Load Carryig Capacity of il-lamiated Timber loaded perpedicular to its plae Volker KRAEMER Dr.-Ig. Lerstul für Igeieurolzbau ud Baukostruktioe Uiversity of Karlsrue Karlsrue, Germay 96 Bor i Tettag / Germay 989-996 Study of Civil Egieerig, Uiversity of Karlsrue sice 996 Scietific assistat, Lerstul für Igeieurolzbau ud Baukostruktioe, Uiversity of Karlsrue Volker.Kraemer@olz.uka.de Summary Te aim of a researc project was to derive desig equatios for te fective bedig stiffess, for te resultig bedig stresses ad for te ail loads occurrig i ail-lamiated timber. It would ave bee quite expesive to obtai te desig equatios by performig a large umber of tests. Tis is wy te tests were simulated o te computer. or te simulatios, te parameters / (spa / eigt of te elemet), te ail diameter ad te ail spacig were varied. Te simulatios were coducted o te basis of a realistic stiffess-beaviour of te lamellas ad of te ailed coectios. To guaratee statistically reliable results, differet systems of ail-lamiated timber elemets were simulated. Eac system was simulated 00 times. Te desig equatios were derived from te results of tese simulatios. Te results of te desig equatios sow a good agreemet wit te results of 4 tests. Keywords: ail-lamiated timber; ailed joits; mecaical fasteers; timber; material properties. Itroductio A ail-lamiated timber elemet is a plae structural compoet composed of sigle, edgewiseorieted lamellas (see figure ). Tese lamellas are mecaically joited usually by ails, alteratively by dowels made of ardwood. I te followig, oly ail-lamiated timber elemets are cosidered, wic are mecaically joited by ails ad loaded by cetral cocetrated loads. I Germay, ail lamiated timber is very popular i ousig costructio, altoug tere are o approved desig rules. Tese elemets are desiged o vague assumptios or i a coservative way. Te aim of a researc project [] was to derive desig equatios for te fective bedig stiffess of te elemets, for te resultig bedig stresses of te lamellas, ad for te ail loads. Te desig equatios were derived from te results of a large umber of simulatios. or tese simulatios te realistic stiffess ad stregt values of te lamellas ad te realistic loaddormatio caracteristics of ailed timber to timber joits were used.
b ig. il-lamiated timber elemet uder cetre sigle load. Basis of te Simulatios. Lamellas Te stregt ad stiffess properties of te lamellas were simulated o te basis of te work of Görlacer []. Studies of lamellas used i glued lamiated timber served as a basis for tese simulatios. A virtual lamella ( = 4.5 m) is subdivided ito 0 segmets wit a legt of 5 cm eac. Te values of MOE, te Kot Area Ratio (KAR) ad te desity are assiged to eac sigle segmet.. ils Te simulatio of te ails was coducted o te basis of a ailed double sear timber-to-timber coectio. Te ail legt cosequetly resulted as tree times te lamella widt. Wit te available smoot ails commoly used, te ail diameter (d N ) used te depeds o te widt (t) of te lamella. Te dimesios of te ails correspoded to dimesios give i Germa codes. or example, for t = 0 mm te ail.4 x 90 mm is used. Te ails are assumed to be arraged i a zigzag patter. Te load dormatio caracteristics were derived from tests. A load dormatio curve ca be approximated by equatio () []. K x K (x) (K K x) e max Te parameters of equatio () are sow i figure. After determiig te parameters K, K, K ad max ad teir statistical distributio, tese parameters could be simulated, takig ito accout te variability witi ad betwee timber members. Te simulated load dormatio caracteristics were used for te simulatios. Terore, te load dormatio curves were approximated usig a polygo. Tis polygo cosists of six idividual geerated poits. ()
max Load [N] K arcta (K ) arcta (K ) Dormatio [mm] x ig. Typical load dormatio curve ad parameters of equatio (). Dimesios of te ail-lamiated timber elemets Te ail-lamiated timber elemets (NLTE) were simulated as simply supported beams (see figure ). Te spa () of te NLTE was kept costat at.6 m. Te dept () of te lamellas was varied i te rage of 40, 60 ad 80 mm. Cosequetly, te /-ratios raged from 0 up to 5.7, wic are close to te ratios used for floors [4]. Te widt (t) of te lamellas was varied i te rage of 0 mm, 5 mm, ad 40 mm. To keep te computig time at a reasoable level, eac virtual NLTE cosisted of 0 lamellas..4 iite Elemet Model ad Simulatio A grid was cose as te mecaical model of te NLTE. Te girders i logitudial directio represet te lamellas, te girders i trasverse directio represet te ails. Te lamellas of te NLTE are supported i x-, y-, ad z-directio (lt ed) ad i y- ad z-directio (rigt ed). Te NLTE s were loaded wit a sigle load or wit a uiformly distributed load, wic was applied i 0 steps. To simulate te spatial distributio of a sigle load (approximately 5cm/5cm), te sigle load was subdivided ito 6 parts. irst, te files wit te material properties of te lamellas ad of te ails were geerated. Te files for te E-calculatio were geerated o te basis of tese material properties ad o cose geometric values of te NLTE. Te calculatios were performed wit te E- program ANSYS.. Evaluatio of te Simulatios or eac of te simulates NLTE s te 98%-fractile-values of te bedig stresses of te lamellas ad of te ail loads ad te mea-values of te dormatios were determied. Te desig equatios were derived from tese 98%-fractile- ad mea-values.. Bedig stresses of te lamellas Te maximum bedig stress of lamellas i a NLTE uder a cetric sigle load ca be calculated usig equatio : M B 4 [N/mm ] () Wˆ t 6 were [N] is te cocetrated load ad [mm] is te spa of te NLTE t ad are te widt ad te dept of te lamellas [mm]
Te equatios to calculate te fective umber of lamellas (bedig stress) were derived for differet butt-joit patters of te lamellas ad for differet types of loadig of te NLTE (see Table ). Table Effective umbers of lamellas (bedig stress) butt-joits cetric sigle load uiformly distributed load o butt-joits, 0, (cotiuous) a alteratig,5 0,,5 0, a ' staggered 0,5,5 0, a 0,9 radom 4,5 0, a 0,9 a 9 were is te dept of te lamellas [mm] is te spa of te NLTE [mm] a is te ail spacig [mm] ' is te locatio of te butt-joits [mm]. Dormatio of te NLTE Te elastic displacemet of te NLTE uder a cocetrated load ca be calculated wit equatio : v [mm] () 48E Iˆ t 48E Te modulus of elasticity is assumed as te mea value of te simulated MOE-values ad resulted as,600 N/mm. Te equatios to calculate te fective umber of lamellas (dormatio) were derived for differet butt-joit patters of te lamellas ad for differet types of loadig of te NLTE (see Table ).
Table Effective umbers of lamellas (dormatio) butt-joits cetric sigle load uiformly distributed load o butt-joits, (cotiuous) a alteratig staggered radom Te parameters are give i paragrap..,9 a 0,86,9 a,9 a 0, ' 0,5 0,9 0,9 a 9 4. il loads Te equatios to calculate te ail loads were derived for differet butt-joit patters of te lamellas ad for differet types of loadig of te NLTE (see Table ). Table il loads butt-joits cetric sigle load uiformly distributed load o butt-joits (cotiuous) alteratig staggered radom a 8, a 8, a 5,, 0,8 0,8 0,8 a q q a q _ ' a d 4,8 4 d N 5 ü 7 a 9 d, N 5,5 N
were a ', ü q d N is te cocetrated load [kn] is te spa of te NLTE [mm] is te dept of te lamellas [mm] is te ail spacig [mm] is te locatio of te butt-joits [mm] is te uiformly distributed load [kn/m] is te diameter of te ils [mm] 4. Discussio, Coclusios A mecaically lamiated timber elemet (NLTE) is a plae structural compoet wic is made of sigle, edgewise-orieted lamellas. Te lamellas are mostly joited by ails. Te aim of a researc project was to derive desig equatios for te bedig stiffess, for te bedig stresses of te lamellas ad for te actio fects of te ails. Te desig equatios were derived from te simulatio of tousads of ail-lamiated timber elemets. I tese simulatios, te parameters / (spa / eigt of te elemet), te diameter of te ails ad te ail spacig were varied. Te simulatios were coducted o te basis of realistic stiffess-values of te lamellas ad te ails. Te lamellas were geerated o te basis of te work of Görlacer, ad te ails were geerated o te basis of test results. To guaratee statistically reliable results, differet systems of ail-lamiated timber elemets were simulated. Eac system of ail-lamiated timber elemets was simulated 00 times. Te desig equatios were derived from te 98%-fractile-values ad from te mea-values of te results of te simulatios. Te results of te desig equatios were compared to test results ad demostrated good agreemet wit eac oter[5]. 5. Rereces [] Görlacer, R.: Klassifizierug vo Brettscictolzlamelle durc Messug vo Logitudialscwiguge; 4.olge Ht, Bericte der Versucsastalt für Stal, Holz ud Steie der Uiversität ridericiaa i Karlsrue; 990 [] Blaß, H.J., Krämer, V.: Lastverteilug, Tragwirkug ud Verformugsveralte für acgiebig miteiader verbudee Brettstapelelemete, orscugsberict, Uiversität Karlsrue (TH), 00 [] Blaß, H.J.; Utersucuge über die Variatio des Last- Versciebugsveraltes i gelverbiduge; Holz als Ro- ud Werkstoff; Spriger Verlag; Nr. 48; Juli 990 [4] Brettstapelbau-Bausystem, Hadbuc, Hiwo Holzidustrie Waldburg zu Wolfegg GmbH & Co. KG; November 997 [5] Krämer, V.; Trag- ud Verformugsveralte geagelter Brettstapelelemete uter Querlast, Dissertatio, ebruar 00