Design resistance of steel expansion anchors under shear loading derived using methods of design assisted by testing

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1 Design resistane of steel expansion anhors nder shear loading derived sing methods of design assisted by testing MACELA KAMAZÍNOÁ Falty of Civil Engineering Brno University of Tehnology eveří St. 331/95, 6 Brno CZECH EPUBLIC karmazinova.m@fe.vtbr.z Abstrat: - This paper deals with the basi reslts of the experimental researh programme realized in the testing laboratory of the Institte of Metal and Timber Strtres of the Falty of Civil Engineering at BUT, whih is direted towards the investigation of atal behavior and ltimate strength of steel expansion anhors to onrete nder shear loading. The problems of failre mehanism, ltimate strength, inflene of edge distane and anhor diameter are disssed, espeially. Based on the test reslts the design formlas an be verified sing the methods of the design assisted by testing. Key-Words: - Fastening, steel expansion anhors, shear loading, experiments, test reslts, design assisted by testing, statistial evalation, probabilisti resistane model, mean vales, harateristi and design resistane. 1 Introdtion The effetiveness and arate plaement together with the new easy tehnologies and tehniqes are the most important advantages of the post-installed fastening systems. For the fastening to onrete in the new onstrtions as well as in repair works the steel expansion anhors are very sitable. Their behavior an be rather ompliated onsidering the inflene of onentrated loading, their different diretions and, espeially, the failre mode depending on the way of the load transfer from anhor body into the onrete base. Ths the experimental verifiation together with statistial and probabilisti analysis of appropriate test reslts shold be an athority for the theoretial modelling and pratial design of the fastening systems. In this paper the brief information on the main reslts (failre mehanisms and adeqate load arrying apaities) of the loading tests of steel expansion anhors nder shear loading and, mainly, their statistial and probabilisti evalation with respet to the random variability of inpt qantities and nmber of tests realized, is presented. Design assisted by testing priniple For the following determination of harateristi and design vales k, d of the resistane (in this ase the load-arrying apaities see below) the statisti parameters of the ratios of experimental and mean vales of the resistane have been obtained sing the statistial analysis. To determine the harateristi and design resistanes, for the test reslts elaboration, so alled standard proedre following the priniples of the design assisted by testing (for more see [13]) has been applied (similarly as e.g. in [1], [15], [16]). This proedre is based on the omparison of the experimental resistanes ex obtained from the loading tests and the theoretial resistanes th obtained from the allation aording to the theoretial resistane model; it is derived from the statisti evalation of the probabilisti resistane model in the form of b (1) = th where b is the redtion fator (see Fig. 1) and the error term is oming from the differenes of experimental and theoretial resistane vales ex, i i = () b, i Then, harateristi and design resistanes are given in the formats of n ( m ) exp( k k = Xj k d, n b α g.5 v ( m.5 v ) ) exp( k ) α k = Xj d, k b g α α (3) () where the expression b g (m Xj ) = m is the mean resistane vale (with the mean vales of the inpt random variables X j ), oeffiients of the prediting ISBN:

method k, k n, k d,, k d,n are depending on the tests nmber (see [13]) and α, α are the weighting fators aording to following formlas v α (5), v v v α (6) For the allation of harateristi and design

2 method k, k n, k d,, k d,n are depending on the tests nmber (see [13]) and α, α are the weighting fators aording to following formlas v α (5), v v v α (6) For the allation of harateristi and design resistane vales it is neessary to know the variation oeffiients v Xj of the inpt random variables X j, whih are sally known from the earlier experienes, and the variation oeffiient v of the resistane. The variation oeffiient v follows from the variation oeffiients v Xj and variation oeffiients v of the resistane model fntion and v of the error term. The variation oeffiient v may be allated as the variation of the resistane fntion and it is depending on this fntion form. The nertainties in the resistane model are taken into aont by the differenes of the experimental and theoretial vales. ex ex = b th ex = th Fig. 1 ex th diagram 3 Basi information of experimental researh programme Dring several last years in or testing laboratory the loading tests of torqe-ontrolled expansion anhors to onrete proded in or ontry have been ondted. Together 368 speimens nder stati loading ations as well as nder dynami loading ations have been tested so far. Among all tests, 77 speimens nder stati and also dynami tensile loading (see [], [6], [7]) and 91 speimens nder stati shear loading have been tested. For the test speimens nder shear loading the expansion torqe-ontrolled anhors see Fig., with following parameters have been sed: For the anhor bolts the steel grade of 8.8 with nominal th vales of ltimate tensile strength f b = 8 MPa, and diameters of d = 1, 1 and 16 mm have been sed. The external diameters of anhor sleeve were D = 1, 18 and mm. Conrete be strength f of the speimen bodies was in the range from 19 to 37 MPa and the effetive anhor embedment depth h ef was in the range from 5 to 8 mm. Fig. Expansion anhor onfigration Analysis of resistane of expansion anhors nder shear loading Dring the test proess the failre mehanism and load-arrying apaity of the tested speimens have been verified. Depending on basi parameters of fastening arrangement different types of failre mode an be established. For the behavior of anhor nder shear loading the edge distane e and onrete strength f together with the bolt dimensions d, D and its strength f b are deisive, espeially. Also the embedment depth h ef an inflene the fastening strength. Depending on the edge distane and embedment depth, both steel failre both onrete fratre, an or. Steel failre by yielding and fratre of the anhor bolt (see Fig. 3a, 3, is harateristi for deep embedment, low steel strength and large edge distane. Conrete failre is haraterized by one of the possible modes: lateral onrete-one failre (see Fig. 3, for the anhors lose to edge, and onrete spalling (see Fig. 3, or onrete rshing (see Fig. 3), respetively, for the large edge distane. The failre by onrete spalling an or for deeper embedment, onrete rshing mostly ombined with sbseqent anhor pll-ot (see Fig. 3d), may or if the anhoring embedment depth is small (h ef D to 6D). Within the framework of this information the reslts overing the set of lateral onrete-one failre and onrete spalling are presented (altogether 33 and 1 tests, respetively). Additionally in 37 ases the other failre modes orred (bolt failre in 9 ases and onrete rshing in 8 ases, respetively). ISBN:

For the primary evalation of the test reslts the basi allation models aording to pblished reslts (see [1], [], [3]) have been sed.

lateral one and f t is the onrete tensile strength. Aording to the 5-Degree Cone Method onsidering 5 lateral failre one (see Fig.

For ACI Method for example, the format of (8) omes to the format of (see [11], [1]) or = π (9).5.137 e f =. (1).5.3 e f Fig. 5-Degree Cone Method ) d) Fig.

3 For the primary evalation of the test reslts the basi allation models aording to pblished reslts (see [1], [], [3]) have been sed. For the sbseqent analysis direted to the determination of harateristi and design vales of anhor resistane the method aording to the normative doments (for detail see [13]) for the design assisted by testing an be sed..1 Lateral onrete-one failre mode Based on Conrete-Cone Method (see [1], [3]) the shear breakot apaity an be expressed by the general basi format of = A f t, (7) where A is projeted area of the lateral one and f t is the onrete tensile strength. Aording to the 5-Degree Cone Method onsidering 5 lateral failre one (see Fig. ), and for the edge distane of e and the tensile strength expressed by the be strength as f t = k f.5, we an write e = π, (8),5 k f where k is nits dependent. For ACI Method for example, the format of (8) omes to the format of (see [11], [1]) or = π (9) e f =. (1).5.3 e f Fig. 5-Degree Cone Method ) d) Fig. 3 Examples of failre modes Based on Conrete Capaity Design Method (CC Method see [1], [3]) the orresponding general expression an be presented in the basi form of = k e f, (11) where the fator of k is sally derived from the test reslts sing the regression analysis (for example, k 5 to 6 aording to [1], [3]). Comparing or experimental reslts with theoretial vales based on (9) the mean vale,m of shear breakot apaity an be given by.5, m =. 16 π e f (1) and the appropriate harateristi vale,k onsidering the nmber of the tests ([], [1]), is.5, k =. 17 π e f. (13) Similarly for the format based on (11) the orresponding mean and harateristi vales of shear breakot apaity are, = 5, (1) m e f ISBN:

4 ,exp [kn],exp [kn] ,m [kn] ,m [kn] Fig. 5 elationships based on (1) and (1) , k =. 38 e f. (15) In Fig. 5 the relationship between experimental strengths,exp and mean vales,m aording to (1) and (1) derived by regression analysis are drawn. The distribtions for the ratios of,exp /,m are shown in Fig. 6. Based on (11) and sing the proedre for design assisted by testing [7] the design vale d of shear breakot apaity determined with respet to the nmber of the tests, an be given by the format of d =. (16) e f For the eqation (9) the design vale annot be determined bease of too high vale of the variation oeffiient (v =.9) together with the relative small nmber of the tests see [1]. The test reslts ompared to the orse of the mean, harateristi and design vales of shear breakot apaity are plotted as a fntion of the edge distane e, for the relationships going ot of (9) in Fig. 7 withot design vale, and for the relationships going ot of (11) in Fig. 8. The experimental vales are normalized for the onrete be strength of f = MPa aording to.5,,exp norm =. (17) f From the evalation mentioned above and from Fig. 6 it implies that the eqation in the format of (11) is more apposite to this type of failre omparing with the format of (9). Freqeny ,,6,8 1, 1, 1, 1,6,exp /,m 1,8, [kn] Freqeny e 1 [mm],,6,8 1, 1, 1, 1,6 1,8,,exp /,m Fig. 6,exp /,m distribtion based on (1) and (1) tests mean vale a. to (6) har. vale a. to (7) Fig. 7 Mean and harateristi vales aording to (1) and (13) ISBN:

5 [kn] 6,exp [kn] [mm] tests mean vale a. to (8) har. vale a. to (9) design vale a. to (1) Fig. 8 Mean, harateristi and design vales aording to (1), (15) and (16). Conrete spalling failre mode The shear apaity for the failre mode by onrete spalling is inflened by the onrete tensile strength, flexral stiffness and diameter of the anhor shaft, embedment depth and by onrete modls of elastiity E. The mean vale an be given aording to [1], [3] as follows π D, m =.5 f E =. 39 D f E, (18) where the ylinder strength of onrete f an be expressed sing the be strength f f. 8. (19) f Based on the format of (18) and sing the regression analysis we an obtain the verifiation of the mean vale for or test reslts as, m =. D f E. () The orresponding harateristi and design vales determined sing design assisted by testing regarding the nmber of the tests then an be written, =. 17 D f E, (1) k d =.117 D f E. () The relationship between experimental strengths,exp and mean vales,m aording to (1) and (1) derived by regression analysis are drawn on the graph in Fig. 9. In Fig. 1 the distribtion for the ratios of,exp /,m is shown. e Freqeny ,m [kn] Fig. 9 elationship based on (18) ,7,8,9 1, 1,1 1,,exp /,m Fig. 1 elationship based on (18) 5 Conlsions The partial reslts above mentioned an be presented as the example of the appliation of experimental methods for the verifiation of atal behavior of steel expansion anhors to onrete nder varios loading ations (of orse, inlding shear loading, as shown here). The ltimate load-arrying apaities implied from the tests an be taken as the basi information for the verifiation of existing known theoretial and pratial models for their allation. The determination of harateristi and design resistanes desribed here indiates the possibility of sing methods based on the design assisted by testing philosophy also in the field of anhorage systems, where load-arrying apaities (available, for example, in anhor proders doments) are often determined only from very limited test nmber of the partilar anhor type, so that the formlas for the design resistane allation are sally very safe bt ineffiient. By sing proedre of the design assisted by testing, sh design resistanes, 1,3 1, 1,5 ISBN:

6 whih are more reliable and together more effetive, an be derived as the generally sable and sitable for the anhor load-arrying apaity determination. Aknowledgement: The paper has been elaborated within the framework of the researh projets of the Czeh Ministry of Edation, Yoth and Sports FAST S-11-3/15 (projet of the niversity speifi researh ) and CZ.1.5/.1./3.97 (Centre AdMaS ). eferenes: [1] Eligehasen,., Malée,. and Silva, J.F. Anhorage in Conrete Constrtion, Ernst & Sohn: Berlin 6. ISBN [] Eligehasen,. Connetions between Steel and Conrete, Proeedings of the 1 st International Symposim, University of Stttgart, ILEM 1. ISBN X. [3] Fastening to einfored Conrete and Masonry Strtres, State-of-art-report, CEB, Blletin d Information, Thomas Telford Servies, 199. [] M. Karmazínová, J. Melher and Z. Kala Design of expansion anhors to onrete based on the reslts of experimental verifiation, International Jornal on Advaned Steel Constrtion, ol. 5, No., Hong Kong Institte of Steel Constrtion, Deember 9, pp ISSN X. [5] M. Karmazínová, Design assisted by testing a powerfl tool for the evalation of material properties and design resistanes from test reslts, International Jornal of Mathematial Models and Methods in Applied Sienes, ol. 6, Isse, 1, pp ISSN [6] M. Karmazínová, J. Melher and M. Štrba, Fastening of steel strtral members to onrete sing post-installed mehanial fasteners, In Pro. of the 9 th International Conferene on Steel-Conrete Composite and Hybrid Strtres held in Leeds, esearh Pblishing Servies: Singapore 9, pp ISBN [7] Karmazínová, M. and Melher, J. Behavior of expansion anhors to onrete, In Proeedings of the nd International Symposim on Connetions between Steel and Conrete, IBIDEM ELAG: Stttgart, 7, pp ISBN [8] Melher, J., Karmazínová, M., The analysis of fastener strength sing the limit state approah, In Proeedings of the 1 st Intl. Symposim on Connetions between Steel and Conrete, University of Stttgart, ILEM 1, pp. 1-19, ISBN X. [9] M. Karmazínová, J. J. Melher, Methods of the design assisted by testing appliable tools for the design resistane evalation sing test reslts, In Pro. of the nd Intl. Conferene on Mathematial Models for Engineering Siene, Institte of Environment, Engineering, Eonomis and Applied Mathematis, WSEAS Press, Perto de la Crz, 11, pp ISBN [1] M. Karmazínová, M. Pilgr, J. J. Melher, Methods based on the approah of the design assisted by testing applied to the determination of material properties, In Proeedings of the nd Intl. Conferene on Mathematial Models for Engineering Siene, Inst. of Environment, Eng., Eonomis and Applied Mathematis, WSEAS Press, Perto de la Crz, 11, pp ISBN [11] Karmazínová, M., Melher, J. and Kala, Z. Atal Behavior and Load-arrying Capaity of Steel Expansion Anhors to Conrete, In Proeedings of the 5 th Intl. Conf. on Advanes in Steel Strtres ICASS 7, esearh Pbl. Servies: Singapore, 7, ol. III, pp ISBN [1] Karmazínová, M., Melher, J. and Kala, Z. Load-arrying apaity of post-installed steel anhors to onrete sbjeted to shear, In Proeedings of 3 rd Intl. Conf. on Steel and Composite Strtres ICSCS 7, Manhester: University of Manhester, 7, pp ISBN [13] EN 199 Basis of strtral design, CEN: Brssels,. [1] M. Karmazínová, Theoretial analysis and experimental verifiation of moment resistane of steel and timber beams strengthened by external CFP omposites, International Jornal of Mehanis, ol. 6, Isse, 1, pp ISSN [15] M. Karmazínová, Analysis of the atal behavior, stress and moment apaity of omposite beams omposed of steel and glassfibre-onrete, International Jornal of Mehanis, ol. 6, Isse, 1, pp ISSN [16] M. Karmazínová, J. J. Melher, Design assisted by testing applied to the determination of the design resistane of steel-onrete omposite olmns, In Proeedings of the 13 th WSEAS International Conferene on Mathematial and Comptational Methods in Siene and Engineering, WSEAS Press: Catania, 11, pp. -5. ISBN ISBN:

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