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1 Structural Analysis of Historical Constructions Jerzy Jasieńko (ed) 2012 DWE, Wrocław, Poland, ISSN , ISBN ToAafTflNAi ClirMN ClNNbCTflNp tfte foln altbip bumbofmbntai ANa NrMbofCAi ANAiYpfp gosip Atalić 1 I aamir iazarević 2 I Marta Šavor 3 ABpToACT Permanent problems with stone columns in Croatia motivated us on comprehensive research. Retrofit of columns, being noted for centuries and existing distinct fractures concentrated around connections with capitals and bases point to some fundamental deficiency of the structural system. Traditional connections consist of carefully smoothed contact areas joined only with centrally placed iron dowel what makes them very sensitive to any disturbance from vertical position. Analyses show that even a small imperfection in the construction process, temperature changes and especially eccentric loads result in the leaning of the contact to one side. Described contacts do not have sufficient rotational stiffness to compensate rotations. Eventually, high edge stresses cause numerous fractures. Performed laboratory tests pointed out additional problem of irregularities of contact areas, which, together with eccentric load, became critical for all specimens. Tests were carried out on almost real scale samples from traditional quarries. Testing procedure ensured separate analyses to centric and eccentric loading with respect to actual stress distribution in structures. All abovementioned assertions were confirmed with a range of numerical models: from simple frame and shell models to complex solid models. All models were calibrated with results of the laboratory tests. This work shows that it is essential to understand real nature of connections behaviour if we want to approximate real stress distributions, positions of thrust lines and finally safety factor in order to form adequate retrofit strategies. heywords: iaboratory testsi kumerical analysisi ptone columni CapitalI BaseI fron doweli ootational stiffnessi Contact stressi bccentric loadi frregularities of contacts areasi cracture propagation NK fntolarctfln NKNK mroblem description Our research of conventionally made columns and column connections started with the reconstruction project of the Rector s Palace in Dubrovnik [1]. Specific vestiges of previous reconstructions like stirrups around columns (Fig. 1a), stone insets and gaps filled with lead or wood, broken parts held with wire (Fig. 1b), different types of stones, various styles of column shapes and capitals were very intriguing. Historical surveys showed that many other researchers in Croatia as well all over the world noticed similar fractures near column connections, but the essence of the observed phenomenon is usually overshadowed by many other issues related to historical structures [2]-[3]. It is convenient to emphasize a sentence from one of the historical reports which describes the nature of the problem: ''Damages of particular parts of columns seem to represent a continuous phenomenon which required unusually large number of interventions'' [4]. Reconstruction is essential to avoid fracture propagation around the column connections, which could eventually endanger the stability of structure [5]. We have performed extensive numerical and experimental research in order to understand the real behaviour of contacts and to establish input parameters needed for adequate retrofit strategies. 1 Senior research assistant, PhD, Faculty of Civil Engineering, University of Zagreb, atalic@grad.hr 2 Associate professor, PhD, Faculty of Civil Engineering, University of Zagreb, damir@grad.hr 3 Teaching assistant, Faculty of Civil Engineering, University of Zagreb, msavor@grad.hr 619

2 af bf cigk NqraditionalcolumnconnectionWaFstirruparounddamagedcolumnI bfwirearoundfracturedcapitalicfcontactmodelxsz cf NKOK Column connections qraditionally madeconnections between columnsi capitals andbases aremade with great carewhat can be noted on carefully smoothed contact areask marts of the column are joined only with iron dowelsi placedcentrallyinaslightlylarger holeandfinallyfilledwithleadkpuchtraditionalcraft is suitable for traditional materials with respect to transmission of vertical load with rather uniform compressionstressesxszk rnfortunatelyiuniformcompressionstressesatthecontactareasareveryrarekconnectionsaremostly eccentricallyloadedoratleastslightlyinclinedfromaverticalpositionkqhereasons arenumerousi ekgk imperfections from the construction processi events throughout history like earthquakesi subsidencexuzitemperaturechangesidifferentrepairsetckqhesejointsarenotdesignedtocompensate such deviations because the rotational stiffness is very small due to the central position and insufficientanchoringofthedoweleusuallyaboutnmcmfkeenceimomentisnegligibleandonlysmall tensileforcescanbetransmittedkqheeccentricload causesrelativerotationofthecolumn elements andbecausethejointhasonlyaverylimitedabilitytocompensaterotationsithisresultsinhighlocal stresses at the edge of a column EcigK NcFK then the stress concentration exceeds the compression strength of stone or the deviation of compression trajectories generates unwanted tensile forcesi fracturesareunavoidablextzk cracturepropagationnearcontactsurfacesleadstosplittingofthecolumnsandcapitalsandtherebyto acompletelossofbendingstiffnessoratleasttoitsverysignificantreductionkqhedescribedproblem isvery localinnatureasthebodyofthecolumnawayfromconnectionsexperiencesonlymoderate uniform compression stresses and a large safety factor is maintained what usually misleads researcherskfngeneraliprejcriticalandpostjcriticalbehaviourofcontactsisoneofthemaingoalsof ourresearchk OK NrMbofCAi ANAiYpbp OKNK mreliminary models jostoftheabovementionedstatementshavebeenconsideredwithaseriesofnumericalmodelswfrom simpleframeandshellmodelstocomplexsolidmodelsiincludingunavoidabletraditionalcalculations by thrust linesk mroblem was identified during analysis of the oector s malace in aubrovnik xnzxvzk kumericalmodelofthecompletestructurewasmadewithtetrahedralfiniteelementsusingcbamtk4 xnmzcombinedwithdiasknkoaxnnzforprejandpostjprocessingpurposesecigkoafkoegardlessofthe greateffort inimplementationofseveralnovelsubroutinesintothebasiclinear elasticcbam model Efor a better description of the connection behaviourfi program code improvements to exclude overstressedfiniteelementsas wellas the definition of failure criterion of materialbythe modified theoryofnormalstresseseoriginallydevelopedbydalileoandoankinefiitwasclear thatadditional parameterswerenecessaryinordertodefinethebehaviourofcolumncontactsk aescription of the complex connection behaviour with all nonlinearities in the global model is complicated because in that case the model becomes completely impractical for applicationk curthermorei complex calculation demands reliable parameters which are always questionable in SOM

3 historical constructions and leads to only qualitative description of the phenomenonk ln the other handitheframeandshellmodelecigkobfistoosimpletodescribethiscomplexbehaviourofcontactsi especially in postjcritical phasesk ConsequentlyI in global models it is difficult to predict the stress distributionandfinallythesafetyfactorkcorpurposesofthisresearchwehavebeenfocusedmostlyon thecontactbehaviouranddetailedlocalmodelskqheimplementationandverificationofresultswere madeonthemathematicalmodelofacharacteristicpartofstructureecigkocfusingpamommmxnozk af bf cf cigk OkumericalmodelsWaFsolidelementsusingcbAmanddiaxRzI bfframeandshellelementsicfdetailedmodelofthespecificpart OKOK Numerical model of laboratory tests AnumericalmodeloflaboratorytestsIwithfocusonthecontactareasIwasmadetakingintoaccountall theabovementionedobservationsecigkpfkftwascreatedwithpamommmwhichwaschosenconsidering theavailabilityofinputdataandassociatedalgorithmskdenerallyiallmodelswereentirelybasedonthe reliableparametersavailablefromlaboratorytestsorcomprehensivesensitivitytestsk qhe main objective of this specific model was to describe the relative rotation between column elementsileaningtoonesideofthecontactandthehighlocalstressesattheedgeofacolumnkpuch nonlinear behaviour at contact areas was described by adjusting the link elements between mesh pointsi which included compressionjonlypropertiesi the friction between contact areas and variable irregularities of the contact areask qhese three carefully tested properties were crucial for the description of the phenomenonk kumerical results correspond to the laboratory tests which will be presentedandclarifiedinthefollowingtextk af bf cf cigk PkumericalmodeloflaboratorytestsWaFdeformedshapeIbFstressdistributionincolumn cfstressdistributionnearcontacts SON

4 PK iabloatloy TbpTp PKNK aescription of the tests PKNKNK deneral kumericalmodelscandepictgeneralbehaviourofcontactsibutifwewantreliabledesignparameters for the consideration of an efficient retrofit processi additional evidence is neededk qaking into consideration the true nature of a historic structurei it was decided to conduct laboratory tests to capturetheactualconditionsinstructuresasmuchaspossiblektetriedtoobtainspecimensfromthe traditionalquarryonsrnikfslandwhichwasusedtobuildtheoector smalaceandmanypartsofthe oldaubrovniktownkrnfortunatelyiitislongbeenabandonedandthereforeispecimensfromanother nearbyquarryontheislandhorčulawereusedk PKNK2K qest setting qhe originally planned arch and vault system for the load implementation was discarded due to the laboratorylimitationsandsafetyreasonskallavailablelaboratoryheightwasusedtokeepthecolumn dimensionsclosetotherealonesiwhatwascrucialforthedeterminationoftheconnectionbehaviour andpropagationoffracturesk ioadswereimplementedbythehorizontallyplacedsteelbeamecigk4f which was adaptedto transmit forces fromtwohydraulic pistonsk lnepiston was placedabove the specimenecentricallyfandtheotheroneatthemidspanofthesteelbeameeccentricallyfklnesideof thesteelbeamelzo4mmmmfwasconnectedtothesupportingstructurewhichrepresentedthebearing ofthevaultsystemkqheconnectionwithsteelbeamwasadjustedtoensurefreerotationswhilefixing ahorizontalmovementkqheothersideofthesteelbeamwasfixedtothespecimenecapitalfwithfour anchorstoensurebothfixedrotationsandfixedhorizontalmovementk cigk 4qestsetting qhe capital Ed Z PMM mmi h Z RMM mmf was placed on the top of the circular column Ed Z ORM mmi hznrmmmmfandconnectedonlywiththecentricallyplacedirondowelkaowelwasplacedinaslightly largerholewithoutfixingitwithleadkfnthesamewayithecolumnwasplacedandconnectedwiththe baseedzpmmmmihzommmmfkboththecapitalandthebasewerewithoutanyornamentsbecausethe focuswastoplacethecarefullyfinishedcontactareaswithoutanydamagesontopofoneanotherkqhe SOO

5 base was placed in a fixed steel ring to prevent horizontal displacements. The described setting ensured testing of the contact behaviour due to centric and eccentric loading, but also ensured safety in postcritical phases when parts of specimen were falling and when specimen lost stability (Fig. 9). PKNKPK ioading phases Several different testing procedures were used, and all were representative of real structure behaviour. Forces were implemented by two hydraulic pistons using displacement control. In the first phase of the experiment centric force is applied (piston above specimen) to maintain an appropriate level of compression stress. Levels of the required stresses were based on previously developed numerical models or defined according to results of measurements on real structures. The second phase was the implementation of an eccentric force (piston at midspan of the steel beam) in order to produce beam deflection and consequently the rotation of the capital (Fig. 3a). The beam deflection was always small but nevertheless enough to cause leaning of the capital to one side of the column. It is important to note that total level of the centric force in column increases in the second phase as well, which needs be taken into account. The final phase was the application of loads until the specimen failed by losing its stability. The procedure was calibrated on three unreinforced concrete (cheaper) specimens. PKNK4K Measuring places Tests on concrete specimens were also very useful for improving measuring procedures. Firstly, tests were performed with only 21 measuring locations and mostly using Linear Variable Differential Transformers (LVDT) sensors with different sensitivity. It was planned to capture displacements along the whole specimen, the rotation of the capital, the deflection of the steel beam and relative deformations on the specimen. Measuring locations for relative deformations (stresses) were placed at the top (10 cm from edge), at the middle and at the bottom of the column (10 cm from edge). After few samples and analyses, we have added several LVDT-s for the control of any out of plane displacements, displacement of the bearing structure and the rotation (torsion) of steel beam. An important change in the procedure was a replacement of LVDT-s used for measuring relative deformations with much more and better placed strain gauges (Fig. 4). Finally, there were over 35 measuring locations. PKOK oesults of the tests a) b) c) cigk R Irregularities of contacts areas: a) usage of FaroArm device, b) measured points in plain views, c) measured points in three dimensional views PK2KNK deneral The behaviour of one of the specimens tested earlier have been presented [7]. The serious problem during the test was to apply an ideal centric force. Despite well controlled laboratory conditions, precision made and installed components and a careful orientation of the piston, it proved impossible to obtain reasonably uniform compression stresses. All specimens presented the same problem and eventually after many attempts, Faro Photon and Faro Arm devices to measure irregularities of the specimen and especially contact areas were adopted. The Faro Arm device with a precision of 2/100 mm finally helped to explain the problem (Fig. 5a). Regardless of the precisely fabricated specimens, contact areas had irregularities below 0.3 mm (Fig. 5b, Fig. 5c). This was enough to prevent ideal leaning of contact areas and uniform stress distribution. Gaps between contact areas on the installed specimens were measured, but only around edges. Gaps inside the cross section were predicted by measurements with the Faro Arm device and corrected with 623

6 results from numerical models. All measured values were assigned to the link elements, used in numerical models which had confirmed the problem and simulation results matched testing results fairly well. One can only imagine many problems the old masterbuilders and stone masons had with traditional construction tools and on real construction sites at the time. PK2K2K Centric force All tests had a control phase at the level of 100 kn and problem of irregularities on contact areas was always detected at the end of phase. Stress distribution at the Top of the Column (TC) and Bottom of the Column (BC) obtained during one of the test is shown (Fig. 6). Red border line represents column edge without gaps (measured) between the column and the capital (Fig. 6a) and between the column and the base (Fig. 6b). The values in white boxes represent gap openings measured before the start of the test. Blue prisms show values for compression stresses [kn/m 2 ] obtained from measured relative deformations. Maximum value at the TC is 9.0 MPa, and at the BC is 10.7 MPa. If a uniform compressive stress is assumed along the whole cross section, it would only amount to about 2.0 MPa. Light gray regions represent contacts obtained by testing and numerical models. Even by these simple results, critical places can be easily predicted for the next phase of experiment. The first crack opened at centric force of 137 kn, near the maximum value of stress at BC (Fig. 6c). The same location was detected by numerical models (Fig. 3). Shades of blue on Fig. 3 represent compressive stresses and the red ones indicate tension stresses in the column. After the crack opening, new contact between the column and base is formed and the new stress redistribution is clearly established. Test was continued until the load level reached 200 kn, which is comparable with the values measured at the Rector s Palace in Dubrovnik. Under the assumption of a uniform compressive stress, the obtained value is only 5% of the capacity load. a) b) c) cigk S a) Stress distribution during control phase at measuring places TC, b) Stress distribution during control phase at measuring places BC, c) First crack at the bottom of the specimen PK2KPK bccentric force Eccentrically placed force caused a relative rotation of the capital (in relation to column) and consequently a complete leaning to one side of the contact (Fig. 3a). This new critical location was detected even at the control phase at the TC (Fig. 6a) and also confirmed by numerical models a) b) c) cigk T a) Stress distribution at measuring places before second crack opened TC, b) Stress redistribution at measuring places after second crack opened TC, c) Position of second crack TC 624

7 cigk Ucracturepropagation topofthecolumneqcf cigk 9Collapsedspecimen EcigKPcFKAtthecentricforceofNU4KRkkandtheeccentricforceofSSKUkkspecimencrackedonce againecigktcfkasallphasesofthetestcannotbepresentedinthearticleiwetriedtopointoutthe specific onesi like the stress distribution before new crack appeared EcigK TaF and redistribution of stressesaroundcrackecigktbfkcrackaftercrackithenewequilibriumstateofspecimenwasalways SOR

8 established and the test was continued. An additional increase of forces (centric and eccentric) caused propagation of present fractures, opening of new ones, leading to the rupture of column parts (Fig. 8) and finally to the collapse of the entire specimen (Fig. 9). Undoubtedly, one can point out to the high sensitivity of contacts with respect to irregularities of contact areas, which governs future behaviour. Any load change, especially eccentricity, causes stress concentration and fracturing. 4K ClNCirpflNp Results presented in the paper emphasize high sensitivity of traditional column connections to the irregularities of contact areas and especially to eccentric forces. The usually assumed uniform or linear stress distribution may grossly overestimate the safety factor. Numerous fractures around column connections with both capitals and bases prove fundamental deficiency of such structural systems. Small rotational stiffness of the contact is unable to maintain a state of equilibrium during many disturbances of the structural system like earthquakes, support settlements, fires (explosions), temperature changes, previous reconstructions, many unknown interventions and possible imperfections emanating from the construction process. Fracture propagation is inevitable and according to present fractures, parts of structure may be in a dangerous post-critical state. Fractures are common in historical constructions, but according to the results of laboratory tests, a collapse is possible if material and structural capabilities to redistribute stresses are exhausted. Therefore, by ignoring or not fully appreciating the real nature of connections we can easily endanger both local as well as global stability of the structure. The importance of a correct analysis must be clearly emphasized, along with complexities and difficulties associated with such a process. Extensive numerical and experimental analyses were and will further be made to assess better the real behaviour of contacts and to provide more realistic parameters needed for adequate analyses and retrofit strategies [7]. AChNltibadbMbNTp The authors would like to thank Department of Technical Mechanics and Department of Materials from Faculty of Civil Engineering, University of Zagreb for supporting the research. Particular thanks are due to the Laboratory for all performed testing of structures, to Fabris Brothers company for provided specimens, to Eugen Lokošek for useful advices and professor Almin Đapo from the Faculty of Geodesy, University of Zagreb, for measurements of specimens. obcbobncbp [1] Lazarević D., Dvornik J., Fresl K. (2004) Analysis of damages to the Rector s Palace Atrium in Dubrovnik. drađevinar 56(10): (in Croatian). [2] Lokošek E., Kleiner I. (2004) Replacement of stone columns at the ground floor of the Veliki Tabor Castle. drađevinar 56(5): (in Croatian). [3] Uglešić D., Banić Ž. (2006) Franciscan Monastery St. Frances in Zadar: Structural repair of cloister vault. In: mrock of the fntk Conference eeritage mrotection J Construction Aspects Dubrovnik, Secon HDGK, [4] Steinman V. (1974) oesearch work on oector s malace in aubrovnik with basic recommendations for reconstruction Book ffk Civil Engineering Institute of Croatia: Zagreb (in Croatian). [5] Atalić J., Lazarević D., Fresl K. (2008) Influence of Rotational Stiffness between Column Elements on Global Stability of Historical Constructions. In: mrock of the 8 th buropean Conference on oesearch for mrotectioni Conservation and bnhancement of Cultural eeritage Ljubljana, National and university library, [6] Lazarević D., Atalić J. Fresl K. (2009) Reconstruction of Rector s Palace Atrium in Dubrovnik: a key role of column connections. In: ptructural ptudiesi oepairs and Maintenance of eeritage Architecture uf Tallinn, WIT Press, [7] Lazarević D., Atalić J., Krolo J., Uroš M., Šavor M. (2010) Experimental and Numerical Analysis of Traditional Column Connections with the Possible Retrofit Concept. Advanced Materials oesearch Vols :

9 [8] Meli R., Sanchez-Ramirez A. R. (1997) Structural aspects of the rehabilitation of the Mexico City Cathedral. In: fntk pemk ptructural Analysis of eistorical ConstructionsK mossibilities of numerical and experimental techniques Barcelona, CIMNE, [9] Lazarević D., Dvornik J., Fresl K., Rak M. (2006) Numerical analysis of damages of the Rectors s Palace atrium in Dubrovnik. In: mrock of the fntk Conference eeritage mrotection Construction Aspects Dubrovnik, Secon HDGK, [10] FEAP (2001) A cinite blement Analysis mrogrami sersion TKPK Programmer Manual, University of California. [11] GiD (2000) qhe universali adaptive and user friendly pre and post processing system for computer analysis in science and engineeringk Reference Manual Version 6, CIMNE. [12] SAP2000 (2011) fntegrated poftware for ptructural Analysis and aesign Analysis reference manualk CSI: Berkeley. [13] Gubane A., Giuriania E. (2004) Structural restoration of vaults with extrados ties. In: fntk pemk ptructural Analysis of eistorical Constructions fsk mossibilities of numerical and experimental techniques Padova, A.A. BALKEMA PUBLISHERS, [14] Theodossopoulos D. (2008) Structural design of high gothic vaulting systems in England. fnternational gournal of Architectural eeritage 2(1):