ORIGINAL RESEARCHPerformance of semirigid timber frame with Lagscrewboltconnections: experimental, analytical, and numerical modelresultsTakuro Mori1 • Makoto Nakatani2 • Solomon Tesfamariam3Received: 25 August 2015 / Accepted: 12 October 2015 / Published online: 13 November 2015 The Author(s) 2015. This article is published with open access at Springerlink.comAbstract This paper presents analytical and numericalmodels for semirigid timber frame with Lagscrewbolt(LSB) connections. A series of static and reverse cyclicexperimental tests were carried out for different beam sizes(400, 500, and 600 mm depth) and column–base connec-tions with different numbers of LSBs (4, 5, 8). For thebeam–column connections, with increase in beam depth,moment resistance and stiffness values increased, andductility factor reduced. For the column–base connection,with increase in the number of LSBs, the strength, stiffness,and ductility values increased. A material model availablein OpenSees, Pinching4 hysteretic model, was calibratedfor all connection test results. Finally, analytical model ofthe portal frame was developed and compared with theexperimental test results. Overall, there was good agree-ment with the experimental test results, and the Pinching4hysteretic model can readily be used for full-scale struc-tural model.Keywords Lagscrewbolt Glulam timber Connection Semirigid portal frame Analytical model Numericalmodel Finite element modelIntroductionIn Japan, there is a push to use timber in residential andnon-residential buildings for consideration of sustainabil-ity. In October 2010, new legislation that promotes the useof wood in public buildings was enacted (Forestry Agency2011). As Japan is located in high seismic zone, rigorousseismic design detailing and quality of construction areimportant considerations. Inoue et al. (1999) highlightedthat, with the number of skilled carpenters decreasing,while meeting stringent performance requirement, con-nection detailing should be easy to construct. Variousconnection types are provided as a viable solution to beused in the timber industry, e.g., glued in rod (e.g., Tlus-tochowicz et al. 2011; Sato et al. 2007; Inoue et al. 1999),drift pins (e.g., Shojo et al. 2004, 2005).The focus of this paper is on versatile connectiondetailing called Lagscrewbolt (Fig. 1, LSB) that wasdeveloped for semirigid connection (Komatsu et al. 1999).The LSBs have thread-like lagscrews on the outside sur-face and thread-like nut in the inside (Fig. 1). The LSBswere developed as a simple and economical fastener formoment-resisting joint of glulam timber (e.g., Fig. 2)(Mori et al. 2009; Nakatani et al. 2008; Komatsu et al.1999). Nakatani et al. (2008) reported experimental andanalytical models for LSBs used in beam–column joint.Figure 3 shows the application of LSB-based connectors ina glulam timber building. The connection details shown inFig. 3 highlight that the LSBs are embedded within the& Solomon Tesfamariamsolomon.tesfamariam@ubc.caTakuro Morimoritakuro@rish.kyoto-u.ac.jpMakoto Nakataninakatani-makoto@pref.miyazaki.lg.jp1 Laboratory of Structural Function, Research Institute forSustainable Humanosphere Kyoto University Gokashou, Uji,Kyoto 611-0011, Japan2 Construction Development Division, Miayazaki PrefecturalWood Utilization Research Center, 21-2 Hanaguri,Miyakonojo, Miyazaki 885-0037, Japan3 School of Engineering, The University of British Columbia,Okanagan Campus, 3333 University Way, Kelowna,BC V1V 1V7, Canada123Int J Adv Struct Eng (2015) 7:387–403DOI 10.1007/s40091-015-0107-4glulam timber and can insulate the connection from fire-induced damage.Nakatani and Komatsu (2005a, b, 2006) have developedanalytical model for the pullout strength of LSBs in bothparallel and perpendicular to grain direction (details areprovided in the analytical model section). This paperextends this study to develop numerical model of theconnections, and portal frame tested under monotonic andreverse cyclic test (Fig. 4). A series of static and reversecyclic experimental tests were carried out for beam–col-umn (Fig. 5, different beam sizes 400, 500, and 600 mmdepth were considered) and column–base (Fig. 6, differentnumbers of LSBs, 4, 5, 8, were considered) connections.The different beam sizes were considered, as the number ofLSBs used varies. Three replicates of each connection andportal frame were considered. The monotonic and reversecyclic load test results were used to calibrate numericalhysteretic model (Pinching4 hysteretic model, McKennaet al. 2000; Lowes et al. 2004). Open System for Earth-quake Engineering Simulation (OpenSees, McKenna et al.2000) finite element program was used to develop theanalytical model of the connection and portal frame. Thenumerical model was developed to represent the cyclicenergy dissipation capacity of the connection. To furtherinvestigate the utility of the calibrated Pinching4 hystereticmodel, reverse cyclic loading test was carried out on aportal frame (Fig. 4), and the corresponding analytical andexperimental load–deformation curve was compared.Experimental testing of connection and frameTest setups of the column–beam connection are shown inFig. 5a, and connector details are shown in Fig. 5b. Thetests were carried out at Kyoto University structural testingfacility. Cyclic load was applied at a beam height of2150 mm. The beam depths considered were 400, 500, and600 mm, denoted as HTA400, HTA500, and HTA600,respectively. The connection details with correspondingLSB locations are shown in Fig. 5c. Specimen HTA400had six LSBs with two connectors, whereas specimensHTA500 and HTA600 had nine LSBs with three connec-tors. Lengths of the LSBs used were 214 and 425 mm,respectively, embedded in the column and beam. For the400-mm beam width, two connectors at a spacing of240 mm were used. For the 500-mm and 600-mm beamdepths, three connectors were used at a spacing of 170 and220 mm, respectively.A schematic and photograph of the test setups of thecolumn–base connection are shown in Fig. 6a, b, respec-tively. For the column–base connection, the column wasinserted into a 200-mm-high and 20-mm-thick steel sleeve.The LSBs were bolted to 20-mm-thick steel plate that waswelded to the steel sleeve. Depth of embedment of theLSBs in the column was 500 mm. Three LSB arrange-ments and numbers were considered (Fig. 6c): 4, 5, and 8LSBs are denoted as HCB4, HCB5, and HCB8, respec-tively. Cyclic load was applied at the column height of2000 mm.Figure 7 shows the cyclic load used for the connectiontest. The loading was defined as story drift angle (R), withR values of 1/300, 1/200, 1/150, 1/100, 1/60, 1/30 (rad).After R = 1/30 rad, testing was continued with monotonicload to collapse. It should be noted that the testing cyclesfollow the Japanese standard loading criteria; however,instead of repeating the loading sequence three times, onlyFig. 1 LagscrewboltsFig. 2 LSB connections388 Int J Adv Struct Eng (2015) 7:387–403123one sequence is used. For this preliminary study of derivinganalytical and numerical solutions, this simplification wassufficient. Further tests are indeed required with the properloading sequence to generalize the model. The load wasmeasured by the 200-kN capacity load cell. Two LVDTsensors, placed on adjacent sides of the column–base(Fig. 5a), were used to monitor the joint rotation. AnotherLVDT, placed at the 2150 mm from the bottom, was usedto measure the tip displacement.Analytical and numerical modelsNumerical and analytical models are developed to simulatethe cyclic energy dissipation capacity of the connectors.Modeling of the connection can be achieved with complexcontinuum or simplified spring models (e.g., Lowes et al.2004; Kouris et al. 2014; Nakatani and Komatsu 2005a, b,2006). The hysteretic model considered can vary from afull characterization of the embedment properties of thebolts (e.g., Foschi 2000; Nakatani and Komatsu 2006) tomacroscopic phenomenological approach of the connec-tions (e.g., Rinaldin et al. 2013; Shen et al. 2013). In thispaper, first, analytical models for the details of the LSBconnections, derived in Nakatani and Komatsu (2005a, b,2006), are provided. Rotational rigidity of both LSBconnections (Figs. 4, 5) was developed in Nakatani andKomatsu (2006). The analytical model for the strength ofbeam–column connection was developed in Nakatani et al.(2008). Details of the derivation are provided in the nextsection. In this paper, the analytical model for the column–base connection is developed. The analytical modelsdeveloped by Nakatani et al. (2008) compute rigidity andmaximum strength, without accounting for the pinchingand hysteretic response. Thus, a robust numerical model,Pinching4 hysteretic model (Lowes et al. 2004), was uti-lized to quantify the stiffness, strength at yield, cyclic(a) Exterior of glulam building (b) Interior of glulam building(c) Column-beam connection (d) Column-base connectionFig. 3 Glulam building withLSB connections (Cafeteria ofKinki University, HiroshimaCampus)Fig. 4 Glulam portal frameInt J Adv Struct Eng (2015) 7:387–403 389123response, and pinching observed from the test results. Thedetails are discussed below.Analytical model: beam–column connectionIn this section, the analytical model of the beam–columnconnection in the elastic range is presented. Schematics ofthe force at the beam–column connection and spring modelrepresentation, respectively, are shown in Figs. 8 and 9.Figure 8 shows that, by applying negative moment (M)at the connection, the LSBs located in the lower and uppersides of the connection are subject to tensile (T) andcompression (C) forces, respectively. The T is computed asa function of tensile semirigidity kT and can be obtainedfrom the deformation geometry shown in Figs. 8 and 9 as(Nakatani et al. 2008):T ¼ kT g kð Þh ð1Þ(a)(b)(c)Fig. 5 Details of beam–columnconnection: a schematic of testsetup, b connector details, andc details of the beam–columnconnections (units are in mm)390 Int J Adv Struct Eng (2015) 7:387–403123kT ¼ ks?kPTksIIks?kPT þ ks?ksII þ kPTksII ð2Þwhere h is the rotation (rad); ks\ and ksII are LSB slipmodulus perpendicular and parallel to the grain (N/mm),respectively; kPT is tensile semirigidity of special con-necters; g is distance from lower edge to the upper LSB(mm); and k is distance from lower edge to the neutral axis(mm). Theoretical slip moduli (ks\ and ksII) were devel-oped based on the Volkersen theory (Volkersen 1938) andare shown to be (Nakatani and Komatsu 2005a, b):ks ¼CpRðEwAw þ EsAsÞ sinh klkðEsAs cosh klþ EwAwÞ ðEwAw EsAsÞCpRðEwAw þ EsAsÞ sinh klkðEwAw cosh klþ EsAsÞ ðEsAs EwAwÞ8>><>:ð3Þ4 LSBs (HCB4) 5 LSBs (HCB5)(c)(a) (b)8 LSBs (HCB8) 55 5595 9555559595Fig. 6 Details of column–baseconnection: a schematic of testsetup, b photograph of testsetup, and c details of thecolumn–base connections (unitsare in mm)-0.04-0.03-0.02-0.0100.010.020.030.040 1 2 3 4 5 6 7R (rad)CyclesFig. 7 Loading protocolInt J Adv Struct Eng (2015) 7:387–403 391123where C is the shear stiffness of LSB connector which isdefined as the ratio of shear stress to displacement (N/mm3). R is the outer diameter of an LSB (mm); Ew ismodulus of elasticity of a glulam timber (kN/mm2); Aw iseffective area of glulam timber that resists pullout force ofLSB (2R) (mm2); Es is modulus of elasticity of steel (kN/mm2); As is the cross-sectional area of an LSB based on theminor diameter (mm2); and l is the effective inserted lengthof a LSB (mm). k is a constant and is computed as:k ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiCpR1EwAwþ 1EsAs sð4ÞThe Aw of beam’s LSBs (perpendicular to the grain, Eq. 5)and Aw of column’s LSBs (parallel to the grain, Eq. 6) arecomputed as:Aw ¼ 4Rð Þ nRð Þ p R2 2ð5aÞn ¼ 2:683eð3:591=3:591h:hÞ ð5bÞAw ¼ 4Rð Þ nRð Þ p R2 2ð6ÞThe C is computed as a function of compression semi-rigidity kC and can be derived from the geometry shown inFigs. 8 and 9 as (Nakatani et al. 2008):C ¼ kC k hð Þh ð7ÞkC ¼ ks?kpc?ks? þ kpc? þksIIkpcIIksII þ kpcII ð8Þwhere h is the distance from lower edge to lower LSB incompression (mm), kpc\ and kpcII are embedment semi-rigidity between steel plate and glulam perpendicular andparallel to the grain, respectively. From the equilibriumcondition, T = C,kTðg kÞ ¼ kTkCðk hÞ ð9ÞThus, location of neutral axis k is computed as:k ¼ kTgþ kChkT þ kC ð10ÞIn the T = C equilibrium condition, the axial force isneglected. From equilibrium forces of T and C, the resul-tant moment M at k is computed asM ¼ kTðg kÞ2 þ kCðk hÞ2h ih ð11ÞThus, rotational semirigidity RJC of the beam–columnconnection isRJC ¼ kTðg kÞ2 þ kCðk hÞ2 ð12ÞMaximum moment (Mmax) of the connection is assumed tobe governed by minimum tensile strength (PTmax). ThePTmax is governed by the minimum pullout strength of LSBembedded in the column (PLSBmax), and tensile strength ofthe special connectors (Pptmax) is computed as:PTmax ¼ minPLSBmaxPptmax(ð13ÞTheoretical PLSBmax of LSB is computed as (Nakatani andKomatsu 2005a, b):PLSBmax ¼fvpRðEwAw þ EsAsÞ sinh klkðEsAs cosh klþ EwAwÞ ðEwAw EsAsÞfvpRðEwAw þ EsAsÞ sinh klkðEwAw cosh klþ EsAsÞ ðEsAs EwAwÞ8><>>:ð14Þwhere fv is the shear strength (N/mm2) of an LSB jointwhich is defined as the shear force divided by the effectivearea. Thus, Mmax is computed as:Fig. 9 Spring model of beam–column connectionFig. 8 Geometry of rotational semirigidity on beam–columnconnection392 Int J Adv Struct Eng (2015) 7:387–403123Mmax ¼ kTðg kÞ2 þ kCðk hÞ2 PTmaxkTðg kÞ: ð15ÞAnalytical model: column–base connectionSchematics of the force at the column–base connection andspring model representation, respectively, are shown inFigs. 10 and 11. To simplify the model, in the preliminaryderivation of the analytical model, effect of shear force wasneglected in deriving the column–base connections. Thisshould be considered in future extension of the model.By applying a rotational angle h, the correspondingtensile force T and compression force C are shown inFig. 10. The tensile force T is computed as in Eq. 1, andcorresponding total tensile semirigidity kT of the column–base connection is computed as:kT ¼ ksIIkpnksII þ kpn ð16Þwhere kpn is tensile semirigidity between special nut andsteel box. The kpn is obtained from tensile test results ofsteel plate and special nutTotal compression force C is computed as:C ¼ CL þ CW þ CCL ð17Þwhere CL is compression force of LSB, CW is compressionforce between the steel box and column parallel to thegrain, and CCL is compression force between the steel boxand column perpendicular to the grain. The CL, CW, andCCL are computed as:CL ¼ ksII k hð Þh ð18ÞCW ¼ bZ k0xkIIkhkdx ¼ bkIIk22h ð19ÞCCL ¼ bZ H0xk?HhHdx ¼ bk?H22h ð20Þwhere b is column width (mm), kII and k\ areembedment semirigidity parallel and perpendicular tothe grain direction, and H is height of steel box (mm).Neglecting the axial force component, from the equi-librium condition T = C, total tensile semirigidity kT iscomputed as:kTðg kÞ ¼ ksIIðk hÞ þ bkIIk22þ bk?H22ð21ÞThus, location of neutral axis k is computed to be:k ¼ ibE0ðkT þ ksIIÞfffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðkT þ ksIIÞ2 2bE0 bE?H22 gkT hksII s )ð22ÞMoment M at k due to T and C isM ¼ kTðg kÞ2hþ ksIIðk hÞ2hþ 2k3Cw þ 2H3CCLð23ÞThus, the rotational semirigidity RJB isRJB ¼ kTðg kÞ2 þ ksIIðk hÞ2 þ bkIIk33þ bk?H33ð24ÞThe Mmax is assumed to be governed by PTmax (shown inEq. 13). Thus, Mmax isFig. 10 Geometry of rotational semirigidity on column–baseconnectionFig. 11 Spring model of column–base connectionInt J Adv Struct Eng (2015) 7:387–403 393123Mmax ¼ kTðg kÞ2 þ ksIIðk hÞ2þ bkIIk33þ bk?H33PTmaxkTðg kÞð25ÞPinching4 hysteretic modelTo model the different connection test results and portalframe, an Open System for Earthquake Engineering Simula-tion (OpenSees) (Mckenna et al. 2000) finite element programwas utilized. The nonlinear hysteretic response of the con-nections in OpenSees was modeled with a 16-parameterPinching4 hysteretic model (Fig. 12; Lowes et al. 2004). Thismodel is composed of piecewise linear curves that represents a‘‘pinched’’ load–deformation response and accounts forLoadDeformaon(ePd3,ePf3)(ePd4,ePf4)(ePd2,ePf2)(ePd1,ePf1)(eNd4,eNf4)(eNd3,eNf3)(eNd1,eNf1)(eNd2,eNf2)(*,uForceN eNf3)(*,uForceP ePf3)(dmax,f(dmax))(dmin,f(dmin)) (x1)=(rDispP.dmax,rForceP f(dmax))(x2)=(rDispN.dmin,rForceN f(dmin))(x2)(x1)Fig. 12 Pinching4 hysteretic model (source: OpenSees Wiki http://opensees.berkeley.edu/wiki/index.php/Pinching4_Material)(a) HCB4 (b) HCB8 – close up Fig. 14 Damage observed onthe column–base connections(a) HTA400 (b) HTA600-1 Fig. 13 Damage observedresponse of the three beam–column connections394 Int J Adv Struct Eng (2015) 7:387–403123stiffness and strength degradation under cyclic loading. ThePinching4 hysteretic model was first developed by Loweset al. (2004) to model RC beam–column joint, and it is suit-able for two-dimensional structures. Shen et al. (2013) havereported the use of the Pinching4 hysteretic model in a cross-laminated timber–steel connector brackets. Rahmanishamsiet al. (2015) have used the Pinching4 hysteretic model forgypsum board to steel stud connection.The 16-parameter piecewise linear curves (Fig. 8) areused to define the positive [(ePd1, ePf1), (ePd2, ePf2),(ePd3, ePf3), (ePd4, ePf4)] and negative [(eNd1, eNf1),(eNd2, eNf2), (eNd3, eNf3), (eNd4, eNf4)] response envel-opes. Two unload–reload paths and pinching behavior aredefined with six parameters [(rDispP, rForceP, uForceP),(rDispN, rForceN, uForceN)], respectively, refer to theFig. 15 Hysteretic response of the beam–column connectionsa HTA400, b HTA500, and c HTA600Fig. 16 Hysteric response of the semirigid column–base connectionsa HCB4, b HCB5, and c HCB8Int J Adv Struct Eng (2015) 7:387–403 395123pinched ratio of the deformation at which reloading orunloading occurs to the historic deformation demand ofeach cycle. rForceP and rForceN individually indicate thepinched ratios of the forces corresponding to the historicdeformation demand of each cycle under reloading andunloading. uForceP and uForceN represent the pinchedratios of strengths under reloading and unloading,respectively.Results and discussionDamage observedThe damage observed for the beam–column connection isshown in Fig. 13. Up to R = 1/30 rad, no appreciabledamage was observed. At higher deformation demand,pullout of the tapered nut was observed for HTA400 andHTA500 (Fig. 13a). This was due to high tensile forcedemand, consequent contraction of the tapered nut andpullout. However, for HTA600-1, as the connection wasstronger with higher moment capacity, the damageobserved was bending inducing cracking of the column(Fig. 13b). The pushover testing was discontinued after themanifestation of this crack. The damages observed in thecolumn–base connection are shown in Fig. 14. Figure 14shows that the failure mode observed in the column–baseconnection is tensile failure (pullout).Hysteretic responsesHysteretic responses of HTA400, HTA500, and HTA600connections are plotted in Fig. 15. All three results indeedshowed pinching, as a result of the tapered nut pullout. Allspecimens showed a gradual strength degradation aftermaximum load capacity was reached. Furthermore, HTA600showed higher capacity but reduced ductility. Furthermore,as shown in Fig. 13b, as the columns were cracked, theHTA600-1 test was discontinued around 150-kNm moment(see Fig. 15c). Hysteretic responses of HCB4, HCB5, andHCB8 connections are plotted in Fig. 16. The column–baseconnection showed similar pinching response as the col-umn–beam connection. Unlike the column–beam connec-tion, all specimens showed a rapid strength degradation aftermaximum load capacity was reached.To examine salient features of the connections (stiffness,strength, ductility, and energy dissipation capacity), first, theload–deformation curves of each test were obtained fromenvelope of the hysteretic curves. Figures 17 and 18 showthe load deformation curves for beam–column and column–base connections, respectively. Finally, the load–deforma-tion curves were fitted with a bilinear curve, and the salientfeatures were computed and summarized in Tables 1 and 2,respectively, for the beam–column and column–base con-nections. Each result is discussed further below.Figure 17 shows that, overall, with beam depth andnumber of connections increasing, the overall stiffness andstrength capacity of the systems increased. The stiffness,yield force, and ultimate force capacity, as expected,increased with increase in the beam depth(HTA600[HTA500[HTA400). It should be noted thatboth HTA500 and HTA600 have the same number ofLSBs, and the difference was only the beam sizes. BothHTA600 and HTA500 showed higher energy dissipationand ductility capacity. Results of HTA500 and HTA600 are051015202530354045500 40 80 120 160Load [kN]Deformaon [mm]HTA 400-1HTA 400-2HTA 400-3HTA 500-1HTA 500-2HTA 500-3HTA 600-1HTA 600-2HTA 600-3Fig. 17 Load–deformation envelope curves of beam–columnconnections051015202530354045500 50 100 150 200Load [kN]Deformaon [mm]HCB4-1HCB4-2HCB4-3HCB5-1HCB5-2HCB5-3HCB8-1HCB8-2HCB8-3Fig. 18 Load–deformation envelope for semirigid column–baseconnection396 Int J Adv Struct Eng (2015) 7:387–403123particularly comparable, as the same number of LSBs wasused. As the HTA600 beam failed prematurely, overall, theHTA500 showed better performance. It should be empha-sized that, in capacity-based seismic design, the columnTable 1 Load deformation properties of semirigid column–base connectionSpecimen Pmax (kN) dPmax (mm) Stiffness K (kN/mm) Energy Pu (kN) Ductility, l = du/dv Ds = 1/sqrt(2l-1)HTA400-1 22.22 83.78 0.44 1758 19.68 2.37 0.52HTA400-2 22.42 101.67 0.43 1544 19.64 2.21 0.54HTA400-3 22.13 75.82 0.48 1594 19.46 2.38 0.52HTA500-1 35.24 83.68 0.63 2431 31.76 2.05 0.57HTA500-2 35.05 84.74 0.62 2748 32.13 2.19 0.54HT500-3 34.46 80.18 0.77 1970 30.39 2.16 0.55HTA600-1 42.00 61.28 1.10 1611 36.32 1.81 0.62HTA600-2 34.27 46.40 1.02 1058 31.73 1.58 0.68HTA600-3 40.92 65.49 1.21 1793 36.47 2.01 0.58Table 2 Load deformation properties of semirigid column–base connectionSpecimen Pmax (kN) dPmax (mm) Stiffness K (kN/mm) Energy Pu (kN) Ductility, l = du/dv Ds = 1/sqrt(2l-1)HCB4-1 28.27 79.12 0.41 1881 28.42 1.47 0.72HCB4-2 28.41 74.86 0.48 1692 26.94 1.71 0.64HCB4-3 26.58 74.56 0.45 1690 24.83 1.80 0.62HCB5-1 33.39 88.54 0.52 2702 31.29 1.99 0.58HCB5-2 28.46 81.08 0.43 2280 27.54 1.83 0.61HCB5-3 32.91 91.30 0.46 2746 31.35 1.84 0.61HCB8-1 45.60 140.61 0.49 5561 43.49 1.99 0.58HCB8-2 44.96 123.77 0.54 4771 41.84 1.98 0.58HCB8-3 44.94 125.38 0.53 4899 42.06 2.00 0.58Table 3 Parameters for the beam–column connection analyticalmodelConnection typeParameters HTA 400-1 HTA 500-1 HTA 600-1Es (MPa) 205,939.65 205,939.65 205,939.65As (mm2) 153.86 153.86 153.86Ew (MPa) 65,000 65,000 65,000Aw (mm2)—beam 3815 3815 3815Aw (mm2)—column 44,959 44,959 44,959l (mm)—beam 425.3 425.3 425.3l (mm)—column 214.3 214.3 214.3fv (N/mm2)—beam 6.5 6.5 6.5C (N/mm3)—beam 10.6 10.6 10.6fv (N/mm2)—column 6.2 6.2 6.2C (N/mm3)—column 9.24 9.24 9.24Pmax (kN)—beam 90.2 90.2 90.2Pmax (kN)—column 62.0 62.0 62.0R (mm) 18 18 18ks (kN)—beam 145.5 145.5 145.5Table 4 Parameters for the column–base connection analyticalmodelConnection typeParameters HCB 4-1 HCB 5-1 HCB 8-1Es (MPa) 205,939.65 205,939.65 205,939.65As (mm2) 153.86 153.86 153.86Ew (MPa) 65,000 65,000 65,000Aw (mm2) 3815 3815 3815l (mm)—column 500 500 500fv (N/mm2)—column 6.2 6.2 6.2C (N/mm3)—column 9.24 9.24 9.24Pmax (kN)—column 93.7 93.7 93.7R (mm) 18 18 18ks (kN)—column 151.2 151.2 151.2Int J Adv Struct Eng (2015) 7:387–403 397123should be stronger than the beam. The HTA600 beam isstronger than the column, and as this did not meet thecapacity-based design requirements, the damage in thecolumn was observed.Figure 18 shows that, overall, with increase in beam depthand number of connections, the maximum load capacity andcorresponding deformation of the systems increased. How-ever, the difference on the stiffness was not appreciable. Thisresult is corroborated with the stiffness values presented inTable 2. From Table 2, it can be seen that the yield force,ultimate force capacity, and energy dissipation capacity hasincreased with increase in the beam depth and number ofLSBs (HCB4[HCB5[HCB8).Analytical model resultsThe parameters needed for the analytical model were obtainedfrom material test results reported in Nakatani et al. (2008).The material properties for the analytical model of the beam–column and column–base connections, respectively, aresummarized in Tables 3 and 4. Following the analyticalderivation shown in the previous section, the rotation semi-rigidity and maximum moments were computed, and theresults are summarized in Tables 5 and 6, respectively. Theseresults are also plotted in Figs. 19 and 20, respectively, for thebeam–column and column–base connections.From Table 5, it can be highlighted that the variation inthe rotation semirigidity of the analytical and experimentalresults was 13–21 %, whereas the variation in the maxi-mum moment between the analytical and experimentalresults was 5–18 %. The maximum moment and rotationalsemirigidity results plotted in Fig. 16 highlight that theproposed analytical model is in good agreement with theexperimental results.From Table 6, the variation in the rotation semirigiditybetween the analytical and experimental results is 27–64 %overprediction, whereas the variation in the maximummoment between the analytical and experimental results is21–30 % underprediction. Results of the analytical modelare plotted in Fig. 20. The results are not in good agreementwith the experimental and numerical results. Possible reasonfor this error is, for HCB5 and HCB8, for example, as theconnection is strong, with the high moment demand on theconnection, the steel support was slightly bent during thetest. This can increase the stiffness of the experimental test.In addition, the steel sleeve was slightly bent with highercyclic demand. The analytical result shows higher semi-rigidity than what is shown from the experiment. This is thesubject of further studies by the authors.Pinching4 hysteretic model resultsThe Pinching4 hysteretic model was calibrated with thehysteretic curves shown in Figs. 15 and 16, and the 16parameters are summarized in Table 7. The Pinching4hysteretic curve results are plotted in Figs. 19 and 20 forthe beam–column and column–base connections, respec-tively. It should be noted that the experimental reversecyclic loads were only applied up to R = 1/30 (rad) only.However, for the numerical model, the reverse cyclic loadswere extended up to the maximum deformation obtainedfrom the monotonic load. The Pinching4 hysteretic modelresults depicted in Figs. 19 and 20 show good agreementwith the experimental hysteretic curves. Beyond R = 1/30 rad, the load–deformation envelope closely matches theexperimental envelop curves.Experimental and numerical resultsof the semirigid framePerformance of timber semirigid frame with LSBs con-nectors shown in Fig. 4 was investigated with initial cyclicand subsequent static pushover analysis. The schematicTable 5 Analytical andexperimental results of therotation semirigidity andmaximum moment for thebeam–column connectionBeam depth (mm) Rotational semirigidity (kNm/rad) Maximum moment (kNm)Experimental result Analytical result Experimental result Analytical result400 4364 3592 75.0 71.3500 8904 7693 122 104600 16,301 12,884 153 141Table 6 Analytical andexperimental results of therotation semirigidity andmaximum moment for thecolumn–base connectionConnection type Rotational semirigidity (kNm/rad) Maximum moment (kNm)Experimental result Analytical result Experimental result Analytical resultHCB4 2672 3396 55.5 43.9HCB5 2828 3607 63.2 47.9HCB8 3546 5805 90.4 63.0398 Int J Adv Struct Eng (2015) 7:387–403123representation of Fig. 4 and instrumentation layout isshown in Fig. 21. The timber used was Japanese cedar,with Japanese Agricultural Standard grade of E65-F255with Young’s modulus and bending strength of 6500 and25.5 MPa. The column height was 3140 mm, and beamspan was 6000 mm. The column and beam dimensionswere, respectively, (300 9 300 mm) and (240 9 400/500 mm). Two beam depths (400 and 500 mm) and threereplicate specimens were tested. A semirigid column–baseconnection and beam–column connection was used. Theframe is tested with the cyclic response shown in Fig. 7 andsubsequently pushed to collapse.For the 400-mm beam depth, the observed failure modeswere partial tensile failure of connection between LSB andplate in beam (Fig. 22a), pullout failure of LSB in columnFig. 19 Hysteric response of the three beam–column connections,a HTA400-1, b HTA500-1, and c HTA600-3 Fig. 20 Hysteric response of the three column–base connections,a HCB4, b HCB5, and c HBC8Int J Adv Struct Eng (2015) 7:387–403 399123Table 7 Monotonic and hysteretic parameters estimation of Pinching4 model for the beam–column connection testsParameters Connection typeHTA 400-1 HTA 500-1 HTA 600-1 HCB 4-1 HCB 5-1 HCB 8-1Positive backboneePf1 (kN) 32 32 50 15 20 20ePf2 (kN) 55 65 100 50 50 70ePf3 (kN) 73 122 160 58 66 90ePf4 (kN) 30 30 30 40 46 60ePd1 (mm) 0.006 0.0025 0.004 0.0045 0.008 0.006ePd2 (mm) 0.015 0.008 0.008 0.020 0.025 0.035ePd3 (mm) 0.029 0.020 0.020 0.032 0.045 0.065ePd4 (mm) 0.065 0.080 0.063 0.046 0.063 0.080Negative backboneeNf1 (kN) -32 -32 -50 -15 -20 -20eNf2 (kN) -55 -65 -100 -50 -50 -70eNf3 (kN) -73 -122 -160 -58 -66 -90eNf4 (kN) -30 -30 -30 -40 -46 -60eNd1 (mm) -0.006 -0.0025 -0.004 -0.0045 -0.008 -0.006eNd2 (mm) -0.015 -0.008 -0.008 -0.020 -0.025 -0.035eNd3 (mm) -0.029 -0.020 -0.020 -0.032 -0.045 -0.065eNd4 (mm) -0.065 -0.080 -0.063 -0.046 -0.063 -0.080PinchingrDispP 0.8 0.8 0.8 0.8 0.8 0.8fForceP 0.1 0.1 0.1 0.1 0.1 0.1uForceP 0.01 0.01 0.01 0.01 0.01 0.01rDispN 0.8 0.8 0.8 0.8 0.8 0.8fForceN 0.1 0.1 0.1 0.1 0.1 0.1uForceN 0.01 0.01 0.01 0.01 0.01 0.01Unloading stiffness degradationgK1 0 0 0 0 0 0gK2 0 0 0 0 0 0gK3 0 0 0 0 0 0gK4 0 0 0 0 0 0gKLim 0 0 0 0 0 0Reloading stiffness degradationgD1 0 0 0 0 0 0gD2 0 0 0 0 0 0gD3 0 0 0 0 0 0gD4 0 0 0 0 0 0gDLim 0 0 0 0 0 0Strength degradationgF1 0 0 0 0 0 0gF2 0 0 0 0 0 0gF3 0 0 0 0 0 0gF4 0 0 0 0 0 0gFLim 0 0 0 0 0 0Energy degradation gE 1 1 1 1 1 1Damage type Energy Energy Energy Energy Energy Energy Energy400 Int J Adv Struct Eng (2015) 7:387–403123(Fig. 22b), and partial tensile failure of connection betweenLSB and column–base joint (Fig. 22c). For the 500-mmbeam depth, similar failure modes as shown in Fig. 22were observed. In addition, for the 500-mm beam depth,the observed failure modes were shear failure at the columnwith subsequent splitting at the top of column (Fig. 23a)and bending failure at the column (Fig. 23b). The failuresin the columns were a direct consequence of the 500-mmbeam depth having a stronger column–beam connectionand weaker column. This indeed reinforces the need tohave strong column–weak beam seismic capacity design.The pushover tests were performed for three replicate ofeach systems. The load–deformation results obtained fromthe pushover test are shown in Fig. 24a, b, for beam depthof 400 and 500 mm, respectively. Figure 24 highlights thatthe three replicate frames showed consistent responses. TheHR500 had higher maximum load carrying capacity thanthe HR400. The average loads were 120 kN for HR400 andFig. 21 Details of semirigid frame and instrumentation(a) Partial tensile failure of connection between LSB and plate in beam (b) Pullout failure of LSB in column (c) Partial tensile failure of connection between LSB and column base joint Fig. 22 Damage observed inthe portal frame test(a) Spilt at the top column (b) Bending crack on the column Fig. 23 Damage observed in the columns of the portal frame testInt J Adv Struct Eng (2015) 7:387–403 401123133 kN for HR500. Once the system reached maximumload capacity, however, there was a big drop for bothsystems. After this drop, the HR400 portal frame continuedto deform without loss of strength and had higher ductility.The HR500 portal frame, however, after the peak load,failed in a brittle manner without showing any ductility.Schematic of the finite element model of the portalframe is depicted in Fig. 25. The frame is modeled inOpenSees using a lumped plasticity approach. The non-linearity was limited within the connection, a zero-lengthspring model was used to model the connection, and thebeam and columns were treated as linear element. Thetimber columns and beam were modeled in OpenSees aselasticBeamColumn element, with the corresponding areaand moment of inertia computed from the sectionalproperties. The timber modulus of elasticity was6500 MPa (Japanese cedar, E65-F255). The plastic rota-tion was modeled with the Pinching4 hysteretic modelcalibrated from the connection tests. A static pushoveranalysis was carried out to a maximum deformation of250 mm. Result of the pushover analysis is plotted inFig. 24. The numerical results, shown in Fig. 24, capturethe overall load–deformation of experimental test resultsup to the maximum load. For the HR500, however, thebrittle failure was not captured. As the brittle failure wasin the column, the use of only lumped plasticity modelwith elastic column assumption did not capture this fail-ure model. As well, in the derivation of the connectionmodels, effects of axial forces in beams and columnswere neglected in the numerical model of the portalframe. Indeed, the modeling can be further enhanced withthe above formulation, but for the overall response anal-ysis, this model can indeed be extended to model build-ings with similar connection types.ConclusionSemirigid frame systems are prevalent in Japanese timberconstruction industry. To develop analytical predictiontools, however, reliability analytical and numerical modelsare needed. In this paper, a series of reverse cyclic andstatic pushover experimental tests were carried out fordifferent sizes of beam–column (depths of 400, 500, and600 mm) and column–base (4, 5, 8 LSBs) connections. Forall connections, both analytical and numerical models weredeveloped. It should be noted that the testing cycles fol-lowed the Japanese standard loading criteria; however,instead of repeating the loading sequence three times, onlyone cycle was used. For this preliminary study of derivinganalytical and numerical solutions, this simplification wassufficient, but further tests are required with the properloading sequence. The following conclusions can be drawn.(a) HR400 0204060801001201401600 50 100 150 200 250Load [kN]Deformaon [mm]Numerical HR400- this studyHR 400-1HR 400-2HR 400-3(b) HR500 0204060801001201401600 50 100 150 200 250Load [kN]Deformaon [mm]Numerical HR500- this studyHR 500-1HR 500-2HR 500-3Fig. 24 Analytical and experimental test load–deformation envelopefor portal frameFig. 25 Details of semirigid timber frame model in OpenSees402 Int J Adv Struct Eng (2015) 7:387–403123• For the beam–column connections, as expected, withincrease in depth of the connection, the overall momentresistance and stiffness increased and ductility reduced.• For the column–base connection, with increase in numberof LSBs, the strength, stiffness, and ductility increased.• The material model available in OpenSees, Pinching4hysteretic model, was calibrated for connections. Thenumerical model shows good agreement with theexperimental test results.• The analytical model for the beam–column connectionshows agreement with the maximum moment andstiffness. However, the analytical model for thecolumn–base connection overpredicted the stiffnessand underpredicted the strength.Furthermore, utility of the numerical models wasexplored for a glulam timber portal frame structure withdifferent beam sizes and connection types. The analyticalmodel of the portal frame was developed in OpenSees. Thefollowing simplification was made in the analytical modelof the portal frame:• The effect of shear force was neglected in deriving thecolumn–base connection models.• As the brittle failure in the column was observed, theuse of only lumped plasticity model with elastic columnassumption did not capture this failure model.• The effects of axial forces in beams and columns wereneglected in the modeling of the portal frame.Despite these limitations, however, there was good agree-ment with the experimental test results. The Pinching4 hys-teretic model can be used in full-scale structural modeling oftimber frames. The authors are carrying out further studies andcalibration to improve the analytical and numerical models.Acknowledgments The research was supported by the Grant-in-Aidfor Scientific research of JSPS (17696048). The authors would like toexpress their sincere thanks to Professor Emeritus Kohei Komatsu ofKyoto University and Hara Tech Co. for their invaluable contribution.Open Access This article is distributed under the terms of the Crea-tive Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use,distribution, and reproduction in any medium, provided you giveappropriate credit to the original author(s) and the source, provide a linkto the Creative Commons license, and indicate if changes were made.ReferencesForestry Agency (2011). Annual Report on Forest and Forestry inJapan: Fiscal Year 2011. Ministry of Agriculture, Forestry andFisheries, Japan, http://www.rinya.maff.go.jp/j/kikaku/hakusyo/23hakusyo/pdf/23_e.pdf. Accessed 17 Jun 2015Foschi RO (2000) Modeling the hysteretic response of mechanicalconnections for wood structures. In: Proc, world conf. on timberengineering (WCTE): Whistler, CanadaInoue M, Okibayshi S, Tanaka K, Yazu S, Goto Y (1999)Development and application of new type connecting systemin timber structures: application to heavy timber structures.J Archit Build Sci 8:91–96 (in Japanese)Komatsu K, Hara Y, Nanami Y, Ikki T (1999) Development ofLagscrewbolt as a connector for Glulam moment-resisting joints.In: Proceedings of Pacific Timber Engineering Conference,14–18 March 1999, Rotorua, New Zealand, pp 2.349–2.354Kouris LAS, Meireles H, Bento R, Kappos AJ (2014) Simple andcomplex modelling of timber-framed masonry walls in Pom-balino buildings. Bull Earthq Eng. doi:10.1007/s10518-014-9586-0Lowes LN, Mitra N, Altoontash A (2004) A beam-column jointmodel for simulating the earthquake response of reinforcedconcrete frames. PEER Report 2003/10, Pacific EarthquakeEngineering Research Center, February 2004McKenna F, Fenves GL, Scott MH (2000) Open system forearthquake engineering simulation, University of California,Berkeley. http://opensees.berkely.edu. Accessed Jan 2015Mori T, Nakatani M, Komatsu K (2009) Development on thestructural performance of one directional timber frame usinglagscrewbolts having an external thread. J Struct Eng B55B:213–218 (in Japanese)Nakatani M, Komatsu K (2005a) Expression mechanism of pull-outperformance in Lagscrewbolted timber joints I. Effects of leadhole diameter, embedment depth, embedment directions andedge distance on the pull-out performance. Mokuzai Gakkaishi51(2):125–130 (in Japanese)Nakatani M, Komatsu K (2005b) Expression mechanism of pull-outperformance in Lagscrewbolted timber joints II. Development oftheory on pull-out properties Parallel to the grain. MokuzaiGakkaishi 51(5):311–317 (in Japanese)Nakatani M, Komatsu K (2006) Expression mechanism of pull-outperformance in Lagscrewbolted timber joints III. Developmentof a theory of pull-out properties perpendicular to the grain.Mokuzai Gakkaishi 52(3):160–167 (in Japanese)Nakatani M, Mori T, Komatsu K (2008) Study on the beam-columnjoint of timber frame structures using lagscrewbolts and specialconnectors. J Struct Constr Eng 73(626):599–606 (in Japanese)Rahmanishamsi E, Soroushian S, Maragakisa M (2015) Cyclic shearbehavior of gypsum board-to-steel stud screw connections innonstructural walls. Earthquake Spectra, in press, http://dx.doi.org/10.1193/062714EQS091M. Accessed 29 Apr 2015Rinaldin G, Amadio C, Fragiacomo M (2013) A component approachfor the hysteretic behaviour of connections in cross-laminatedwooden structures. J Earthq Eng Struct Dyn. doi:10.1002/eqe.2310Sato M, Isoda H, Sugaya Y (2007) Experimental study for timber-based semi-rigid frame with bolt and bond. J Archit Build Sci13(26):539–544 (in Japanese)Shen YL, Schneider J, Tesfamariam S, Stiemer SF, Mu Z (2013)Hysteresis behavior of bracket connection in cross-laminated-timber shear walls. Constr Build Mater 48:980–991Shojo N, Fujitani Y, Makishima Y, Nogomi H, Ohno Y, Ohashi Y(2004) Study on the beam-column joint of timber framestructures using drift pins. J Struct Constr Eng 578:91–97 (inJapanese)Shojo N, Ohno Y, Fujitani Y, Ohashi Y (2005) Experimental study onthe two story timber frame structure using drift pin joints(structures). J Archit Building Sci 22:185–188 (in Japanese)Tlustochowicz G, Serrano E, Steiger R (2011) State-of-the-art reviewon timber connections with glued-in steel rods. Mater Struct44(5):997–1020Volkersen O (1938) Die Nietkraftverteilung in zugbeanspruchtenNietverbindungen mit konstanten Laschenquerschnitten. Luft-fahrtforschung 15:41–47Int J Adv Struct Eng (2015) 7:387–403 403123
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Performance of semirigid timber frame with Lagscrewbolt connections: experimental, analytical, and numerical… Mori, Takuro; Nakatani, Makoto; Tesfamariam, Solomon Nov 13, 2015
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Title | Performance of semirigid timber frame with Lagscrewbolt connections: experimental, analytical, and numerical model results |
Creator |
Mori, Takuro Nakatani, Makoto Tesfamariam, Solomon |
Publisher | Springer Berlin Heidelberg |
Date Issued | 2015-11-13 |
Description | This paper presents analytical and numerical models for semirigid timber frame with Lagscrewbolt (LSB) connections. A series of static and reverse cyclic experimental tests were carried out for different beam sizes (400, 500, and 600 mm depth) and column–base connections with different numbers of LSBs (4, 5, 8). For the beam–column connections, with increase in beam depth, moment resistance and stiffness values increased, and ductility factor reduced. For the column–base connection, with increase in the number of LSBs, the strength, stiffness, and ductility values increased. A material model available in OpenSees, Pinching4 hysteretic model, was calibrated for all connection test results. Finally, analytical model of the portal frame was developed and compared with the experimental test results. Overall, there was good agreement with the experimental test results, and the Pinching4 hysteretic model can readily be used for full-scale structural model. |
Subject |
Lagscrewbolt Glulam timber Connection Semirigid portal frame Analytical model Numerical model Finite element model |
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Article |
Type |
Text |
Language | eng |
Date Available | 2016-08-19 |
Provider | Vancouver : University of British Columbia Library |
Rights | Attribution 4.0 International (CC BY 4.0) |
DOI | 10.14288/1.0308646 |
URI | http://hdl.handle.net/2429/58878 |
Affiliation |
Non UBC Applied Science, Faculty of Engineering, School of (Okanagan) |
Publisher DOI | 10.1007/s40091-015-0107-4 |
Peer Review Status | Reviewed |
Scholarly Level | Faculty |
Copyright Holder | The Author(s) |
Rights URI | http://creativecommons.org/licenses/by/4.0/ |
Aggregated Source Repository | DSpace |
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