [] Level I provide the implet alulation herea thi i the mot onventional method among the other [] Level II i a balaned model in omplexity and auray hile Level III i the mot aurate and general approximation but need more omplex omputation than that of the other Level [] All the firt three level an be ued in the everyday engineering pratie ithout uing omputer Level I i a further option hih an be ued in nonlinear finite element analyi or generalized tre-field approahe [][] Thi paper preent the bai trutural keleton of the Level of Approximation I to III Baed on a ide ale experimental proedure aimed to invetigate the hear propertie of reinfored onrete beam tet Coll Prof Dr Imre Ková PhD Head of Department Univerity of Debreen Faulty of Engineering Department of Civil Engineering Ótemető uta -4 Debreen 408 Hungary tel: e mail: drkovaimre@gmailom 5

2 4 th ANNIERSARY FACULTY OF CIIL ENGINEERING SUBOTICA International onferene Contemporary ahievement in ivil engineering 4 April 05 Subotia SERBIA reult are alo ompared to the reult of the multilevel hear approximation of fib MC 00 SHEAR MODEL OF fib MC 00 The tate equation of hear behaviour aording to fib MC 00 i the folloing: Ed max here i the deign hear reitane hih inlude both the deign hear reitane attributed to the onrete ( ) and the deign hear reitane provided by the hear reinforement ( ) hih mut not be taken grater than max Ed i the deign hear fore Component of the tate equation above an be derived: fk A 09 kv b d 09 f yd d ot ot in Aording to the model the deign hear reitane of onrete ontribution ( ) affeted by the harateriti value of onrete ompreive trength ( f k ) the idth of the eb ( b ) the effetive dept of the etion ( d ) the partial afety fator of the onrete aording to the deign ituation ( ) and the firt parameter of the model k v defined by the level of approximation and indiate the ability of the eb to reit aggregate interlok tree hih provide the onrete ontribution to hear trength [][][3] Hoever the value of annot exeed the ruhing apaity of the onrete alulated a: fk ot ot max 09 k b d ot here defined by the different level of approximation eond parameter of the model and indiate the angle of prinipal ompreive tre in the eb hile i the angle of the tirrup or bended bar from the beam axi The onrete trength redution fator k taking into onideration the effet of raked onrete i defined a: 30 k k f k fk here k an be alulated aording to the level of approximation hile f The deign hear reitane provided by hear reinforement ( ) i generally defined by the amount of hear reinforement ( A 3 ) and the trength propertie of 6

3 4 ГОДИНА ГРАЂЕВИНСКОГ ФАКУЛТЕТА СУБОТИЦА Савремена достигнућа у грађевинарству 4 април 05 Суботица СРБИЈА reinforement ued ( f yd f yk detailing rule [] hould be applied / ) Minimum hear reinforement aording to the 3 LEEL OF APPROXIMATION I Level of Approximation I i uitable for pre-deing or initial izing of trutural element here a onervative alulation method i aeptable [] In ae that f 600 N/mm and yk f 70 N/mm a ell a the maximum aggregate ize ( d g ) i k not le than 0 mm deign hear reitane of reinfored onrete ro etion ith no ignifiant axial load ith no hear reinforement an be detered by the folloing equation []: fk 6 fk 09 kv b d b d d Further the deign hear reitane of a reinfored onrete ro-etion ith hear reinforement an be alulated a [] negleting the onrete ontribution: max here if there i no oniderable axial fore the inlination of the fitional ompreed tru ( ) aording to the propoal to be at leat ( 30 ) The ruhing apaity of the onrete at that angle ( 30 ) of the prinipal ompreive tre an be alulated by the ue of k 0 55 Reult of thi level of approximation an M Ed only be aeptable if the longitudinal train deformation x Ed / E A 09 d alulated at the middle of the effetive orking dept ( ~ d / ) i not exed of ( x f yk E 0 3 ie in ae of B500 teel quality the tenioned teel bar are in elati tate ): A 09 f yd d ot ot in max here after implifiation and onolidation e have for the ruhing apaity: max 09 k fk b ot ot fk d 55 ot 3 b ot ot d ot 7

4 4 th ANNIERSARY FACULTY OF CIIL ENGINEERING SUBOTICA International onferene Contemporary ahievement in ivil engineering 4 April 05 Subotia SERBIA 4 LEEL OF APPROXIMATION II In addition to the validity of the material propertie peifield at the Level of Approximation I ith a more aurrate deteration of the axial train ( x ) defined at the middle of the effeetive dept the deign hear reitane of a reinfored onrete ro-etion ith no hear reinforement an be ritten at the Level of Approximation II []: fk fk 09 kv b d b d k d here k dg if d g d max 6 mm and kv / kdg d or k / k d 3 v 95 dg if x x dg 50 if 0 When hear reinforement i applied the deign hear reitane of a reinfored onrete an be alulated negleting alo the onrete ontribution a: A 09 f yd d ot ot in max here the imum angel of the prinipal ompreive tre in the eb an be alulated on a more preiiou ay than in the ae of LoA I by the ue of x hile the maximum hear apaity defined by the failure of the ompreed onrete trut: max 09 k fk b here / ot ot 80 fk d ot 55 3 k and 0 x ot 3 b x ot ot d ot x 5 LEEL OF APPROXIMATION III At LoA III Model Code 00 provide an opportunity to take into aount the hear 4 fore ontributed by the onrete [] When max 0 0 x the deign hear apaity of a reinfored onrete ro-etion applying alo hear reinforement aording to the LoA III an be alulated a: here: max fk 036 Ed fk 0 9 kv b d b d 500 x max 8

5 4 ГОДИНА ГРАЂЕВИНСКОГ ФАКУЛТЕТА СУБОТИЦА Савремена достигнућа у грађевинарству 4 април 05 Суботица СРБИЈА max 09 k A 09 f yd d ot ot in fk b ot ot 80 fk d ot 55 3 b ot ot d ot 6 EXPERIMENTAL OBSERATIONS Some reult of earlier hungarian hear tet arried out on beam having mm ro-etion and m length together ith Ø6 longitudinal teel bar [4] ere ompared to the hear model of fib Model Code 00 Experimental variable ere the ued teel fibre type (Dramix ZC 30/5 hooked-end D&D ~30/5 rimped) the applied teel fibre ontent (0% 05 % and 0%) and the amount of tirrup reinforement (Serie A: no trirrup Ø6/40 and Ø6/0 and for Serie B: no tirrup Ø4/40 Ø4/0 ) Comparion of beam ith only longitudinal teel bar (-A and -B) a ell a beam ith different tirrup reinforement for Serie B (-- Ø4/40 --Ø4/0) are onidered hereafter in Table and Table Table Shear tet reult on beam made ith hear reinforement and their omparion to the hear deign propoal of fib MC 00 Experimental EC No f m Rexp A / k dg f R= R Rmax Rexp/ R N/mm kn mm /mm 0 /00 0 / kn kn No No fib MC 00 LoA I k k R= R Rmax Rexp/ R kn kn fib MC 00 LoA II x k k R= R Rmax Rexp/ R 0 / / kn kn No fib MC 00 LoA I k v R R R= R + R Rmax Rex/ R 0 kn kn

6 4 th ANNIERSARY FACULTY OF CIIL ENGINEERING SUBOTICA International onferene Contemporary ahievement in ivil engineering 4 April 05 Subotia SERBIA 7 CONCLUSIONS Shear deig model of the fib Model Code 00 i an attempt to ombine and harmonize many earlier different approahe [5-] For the alulation to parameter and k v mut be detered and three different level of approximation (LoA ILoA III) to alulate the hear deign fore are reommended depending on the ombination of the auray of predition and the ot of alulation proe a ell Baed on ome earlier hear tet ummaried in Table and Table it i found that preiion of alulation inreae a the level of approximation i inreaed Table Shear tet reult on beam made ith no hear reinforement and their omparion to the hear deign propoal of fib MC 00 No Experimental fib MC 00 LoA I fib MC 00 LoA II EC A B f m Rexp k dg k v R Rex/ R x k v R Rexp/ R R Rexp/ R N/mm kn kn - 0 /00 - kn - kn REFERENCES [] Fédération Internationale du Béton (fib): fib Model Code for Conrete Struture [] Fédération Internationale du Béton (fib): Shear and punhing hear in and F element fib Bulletin [3] Walraven J C: Fundamental analyi of aggregate interlok Journal of the Strutural Diviion ASCE 98 07(ST) pp [4] Ková I: Effet of teel fibre on the trutural behaviour of onrete member PhD Thei Tehnial Univerity of Budapet 005 [5] Collin M P: Toard a rational theory for reinfored onrete member in hear Journal of the Strutural Diviion ASCE (4) pp [6] Thurlimann B: Shear trength of reinfored and pretreed onrete-ceb Approah ACI Speial publiation 979 ol 59 pp 93-6 [7] Nielen M P: On the trength of reinfored onrete di Ata Polithnia Sandinavia Civil Engineering and Building Contrution Serie 97 No 70 Copenhagen Denmark 6 p [8] Muttoni A: The appliability of the theory of platiity in the deign of (German: Die Andendbarkeit der Platizitättheorie in der Bemeung von Stahlbeton) IBK 76 ETH Zürih Sitzerland p [9] Sigrit : On the deformation apaity of reinfored onrete girder (German: Zum erformungvermögen von Stahlbetonträger) Di IBK ETH Zürih Sitzerland p 30

7 4 ГОДИНА ГРАЂЕВИНСКОГ ФАКУЛТЕТА СУБОТИЦА Савремена достигнућа у грађевинарству 4 април 05 Суботица СРБИЈА [0] Bentz E C ehio F J Collin M P: The implified MCFT for alulating the hear trength of reinfored onrete element ACI Strutural Journal (4) pp [] ehio F J Collin M P: The modified ompreion field theory for reinfored onrete element ubjeted to hear ACI Journal () pp 9-3 ISKUSTA NA MODELU SMICANJA fib MODEL CODE 00 Rezime:Međunarodna organizaija fib je uvela novi tandard (Model Code 00) za mianje armiranog betona i prednapregnutog betona Jednačina koja opiuje model koriti dva parametra: ugao pukotine koja e tvorila pod utiajem ila mianja k v koefiijent doprinoa betona Standard (MC00) opiuje tri nivoa kod približnog određivanja ovih parametara Prvi i treći nivo e olanja na teoriju modifiiranog polja napona dok drugi nivo na teoriju modifiiranog polja platične deformaije Rad prikazuje i opiuje primenjene metode u toku velikog broja praktičnih merenja mianja izvršenih u laboratoriji za ipitivanje kontrukija i materijala Cilj ekperimenta je bio da e uporede mađarki rezultati merenja dobijeni na betonima koji u bili armirani a polipropilenom i a čeličnim vlaknama Keyord: pomična čvrtoća razina približavanja 3