67  Advances in Production Engineering & Management ISSN 1854 ‐6250 Volu me 16 | Number 1 | March 2021 | pp 67–8 1 Journal ho me: a p em‐journal.or g https://doi.org /10.14743/apem2021.1.385 Original s cientif i c paper Study of load‐bearing timber‐wall elements using  experimental testing and mathematical modelling   Premrov, M. a , Ber, B. b , Kozem Šilih, E. a,*   a University of Maribor, Faculty of Civil Engineering, Transportation Engineering and Architecture, Maribor, Slovenia  b Jelovica hiše d.o.o., Preddvor, Slovenia      A B S T R A C T   A R T I C L E   I N F O C o m b i n i n g t i m b e r a n d g l a s s i n t h e w a l l e l e m e n t s o f t h e b u i l d i n g e nvelop e with the p roper orientati o n of s uch transparent façade e lem e nts e n a b l e s t h e utilization of solar energy for h eating and inter nal illum i nati on of the building. However, the a symmetrical l ayout of t i m ber‐glass wall e l e ments in s uch buildings can result i n problems w ith the horizontal stabilit y of the s tructure, so their p artici pation t o load‐ b earing c apacity of the s truc tu re i s u s u a l l y n e ‐ g l e c t e d . T h e s t u d y d e a l s w i t h s o l u t i o n s f o r s u c h e l e m e n t s a s h o rizontal l oad ‐ bearing members with proper c onnectio n det a ils . F irs t, s p ecific ally d evelope d timber‐glass w a ll e lements we re e xperimentally tested u nder m on oto n ic a nd cyclic h orizon tal poin t l o ad, an d further in c o m binatio n w i t h c lassical timbe r ‐ framed w all elements i mplemented i nt o special single a nd t wo‐st orey b ox ‐ house models, which were fur ther e x p e r i m e n t a l l y t e s t e d o n t h e s haking t able. In the s econd part a s the m ain goal o f the s tudy, a quite simpl e mathematical m o d e l o f t h e b o x ‐ h o u s e p r o t o t y p e s i s d e v e l o p e d u s i n g a f i c t i v e diagonal e le ‐ m e n t f o r s i m u l a t i n g t h e r a c k i n g s t i f f n e s s o f t h e b r a c i n g t i m b e r ‐glass wall element. The calculated r esults f or the 1 st v ibra tion p eriod are compared w ith the p reviousl y measured e xperimental result s to p rove an  accuracy o f the developed model. F inally, a line ar time‐his tor y calculatio n is do ne a s a samp le presentation o f the d eveloped m a thematical model using La nders accelera‐ tion spectrum. The developed m a thematical model enables a simpl e and effec‐ tive s eis m ic r es pons e calculation of t imber buildings cons id eri ng the d evel‐ oped t imber‐gl ass wall e lements as l oad‐bearing bracing element s against h o r i z o n t a l l o a d a c t i o n s . T h e m o d e l c a n a l s o b e r e c o m m e n d e d f o r using i n further parametric n umerical a cademic studi e s analysing the i nf luence o f various parameters.   Keywords: Wall elements; Timber; Timber‐glass building ; Stiffness; Vibratio ns ; Ex periments; Modelling; Landers accelerogram *Corresponding author: erika.kozem@u m.s i (Kozem Šilih, E.) Article history: Received 6 October 2020 Revised 26 February 2021 Accepted 7 Mar ch 2021 C o ntent fro m th i s w o rk may be us ed und er th e ter m s o f the Cre a ti ve C o m mons At tri bution 4.0 Internat i ona l Li c e n c e (C C BY 4.0). Any furth er d i s tr i b ut i o n of t h i s work m u s t mai nta i n attri b ut i o n to th e auth o r( s ) and th e t i t le of the work, journa l c i t a tion and DOI.      1. Introduction   C l i m a t e c h a n g e s o f t h e l a s t f e w d e c a d e s d o n o t o n l y e n c o u r a g e r esearch i nt o the origins of t hei r onset, but th ey a lso mean a w arnin g a nd a n ur gent c all for a nee d t o r e m o v e t h e i r c a u s e s a n d alleviat e the conseque nces a ffec tin g the e nviro n ment. Eco‐frien dly solutions i n residential an d public b uilding construct i on remains our most v ital task, w hose holistic problem sol v ing re‐ quires k now ledge inte gr ation [1 ]. T h e refor e , the domain o f e n er gy c onsu m ption is w itnessing a w o r l d w i d e t r e n d w h o s e a i m i s t o r e d u c e p r i m a r y e n e r g y c o n s u m p t i o n a nd g r eenh o use gas emissions. C onsequ e ntly, many i nvest i gatio n s h a ve b een c arri ed o u t t o w a r d s 1 0 0 % r e n e w a b l e a n d s u s t a i n a b l e e n e r g y s o l u t i o n s i n m a n y d i f f e r e n t a r e a s [ 2 ‐ 5 ] . C onstruc tions a r e , besides th e f i e l d s o f t r a n s p o r t a n d i n d u s t r y , o n e o f t h e m a i n u se r s o f t h e primary ener gy f rom fossil sources. However, i t i s i mportant t o set out that r esidential b uildings forming 70 % o f the total buildings ’ Premrov, Ber, Kozem Šilih    68  Advances in Production Engineering & Management 16(1) 2021 surface co nsume and are responsib le for 6 3 % of the tota l ene rg y de ma nd require d to sa t isf y the requests o f t h e hosin g st o ck [6 ] . Moreo v er, the time o f significan t climate c hanges d emands a ctive search f or e nergy efficient s t r u c t u r a l s y s t e m s w i t h a s l o w C O 2 e missions a s possible in the p hases of o bject construction, i ts exploit a tion, a nd i ts d ecomposition. A s a natural raw materi al requiring minimal energy i nput into the p rocess of b ecoming construction material, timber s how s indisputable e nvi r onmental excellence w i th v er y low CO 2 e missions. T her e for e , the pr efabricated timber b uildings a re s uit a ‐ ble for buildi ng th e ener g y savi ng obje c ts of differe n t stand a r ds. T h e u s e o f g l a z i n g i n b u i l d i n g s h a s a l w a y s c o n t r i b u t e d t o o p e n n e s s , v i s u a l c o m f o r t , a n d b e t t e r daylight situation. Although char act e r i zed by w e a k thermal pro p erties i n th e past, glass has be en gaini n g a n e ver‐gre a ter significa n ce a s a building m ateri a l due to its improved ther m al, optical a n d s t r e n g t h p r o p e r t i e s , r e s u l t i n g f r o m y e a r s o f d e v e l o p m e n t . M anu f act urers h ave i m prove d thermal insu lation and strength o f th e glass over y ears [ 7] a nd t he f actor of e ner g y transmission of s olar r adi a tion which enabled not only the i n ternal i lluminat i o n o f t h e b u i l d i n g w i t h b i g g l a s s surfaces, pri m arily orien t ed tow ard t h e south, but also th e sol ar e nerg y heating . Nowadays, timber c onst r uction com b ined w ith the usage of s uitab le a nd p roperly o riented glass surfaces r epresents a huge p otential i n residential and p ublic building c onstruct ion. T he fact t hat location of S lovenia on the so uthern s ide of t he A lpin e r a n g e e n a b l e s c o n s i d e r a b l y h i g h portion of t h e s olar p otential i n the ti me o f h e ati n g season re s u lts in high portions o f solar gains with t he p roper installation of bigger glass surfaces in the s o uthern s ide of the b uilding envelope [8‐10]. Consequently, so‐ c alled timber‐glass build ings have b ee n developed in o rder t o provide the highest possible solar potential and internal n atural i llum inati on. I n that w ay , f i x e d g l a s s surfaces a re installed besides windo w s primary in the s outhern part o f t he building e nvelope (Fig. 1). Such w all elements w ere e a rlier not c onsidered a s loa d ‐ bearing to horizontal loads b e c a u s e o f t h e e x t r e m e l y b r i t t l e b e h a v i o u r o f t h e g l a s s . O n l y c onvention al p refabricated f rame‐ panel wall elements w ith classica l OSB or f ibre‐plaster b oar d s were m ostly installed on other three sides of the building envelope. H o w e v e r , i t i s i m p o r t a n t t o e m p h a s i z e t h a t c o n s e c u t i v e a s y m m e t r ical i nstallation o f load‐ bearin g w a ll ele m ents o f the b u ilding e nv elope, i f t i mber‐ g lass e lements are considered a s com‐ pletely no n load b earing, leads to t he p heno men o n of t orsio n i n s i n g l e f l o o r s d u e t o t h e s e i s m i c l o a d . A s s c h e m a t i c a l l y p r e s e n t e d i n F i g . 2 , t h e p o s i t i o n o f t h e m a s s f l o o r c e n t r e ( M ) i n s u c h c a s e can significa n tly devi ate from th e ce n t r e of stiffnes s (R) of the l oad‐be aring elem ents. N a m e l y , t h e p o s s i b l e p h e n o m e n o n i n t h e m e n t i o n e d c a s e c a n b e t h e so‐called soft f loor, which should b e avoided when d esignin g m ulti‐ s torey buildings in seismic areas [11]. This p h e n o m e n o n c a n b e c o n s t r u c t i o n a l l y s o l v e d i n t w o k n o w n a n d i n e ngineering practice common used met hod s :  Inner conventional pr efabricated fr ame‐panel w a ll eleme n ts c an be a dditionally i nstalled; h o w e v e r , t h i s i s n o t i n l i n e w i t h contemporary a rc hitecture of residential b u ildings aimi ng to enl arge n a t ural illumin a tion and general living comfort.  Special a dditional load‐bearing d iag o na l e lem ents ca n b e instal led in t imber‐glass wall el‐ e m e n t s o f t h e b u i l d i n g e n v e l o p e , w h i c h a r e e v i d e n t l y v i s i b l e ( F ig. 3). Still, t his practice is mostly us e d in public buildings only. Subsequentl y , lots o f res e archers deal w ith the solution of t he problem b y me a n s of loa d‐ bearin g tim b er‐glass wall elements . In this case, studies of n o n‐linear s ei smic r esponse of t he buildings on o bject classes should b e done, and accordingly suc h design m ethods s hould be d e‐ veloped th at a re r eli a ble enou gh f or i ntroduction in c onstructi on. I mp ortantly, the bas i c stand‐ ard conditio n [1 2] – li f e s a fet y sho uld be m et. Study of load‐bearing timber‐wall elements using experimental testing and mathematical modelling   Advances in Production Engineering & Management 16(1) 2021  69 Fig. 1 Timber‐g l ass houses wit h so uth‐or iente d fixed glazing Fig. 2 Phenome non of t orsion o n the floor due t o deviatio n of mas s (M ), and centre o f stiffness (R ), ran d omly chosen case Fig. 3 Detached house with fixe d glazing with south‐ oriented a nd addi tionally i nstalled visible diagonals; designed and photographed by Arc hitekturbür o Reinberg ZT G mbH V ienna The timber‐glass wall el ements a r e f ormed as a lt ernative l o a d‐b earing m embers o n horizon‐ tal weight w hich c an s ignificantl y c ontribute t o additional hor izontal l oad ‐ bearin g cap a city a nd s t i f f n e s s o f t h e w h o l e b u i l d i n g . M o r e o v e r , t h e y r e d u c e t h e t o r s i on impact o n single f lo o r s and at t h e s a m e t i m e t h e i n s t a l l a t i o n o f t h e v i s i b l e d i a g o n a l s c a n b e a v o i d e d . T h i s r e q u i r e s t h e f a i l u r e not t o r u n a t t h e g l a s s p a n e l , w h i c h i s a s a v e r y u n ‐ d u c t i l e s t r u c t u r a l elem ent, b ut on the joint surface bet w een t h e g lass and ti mber f r a me o r on the steel corn er j oi nt i nter‐stor e y el em ents which can ensure h igh level of d uctility o f such l oad‐bearing w all elem ent s . An i nteres ting a lt er ‐ native m eth o d of t h e d evelopment o f timb er‐glas s w all panels w i thout any adhesive is shown in [13]. In [ 14] innovative hybrid s tructural comp onents co mposed of cross‐laminated timber Premrov, Ber, Kozem Šilih    70  Advances in Production Engineering & Management 16(1) 2021 fram e a n d la minat e d glas s infill without using any adhesive t o examin e th eir response on the reverse‐cyclic loading. A s a result, in the c ase of s pecimens wi t h l o w v e r t i c a l l o a d , t h e s t r e n g t h degradati on demonstrat ed on aver age twice high er than i n t he c a ses of s pecimens w ith high v e r t i c a l l o a d . T h e s t i f f n e ss d e g r a d a t i o n w a s n o t i n f l u e n c e d e i t h e r b y t h e i n t e n s i t y o f v e r t i c a l l o a d or b y the nu mber o f glaz ing pan e ls. There f or e, i t was possible to f ormulate this phen omenon with a c ommon equation, w hich is imp o rtant for th e development o f f uture math ematical m odel of th e t ested type o f struc t ural comp o nents. T h e g o a l o f t h e s t u d y a n a l y s i s i n t h i s c o n t r i b u t i o n a i m s t o f i n d a solution to c hange a conven‐ tional board (plaster‐fibre, OS B) of f ramed‐panel wall elements w ith fixed thermal‐insolation glazin g. I mp ortantly, by t h e right pro c edure of c o nnection det a ils in t he c onnectin g pla ne o f th e timber‐ g lass frames, these can be c onsidered as a dditional load ‐bearing v ertical elements on known horiz ontal s train with p roper level of d uct i lity. This i s briefly presented in t he f orm of experi ment al s tudy i n Section 3. S o‐called timber ‐glass wall el emen ts w er e dev e loped and ex‐ p e r i m e n t a l l y a n a l y s e d i n d e t a i l o n n u m e r o u s s p e c i m e n s i n t h e f r ame o f i nternati onal resear c h project WoodWisdom L BTGC [15] . However, it h a s to b e emphasized th a t the costs of s uch ex‐ periments are too hi gh t o b e r eco g nized as u se ful in e n g in eerin g practice u sing a lso various t y p e s o f u n ‐ t e s t e d w a l l s a n d b o x ‐ h o u s e m o d e l s . T h e r e a r e a l s o m any various parameters, such t h e a d h e s i v e a n d g l a s s t y p e a n d t h i c k n e s s , t h e b o n d i n g c o n n e c t i on type, etc., which significantl y a f f e ct ra cking stif f n e ss of t im be r‐g la ss wa ll e le m ents a nd ha v e to be very car e fully analys e d, [15‐ 18]. O n t h e o t h e r c a s e , t h e g r o u p o f a u t h o r s w i d e l y i n v e s t i g a t e d a c ase w h ere the glass pane s we re com plete ly no t bo nd ed to the ti mber frame, [19, 14] . T h e r e f o r e , t h e s e c o n d p a r t i n S e c t i o n 4 a s t h e m a i n a n d f i n a l g oal of t he p resented s tudy, a q u i t e s i m p l e m a t h e m a t i c a l m o d e l o f t h e b o x ‐ h o u s e p r o t o t y p e s i s developed using a fictive diag‐ onal el emen t for simulat i ng t he r ack i ng s tiffness o f the braci n g tim b er‐gl a ss wall ele m ent. I t enables designers its application in a q uite simple c alculaculation softwar e in order to determine the horizontal l oad‐bearing capacity a n d s t i f f n e s s o f s u c h t i m b e r ‐ g lass w a ll element and further also the calc ulation of os c illating for m o f th e wh o le timb e r‐gla ss build ing model. Such math em at‐ ical m odel c an b e l a ter us ed f or d eter minati on o f c omplete s e is mic response o f such b uildings. A simple e xam p le p erform ed on previo usly e xperi m ental b o x‐h o use mo d e l i s p r e s e n t e d a t t h e e n d of the study. Howe ve r, t he b eh av io u r f a c t o r (q ) should be de term ine d f irst in tha t ca se . Only the n such d esign methods can be f ina lly d eveloped t hat ar e reliable en ou gh t o be i ntroduced in common en gineering practice f or a c omplete s e ismic calculation analysis o f such timber‐glass structures. However, i t should b e especially f i n a l l y e m p h a s i z e d t h a t t h e s e t o p i c s a r e n o t y e t i n c l u d e d i n Europe an s t a ndards s uch as [11] o r [12], s i n c e t h e y a r e t h e f i r s t s u c h i m p l e m e n t i n g E u r o p e a n guidelines i n terms of g l a ss construction as s uppo rt a nd i mplem entation of e xisting Eur o codes [20] . Nevertheless, s tudies a re a lread y mentioned in these g ui delin es w hich e xplicitly s tate that the y a re still in the stag e o f an a ca dem i c le ve l only. Ge n e ra lly, e a ch obje ct is unique , so a de sig ne r should p rovide s ufficientl y high r esist a nce t o a ll e x pected l o a d cases, a s determined b y Europe ‐ an s tand ard. A ll presente d and developed timber‐ g lass wall elem ents f rom our article, separate‐ ly l isted in [ 20] , can only increase t h is k ind of c alculated loads on request an d at s uitable con‐ structor k no wledge w h o d oes not n eed to use onl y kn own lo ad‐bea ring w all elements o r other strength ening meth ods (e. g. d ia gonals) in o rder to ensure s uff icientl y high resistance to ex‐ p e c t e d h o r i z o n t a l l o a d s ( w i n d , e a r t h q u a k e ) , w h i c h a r e n o t t h e t opics of this study. H er eby the p r o b l e m o f t h e s o ‐ c a l l e d s o f t f l o o r c a n b e a v o i d e d , a n d a l l p a r ameters o f m odern en ergy e fficient prefabricated timber buil d ing ca n also be tak e n i n t o considerat i on. 2. Materials and methods  Prefabricate d framed‐p anel w all ele m ents a re m ade of ti m b e r fra mes composed b y s t uds and longitudin al p osts a nd s h e athin g b oar d s (fibre‐plaster o r OSB), w h i c h m a y b e u n i l a t e r a l o r b i l a t ‐ eral w ith nai l s or s taples a ttach ed t o t h e ti mber f r a me. Th e sof t t h e r m a l i n s u l a t i o n i s i n s t a l l e d i n t h e s p a c e b e t w e e n t h e f r a m e s t r u c t u r e w h i c h t o g e t h e r w i t h o u t e r s tiff thermal insulati on pro‐ Study of load‐bearing timber‐wall elements using experimental testing and mathematical modelling   Advances in Production Engineering & Management 16(1) 2021  71 vides sufficie n t therm a l insulation o f the o ut er w all elements. S uch prefabricated ele m e n ts w ere in their o riginal form tec hnologic ally m anufactured only as s in gle‐pan e l ele m ents ( Fi g. 4 a) w ith the standard l ength 12 50 m m whic h was the standard length of s h eathin g boards. In 1 99 0s, th e single‐panel system b ecame a macro‐ p anel s ystem (Fig. 4b) for t echnolo g ical r equirements after f a s t e r m a n u f a c t u r e , s o t h e e n t i r e w a ll systems were m anufacture d in one p iece o f 12500 mm length w ith mostly b uilt‐ i n window a nd d oors openin gs. In terms o f horiz ontal l oads, a macro‐ panel system i s statically c onsidered a s the sum of s epar ate s i ngle p anel w all elem ent s . Howev‐ er, the meth od A i n Eurocode 5 [ 12] requires onl y the considera tion for the contribut i on of t h e single‐pan e l elem ents wit hout a ny win dow and do o r s openin gs. a) b) Fig. 4 a) Single‐panel, and b) m acro‐panel wall system Sever a l studies [21‐24] in the k nown literature p rove that el em ents w ith window a nd d oors openin gs c an c ontribut e t o a cert ain ext e nd t o ho rizontal l o a d‐ bearin g cap a city a nd s tiffn ess of such w all el e m ents. Ther efore, timb e r‐glass ele m ents, where con ventional sheathing is r eplaced by i nsul atio n glazin g (Fi g . 5 a ), c an b e considered a s load‐b ear ing to h orizontal loads to a c ertai n ext e nd. Obviously, horizo n tal fo rce tr a nsfer should b e assured b o t h o v e r c o n n e c t i n g p l a n e g l a s s ‐ timber w ith the help o f t he suitabl e a dhesive and over f ictiv e t e nsile diago n al o f th e gl a ss panel, as s chematic ally s hown i n Fig. 5 a [25‐27]. Furthermore, i t shou ld b e emph asized that s u ch l oad‐ bearing timber‐glass wall elements s h o u l d b e t h e n i n c o r p o r a t e d i n a l o a d ‐ b e a r i n g w a l l s y s t e m of prefabricated frame‐panel macro ‐wall systems and used in th e models o f timber‐glass prefabri‐ cated object s, p resented i n the shap e of the simplified box ‐house m odels in F ig. 5b, which were experi ment a lly tested in t he fr a m e o f t h e project [1 5] o n th e s ha king t able o f IZI I S in Skop j e [2 8]. a) b) Fig. 5 a) Type single panel wall elemen t with fi xed glazing and schem atic presentation of hor izontal load transfer, b) Box ‐house m odel of a timber glass building 1250 mm  Premrov, Ber, Kozem Šilih    72  Advances in Production Engineering & Management 16(1) 2021 3. Results and discussion   3.1 Experimental analysis  Experimental analysis of timber ‐glass wall elements  Prefabricated single f rame p anel w all elemen ts w ith fixed th ree ‐layered i nsulation glazing p a nel w e r e f i r s t t e s t e d f o r m o n o t o n o u s s t a t i c l o a d a c c o r d i n g t o t h e s tandard E N 594 :2 01 1, [29]. The vertical s tatic load w as c onstant a nd s caled up t o 25 kN/m. The t ests w er e the n r esu m ed w ith cyclic horizontal point l oad unde r the same l oad. I n addition, the Nieder maier end ‐joint t y p e 1 [ 3 0 ] w a s u s e d t o p r o v i d e t h e j o i n t b e t w e e n g l a s s p a n e l a n d t i m b er f rame. Two‐component poly‐ urethane a dhesive of 5 m m t hickn e ss and the an ne aled g lass o f 3 x 6 mm thic k ness were u sed, and the space b e twee n glazi n g was 1 6 mm thick. T wo t ypes o f specime ns w ere tested; they a re schematic a lly shown in F i g. 6:  wall ele m ent s with insulating g lass u n it (IGU) in on e piece (TG WE‐1),  wall ele m ent s of equ a l di mensio ns wi t h a glass p a nel in two pi e ces (TGW E‐ 2). Fig. 6 Geometr y of tested timber‐glass wall specimens The r e sults for all obtained h ys teresis of c yclic tests for both t y p e s o f a l l t e s t e d s p e c i m e n s w i t h drawn first envelopes of hystere sis cu rves ar e sho wn in Fig. 7 . I t c a n b e o b s e r v e d t h a t t h e t e s t s a m p l e s w i t h g l a z i n g i n o n e p i ece (TGW E‐1) not ably p rove slightly h igher horizontal l oad‐ bearing capacity a nd e specially h igher stiffness. H owever, hyste‐ resis curves s how t h a t t h e d u c t i l i t y f o r T G W E ‐ 1 i s s i g n i f i c a n t l y l o w e r , w h i c h c o u ld s ignificantly influe nce o n s eismic r esistance of s uch type o f load‐bearin g ti mber‐ g lass wall ele m ent s . The av‐ erage ductility calculated according to E N 12512 [31] a mounts f or d = 2.8 for TGWE‐ 1 a nd d = 3 . 1 f o r T G W E ‐ 2 . T h e d e t a i l e d p r e s e n t a t i o n o f t h e r e s u l t s u n d e r s t a t i c h o r i z o n t a l l o a d , c a l c u l a t e d values f or h orizont al s tiffness an d detailed a nalysis of m easure d v a l u e s w i t h a d d i t i o n a l r e c o m ‐ mendations for practical usage can b e fou n d in d et ail in [ 15 ] a n d [28]. The reduction in l oad c a pacity i n repetitive cycles is presented i n F i g u r e 8 , w h e r e t h e f o r c e ‐ d i s p l a c e m e n t d i a g r a m s h o w s t h e e n v e l o p e s o f t h e f i r s t , s e c o n d a nd t hird c ycles for all tested samples. T he c urves ar e markedly a ntisymmetric, and a cycl ic d e crease in s tiffness is a lso ob ‐ served. Additionally, the calcula ted m e an v alues o f t he r ackin g s t i f f n e s s w i t h t h e s t i f f n e s s r e d u c ‐ tion chart for the first thr ee en v e lopes are also pre sented f or T GWE‐1 and TGWE‐2 test samples. The stiffness diagram in F ig. 8 shows a slightly l arger decrease i n s t i f f n e s s f r o m t h e f i r s t t o t h e s e c o n d c y c l e f o r T G W E ‐ 2 t y p e ( 1 6 . 3 % ) . F r o m t h e s e c o n d t o t he thir d c ycle, the decrease in s t i f f n e s s i s m o r e p r o n o u n c e d i n t h e T G W E ‐ 1 t y p e ( 8 . 6 % ) . T h e t o tal decrease in s tiffness, i.e., difference between the first and thir d cycle r anges from 19. 1 % ( TGWE‐2 ) to 21.2 % (TGWE‐1), respectively. Study of load‐bearing timber‐wall elements using experimental testing and mathematical modelling   Advances in Production Engineering & Management 16(1) 2021  73 Fig. 7 Presentation of the response to horizontal cycli c load for bot h gro u ps of spe ci m ens and calculated sti f f ness Fig. 8 Presentation of the response to horizontal cycli c load for bot h gro u ps of spe ci m ens and calculated sti f f ness Premrov, Ber, Kozem Šilih    74  Advances in Production Engineering & Management 16(1) 2021 Experimental analysis of box ‐house timber ‐glass specimens The further analysis connects to g e the r the pre viously e x pe rime n ta lly te sted T GWE ‐1 and T GWE ‐ 2 tim b er‐gl a ss wall elem ents i n diffe r ent ways b y conv entio n al tim b er‐framed w a ll elem ent s s h e a t h e d w i t h O S B ( T F W E ‐ 1 ) b o a r d s . C o n s e q u e n t l y , a s t h e f i n a l p roduct s o‐called box ‐house timber‐ g lass building m o d els are developed, s chematically p r e se nted i n Fi gure 5 b, a nd t ested on the shaking table IZIIS in the S kopje institute. S ingle and two ‐storey composed box ‐house m o d e l s w i t h d i f f e r e n t s e t t i n g s o f T G W E a n d T F W E w a l l e l e m e n t s a r e p h o t ogr a phi c ally p resent ed i n Fig‐ u r e 9 . I t s h o u l d b e m e n t i o n e d t h a t i n s u l a t i n g t h r e e ‐ l a y e r e d g l a ss panels f rom non‐laminate g lass were u sed j u st f or the e conomic r easons, while lamin a te g las s s hould be u sed in p ractice for safety r easons b ecause i t signif icantl y increases the g lass duc tility. Anyway, failure mechanism s h o u l d b e c r e a t e d i n o r d e r t o g e n e r a t e t h e f a i l u r e a l o n g d u c t i l e steel inter‐storey h old‐downs or at l east a lo n g a dhesive in c onnectin g plane glass‐ timber, and b y no means the failure along t he glazin g, whic h would le a d to th e inst a n t brittle fract u re. Four s in gle‐ storey a nd f our two‐stor ey o bjects w ith grou nd p lan 2 . 4  3 . 4 m a n d h e i g h t 2 . 5 and 5.0 m, w ere constr ucted from w all eleme n ts, type T G W E‐1, T GW E ‐ 2 a n d T F W E ‐ 1 . T h r e e ‐ layered cros s g lued p anel o f dimension 2.4 m  3 . 4 m a n d t h i c k n e s s 1 0 0 m m s e r v e d f o r t h e c o n ‐ n e c t i o n o f w a l l e l e m e n t s . T h e a d d i t i o n a l m a s s o f 1 6 0 0 k g w a s a p p l i e d t o t h e p a n e l w h i c h s i m u ‐ lated the impact o f its own weight a nd l ive load i n the floor el e m e n t . D u e t o t h e h i g h e r s t i f f n e s s i n s h o r t e r d i r e c t i o n , t h e p a n e l t r a n s f e r r e d t h e m a j o r i t y o f v e r tical loads onto wall el ements, in‐ stalled perpendicularly t o the direction of e xcitation. T he w al l elemen ts t hat were s ei smically loaded i n t heir planes r ec eived only a minor p ortio n o f vertica l l o ad. This is an import a nt b ound‐ ary conditio n which affects the behaviour of th e se w all elements . T h e w a l l e l e m e n t s w e r e a t ‐ t a c h e d t o t h e A B f o u n d a t i o n w i t h W K R ‐ 2 8 5 t y p e o f a n g l e b r a c k e t s a n d w i t h a d d i t i o n a l M 1 2 a n ‐ c h o r s a l o n g t h e l e n g t h o f t h e b o t t o m s i l l . T h e c e i l i n g p a n e l s w ere joint to t he w all ele m e nts by self‐tappin g w ood s crews 8 /180 m m on mutu al d istance o f 1 50 m m. U pper and low e r walls were j oint t oget her in c orners b y metal an gle br ackets a nd M 12 s c r e w s . I n a d d i t i o n , d y n a m i c tests were d ivided i nto two basic modules: i ) lower intensity t esting w ithout f ailure i n the struc‐ ture o r in t he so‐called elastic state (together w ith a ll joints ) and ii) h ighe r i n t e n s i t y t e s t i n g , where th e gr ound acc eler ation w a s sc aled up eno u gh to caus e fai lure in the structure. After the str u cture was loaded w ith recorded Petrovac a n d Landers a ccelerograms, the s truc‐ ture d id not e xhibit v isibl e d am ages. I n o rder to in tensify the r esponse of t he s tructure, rando m ‐ l y g e n e r a t e d g r o u n d m o t i o n i n f r e q u e n c y r a n g e 2 . 0 ‐ 1 5 H z a n d g round acc e leration f r o m 0. 1 to 0.4 g was ap plied, as sho w n in T a b le 1 . Fig. 9 Photo of tested sin gle‐ and two‐storey box ‐house timber‐ glass models Study of load‐bearing timber‐wall elements using experimental testing and mathematical modelling   Advances in Production Engineering & Management 16(1) 2021  75 Table 1 Protoc o l of GLS m odel loading Low ‐intensity testing High ‐intensity testing GLS1 ‐ GLS4 and GLS6 ‐ GLS9 GLS5 G LS10 Modified Landers 0.15 g modified Landers 0 .50 g modified Landers 0 .50 g Modified Landers 0.25 g modified Landers 0 .75 g modified Landers 0 .75 g Petrovac 0.22 g sine‐beat 9.856 Hz 0 .10 g random 2‐15 Hz 0 .25 g sine‐beat 9.856 Hz 0.50 g random 2‐15 Hz 0 .35 g s ine‐beat 9.856 Hz 1 .00 g r andom 2‐15 Hz 0 .10 g r andom 2‐15 Hz 0 .25 g r andom 2‐15 Hz 0 .40 g Deformati o n s c an b e not iced i n the glue l ine b e t w een t h e g lass panel an d timber f r a me, she a r d r i f t a n d c o r n e r u p l i f t i n g . F i g . 1 0 ( l e f t ) s h o w s t h e v a l u e s o f these d e for m atio ns f or t he G LS 5 model at r andom excitation (2.0‐15 H z ) with a cceleration 0.4 g. T he v ertical displacement o f the corner w as 1 .0 mm, how ever, shear wall drift (1. 9 m m) a nd d efor mations of t he g lue line in the size o f 1.2 m m wer e also noticed. The tests of s tructure e xcitation or th e so‐called sweep tests w ere carried o ut i n the freq uency a r e a 1 . 0 ‐ 3 2 H z a n d t h e i n tensity acc e leration 0 .01 g. B ased o n thes e, v ibr a tion p eriod s of t he structure were c alculated; this could serve also f or t he e valua t ion o f t he r eduction level of t he s t r u c t u r a l s t i f f n e s s a n d d a m a g e l e v e l s . T h e m e a s u r e d v a l u e s b e f ore and aft e r high i ntens i ty e xci‐ tation are gr a phically pre sented in Fi g. 11. Fig. 10 Values of displacements and def ormati ons of the GLS 5 and GLS 1 0 mod els for a high intensity dynam i c test Premrov, Ber, Kozem Šilih    76  Advances in Production Engineering & Management 16(1) 2021 Fig. 11 Measured values of basic vibrat io n p e riods of the bef ore and a fter high intens it y tes t i n g A d e t a i l e d a n a l y s i s o f a l l r e s u l t s c a n b e f o u n d i n [ 1 5 ] a n d [ 2 8 ] , h o w e v e r , i t s h o u l d b e m e n ‐ tioned that t he high intensity excitati on did not r esult in a ny v i s i b l e d e f o r m a t i o n i n g l a z i n g , y e t ductile failure mechanis m with y ielding of s teel hold‐downs betw e e n f l o o r s , t h e so‐c alled rock‐ i n g m e c h a n i s m w a s g e n e r a t e d a t a l l t e s t s p e c i m e n s . T h e m a j o r i t y o f s e i s m i c e n e r g y w a s a b ‐ sorbed i n th e steel c orne r faste ners which function as ductile protectors of wall elements. In fact, t h i s w a s a l s o o n e o f t h e g o a l s o f t h i s s t u d y . T h e m e a s u r e d v a l u es o f vibr ation periods b e fore a nd after excitati on (Fig. 11) also p rove t hat there w a s no signific a n t d e c r e a s e i n s t r u c t u r e s t i f f n e s s . The slight i n crease in t h e me asured 1 st time periods can result only from t he y ielding process in steel corner fasteners. 3.2 Mathematical modelling and numerical analysis of the single and two‐storey box‐ house model  First, in order to pe rform t he num e rica l a na lysis, it wa s ne ce s sary to define a suitable mathemat‐ i c a l m o d e l o f t h e s t r u c t u r e . F o r t h i s p u r p o s e , t h e p r e v i o u s l y i ntroduced mathematical m odel w i t h a f i c t i v e d i a g o n a l f o r d e t e r m i n a t i o n o f t h e r a c k i n g s t i f f n es s of t imber‐framed w all e l emen ts with classical OSB or f ibr e ‐plaster (FPB) sheathing material [ 3 2] w as a pplied and further devel‐ oped f or the timber‐ glass wall elemen ts s tiffness simulatio n . F ollowing the e xpressions p resent‐ ed i n [ 3 2 ] , t h e ficti v e di ago n al d iameter for clas s ical s heathi ng b oards (OSB o r FPB) is deter‐ m i n e d i n t h e w a y t h a t h o r i z o n t a l d i s p l a c e m e n t o f t h e a c t u a l w a l l e l e m e n t i s t h e s a m e a s a h o r i ‐ zonta l displa ce m ent of the sim plif ie d m o de l with a f ictive dia g o n al, as s chematically p r e sented i n Fig. 1 2. L astly, the f ictive d iagon a l dia m eter ( ) is expressed in t he fi n al for m of: , ⋅ ⋅ (1a) 1 3⋅ (1b) 2⋅ , (1c) with b e i n g t h e m o d u l u s o f e l a s t i c i t y o f t h e d i a g o n a l , , t h e f i c t i v e c r o s s ‐ s e c t i o n o f t h e d i ‐ ago n al a nd th e le ng t h o f th e diag o na l . However, i t i s i mportant t o point out that t h e a lready develop e d mathematical m odel b y [32] can be u sed only for sheets w hich a re m echanically f astened to the timber f rame by s taples o r n a i l s . T h e e f f e c t i v e s t i f f n e s s is n amely calculated using the gamma‐method f ollowing the Eurocode 5 [12] expressions. Study of load‐bearing timber‐wall elements using experimental testing and mathematical modelling   Advances in Production Engineering & Management 16(1) 2021  77 EA= ∞ EA= ∞ EA= ∞ α F H h b F H EA= ∞ F D u d u H α F H Fig. 12 Schematically presented transfo rmation of a frame‐pa n el wall m odelled with truss members and a fictive diagonal However, i n case o f timb er‐glass wall elements, where the glas s p a n e i s c o n t i n u o u s l y b o n d e d t o t h e t i m b e r f r a m e , i t i s n o t p o s s i b l e t o d e t e r m i n e t h e g a m m a coefficient and the effect ive stiff‐ ness in E q. 1 b directly with the known e x pre ssions f rom the Eurocode s. S ome alread y de‐ veloped m a t hem atical m odels with s pring elem e n ts s imulate the f lexibility o f the bonding line between the glass pane a nd t he t imber frame [ 25], followed by a n extensive numerical paramet‐ ric study [27], albeit t he c alculation ti me i s too long t o be i mplement ed i nto the whole bo x‐house building m o d el. There f o r e, f or ti m b e r‐glass wall elem ents th e d iameter of the f ictive d iagonal c a n b e d e t e r m i n e d u s i n g e x p e r i m ental results fr om S ubsection 3 .1 u pon derived equation only: 4∙ ∙ ∙ cos ∙∙ (2) where r epresents the force u pon appe arance o f the first crac k a nd w cr r epresents the corre‐ sponding displacement u pon appearance o f the fir s t crack. The v alues for and w cr c a n b e d e ‐ termined onl y according to e xperim en tal testin g. The diamet e r s of t he d iagon a ls w ere calculated in this way for each type of w all panel. A s the box ‐ house model is c omposed as a c ombination o f classical timbe r‐fr amed w all ele m ents w ith OSB sheathi n g bo ards ( TFWE‐1) and the ti mber‐ g lass wall ele ment s ( T G WE ‐ 1 a n d T GW E ‐ 2 ) , t h e diamet er o f the substitu t i onal fi ctive diagon al i s d e termin ed fo r t h e O S B w a l l e l e m e n t s i n s e m i ‐ a n a l y t i c a l f i n a l e x p r e s s i o n s u s i n g E q . 1 a n d f o r t h e t i m b e r ‐ g l a s s T G W E ‐ 1 a n d T G W E ‐ 2 w a l l e l e ‐ ments from t he e xperi m ental resul t s u s i n g E q . 2 . T h e r e s u l t s f o r a r e p r e s e n t e d i n T a b l e 2 . A c c o r d i n g t o t h e r e s u l t s p r e s e n t e d i n T a b l e 2 , t h e h o r i z o n t a l s tiffn ess of T GWE‐2 and conven‐ tional TFWE‐1 wall pane l s are practically e qual, the stiffness of the TGWE‐ 1 does not differ much a s w e l l . I t a l s o m e a n s t h a t s t i f f n e s s c e n t r e () a n d m a s s c e n t r e ( ) of t he b ox‐h ouse m od el c oin‐ c i d e r e l a t i v e l y w e l l . B a s i c a l l y , t h i s w a s o n e o f t h e g o a l s o f o ur s tudy, because co nsecutive hi gh torsion loads along t he b uilding floor c an b e avoided in t he c ase o f an e arth quak e. S teel w ith the elasticity module E = 21 0 GPa was con s idered as m a terial for di a go nals. Table 2 The diameter of the fictive dia gonal for different wall elemen ts Wall elements R (N/mm) (mm) TGWE‐1 6704 16.60 TGWE‐2 3595 12.16 TFWE‐1 3636 12.23 Premrov, Ber, Kozem Šilih    78  Advances in Production Engineering & Management 16(1) 2021 I n t h e m a t h e m a t i c a l m o d e l o f t h e b o x ‐ h o u s e a r e c o n s i d e r e d a s r i g i d . A l s o , t h e t i m b e r f r a m e e l e m e n t s a r e c o n s i d e r e d a s a x i a l l y r i g i d i n o r d e r t o e l i m i n a t e the frame flexibility and only the flexi b ility of the d iagonals i s taken i n to a ccount [32]. How e ve r, they ar e already further devel‐ oped i n [33] a n up graded m athema tical approach f or classical timber‐fr a med wall buildings by including d ifferen t c ontri butions t o th e stiffn ess of t he t imb e r‐framed w alls, such a s floor bend‐ ing flexibility and flexibil it y in all floor to walls connectio ns, w hich are not i ncluded in t his study. The math em atical m od el d efined b y t h is m ethod was then u s e d for t h e n u m e r i c a l a n a l y s i s o f the single‐storey GLS5 a nd two‐s torey mod e l GLS10. T he n umerica l an al yses w ere p e rform e d using the str u ctural a nalysis softwar e S AP 2 000 v.17. T imber co lumns were m odelled as a xially rigid, w hile the timber c r oss‐glued fl oor p anels were c onsid ere d as isotr opic thin slabs board. T h e f l o o r s l a b s w e r e s u b j e c t e d t o a s u r f a c e l o a d o f 2 . 0 k N / m 2 . Fig. 13 shows the numeric a l mod‐ e l s o f t h e o n e ‐ s t o r e y a n d t h e t w o ‐ s t o r e y b o x ‐ h o u s e u s i n g t h e f i ctive diagonals, w hile T able 3 presents the c alculated fundamen tal vibration periods for both m o d e l s a n d c o m p a r i s o n with the measur ed f u n dame ntal p eriods a s ob tained f rom the e x peri m e ntal an alysi s ( see Subs e c tion ti‐ tled Experimental analysis of box ‐house timber ‐glass specimens). Ta ble 3 sho w s that t he r esults o f th e numerica l analysis c oincide well with t he m easured o n e s . M i n o r d i f f e r e n c e s c a n b e o b s e r v e d d u e t o t h e f a c t t h a t r i gid supports were u sed in n umeri‐ cal models, while anchor e lements i n t h e e x p e r i m e n t a l m o d e l s h a v e a c e r t a i n f l e x i b i l i t y w h i c h gives rise to a higher d eformability o f the structure and cons e quently slightly l onger vibration periods. S ubsequentl y, w ith the appli c ation o f t h e d eveloped m a th ematical m odels time‐history analys es c an b e furth e r p e rform ed using the Landers accelerogr a m, F ig. 13. T h e calculated hori‐ z o n t a l d i s p l a c e m e n t s o f t h e t o p o f t h e s t r u c t u r e s a s a functio n of t i m e are shown in F i g . 14 f or the single‐st o rey models G LS5 and two‐storey G LS10, r espec t ively . T h e m a x i m a l h o r i z o n t a l d i s ‐ placement amount ed to 2.67 mm for the mode l G LS5 a n d 1 1 . 86 m m f or th e model G LS1 0 . Fig. 13 Simplified numerical model of s ingle‐storey and two‐storey mod el with a fictive diagonal (presentation o f fundame ntal vibration forms) Table 3 Review of fundamental vibration period of experimentally and n umeri c ally tested mo dels Model Fundamental vi bration period T 1 (s) E xperimental Numerical Single‐storey GLS5 0 .095 0.096 Two‐storey GLS10 0 .167 0.173 Study of load‐bearing timber‐wall elements using experimental testing and mathematical modelling   Advances in Production Engineering & Management 16(1) 2021  79 Fig. 14 Numerical values of the top hor izo n tal displacements of the GL S5 and GLS10 models as the result of the time hist ory analyses usi ng the Landers acc elerogram 4. Conclusion  The us age o f e nlarged po rtion of g lass s urfaces in m odern ti mbe r objects p r ovides s olar thermal gains and impacts living c omfort p osi t ively. H owe v er, large no n ‐ load‐bearing g lass surfaces u n‐ der wind a nd s eismic f or ces cause str u ctural problems, a bove a l l in ter ms o f uneven d istribution of the horizontal forc e due to i rregularity o f the structure in i t s g r o u n d p l a n . T h e r e f o r e , i t i s r e a ‐ sonable to e nsure that s uch wall ele m ents c an p rovide c ertai n h orizo n tal load c apacit y and sti ff‐ ness and als o certai n level of ductility in s eismic active area s. Firstly, d iscu ssed timber‐ g lass el e m en ts w ere e x p e riment ally t e sted. Secondly, timber ‐glass wall elem ent s w ere studi e d with c om binatio n o f c onve n tion al f ram e w a l l e l e m e n t s w h i c h w e r e used i n th e t e st b o x m od els of s in gle‐ storey a nd t wo‐storey o b j ects. The t i mber‐ g lass wall ele‐ m e n t s , u s e d i n t h e b o x m o d e l s a n d s u b j e c t e d t o h i g h l y i n t e n s i v e s eismic i mpact show ed s uffi‐ ciently hi gh l evel o f robu stness bec a u s e the e n ergy a bsorption w a s n o t e d i n u p l i f t e d a n d s h e a r s t e e l c o r n e r f a s t e n e r s , w h e r e a s t h e w a l l p a n e l r e m a i n e d i n e l a s t i c a r e a w i t h o u t a n y v i s i b l e s i g n s of d eformati on of t he g lu e line. In S u b section 3. 2, s pecial m at hematical models u sing f ictive d i‐ agonal e lements for prefabricate d ti mber‐ g lass wall eleme n t s a re developed and upgraded f rom the alread y known stud y in [ 32 ], h owever, they a re a pplicabl e f or t imb e r‐ fram ed w all elem ents with classical sheathing boards only. C onseq uent ly, previousl y e x perim e n t ally d ev elo p ed l oad‐ bearin g tim b er‐glass wall elements w ith insulating three‐l a y e red g l a s s p a n e a r e i m p l e m e n t e d ‐0,5 0 0,5 1 0 5 10 15 20 25 30 35 40 45 Acceleration (in units of g) Time [s] Landers Accelerogram  ‐4 ‐2 0 2 4 0 5 10 15 20 25 30 35 40 45 Displacement [mm] Time[s] GLS5‐top horizontal displacements ‐15 ‐10 ‐5 0 5 10 15 0 5 10 15 20 25 30 35 40 45 Displacement [mm] Time[s]  GLS10‐top horizontal displacement Premrov, Ber, Kozem Šilih into the linear seismic analysis of the whole timber-frame building by using a fictive diagonal approach for the first time in this study. The developed new models for timber-glass elements however enable numerical simulation of seismic behaviour of single and two-storey timber-glass box-house models and demonstrated very good agreement with the previously experimentally measured results. Therefore, the mod- els can be recommended for further parametric numerical academic studies analysing the influ- ence of many various parameters. Our further work will base on existing experimental results and expand numerical models in terms of actual nonlinear behaviour of single-wall and anchorage elements and determination of the factor for structural behaviour. Only then numerical analyses could simulate real structural behaviour as a whole and develop reliable design methods which could be introduced in prac- tice. It is important to highlight once more that the basic requirement of the standard [11] should be fulfilled – that is life safety. Finally, discussed timber-glass panels are in the development phase and at the level of im- plementing guidelines [20] in European standardization, even though some companies have started to use them in practice as additional panels after they were awarded international patent [34]. 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