Experimental assessment of damping factors in concrete housing walls

Transcription

1 IGEIERÍA E IVESTIGACIÓ VOL. o., DECEMBER 1 (-) Experimetal assessmet of dampig factors i cocrete housig walls Evaluació experimetal de los factores de amortiguamieto e muros de cocreto para vivieda J. Carrillo 1, S. M. Alcocer, G.Gozalez ABSTRACT Thi walls havig low cocrete stregth, miimum web steel ratios ad web shear reiforcemet made of welded wire meshes are commoly used i low-rise cocrete housig. The dampig factor commoly used for code-based dyamic aalysis was evaluated based o seismic respose measured durig shae table tests of six low-rise cocrete walls. The variables studied were the type of cocrete (ormal ad light), the web steel shear ratio (.15% ad.5%), the type of web shear reiforcemet (deformed bars ad welded wire meshes) ad the effect of opeigs (doors ad widows). Dyamic properties were evaluated cosiderig the advatages of frequecy-domai system idetificatio, usig the dyamic trasfer fuctio amplitude fittig method. The effect of failure mode o dampig factor is discussed. A equatio for estimatig dampig associated with a particular vibratio period value is also proposed. It was observed that a 5% dampig factor (assumed for dyamic aalysis of cocrete housig i the rage of lieal elastic behaviour) was cosistet with the values measured here. Keywords: cocrete wall, vibratio period, dampig factor, dyamic trasfer fuctio, shae table test. RESUME E viviedas de cocreto de baja altura se emplea usualmete muros delgados co baja resistecia del cocreto, cuatías míimas de refuerzo y mallas de alambre soldado para refuerzo a cortate e el alma. Co base e la respuesta sísmica medida durate el esayo e mesa vibratoria de seis muros de cocreto de baja altura se evalúa el factor de amortiguamieto que se utiliza usualmete e el aálisis diámico especificado e los reglametos. Las variables estudiadas fuero el tipo de cocreto (peso ormal y ligero), la cuatía,15% y,5% y el tipo de refuerzo a cortate e el alma barras corrugadas y malla de alambre soldado y el efecto de aberturas (puerta y vetaa). Tomado e cueta las vetajas de los sistemas de idetificació e el domiio de la frecuecia, las propiedades diámicas se evaluaro utilizado el método de ajuste de amplitud de la fució de trasferecia diámica. E el artículo se discute el efecto del modo de falla sobre el factor de amortiguamieto y se propoe ua ecuació para estimar el amortiguamieto asociado a u determiado valor del periodo de vibració. Se observó que el factor de amortiguamieto del 5%, supuesto e el aálisis diámico de viviedas de cocreto e el itervalo de comportamieto elástico lieal, es cosistete co los valores medidos. Palabras clave: muros de cocreto, periodo de vibració, factor de amortiguamieto, fució de trasferecia diámica, esayos e mesa vibratoria. Received: December 1th 11 Accepted: ovember th 1 Itroductio 1 Costructig cocrete wall housig has become a welldeveloped techique i some Lati-America coutries. Because of these housig uits typical large wall-to-floor area ratio, seismic demad is relatively low i terms of forces ad displacemet. Therefore, thi walls havig low cocrete stregth are commoly used. Welded-wire mesh ad web shear reiforcemet ratios 1 Julia Carrillo. Affiliatio: Uiversidad Militar ueva Graada, Colombia. PhD. i Structural Egieerig. Civil Egieer. wjcarrillo@gmail.com Sergio M. Alcocer. Affiliatio: Istituto de Igeiería, Uiversidad acioal Autóoma de México, UAM, México. PhD. i Structural Egieerig. Civil Egieer. E- mail: salcocerm@i.uam.mx Giovai Gozalez. Affiliatio: Uiversidad Militar ueva Graada, Colombia. Esp. i Structural Egieerig. Civil Egieer. gozalez.giovai@gmail.com How to cite: J. Carrillo, S. M. Alcocer, G.Gozalez. (1). Experimetal assessmet of dampig factors i cocrete housig walls. Igeiería e Ivestigació. Vol., o.. December 1, pp. -. lower tha the miimum ratio prescribed by ACI-18 (11) are used i low-hazard seismic areas. Thi walls, steel ratios lower tha the miimum prescribed by codes ad web shear reiforcemet made of welded-wire mesh are also the cosequece of demads for costructio speed ad ecoomy. Cosiderig these houses particular characteristics, most desig parameters ad requiremets i curret codes are ot all directly applicable. Ufortuately, most curret codes are more liely iteded to desig medium- ad high-rise buildigs ad thus, some cocepts have become geeralised i the literature. The aim of this study was to evaluate the dampig factor usually used for the dyamic aalysis of cocrete housig. The research icluded aalysig respose measured durig shae table tests of six walls with ad without door ad widow opeigs. Wall failure modes, vibratio period ad dampig factors are discussed. Give the advatages of frequecy-domai idetificatio

2 CARRILLO, ALCOCER, GOZALEZ techiques, the dyamic trasfer fuctio (DTF) amplitude fittig method was used for idetifyig vibratio frequecies ad dampig factors. The effect of walls failure mode o dampig factor was also evaluated ad a equatio was proposed for estimatig a damaged house s dampig factor with vibratio period. Evaluatig dampig i the frequecy domai Dampig is usually idealised as a equivalet viscous dampig factor for computig a elastic respose. Dampig factors ca be computed i experimetal studies by usig the free vibratio respose, dissipated ad strai eergy or the DTF. Logarithmic decremet ad expoetial regressio methods use free vibratio respose. Half power badwidth ad amplitude fittig methods mae use of the DTF which correlates spectral amplitudes of acceleratio recorded at two poits i the structure. The half power badwidth method directly uses DTF shape to estimate the dampig factor (Chopra, 1). atural vibratio frequecy (f) is estimated by idetifyig DTF pea maximum amplitude. Figure 1 shows frequecies fa ad fb. Figure 1. Defiitio of the half power badwidth method Both the half power badwidth ad the amplitude fittig (Riawi ad Clough, 1) methods use DTF shape to evaluate atural vibratio frequecies ad the dampig ivolved i measured respose (Figure 1). However, whe TF amplitude is more accurate tha phase, results reliability becomes improved by usig the amplitude fittig method. The theoretical sigle degree of freedom system DTF is fitted to the experimetal shape of a similar DTF i this approach. Accordig to Riawi ad Clough, (1), a well-separated pea i the DTF ca be approximated by the respose of a sigle mode as: x x x P ei t (1) where ad are agular frequecy ad dampig for particular mode, ad P is the participatio factor for the mode uder cosideratio. At a give iput agular frequecy, the steady state amplitude of the respose x is give by: P P A ) () ( ) ( D By usig arithmetic simplificatios, for a set of frequecies, equatio () ca be writte as: A A A A A A A A A y 1 A 1 y A () 1 y A 1 Oce equatio () has bee solved, atural vibratio frequecy (f) ad dampig factor () ca be computed from: ( ) 1/ y f 1, y 1 () Experimetal programme The three-dimesioal prototype was a two-story house havig 1-mm thic,,-mm high cocrete walls ad 15 MPa specified cocrete compressive stregth (fc ). Shae table tests are curretly the most effective method for assessig the experimetal performace of specimes subjected to seismic actio. The experimetal programme thus ivolved a shae table test of six thi cocrete walls. The variables studied were the type of cocrete (ormal ad light), the web steel shear ratio (.15% ad.5%), the type of web shear reiforcemet (deformed bars ad welded wire meshes) ad the effect of opeigs (doors ad widows). Geometry, reiforcemet layout ad materials Due to limitatios i shae table payload capacity, lightly-reduced ad isolated wall models were built (i.e. geometry scale factor, SL=1.5). The simple law of similarity was chose because specime size was very similar to that of isolated walls i the prototype (8% prototype size). The models were built with the same material as the prototype i this type of similarity (i.e. material properties were ot chaged) ad oly the models dimesios were altered. Table 1 shows the mai simple law of similarity scale factors. Table gives the specimes characteristics. The specimes height-to-legth oe-to-four ratio was equal to oe (hw/lw=1). Door ad widow opeig cofiguratio was typical of the prototype house for last two specimes. Three specimes geometry ad reiforcemet layout are show i Figure. omial web steel ratio correspoded to the miimum web steel ratio prescribed by ACI-18 buildig code (11) for MC1, MCL1 ad MV1 walls, ad deformed bars were used to provide web shear reiforcemet. omial web steel ratio was approximately 5% of the miimum web steel ratio prescribed by ACI- 18 for MC5m, MCL5m ad MV5m walls, ad weldedwire mesh was used to provide web shear reiforcemet. Logitudial reiforcemet at the boudary elemets was purposely desiged ad detailed to prevet flexural failure prior to achievig shear stregth. Table 1. Mai scale factors for the simple law of similarity Quatity Equatio Scale factor Legth (L) SL = LP / LM SL Strai () S = P / M 1 Stress () S = fp / fm 1 Time (t) St = SL (S S / Sf) 1/ SL Acceleratio (a) Sa = Sf / SL St 1 / SL Dampig ( ) S = P / M 1 Table shows the mea value of measured mechaical properties of cocrete. These properties were measured at the time of wall testig. Seismic demad Three types of record were used for testig walls: lowfrequecy, forced vibratio ad seismic excitatio (Table ). Tests started with sie-curve ad ramp (RM) sigals which were used to evaluate the mass-carryig system frictio level durig IGEIERÍA E IVESTIGACIÓ VOL. o., DECEMBER 1 (-)

3 EXPERIMETAL ASSESSMET OF DAMPIG FACTORS I COCRETE HOUSIG WALLS Table. The walls geometry ad reiforcemet o. Wall hw / lw Cocrete Web reiforcemet Boudary reiforcemet Layout 1 ad v = h, % Flexural Stirrups 1 MC5m 1. MC1 1. ormal ormal Table. The cocrete s mechaical properties Wall Mechaical property MC5m, MC1, MCL5m, MCL1 MV5m, MV1 Type / slump, mm ormal / 1 Light / 15 Compressive stregth, MPa.8 1. Modulus of elasticity, MPa Splittig tesile stregth, MPa. 1. Flexural stregth, MPa.75. Specific, /m. 1.8 Table. Characteristics of records for the prototype house ad testig stages Pea groud Magitude, acceleratio, Itese Total Stage Record PGA, g phase MW duratio, s duratio, s % g S RM W CALE CALE CALE mesh -8/8.11 # 5 S mm mm.8 8 # 5 S mm MCL5m 1. Light mesh -8/8.11 # 5 S mm MCL1 1. Light mm.8 # 5 S mm 5 MV5m Opeigs ormal mesh -8/8.11 # S mm MV1 Opeigs ormal mm.8 # S mm 1-8/8: sigle mesh made of wires with 15 mm (~ i.) spacig, gage 8 (diameter =.1 mm) #@: o. vertical ad horizotal deformed bars (diameter =.5 mm = /8 i) spaced at mm # 5: o. o. 5 deformed bars at each boudary elemet (diameter = 15. mm = 5/8 i.) S o. smooth bars (diameter =. mm = /8 i.) spaced at 18 mm. Figure. Geometry ad typical reiforcemet of walls: (a) MC5m ad MCL5m, (b) MV W low-velocity excitatio. Both sie (S) ad ramp (RM) sigals havig.5 Hz ad. Hz frequecies were used. A radom acceleratio sigal (white oise (W)) at 1 cm/s (.1 g) RMS at the begiig ad the ed of the seismic tests was used to idetify the mai dyamic properties. Specimes were subjected to three earthquae hazard levels to study wall performace uder differet limit states, from oset of cracig to collapse, usig both atural ad umerically-simulated acceleratio records. A earthquae record from a epicetre regio i Mexico (MW 7.1, CALE71) was used for seismic demad i elastic limit state. This record was cosidered a Gree s fuctio for umerically simulatig larger-magitude evets. Two earthquaes havig 7.7 (CALE77) ad 8. (CALE8) MW magitude were umerically simulated for stregth ad ultimate limit states, respectively. Table gives the mai characteristics of records for prototype house ad testig stages. Accordig to the simple law of similarity, acceleratio ad time scale factors were applied to these records for testig models (Sa =.8 ad St = 1.5, Table 1). Models were tested uder progressively more severe earthquae actios by scalig up the value of pea acceleratio as the referece factor, util the fial damage stage was attaied. The results of both forced vibratio ad seismic excitatio tests were used for idetifyig the wall specimes vibratio period ad dampig factor. Dyamic similarity For adequately extrapolatig the specimes respose to a prototype s respose, isolated wall models were desiged cosiderig a prototype house s fudametal vibratio period. Mathematical models were developed ad calibrated through ambiet vibratio testig to establish such dyamic characteristics. Hece, a two-story house s fudametal vibratio period was estimated as beig.1 s (Carrillo, 11). Taig the simple law of similarity scale factors ito accout (St = 1.5, Table 1), isolated wall models were desiged to achieve a iitial i-plae vibratio period close to.1 s. The dyamic (mass gravity acceleratio) used for achievig the desired desig period thus varied from 15 to 8. Test setup If the dyamic were to rest at the top of the models, it sigificatly icreased the actig o the table platform ad thus made cotrollig movemets more complex ad difficult. A exteral device for trasmittig iertia forces to the models usig a mass-carryig slidig system was thus used to avoid the ris of models lateral istability to remove oise i recorded sigals ad eep test specimes withi table payload. The device allowed horizotally guidig mass withi a fixed supportig structure istalled outside the shae table (Carrillo ad Alcocer, 11). Additioal mass blocs (dyamic ) were placed i a steel box which, i tur, was supported by a very low frictio liear motio guide system (LMGS) (Figure ). A.5 MPa axial compressive stress was uiformly applied to the walls ad was ept costat durig testig. This value was % of IGEIERÍA E IVESTIGACIÓ VOL. o., DECEMBER 1 (-)

4 CARRILLO, ALCOCER, GOZALEZ the cocrete s omial compressive stregth. Fiite elemet models of two-story houses were used for determiig the average axial stress at service loads o the housig prototype s first storey walls (Carrillo, 11). The axial load was exerted through the of the load ad coectio beams, ad lead igots bolted to the load beam (Figure ). Although lead igots resulted i a triagular load distributio, addig the of the coectio beam provided uiform axial load distributio o the walls. ' (5) eq eq eq Dampig factors geerated i the LMGS durig shae table testig were calculated i lie with Carrillo ad Alcocer (11). The highest dampig value added by LMGS was.% (i.e. % of the dampig i the specimes respose). It ca thus be cocluded that the mass-carryig load system LMGS did ot add a sigificat amout of dampig to a specime s respose. atural vibratio frequecies Durig excitatio of both white oise sigals ad earthquae records, DTFs were estimated as the ratio of the spectral amplitude of acceleratio recorded at the top of specimes (loadig beam) to that recorded at the base (shae table). Figure shows ratios of measured spectral amplitude for three walls of up to 75% of CA77 earthquae records; DTFs for all the specimes may be foud elsewhere (Carrillo, 1). Acceleratio records were measured durig white oise excitatio durig the iitial (a) MC5m 7. Hz. % Iicial 5. Hz 7. % 71-5% Figure. Test setup Failure modes Prior to testig, all walls exhibited early-age cracig, maily at the corers of the wall web. Crac width was smaller tha.5 mm; such cracs may have bee caused by cocrete shriage. Accordig to these cracs locatio ad slope at wall surface, early-age cracig may have bee triggered by steel costrait of logitudial reiforcemet at the boudary elemets. I ay case, these cracs oly affected iitial wall stiffess (Carrillo, 11). Web reiforced walls usig welded-wire mesh at 5% of the miimum code-prescribed web steel ratio had diagoal tesio (DT) failure. Failure mode was brittle ad govered by web iclied cracig at aroud 5, plastic yieldig of most of web shear reiforcemet ad subsequet wire breaig. By cotrast, walls reiforced by usig deformed bars ad havig the miimum web steel ratio exhibited a mixed failure mode, where diagoal tesio ad diagoal compressio (DT-DC) were observed; yieldig of most web steel reiforcemet ad oticeable web crushig of cocrete was observed i these walls. Results ad Discussio The mass-carryig load system simplified the test setup. However, whe a slidig system was used, the models atural vibratio period prior to ad after each test could ot be estimated usig hammer impact testig (or similar methods), sice ay small displacemet demad o the models became almost istataeously damped to zero (Carrillo et al., 1a). The specimes dampig factors were thus idetified by usig DTF amplitude fittig. Accordig to Chopra (1), the atural vibratio period for a system havig Coulomb dampig is the same as a system with o dampig. Hece, the device used for testig had o effect o the specimes vibratio period. However, for calculatig the specimes effective equivalet viscous dampig ratio (eq'), it was ecessary to subtract the dampig geerated i the LMGS ( eq), from a specime s equivalet viscous dampig ratio (eq): (b) MCL1 (c) MV1.5 Hz 7.5 % 7.8 Hz. % 71-1% Iitial Hz 7. % 71-1% Hz.5 % 7. Hz. % Iicial 71-1% Figure. Three walls vibratio frequecies ad dampig factors of up to 75% of CA77 record 1 8. Hz. %. Hz.8 % 71-5% Hz 7. % Hz 5. % 71-5% Hz 7. % IGEIERÍA E IVESTIGACIÓ VOL. o., DECEMBER 1 (-) 5

5 Dampig factor, % EXPERIMETAL ASSESSMET OF DAMPIG FACTORS I COCRETE HOUSIG WALLS testig stage. The procedure proposed by Riawi ad Clough (1) was followed for idetifyig the frequecy ad dampig factor from curves i Figure (thus showig both measured ad computed DTFs). atural vibratio frequecies ad effective dampig factors are icluded i the Figures. Dampig factors The chage of effective dampig factors with specimes vibratios period is show i Figure 5. The period was calculated as the vibratio frequecy s iverse value. Accordig to the simple law of similarity, the dampig scale factor (S = 1, Table 1) did ot eed to be applied to the results of walls tested through shae table excitatio. However, vibratio periods became icreased by 1.5 because of period scale factor (ST = 1.5). The fitted curve had very good agreemet with test data, as ca be observed from the correlatio coefficiet, r. Figure 5 shows that the dampig factor became slightly icreased with vibratio period; for example, dampig factors associated with iitial loadig stage were roughly %, but icreased to % o failure. Dampig factors measured durig the iitial stage were related to very small amplitudes applied durig white oise excitatio. It should be also oted that the dampig factors i Figure 5 were ot related to total dampig of low-rise reiforced cocrete wall housig. Total dampig of a cocrete house would deped o structural system dampig ad o-structural elemets (if preset), as well as frictio betwee differet elemets (Aristizabal-Ochoa, 18). However, a startig poit was to estimate structural elemet dampig because a house s total dampig may be similar or slightly higher tha that of structural elemets. Figure 5 shows that dampig factors associated with the udamaged stage were close to % ad thus, total cocrete house dampig would be similar or slightly higher tha this value DT failure DT-DC failure Dampig factor, % = 1. T. r = Period, T, s Figure 5. Chage i dampig factor with walls vibratio period After cocrete cracig, measured dampig was primarily credited to steel reiforcemet yieldig (of deformed bars) or plasticity (of welded-wire mesh), as well as the eergy dissipated by frictio betwee crac surfaces ad cocrete crushig. Figure 5 shows that the dampig factors of walls sufferig DT failure were roughly 8% higher tha those of walls havig a mixed DT-DC failure mode. For istace, whe the failure mode was govered by cocrete crushig (i.e. DT-DC failure), hysteresis loop pichig became more sigificat (Carrillo ad Alcocer, 1b) ad, thus, dampig factors were smaller tha those of failures govered by web steel reiforcemet yieldig/plasticity (walls failig through diagoal tesio). Coclusios Durig the last few years, costructig low-cost housig made of cocrete walls has oticeably icreased i some Lati-America coutries. This study has experimetally assessed the dampig factor usually assumed for dyamic aalysis of cocrete houses. The amplitude fittig method provided sigificat advatages i estimatig the dampig factors of low-rise cocrete walls subjected to characteristic seismic excitatio because both vibratio frequecy ad dampig factor were directly computed from measured DTF values. It was thus ot ecessary to carry out free vibratio tests or compute the dissipated eergy ivolved i each hysteretic loop durig seismic excitatio. Assessig the measured respose revealed that dampig factors associated with the udamaged stage of low-rise cocrete walls was close to %. The total dampig of a cocrete house would be at least equal to that value ad thus the 5% dampig factor commoly used for lieal dyamic aalysis may be cosidered suitable for the code-based seismic desig of cocrete housig. The equatio proposed i Figure 5 proved a useful tool for estimatig the dampig factor associated with a cocrete house s particular vibratio period value. Acowledgmets The authors gratefully acowledge the fiacial support provided by Grupo CEMEX ad extesive assistace i experimetal testig provided by staff ad studets at UAM s Istituto de Igeiería Shae Table Laboratory. Refereces America Cocrete Istitute (ACI), Buildig code requiremets for structural cocrete (ACI 18-11) ad commetary, Farmigto Hills, MI, 11. Aristizabal Ochoa, J., Cracig ad shear effects o structural walls. Joural of Structural Egieerig ASCE, Vol. 1, o. 5, 18, pp Carrillo J., Evaluatio of shear behavior of cocrete walls usig dyamic tests, PhD thesis, Uiversidad acioal Autóoma de México, UAM, 11 (i Spaish). Carrillo, J., Gozalez, G., LLao, L., Evaluatio of mass-carryig systems for shaig table experimets., DYA Joural, Vol. 7, o. 17, 1a. Carrillo, J., Alcocer, S., Experimetal ivestigatio o dyamic ad quasi-static behavior of low-rise reiforced cocrete walls., Joural of Earthquae Egieerig ad Structural Dyamics, DOI: 1.1/eqe., 1b. Carrillo, J., Alcocer, S., Improved exteral device for a masscarryig slidig system for shaig table testig., Joural of Earthquae Egieerig ad Structural Dyamics, Vol., o., 11, pp Chopra, A., Dyamics of structures Theory ad applicatios to earthquae egieerig., Seguda Edició, Editorial Pretice Hall, ew Jersey, 1. Riawi, A., Clough, R., Improved amplitude fittig for frequecy ad dampig estimatio., 1th Iteratioal Modal Aalysis Coferece - Society for Experimetal Mechaics, Bethel, CT, 1, pp Church, R., Geographical iformatio systems ad locatio sciece., Computers & Operatios Research, Vol., o., Ju.,, pp IGEIERÍA E IVESTIGACIÓ VOL. o., DECEMBER 1 (-)