Cross laminated timber elements in contemporary timber structures of buildings: Application and design

Abstract

This work analyses cross laminated timber (CLT), contemporary building material produced of dried wooden elements - laminates. Laminates in CLT panels are equally wide and timber fibers are rectangularly plated within layers. Paper shows basic physical - mechanical characteristics of CLT panels and analytic models that are most commonly used in designing of CLT floor and wall construction elements. Advantages and disadvantages of this new construction system are stated according to contemporary requirements in designing environmentally and ecologically acceptable constructions.

Full text

GRAĐEVINSKI MATERIJALI I KONSTRUKCIJE 58 (2015) 4 (51-69)
BUILDING MATERIALS AND STRUCTURES 58 (2015) 4 (51-69) 51
UNAKRSNO LAMELIRANI DRVENI ELEMENTI U SAVREMENIM DRVENIM
KONSTRUKCIJAMA ZGRADA – primena i proračun
CROSS LAMINATED TIMBER ELEMENTS IN CONTEMPORARY TIMBER
STRUCTURES OF BUILDINGS – application and design
Ljiljana KOZARIĆ
Aleksandar PROKIĆ
Miroslav BEŠEVIĆ
STRUĆNI RAD
PROFESSIONAL PAPER
UDK: 624.011.1
doi: 10.5937/grmk1504051K
1 UVOD
Drvo je jedan od najstarijih građevinskih materijala i
pored kamena je dugi niz godina bio osnovni materijal za
građenje. Njegove karakteristike omogućavaju visok
stepen prefabrikacije, brzu montažu na terenu i trenutnu
useljivost. Zbog velike požarne otpornosti u požaru ne
gubi nosiva svojstva, odnosno mehaničke karakteristike
ne menjaju se bitno prilikom visokih temperatura. Drvene
konstrukcije su pet puta lakše od armiranobetonskih, pa
mogu lakše preuzeti seizmičke sile i predstavljaju doba
r
izbor u trusnim područjima. Objekti izgrađeni od drveta
imaju visoku energetsku efikasnost.
Poslednjih decenija, drvo se sve više primenjuje u
izgradnji modernih arhitektonskih građevina (npr.
sportskih objekata, stambenih zgrada, mostova)
zahvaljujući boljem poznavanju drveta kao materijala,
primeni savremenih drvenih konstrukcija i upotrebi
kvalitetnih spojnih sredstava. Konstruktivni elementi
savremenih drvenih konstrukcija bazirani su prvenstveno
na savremenim proizvodima od drveta kao što su
lepljeno lamelirano i unakrsno lamelirano drvo.
Ljiljana Kozarić, dipl. inž. građ., Univerzitet u Novom Sadu,
Građevinski fakultet Subotica, Kozaračka 2a, Subotica,
Srbija, tel.: 024 554 300, e-mail:kozaric@gf.uns.ac.rs
Prof.dr Aleksandar Prokić, dipl. inž. građ., Univerzitet u
Novom Sadu, Građevinski fakultet Subotica, Kozaračka 2a,
Subotica, Srbija, tel.: 024 554 300
e-mail: aprokic@eunet.rs
Prof.dr Miroslav Bešević, dipl. inž. građ., Univerzitet u
Novom Sadu, Građevinski fakultet Subotica, Kozaračka 2a,
Subotica, Srbija, tel.: 024 554 300
e-mail miroslav.besevic@gmail.com
1 INTRODUCTION
Wood is one of the oldest building materials and
along with stone it is the basic building material. Its
characteristics allow for a high degree of prefabrication,
quick assembly, and immediate utilization. Wood has
great fire resistance, and during the fire retains its
characteristics, i.e. its mechanical properties do not
change significantly due to high temperatures. Timbe
r
constructions are five times lighter than reinforced
concrete, thus they are better capable of weathering
seismic forces and stand out as material of choice fo
r
earthquake prone areas. Timber constructions have high
energy efficiency.
Within last few decades, wood has been increasingly
used in modern architectural buildings (sports’ arenas,
residential buildings and bridges) thanks to bette
r
understanding of wood as a material, utilization o
f
modern timber construction and high quality
connections. Construction elements for contemporary
timber constructions are primarily based upon
contemporary products such as glued laminated timbe
r
and cross laminated timber.
Ljiljana Kozarić, dipl.inž. građ., University of Novi Sad,
Faculty of Civil Engineering, Subotica, Kozaračka 2a,
Serbia, tel: 024 554 300, e-mail: kozaric@gf.uns.ac.rs
Prof.dr Aleksandar Prokić, dipl.inž. građ., University of Novi
Sad, Faculty of Civil Engineering, Subotica, Kozaračka 2a,
Serbia, tel: 024 554 300, e-mail: aprokic@eunet.rs
Prof.dr Miroslav Bešević, dipl.inž. građ., University of Novi
Sad, Faculty of Civil Engineering, Subotica, Kozaračka 2a,
Serbia, tel: 024 554 300
e-mail: miroslav.besevic@gmail.com

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Cilj rada jeste da se stručna javnost u Srbiji upozna s
primenom unakrsno lameliranih drvenih panela u
konstrukcijama, kao i s načinom proračuna pojedinih
konstruktivnih elemenata.
2 UNAKRSNO LAMELIRANO DRVO ‒ CLT
Unakrsno lamelirano drvo je moderan proizvod,
visoke tehnologije koji je u mnogome unapredio fizičke
osobine monolitnog drveta. CLT se proizvodi od
kontrolisano sušenih drvenih elemenata podjednake
širine - lamela, kojima su uklonjeni nedostaci (npr.
čvorovi, smola). Izdvajanjem tih nedostataka i slojevitim,
unakrsnim lepljenjem, dobija se materijal koji ima
mehaničke karakteristike ujednačenije od mehaničkih
karakteristika monolitnog drveta - slika 1.
Objective of this paper is to introduce possibilities o
f
application of cross laminated timber panels in structures
in Serbia, as well as the way the individual structural
elements can be calculated.
2 CROSS LAMINATED TIMBER – CLT
Cross laminated timber (CLT) is a sophisticated
modern product that greatly improved the physical
properties of traditional wood as building material. CLT is
made of controlled dried wooden elements – laminates
of uniform width, free of defects (knots, resin etc.). By
removing all of the defects and cross-gluing the
laminates it is possible to produce the material that has
more uniform mechanical properties than the traditional
wood, Figure 1.
Slika 1. Unakrsno lamelirano drvo [1]
Figure 1. Cross laminated timber [1]
Kao kod šperploča, slojevi mekog drveta postavljaju
se tako da vlakna drveta budu međusobno pod pravim
uglom. Unakrsno slaganje drveta pruža stabilnost, kao i
kod obične šperploče, ali veća debljina slojeva stvara
panele koji su dovoljno jaki da budu korišćeni kao
konstruktivni elementi, bez potrebe za ojačanjem
konstrukcije upotrebom opeke ili betona - slika 2.
Just like with plywood, the layers of soft wood are
positioned in such manner that the wooden grain o
f
adjacent layers are mutually perpendicular. As with
plywood, perpendicularly positioned elements create
stability; however, greater layer thickness creates panels
that are strong enough to be used as a primary structural
elements without the need for brick or concrete as
reinforcement, Figure 2.
Slika 2. CLT konstrukcija [2]
Figure 2. CLT construction [2]



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Poprečni preseci CLT panela sadrže najmanje tri
unakrsno zalepljene lamele, a najčešće pet ili sedam.
Slojevi s lamelama postavljeni su naizmenično pod
pravim uglom, ali se pojedini slojevi mogu i duplirati,
stvarajući tako panele s većom nosivošću u potrebnom
pravcu - slika 3. Visina lamela u CLT panelima varira od
16 mm do 51 mm, a širina od 60 mm do 240 mm.
Spoljne lamele u zidnim CLT panelima postavljaju se
uspravno, paralelno sa silom gravitacije, radi
maksimalnog iskorišćenja vertikalne nosivosti panela.
Kod podnih i krovnih CLT panela, spoljne lamele
postavljaju se paralelno s pravcem dominantnog
opterećenja. Spoljašnje površine panela - zbog estetskih
zahteva, te zbog zahteva vatrootpornosti i zvučne
izolacije - mogu se obložiti gips-kartonskim pločama ili
nekom drugom pogodnom oblogom.
A CLT cross section contains a minimum of three
cross-glued laminates, but most often five or seven.
Alternate layers are mutually perpendicular; however, it
is possible to double certain layers so that greate
r
strength can be achieved in a desired direction, Figure 3.
Laminate height within a CLT varies from 16 to 51 mm
while width varies between 60mm and 240mm.
Outside laminates within a CLT wall are positioned
vertically, parallel with the gravitational forces so that
vertical potential of the panel can be maximized, while in
CLT panels for floor and roof applications are placed
parallel with the direction of dominant forces. To meet
aesthetic, fireproof, and insulation requirements, the
exposed surfaces of the panels can be covered with
gypsum or similar appropriate finish.
Slika 3. Poprečni preseci CLT panela [3]
Figure 3. CLT Panel cross sections [3]
U Evropi, CLT paneli najčešće se proizvode od
četinara klase čvrstoće C24, vlažnosti 12±2% - [4].
Dimenzije panela zavise od raspoložive tehnologije
proizvođača, ali i od načina transporta.
Zidni CLT paneli isporučuju se na gradilište s već
formiranim otvorima po projektu. Tipičan zidni CLT panel
prikazan je na slici 4.
In Europe, CLT is most often manufactured from
conifers grade C24, and moisture content 12±2%, [4].
Panel dimensions are dictated by manufacture
r
technology and mode of transportation.
Wall CLT panels are delivered to a construction site
where the wall openings have already been formed
according to design. A typical CLT wall panel is shown in
Figure 4.
Slika 4. Zidni CLT paneli [3]
Figure 4. Typical Wall CLT panel [3]
4,8
∼
15 cm
do 3 m
to 3 m
do 18 m
to 18 m

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Podne i krovne konstrukcije dobijaju se horizontalnim
ili kosim slaganjem osnovnih panela. Tipične dimenzije
osnovnog podnog i krovnog panela prikazane su na slici
5.
Među najveće evropske proizvođače CLT panela
svrstavaju se: KLH (Austrija, UK, Švedska), Binderholz
(Austrija), Martinsons (Švedska), Moelven (Norveška),
Stora Enso (Austrija), Thoma Holz GmbH (Austrija),
FinnForest Merk (Nemačka, UK), HMS (Nemačka).
Svi navedeni proizvođači koriste isti proces
proizvodnje, glavna razlika je u dimenzijama CLT panela
i u izboru lepka.
Osnovne fizičko-mehaničke karakteristike CLT
panela s daskama od četinara klase čvrstoćeC24
(minimalno 90%) i C16 (maksimalno 10%) date su u
Tabeli 1.
Floor and roof construction are manufactured by
arranging the basic panels in horizontal or angula
r
pattern. Typical dimensions of basic floor or roof panel
are depicted in Figure 5. Some of the biggest European
CLT panels manufacturers are: KLH (Austria, UK,
Sweden), Binderholz (Austria), Martinsons (Sweden),
Moelven (Norway), Stora Enso (Austria), Thoma Holz
GmbH (Austria), FinnForest Merk (Germany, UK) and
HMS (Germany).
All of the above listed manufacturers use the same
manufacturing process, while the main differences are
panels’ dimensions, and the choice of glue.
Basic physical and mechanical properties of CLT
panels with planks made out of conifers grade C24
(minimum 90%) and C16 (maximum 10%) are listed in
Table 1.
Slika 5. Podni i krovni CLT paneli [3]
Figure 5. Floor and Roof CLT panel [3]
Tabela 1. Osnovne fizičko-mehaničke karakteristike CLT panela [5]
Table 1. Basic physical and mechanical properties of CLT panels [5]
Karakteristične čvrstoće [N/mm²] / Characteristic strength [N/mm²]
Savijanje / Bending fm,k 24
Zatezanje paralelno s vlaknima / Tension along the grain ft,0,k 16,5
Zatezanje upravno na vlakna / Tension across the grain ft,90,k 0,12
Pritisak paralelno s vlaknima / Compression along the grain fc,0,k 24‒30
Pritisak upravno na vlakna / Compression across the grain fc,90,k 2,7
Karakteristične krutosti [N/mm²] / Characteristic stiffness [N/mm²]
Srednja vrednost modula E paralelno s vlaknima
Median value of modulus of elasticity E along the grain E0,mean 12000
Srednja vrednost modula E upravno s vlaknima
Median value of modulus of elasticity E across the grain E90,mean 370
Zapreminska masa [kg/m³] / Specific weight [kg/m³] ρ 480‒500
Koeficijent toplotne provodljivosti [W/(mK)]
Thermal conductivity coefficient [W/(mK)] λ 0,13
Dopušteni ugib / Allowable deflection umax l/250
do 3 m
to 3 m
do 18 m
to 18 m
4,8∼50 cm

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U svetu, CLT konstrukcije doživele su veliki uspon iz
sledećih razloga: neuporedivo su čvršće i imaju bolje
statičke osobine od monolitnog drveta, nemaju sklonost
ka uvijanju, pojava napuklina svedena je na minimum,
velika požarna otpornost, visoka otpornost na potres.
Upotrebom CLT panela smanjuje se vreme
izgradnje, jer se drveni elementi isporučuju kao
prefabrikovani zidovi ili moduli, koji se zatim brzo
uklapaju na gradilištu. Izgradnja CLT konstrukcije je oko
30% brža u poređenju sa odgovarajućom betonskom
konstrukcijom. Takođe, drvo je „suv” građevinski
materijal, njemu ne treba vreme da se osuši ili očvrsne,
kao što je to slučaj s betonom ili opekom. Za CLT panele
koristi se mekano drvo koje raste brzo i kog ima u
izobilju, pa je i cena CLT konstrukcija niža od 5 do 10%
od odgovarajućih betonskih ili čeličnih [6].
Drvo je obnovljiv izvor, što je velika prednost, kao i to
što u toku rasta vezuje velike količine ugljen-dioksida. Za
proizvodnju tone betona potrebno je pet puta, za čelik 24
puta, dok je za tonu aluminijuma potrebno 126 puta više
energije nego za proizvodnju materijala od drveta. Drvo
je i mnogo bolji izolator i to pet puta bolji od betona i čak
350 puta bolji nego što je to čelik [7].
3 PRIMERI IZVEDENIH CLT KONSTRUKCIJA
3.1 Stambena zgrada Forte u Melburnu
Zgrada Forte trenutno je najviša stambena zgrada
izgrađena od drveta na svetu. Projektovala ju je i
izgradila kompanija Lend Lease 2013. godine. Visoka je
32,17 metara. U prizemlju su poslovni prostori, a na
spratovima ima 23 stana - slika 6.
Worldwide, CLT became greatly popular for the
following reasons: CLT is much stronger with far more
superior mechanical properties than traditional wood, no
bending tendency, minimal fractures appearance, high
resistance to fire, and resilience to earthquakes.
Since CLT is delivered to construction site in
prefabricated or modular form it takes on average 30%
less time to complete CLT than a comparable concrete
or brick and mortar project. Contributing to the speed o
f
completion is also the fact that unlike concrete, timber is
“dry” building material that does not require either the
time to dry, or the time to cure and achieve its final
strength. Fast growing easily accessible softwood keeps
the price of CLT 5 to 10% lower than the competing
concrete or steel construction [6].
Timber’s great advantage is that it is a renewable
resource, and in the process of growth trees absorb
great amount of carbon dioxide. To produce one ton o
f
concrete, steel or aluminium it takes 5, 24 and 126 times
more energy respectively than for the production o
f
timber. Timber is 5 times better insulator than concrete
and up to 350 times better than steel [7].
3 EXAMPLES OF CLT APPLICATIONS
3.1 Apartment building Forte in Melbourne,
Australia
Forte is currently the tallest residential timbe
r
building in the world. The design and construction has
been done in 2013 by Lend Lease. The apartment
building is 32,17m tall. At the ground floor there are
commercial spaces, and 23 apartments in the above
floors, Figure 6.
Slika 6. Zgrada Forte u Melburnu
Figure 6. Forte Residential Building in Melbourne, Australia
Osnovni konstruktivni elementi su drveni zidni paneli
i podne ploče. Za izgradnju je bilo potrebno 759 CLT
panela, odnosno 485 tona drvene građe. Zgrada Forte je
prva stambena zgrada sertifikovana s pet zvezda
programa Green Star As Built u Australiji.
Drvena građa u ovom objektu skladišti 761 tonu
ugljenika, a odabirom CLT konstrukcije količina ugljen-
dioksida u atmosferi se smanjila ukupno za oko 1 451
tonu, jer bi se pri izgradnji sličnog objekta od betona ili
čelika, u atmosferu ispustio dodatan ugljen-dioksid. Ta
Basic design elements are wooden wall and floo
r
panels. It took 759 CLT panels, or 485 tons of wooden
material for construction. Forte residential building is the
first Five Star Green Star as built rating in Australia. The
wooden material in this building stores 761 ton o
f
carbon, and by choosing CLT over concrete or steel the
total amount of carbon dioxide released in the
atmosphere has been reduced by 1,451 tons. This
amount represents the equivalent of the carbon dioxide
released by 345 cars during one year [8].

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količina ugljen-dioksida predstavlja 345 automobila
manje na ulici u toku jedne godine [8].
3.2 Stambena zgrada Stadthaus u Londonu
Zgrada Stadthaus sagrađena je 2008. godine u
Londonu i pune dve godine bila je najviša drvena
stambena zgrada na svetu. Ovu devetospratnicu
projektovala je kompanija Waugh Thistleton Architects.
Podovi, plafoni, kućište lifta i stepeništa izrađeni su u
potpunosti od drveta - slika 7.
3.2 Stadthaus Residential Building in London, UK
Stadthaus Residential building was built in 2008 and
for full two year was the world’s tallest timber residential
building. This nine story building has been designed by
Waugh Thistlton Architects. Floors, ceilings, elevato
r
shaft and stair flights were built completely out of timber,
Figure 7.
Slika 7. Zgrada Stadthaus u Londonu
Figure 7. Stadthaus Residential Building in London, UK
Korisna površina stambene zgrade jeste 2.352 m2 i
za izgradnju bilo je potrebno 950 m3 CLT panela. Zidni
paneli bili su debljine 128 mm, a podni - 146 mm. Za
izgradnju jednog sprata bilo je potrebno tri dana. U
poređenju s betonskom konstrukcijom, projektanti su
izborom CLT konstrukcije uštedeli dvadeset dve nedelje
gradnje, što predstavlja uštedu u vremenu od oko 30%.
Drvo ugrađeno u Stadthaus čuva oko 186 tona
ugljenika, dok bi se za čelik i beton koji se koriste u
konvencionalnom građevinarstvu, za sličnu građevinu, u
atmosferu ispustilo oko 137 tona ugljen-dioksida u
procesu proizvodnje. Dakle, ovakav način gradnje
smanjio bi količinu ugljen-dioksida u atmosferi za oko
323 tone [9].
3.3 Srednja škola u Noriču UK
Objekat se nalazi u Noriču i trenutno je najvećaCLT
konstrukcija u Ujedinjenom kraljevstvu. Sagrađena je
krajem 2009. godine. Glavni arhitekta bio je Sheppard
Robson. Korisna površina objekta iznosi 9.500 m2,a za
izgradnju bilo je potrebno 3.065 m3 CLT panela.
Kompletna konstrukcija ovog trospratnog objekta
izgrađena je za šesnaest nedelja. Fiskulturnu salu u
sklopu škole od 600 m2 (slika 8) montirala su četiri
radnika za četiri dana. Za montažu jednog zidnog CLT
panela dimenzije 3 m x 6 m debljine 15 cm, bilo je
potrebno samo tri sata.
Buildings used area is 2,352 m2 and it took 950 m3
of CLT panels for construction. Wall panels’ thickness
varies from 128 mm to 146 mm. It took three days fo
r
completion of one story. Compared to a concrete
building construction, the CLT method is 22 weeks
faster, which amounts to total time reduction of about
30%.
The amount of wood in Stadthaus stores 186 tons o
f
carbon, while for construction of conventional steel o
r
concrete building of this size 137 tons of carbon dioxide
would have been released in the atmosphere. As a
result, CLT method reduces the total carbon dioxide foot
print for 323 tons [9].
3.3 High School in Norwich, UK
The School is located in Norwich and currently is the
largest CLT construction in the United Kingdom. It was
built in 2009. The lead architect was Sheppard Robson.
Building’s used area is 9,500 m2, and it took 3,065 m3 o
f
CLT panels for its completion. The construction of this
three story building was completed in 16 weeks. The 600
m2 gymnasium within the school building was
assembled by 4 workers in 4 days, Figure 8. It takes only
3 hours for the installation of one 3 m by 6 m wall CLT
panel.

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Slika 8. Srednja škola u Noriču UK
Figure 8. High School in Norwich, UK
Zidovi i podovi su CLT paneli, dok su gredni nosači
izvedeni od lepljenog-lameliranog drveta - slika 6. Prose-
čan raspon međuspratnih CLT ploča iznosi 7,5 metara,
sa osnovnom frekvencijom oscilovanja od 8 Hz - slika 9.
CLT panels were used for the walls and floors, while
the girders were built from glued laminated timber,
Figure 9. The average span of the floor CLT panels is
7,5 meters with base frequency of 8 Hz, Figure 17.
Slika 9. Izgradnja srednje škole u Noriču UK
Figure 9. Construction of High School in Norwich, UK
4 DIMENZIONISANJE ELEMENATA CLT
KONSTRUKCIJA
Proizvođači CLT panela u Evropi nemaju jedinstveni
analitički pristup prilikom dimenzionisanja elemenata
CLT konstrukcija. Za dimenzionisanje međuspratnih i
krovnih konstrukcija od CLT panela najčešće se koriste
[1] [10]: Gamma metod (Evrokod 5), K-metod (Teorija
kompozita), Kreuzinger-ova analogija i Uprošćen
postupak proračuna.
Zidni CLT paneli dimenzionišu se kao pritisnuti
štapovi složenog preseka, spojeni mehničkim spojnim
sredstvima (Evrokod 5).
4 DESIGNING THE ELEMENTS FOR CLT
CONSTRUCTION
CLT manufacturers in Europe do not have unified
analytical approach for the design of elements for CLT
construction. The following methods are most frequently
used for the floor and roof CLT design, [1] [10]: Gamma
Method (Eurocode 5), K – Method (Composite theory),
Kreuzinger Analogy and Simplified Design Methods.
CLT wall panels are calculated as mechanically
joined compressed columns with complex cross section
(Eurocode 5).

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4.1 Gamma metod
Gamma metod zasnovan je na Aneksu B Evrokoda 5
(EN 1995-1-1:2004) [11] koji je razvijen za gredne
nosače složenog poprečnog preseka, spojene mehani-
čkim spojnim sredstvima krutosti k postavljenim na
jednakim rastojanjima
s
. Prilikom proračuna CLT pane-
la, uzimaju se u obzir samo podužne lamele to jest
lamele u pravcu delovanja opterećenja. One se modeli-
raju kao gredni nosači koji su povezani „imaginarnim”
mehaničkim spojnim sredstvima čija je krutost jednaka
modulu smicanja upravno na vlakna poprečnih lamela.
Smicanje podužnih lamela zanemaruje se ako je odnos
raspona i visine lamele 30≥.
Ovaj metod proračuna prikladan je za slobodno oslo-
njene međuspratne i krovne CLT panele sa 3 ili 5 lamela.
4.1 Gamma method
Gamma method is based upon annex B of Eurocode
5(EN 1995-1-1:2004) [11] which has been developed fo
r
a girders with composite cross section joined with
mechanical connectors with stiffness k distributed evenly
over distance s. During the CLT design process only the
longitudinal laminates are taken into consideration i.e.
the laminates parallel with the loading direction. The
laminates are modelled like beams whose stiffness is
equal to the shear modulus along the grain of lateral
laminates. Shearing of longitudinal laminates can be
neglected of the ration of span to height of the laminate
is 30≥.
This design method is adequate for freely spanned
floor and roof CLT panel with 3 or 5 laminates.
Legenda / Legend:
(1) razmak / span 1
s
modul pomerljivosti / displacement modulus 1
K opterećenje / load 1
F
(2) razmak / span 2
s
modul pomerljivosti / displacement modulus 2
K opterećenje / load 2
F
Slika 10. Model CLT panela sa 5 lamela [11]
Figure 10. CLT Panel with 5 laminates [11]
Efektivna krutost na savijanje računa se prema
izrazu
Effective stiffness can be calculated based on the
following expression:
()
()
32
1
ii i i ii
ef i
EI E I E A a
γ
=
=+
∑ (1)
gde su simboli definisani na slici 10, a
γ
predstavlja
meru efikasnosti veze i ima vrednost od 0 do 1. Kad
nema spojnog sredstva u vezi 0
γ
=a kod potpuno
krute veze (potpunog sprezanja) 1.
γ
= Kod CLT
panela 0,85 0,99
γ
=÷.
U Evrokodu 5
γ
definisana je kao
where the symbols have been defined in Figure 10, and
γ
represent the effectives of the connection with its
value ranging from 0 to 1. For the connection with no
connectors, 0
γ
=
, while for fully fixed connection
(coupling) 1.
γ
=
. For CLT panels 0,85 0,99
γ
=÷
Eurocode 5 defines as:
21
γ
=
1
2
2
1
iii
ii
EAs
Kl
π
γ
−
⎡
⎤
=+
⎢
⎥
⎣
⎦
(2)
za 1i= i 3i= for 1i
=
and 3i
=
spojno sredstvo
connector
spojno sredstvo
connector

GRAĐEVINSKI MATERIJALI I KONSTRUKCIJE 58 (2015) 4 (51-69)
BUILDING MATERIALS AND STRUCTURES 58 (2015) 4 (51-69) 59
Uzimajući u obzir da je krutost „imaginarnih”
mehaničkih spojnih sredstava jednaka modulu smicanja
upravno na vlakna poprečnih lamela
If taken into consideration that the stiffness o
f
“imaginary” mechanical connectors is equal to the shea
r
modulus along the grain of lateral laminates then:
i
iR
i
sGh
Kb
⋅
=(3)
gde je b širina panela (obično 1 m)
i
h visina poprečne lamele
R
G modul smicanja upravno na vlakna poprečnih
lamela
za CLT panele dobija se da je
where b is width of a panel (usually 1 m)
i
h is height of the lateral laminate
R
G is shear modulus along the grain of lateral
laminates
Expression for CLT panels is given as:
21
γ
=
1
2
2
1
ii
ii
R
hEA
lGb
π
γ
−
⎡
⎤
=+ ⋅
⎢
⎥
⎣
⎦
⋅
(4)
za 1i= i 3i= for 1i
=
and 3i
=
Normalni napon računa se kao Normal stress can be calculated as
i max i globa l i local
σ
σσ
=
+ (5)
gde je where
()
iii
i global
ef
E
aM
EI
γ
σ
=
()
0,5 ii
i local
ef
E
hM
EI
σ
=
(6)
4.2 K- metod (Blass&Fellmoser)
Prilikom proračuna ovom metodom, u obzir se uzima
krutost svih lamela. Modul elastičnosti poprečnih lamela
računa se kao
4.3 K- method (Blass&Fellmoser)
This design method includes the stiffness of all
laminates. Modulus of elasticity of lateral laminates can
be calculated as:
90 0 /30 EE
=
(7)
Princip proračuna sličan je proračunu šperploča.
Efektivne vrednosti napona i krutosti dobijaju se pomoću
koeficijenata i
k - Tabela 2.
The method is similar to the design method fo
r
plywood. The values for stress and stiffness can be
calculated by using the coefficient i
k, Table 2.
Tabela 2. Efektivne vrednosti napona i krutosti CLT panela [12]
Table 2. Normal Stress and Effective Stiffness Values [12]
Opterećenje
Load
Pravac vlakana
Grain direction
Efektivni napon
Normal Stress
Efektivna krutost
Effective Stiffness
Opterećenje normalno na ravan panela
Load perpendicular to a panel
Paralelno s vlaknima
Along the grain fm,0,ef = fm,0 ⋅ k1 Em,0,ef = E0 ⋅ k1
Savijanje
Bending Upravno na vlakna
Across the grain fm,90,ef = fm,0 ⋅ k2 ⋅ am / am-2 Em,90,ef = E0 ⋅ k2

GRAĐEVINSKI MATERIJALI I KONSTRUKCIJE 58 (2015) 4 (51-69)
BUILDING MATERIALS AND STRUCTURES 58 (2015) 4 (51-69)
60
Opterećenje u ravni panela
Load in the plane of a panel
Paralelno s vlaknima
Along the grain fm,0,ef = fm,0 ⋅ k3 Em,0,ef = E0 ⋅ k3
Savijanje
Bending
Upravno na vlakna
Across the grain fm,90,ef = fm,0 ⋅ k4 Em,90,ef = E0 ⋅ k4
Paralelno s vlaknima
Along the grain ft,0,ef = ft,0 ⋅ k3 Et,0,ef = E0 ⋅ k3
Zatezanje
Tension Upravno na vlakna
Across the grain ft,90,ef = ft,0 ⋅ k4 Et,90,ef = E0 ⋅ k4
Paralelno s vlaknima
Along the grain fc,0,ef = fc,0 ⋅ k3 Ec,0,ef = E0 ⋅ k3
Pritisak
Compression Upravno na vlakna
Across the grain fc,90,ef = fc,0 ⋅ k4 Ec,90,ef = E0 ⋅ k4
Koeficijenti i
k definisani su u zavisnosti od
opterećenja - Tabela 3.
Depending on the load coefficients i
k are defined in
Table 3.
Tabela 3. Vrednosti koeficijenata i
k [12][3]
Table 3. Coefficients i
k Values [12][3]
Opterećenje / Load i
k
33 3
90 2 4 1
13
0
11 mm
m
Ea a a
kEa
−−
⎛⎞
−
+…±
=− − ⋅
⎜⎟
⎝⎠
33 3
90 90 2 4 1
23
00
1mm
m
EEaa a
kEE a
−−
⎛⎞
−
+…±
=+− ⋅
⎜⎟
⎝⎠
90 2 4 1
30
11 mm
m
Ea a a
kEa
−−
⎛⎞
−
+…±
=− − ⋅
⎜⎟
⎝⎠

GRAĐEVINSKI MATERIJALI I KONSTRUKCIJE 58 (2015) 4 (51-69)
BUILDING MATERIALS AND STRUCTURES 58 (2015) 4 (51-69) 61
90 90 2 4 1
400
1mm
m
EEaa a
kEE a
−−
⎛⎞
−
+…±
=+− ⋅
⎜⎟
⎝⎠
Način određivanja rastojanja a CLT panela s pet
lamela ( 5m=) prikazan je na slici 11.
Figure 11. Depicts the method to determine spans a
CLT panels with 5 laminates ( 5m=).
Slika 11. CLT panel sa 5 lamela [3]
Figure 11. CLT Panel with 5 laminates [3]
Efektivna krutost na savijanje od opterećenja
upravno na ravan panela jeste:
− paralelno s vlaknima
Effective bending stiffness perpendicular to the panel
can be calculated as:
− along the grain
()
3
01
12m
ef
ba
E
IE k
⋅
⋅
⋅= (8)
− upravno na vlakna − across the grain
()
3
02
12m
ef
ba
E
IE k
⋅
⋅
⋅= (9)
gde b predstavlja širinu panela opterećenog upravno na
svoju ravan.
Normalni napon savijanja od opterećenja upravno na
ravan panela jeste:
− paralelno s vlaknima
where brepresents the width of the panel perpendicula
r
to its own plane.
Normal bending stress from the load perpendicular to
the plane of the panel can be calculated as:
− along the grain
()
0
2
m
m
ef
a
ME
EI
σ
=⋅
⋅
(10)
− upravno na vlakna − across the grain
()
2
0
2
m
m
ef
a
ME
EI
σ
−
⋅⋅=(11)

GRAĐEVINSKI MATERIJALI I KONSTRUKCIJE 58 (2015) 4 (51-69)
BUILDING MATERIALS AND STRUCTURES 58 (2015) 4 (51-69)
62
4.3 Kreuzinger-ova analogija
Kreuzinger pri proračunu uzima različite module
elastičnosti i module smicanja podužnih i poprečnih
lamela. Smicanje podužnih lamela se ne zanemaruje.
Modul elastičnosti poprečnih lamela računa se po izrazu
(7). Kreuzinger-ova analogija nije ograničena brojem
lamela u panelu.
Ovom analogijom, CLT panel deli se u dve virtuelne
grede A i B - slika 12.
4.3 Kreuzinger Analogy
Design according to Kreuzinger considers different
modules of elasticity and shear for longitudinal and
lateral laminates. Longitudinal shear of laminates is also
considered. Modulus of elasticity of lateral laminates can
be calculated by using expression (7). Number o
f
laminates is not a limiting factor in Kreuzinger Analogy.
This method divides the CLT panel into two virtual
beams A and B as in Figure 12.
Slika 12. Kreuzinger-ova analogija [1]
Figure 12. Kreuznger Analogy [1]
Efektivna krutost Effective stiffness
() () ()
32
11
12
nn
i
ii i i i
ef A B ii
h
E
IEIEI Eb EAZ
==
=+
⋅
⋅⋅=+
∑∑ (12)
gde je i
b širina panela (obično 1 m)
i
h visina lamele
i
Z
rastojanje od težišta lamele do neutralne ose
- slika 13.
where i
b is width of a panel (usually 1 m)
i
h is height of the laminate
i
Z
is the distance from the centroid of the
laminate to the neutral axis, Figure 13.
Slika 13. Rastojanja i
z
kod CLT panela sa 5 lamela [10]
Figure 13. Distance i
z
with CLT panels with 5 laminates [10]
4.4 Proračun zidnih CLT panela
Zidni CLT paneli dimenzionišu se kao pritisnuti
štapovi složenog preseka, spojeni mehničkim spojnim
sredstvima. Postupak proračuna izložen je u Aneksu C
Evrokoda 5 (EN 1995-1-1:2004) [11].
Metod proračuna zasnovan je na sledećim
pretpostavkama:
− elementi su sistema proste grede, dužine l
− elementi složenog preseka idu kontinualno duž
štapa.
Efektivnu vitkost treba uzeti prema izrazu
4.4 Design Method for CLT Wall Panels
CLT wall panels are calculated as mechanically
joined compressed columns with complex cross section.
Design method is presented in annex C of Eurocode 5
(EN 1995-1-1:2004) [11].
The method is based upon following assumptions:
− The elements are simple beams with length l,
− The elements with the complex cross section run
longitudinally with the member.
Effective slenderness shall be calculated using the
following expression:
tot
ef ef
A
lI
λ
=(13)
Greda A
Beam A
Greda B
Beam B

GRAĐEVINSKI MATERIJALI I KONSTRUKCIJE 58 (2015) 4 (51-69)
BUILDING MATERIALS AND STRUCTURES 58 (2015) 4 (51-69) 63
gde je tot
A ukupna površina poprečnog preseka
panela
l visina panela (dužina izvijanja)
ef
I
efektivni momenat inercije
Efektivni momenat inercije dobija se pomoću
sledećeg izraza
where tot
A the total area of the cross section of the
panel
l the height of the panel (bending length)
ef
I
the effective moment of inertia
Effective moment of inertia shall be calculated based
on the following expression:
(
)
ef
ef mean
EI
IE
=(14)
gde je
()
ef
E
I efektivna krutost
mean
E srednja vrednost modula elastičnosti
vertikalnih lamela
Efektivna vitkost ef
λ
uvrštava se u izraz 6.21
Evrokoda 5, a proračun nosivosti CLT panela vrši se po
poglavlju 6 Evrokoda 5.
5 PRIMER
Sračunati efektivnu krutost
()
ef
E
I slobodno
oslonjenog podnog CLT panela dužine 4,5 metara, a
širine 1 metar. Poprečni presek panela prikazan je na
slici 14. Ukupna visina panela je 14 centimetara.
Opterećenje deluje upravno na ravan panela paralelno s
vlaknima spoljnih lamela [3].
where
(
)
ef
E
I effective stiffness
mean
E median value of modulus of elasticity of the
vertical laminates
Effective slenderness ef
λ
is used in expression 6.21
of Eurocode 5 while bearing capacity of a CLT panel
shall be calculated following chapter 6 of Eurocode 5.
5 EXAMPLE
Calculate the effective stiffness
()
ef
E
I of the simply
supported CLT floor panel 4,5m long and 1m wide.
Panel’s cross section is depicted on Figure 14. The total
height of the panel is 14 centimetres. The load is acting
perpendicularly to the panel and along the grain of the
exterior laminates [3].
Slika 14. Geometrijske karakteristike panela
Figure 14. Geometric characteristics of the panel
Fizičko-mehaničke karakteristike podužnih lamela: Physical and mechanical properties of the
longitudinal laminates:
011000
E
MPa
=
0
90 11000 367 370
30 30
E
E
MPa≈= = ≈
0
011000 688 690
16 16
E
GMPa≈= = ≈
0690 69
10 10
RG
GMPa≈= =
širina (b)
with (b)

GRAĐEVINSKI MATERIJALI I KONSTRUKCIJE 58 (2015) 4 (51-69)
BUILDING MATERIALS AND STRUCTURES 58 (2015) 4 (51-69)
64
Fizičko-mehaničke karakteristike poprečnih lamela: Physical and mechanical properties of the lateral
laminates:
09000
E
MPa
=
0
90 9000 300
30 30
E
E
MPa≈= =
0
09000 563 560
16 16
E
GMPa≈= = ≈
0560 56
10 10
RG
GMPa≈= =
Odnos raspona i visine lamele CLT panela jeste Ratio of the span to the height of the panel is:
450 32 30
14
l
h
=
=>
pa se smicanje podužnih lamela zanemaruje.
5.1 Gamma metod
Thus the shear of the longitudinal laminates can be
neglected.
5.1 Gamma method
Slika 15. Geometrijske karakteristike panela (Gamma metod)
Figure 15. Geometric characteristics of the panel (Gamma method)
123 12
34 19 140 hhh mm hh mm h mm=== == =
123
11000
E
EE MPa===
56
R
GMPa=
Efektivna krutost računa se po jednačini (1) The effective stiffness shall be calculated by using
the expression (1):
()
()
32
1ii i i ii
ef i
E
IEIEAa
γ
=
=+
∑
Ako su If
13
γ
γγ
=
= i / and 21
γ
=
dobijamo then
(
)
()
(
)
(
)
22
11 1 1 1 1 2 2 33 3 3 3 3
ef
E
IEIEAaEIEIEAa
γγ
=+ + ++
gde je where
13
AAA==
123
E
EEE===
neutralna osa
neutral axis

GRAĐEVINSKI MATERIJALI I KONSTRUKCIJE 58 (2015) 4 (51-69)
BUILDING MATERIALS AND STRUCTURES 58 (2015) 4 (51-69) 65
3
1
123 12
bh
IIII====
20a=
3
122
13 1 2
2222
h
hhh
aaa h h===++ =++
pa se za efektivnu krutost dobija Then the effective stiffness is:
()
2
2
3
ef
Aa
EI EI I
γ
⎡
⎤
=+
⎢
⎥
⎣
⎦
Ako je If
()
2
2
22
11
0,9418
11000 1000 34 19
11
4500 56 1000
R
EA h
lGb
γπ
π
== =
⋅⋅
⎡⎤
+⋅ + ⋅
⎢⋅
⎣⎦
⋅⎥
2
1000 34 34000
A
bh mm== ⋅=
3
122
13 1 2 34 34
19 53
22222 2
h
hhh
aa a h h mm===++ = ++ = ++ =
33 64
11000 34 3,275 10
12 12
bh
Imm
⋅
== = ×
dobijamo Then
()
2
692
6
2 0,9418 34000 53
11000 3,275 10 3 2087 10
3,275 10
ef
E
INmm
⎡⎤
⋅⋅⋅
=⋅×+ =×
⎢⎥
×
⎣⎦
5.2 K- metod (Blass&Fellmoser)
5.2 K- method (Blass&Fellmoser)
Slika 16. Geometrijske karakteristike panela (K-metod)
Figure 16. Geometric characteristics of the panel (K– method)
011000
E
MPa
=
90 300
E
MPa
=
Iz Tabele 3 dobijamo From Table 3 we get:
5140
m
aa mm
=
=
23
19 34 19 72
m
aa mm
−==++=
41
34
m
aamm
−==

GRAĐEVINSKI MATERIJALI I KONSTRUKCIJE 58 (2015) 4 (51-69)
BUILDING MATERIALS AND STRUCTURES 58 (2015) 4 (51-69)
66
33 33
90 3 1
133
05
300 72 34
1 1 1 1 0,8816
11000 140
Eaa
kEa
⎛⎞ ⎛⎞
−−
⎛⎞
=− − ⋅ =− − ⋅ =
⎜⎟ ⎜⎟
⎜⎟
⎝⎠
⎝⎠
⎝⎠
a iz Tabele 2 And from Table 2
,0, 0 1 11000 0,8816 9698
mef
E
Ek MPa==⋅
⋅
=
pa je efektivna krutost CLT panela širine 1000 bmm= Finally the effective stiffness of the CLT panel with
width 1000 bmm
=
()
392
1000 140
9698 2218 10
12
ef
E
INmm
⋅
=⋅ =×
5.3 Kreuzinger-ova analogija 5.3 Kreuzinger Analogy
Slika 17. Geometrijske karakteristike panela (Kreuzinger-ova analogija)
Figure 17. Geometric characteristics of the panel (Kreuzinger Analogy)
(
)
10 90
34 11000 370 11000 /30h mm E MPa E MPa== =≈
(
)
20 90
19 9000 300 9000 /30h mm E MPa E MPa== =≈
(
)
30 90
34 11000 370 11000 /30hmm E MPa E MPa== =≈
(
)
40 90
19 9000 300 9000 /30h mm E MPa E MPa== =≈
(
)
50 90
34 11000 370 11000 /30hmm E MPa E MPa== =≈
12345
140 hhh h h h mm=++++=
1000 bmm=
Efektivna krutost dobija se iz jednačine (12) The effective stiffness shall be calculated by using
the expression (12)
() () ()
32
11
12
nn
i
ii i i i
ef A B ii
h
E
IEIEI Eb EAZ
==
⋅
⋅⋅=+= +
∑∑
Položaj neutralne ose
Z
The location of the neutral axis
Z
is:
()
()
1
1
n
ii i
in
ii
i
E
AY
Z
E
A
=
=
⋅
=∑
∑
8
11 1 1 11000 1000 34 3,74 10
E
AEbh N=⋅= ⋅⋅=×⋅
6
22 2 2 300 1000 19 5,7 10 EA E bh N=⋅=⋅⋅=×⋅
neutralna osa
Neutral axis

GRAĐEVINSKI MATERIJALI I KONSTRUKCIJE 58 (2015) 4 (51-69)
BUILDING MATERIALS AND STRUCTURES 58 (2015) 4 (51-69) 67
8
33 3 3 11000 1000 34 3,74 10 EA E b h N=⋅= ⋅⋅=×⋅
6
44 4 4 300 1000 19 5,7 10 EA E bh N=⋅=⋅⋅=×⋅
8
55 5 5 11000 1000 34 3,74 10
E
AEbh N=⋅= ⋅⋅=×⋅
()
58
111,334 10
ii
i
E
AN
=
=×
∑
1
134 17
22
h
Ymm== =
2
21 19
34 43,5
22
h
Yh mm=+ = + =
3
312 34
34 19 70
22
h
Yhh mm
=++ = + + =
4
4123 19
34 19 34 96,5
22
h
Yhhh mm=+++ = ++ + =
5
51234 34
34 19 34 19 123
22
h
Yhhhh mm=++++ = + + ++ =
89
111 3,74 10 17 6,358 10
E
AY Nmm=× = ×⋅
68
222 5, 7 10 43,5 2, 48 10 EAY Nmm=× = ×⋅
810
333 3,74 10 70 2,618 10 EAY Nmm=×⋅=×
68
444 5,7 10 96,5 5,501 10 EAY Nmm=× = ×⋅
810
555 3,74 10 123 4,6 10
E
AY Nmm=×⋅=×
()
510
17,934 10
ii i
i
E
AY Nmm
=
⋅= ×
∑
pa je then
()
()
510
1
58
1
7,934 10 70
11,334 10
ii i
i
ii
i
EA Y
Z
mm
EA
=
=
⋅×
===
×
∑
∑
1
134
70 53
22
h
Z
Zmm=− = − =
2
21 19
70 34 26,5
22
h
Z
Zh mm=−− = − − =
3
312 34
70 34 19 0
22
h
Z
Zhh mm=−−−=−−− =
42
26,5
Z
Zmm=− =−
51
53
Z
Zmm=− =−
Proračun krutosti virtuelne grede A Stiffness calculation for the virtual beam A
()
3
112
ni
ii
Ai
h
EI E b
=
⋅= ∑
33
10 2
1
134
11000 1000 3,603 10
12 12
h
E
bNmm=⋅ =×

GRAĐEVINSKI MATERIJALI I KONSTRUKCIJE 58 (2015) 4 (51-69)
BUILDING MATERIALS AND STRUCTURES 58 (2015) 4 (51-69)
68
33
82
2
219
300 1000 1,715 10
12 12
h
E
bNmm=⋅ = ×
3310 2
3
334
11000 1000 3,603 10
12 12
h
E
bNmm=⋅ =×
33
82
4
419
300 1000 1,715 10
12 12
h
E
bNmm=⋅ = ×
3310 2
5
534
11000 1000 3,603 10
12 12
h
E
b Nmm=⋅ =×
()
11 2
1, 0 84 1 0
A
E
INmm=×
Proračun krutosti virtuelne grede B Stiffness calculation for the virtual beam B
()
2
1
n
iii
Bi
E
IEAZ
=
⋅=
⋅
∑
22122
11111000 1000 34 53 1,051 10
E
AZ Nmm=⋅⋅⋅=×⋅⋅
2292
22230010001926,5 4,003 10
E
AZ Nmm=⋅ ⋅⋅ = ×⋅⋅
22
33311000 1000 34 0 0
E
AZ Nmm=⋅⋅⋅=⋅⋅
()
2
292
444300 1000 19 26,5 4,003 10EAZ Nmm=⋅ ⋅⋅− = ×⋅⋅
()
2
2122
55511000 1000 34 53 1,051 10EAZ Nmm=⋅⋅⋅−=×⋅⋅
()
12 2
2,110 10
B
E
INmm=×
Efektivna krutost je Effective stiffness is:
() () ()
11 12 9 2
1,084 10 2,110 10 2218 10
ef A B
E
IEIEI Nmm=+=×+×=×
6 ZAKLJUČAK
Primenom CLT u konstrukcijama postiže se zdrav i
prirodan ambijent. CLT konstrukcije su čvršće i imaju
bolje statičke osobine od monolitnog drveta, nemaju
sklonost ka uvijanju, a pojava napuklina svedena je na
minimum. Karakteriše ih velika požarna otpornost, kao i
visoka otpornost na potres. Izgradnja CLT konstrukcije
brža je oko 30% nego kada se koristi odgovarajuća
betonska konstrukcija, jer se drveni elementi isporučuju
kao prefabrikovani, koji se zatim brzo uklapaju na
gradilištu. Za CLT panele koristi se mekano drvo koje
raste brzo i kog ima u izobilju, pa je i cena CLT
konstrukcija niža od 5 do 10% od odgovarajućih
betonskih ili čeličnih. Drvo je i mnogo bolji izolator - pet
puta bolji od betona i čak 350 puta bolji od čelika.
6 CONCLUSION
Use of CLT creates healthy and natural ambiance.
Compared against traditional wood, CLT construction
are stronger, have better mechanical properties, no
bending tendency, and minimal fractures appearance.
CLT constructions are characterized by high fire
resistance, and resilience to earthquakes. Since the
elements are delivered prefabricated and can be
assembled quickly on the construction site, CLT
constructions can be completed roughly 30% faster than
comparable concrete projects. Fast growing easily
accessible softwood keeps the price of CLT 5 to 10%
lower than the competing concrete or steel construction.
Timber is 5 times better insulator than concrete and up
to 350 times better than steel.
U radu su prikazane analitičke metode proračuna
koje se najčešće koriste prilikom dimenzionisanja CLT
konstrukcija. Gamma metod daje jednostavan postupak
proračuna, ali vrednost efektivne krutosti panela u
prikazanom primeru manja je za oko 6% u poređenju s
druge dve metode. Efektivne krutosti panela sračunate
K-metodom i Kreuzinger-ovom analogijom imaju istu
vrednost, ali je postupak proračuna K-metodom znatno
kraći i jednostavniji.
Usvajanjem predloženog međunarodnog standarda
EN 16351 Timber structures - Cross laminated timber -
Requirements u svim državama Evrope postigao bi se
jedinstveni analitički pristup prilikom dimenzionisanja. U
This work presents the most frequently used
analytical design methods. Even though Gamma method
is a simple design procedure for CLT constructions,
result in the shown example for effective stiffness of the
panel is about 6% lower compared to other two
methods. When calculated using both K-method, and
Kreuziner analogy, panels’ effective stiffness values
yield same results; however, K-method design
procedure is considerably shorter and simpler.
By adopting the international standard EN 16351
Timber Structures – Cross laminated timber –
Requirements across all European countries the unified
design approach could be achieved. In Serbia the

GRAĐEVINSKI MATERIJALI I KONSTRUKCIJE 58 (2015) 4 (51-69)
BUILDING MATERIALS AND STRUCTURES 58 (2015) 4 (51-69) 69
Srbiji, prevod ovog standarda obuhvaćen je planom rada
Instituta za standardizaciju Srbije, a njegovo prihvatanje
očekuje se krajem 2015. godine.
proposal of the standard has been made the part of the
agenda of the Institute for Standardization and its
adoption could be finalized by the end of 2015.
7 LITERATURA
REFERENCES
[1] Sylvain Gagnon, M. Mohammad: Structura
l
Performance and Design of CLT Building, CLT
Symposium and Workshop, Moncton, NB, Octobe
r
12, 2011.
[2] Ian Smith, Andrea Frangi: Use of Timber in Tal
l
Multi-Storey Buildings, International Association fo
r
Bridge and Structural Engineering (IABSE), Zurich,
Switzerland, 2014.
[3] Handbook cross-laminated timber, FPInnovations
and Binational Softwood Lumber Council, 2011.
[4] Gerhard Shickhofer: CLT - European Experience,
Presentation in the frame of the CLT Forum 2013
in Tokyo.
[5] European technical approval ETA-06/0138 Validity
from 01.07.2011 to 30.06.2016, extends ETA-
06/0138 with validity from 27.07.2006 to
26.07.2011.
[6] Ben Toosi: Cross Laminated Timber, The Market
Opportunities in North America, FPInnovations,
Canada, May 12th 2011.
[7] http://www.drvotehnika.info/clanci/drvo-kao-
gradjevinski-materijal-zgrada-od-drveta,
15.03.2015
[8] http://www.woodsolutions.com.au/Inspiration-Case-
Study/forte-living, 17.03.2015.
[9] http://www.drvotehnika.info/clanci/drvo-kao-
gradjevinski-materijal-zgrada-od-drveta,
15.03.2015.
[10] Sylvain Gagnon: Structural Design of CLT in
Canada, Québec City, May, 2010.
[11] Evrokod 5 - Proračun drvenih konstrukcija - Deo 1-
1: Opšta pravila i pravila za zgrade, EN 1995-1-
1:2004, Beograd, 2009.
[12] Hans Joachim Blass, Peter Fellmoser: Design o
f
solid wood panels with cross layers, Proceedings,
8. World Conference on Timber Engineering, Lahti,
Finnland, 2004.
REZIME
UNAKRSNO LAMELIRANI DRVENI ELEMENTI U
SAVREMENIM DRVENIM KONSTRUKCIJAMA
ZGRADA - primena i proračun
Ljiljana KOZARIĆ
Aleksandar PROKIĆ
Miroslav BEŠEVIĆ
U radu se analizira unakrsno lamelirano drvo (CLT),
moderan građevinski materijal koji se proizvodi od
osušenih drvenih elemenata - lamela. Lamele u CLT
panelima su podjednake širine i postavljene su tako da
vlakna drveta u lamelama po slojevima budu
međusobno pod pravim uglom.
Prikazane su osnovne fizičko-mehaničke
karakteristike CLT panela, kao i analitički modeli koji se
najčešće koriste prilikom projektovanja CLT podnih i
zidnih elemenata u konstrukcijama. Navedene su
prednosti i nedostaci ovog novog konstruktivnog
sistema, u skladu sa savremenim svetskim zahtevima pri
projektovanju modernih, ekološki prihvatljivih
konstrukcija.
Ključne reči: unakrsno lamelirano drvo, savremene
drvene konstrukcije
SUMMARY
CROSS LAMINATED TIMBER ELEMENTS IN
CONTEMPORARY TIMBER STRUCTURES OF
BUILDINGS - application and design
Ljiljana KOZARIC
Aleksandar PROKIC
Miroslav BEŠEVIC
This work analyses cross laminated timber (CLT),
contemporary building material produced of dried
wooden elements - laminates. Laminates in CLT panels
are equally wide and timber fibers are rectangularly
plated within layers.
Paper shows basic physical - mechanical
characteristics of CLT panels and analytic models that
are most commonly used in designing of CLT floor and
wall construction elements. Advantages and
disadvantages of this new construction system are
stated according to contemporary requirements in
designing environmentally and ecologically acceptable
constructions.
Key words: cross laminated timber, contemporary
timber structures