Ci a ion: Nespˇešný, O.; Beˇcko ský,
D.; Vys ˇcil, J.; Vanˇek, V.; No o ný,
M.; Pˇenˇcík, J. Expe imen al Loading
o S ai case Made om Cemen Fibe
Boa ds wi h Cellulose Fibe s Using
Full-Scale Model. Buildings 2023,13,
704. h ps://doi.o g/10.3390/
buildings13030704
Academic Edi o s: K is ýna
Va ušo á, Pe Myna ˇcík and
Lucie Myna zo á
Recei ed: 18 Janua y 2023
Re ised: 24 Feb ua y 2023
Accep ed: 3 Ma ch 2023
Published: 7 Ma ch 2023
Copy igh : © 2023 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
buildings
A icle
Expe imen al Loading o S ai case Made om Cemen Fibe
Boa ds wi h Cellulose Fibe s Using Full-Scale Model
Ondˇ ej Nespˇešný* , Da id Beˇcko ský, Jan Vys ˇcil, Voj ˇech Vanˇek, Milosla No o nýand Jan Pˇenˇcík
Facul y o Ci il Enginee ing, Ins i u e o Building S uc u es, B no Uni e si y o Technology, Ve eˇ í331/95,
602 00 B no, Czech Republic
*Co espondence: ond [email p o ec ed]
Abs ac :
The s udy p esen s a possible inno a i e use o cemen ibe boa ds (CFBs) ein o ced wi h
cellulose ibe s o cons uc ion o an in e io p e ab ica ed s ai case. Rega ding he unusual use o
adi ional ma e ial ha was used in all bea ing elemen s o he s ai case, a nume ical simula ion wi h
he use o a ma e ial model SBETA was ca ied ou and, subsequen ly, mul iple expe imen al s a ic
loading was applied. In o de o ca y ou expe imen al es ing o s a ic load capaci y, a ull-scale
expe imen me hod was chosen and pe o med on a eal s ai case s uc u e o amily houses. The
ull-scale expe imen is conside ed he mos p ecise me hod o es s uc u es o ma e ial beha io .
The ob ained esul s show ha he designed and es ed s ai case s uc u e o CFBs is able o mee he
equi emen s o echnical s anda ds ela ed o s a ic loading o s ai cases. The load es con i med he
po en ial use o cemen ibe boa ds p oduced by he Ha schek p ocess o eal bea ing s uc u es
unde s a ic loading.
Keywo ds: s ai case; ull-scale expe imen ; cemen ibe boa d; CFB; cellulose ibe
1. In oduc ion
In mos cases, s ai case s uc u es a e dominan ea u es o in e io s and comple e
in e io cha ac e . The igh choice o s ai case s uc u e sys em, o ype o s ai case,
con ibu es o he elegance, o iginali y, and unique s yle o a building. The e o e, he
cu en end is o design sub le and ligh weigh s ai cases wi h a ac i e and mode n
s yles. When designing a s ai case, i is necessa y o ake in o accoun he ype o building
and economic ac o s, and co ec ly design dimensions o he s ai case a ea, dimensions
o s eps and hei shape, e c. The designed s ai case should be com o able o use s and
should gua an ee p opo ionali y, egula i y, hy hm, and o de , as s a ed in [1].
Nowadays, he s ai case is an in eg al pa o all mul iple loo s uc u es in a wide
ange o esiden ial, public, and indus ial buildings. Based on place o use, i s geome ic
equi emen s ela ed o echnical s anda ds and o locali y di e . Geome ic equi emen s
o s ai cases and hei compa isons acco ding o na ional equi emen s [
2
–
4
] and ypes
o buildings a e summa ized by Veseláin [
5
]. Conside ing he ac ha s ai cases a e
load-bea ing s uc u es, hey a e subjec ed o s ic equi emen s o mechanical du abili y
and s abili y unde a ious e ec s o ex e nal loading. The s a ic load-bea ing capaci y o a
s ai case can be p o ed by di e en me hods, mos commonly wi h he use o a nume ic
analysis using FEA and assessmen acco ding o s anda d equi emen s o s ai case ma e-
ial. Ano he me hod ha can be used and is accep ed by s anda ds and egula ions is he
use o a load es in educed scales, which uses model simila i ies [
6
], o he use o cu ou
models in he scale o 1:1, o he use o a eal model in 1:1 scale, i.e., a ull-scale expe imen .
The ull-scale expe imen is conside ed he mos p ecise me hod o e i y beha io o a
s uc u e o ma e ial. The me hod o he ull-scale expe imen is e y popula in ci il
enginee ing esea ch, which is con i med by a ange o ecen scien i ic publica ions [
7
–
12
]
an example o expe imen al loading o s ai cases is gi en a Figu e 1.
Buildings 2023,13, 704. h ps://doi.o g/10.3390/buildings13030704 h ps://www.mdpi.com/jou nal/buildings
Buildings 2023,13, 704 2 o 16
Buildings 2023, 13, x FOR PEER REVIEW 2 o 16
enginee ing esea ch, which is con i med by a ange o ecen scien i ic publica ions [7–
12] an example o expe imen al loading o s ai cases is gi en a Figu e 1.
A combina ion o he abo emen ioned me hods o e i ica ion o s ai case s a ic
bea ing capaci y, i.e., a nume ical analysis wi h ull-scale expe imen s, was used by Pěnčík
e al. in [7] o analysis o he beha io o p e ab ica ed wooden s ai cases wi h one-sided
suspended s ai s made om Sco s pine (Pinus syl es is L.), by La ický e al. in hei anal-
ysis o a p e ab ica ed winde wooden s ai case wi h cen al s inge made om Sco s
pine (Pinus syl es is L.) [13], and by Pouse e in [14] o es ing and modeling o he be-
ha io o wooden s ai s and s ai join s. The nume ically de e mined esul s in [13]
showed he sui abili y and necessi y o idealize he cons uc ion (Figu e 2) in ques ion by
he nume ic s a ic model in mo e de ail and wi h highe accu acy.
(a) (b)
Figu e 1. (a) P o o ypes o wooden s ai case du ing s a ic load es , ull-scale expe imen [7]; (b) 3D
wooden s ai case FEA model [7].
(a) (b)
Figu e 2. (a) P o o ypes o wooden s ep du ing s a ic load es , semi-scale expe imen [13]; (b) 3D
wooden s ep FEA model [13].
Acco ding o Sachs e al. [15], apa om he s ai case s uc u e s a ic load, i is nec-
essa y o pay a en ion o ib a ions caused by people walking, i.e., dynamic e ec s on he
s uc u e. The assessmen o he e ec o he p esence o people on dynamic beha io o
s eel s ai cases was published by Cappellini e al. in [16], whe e a me hodology o quan-
i ica ion o modal pa ame e changes due o he p esence o passi e people on a na ow
s uc u e was applied. Dynamic es s can be conside ed as an ad anced le el o a s uc u e
analysis, which is p eceded by a s a ic load es , a ull-scale expe imen , and a nume ic
simula ion [17,18].
In cons uc ions, he mos equen ly used s ai cases a e monoli hic ein o ced con-
c e e s ai cases. In o de o speed up he cons uc ion p ocess and emo e he we p ocess,
p e ab ica ed s ai cases [19] a e cu en ly used mo e o en han monoli hic s ai cases.
They a e made om s eel, conc e e, o wood. In Eu opean Union coun ies, he
Figu e 1.
(
a
) P o o ypes o wooden s ai case du ing s a ic load es , ull-scale expe imen [
7
]; (
b
) 3D
wooden s ai case FEA model [7].
A combina ion o he abo emen ioned me hods o e i ica ion o s ai case s a ic bea -
ing capaci y, i.e., a nume ical analysis wi h ull-scale expe imen s, was used by Pˇenˇcík e al.
in [
7
] o analysis o he beha io o p e ab ica ed wooden s ai cases wi h one-sided sus-
pended s ai s made om Sco s pine (Pinus syl es is L.), by La ickýe al. in hei analysis
o a p e ab ica ed winde wooden s ai case wi h cen al s inge made om Sco s pine
(Pinus syl es is L.) [
13
], and by Pouse e in [
14
] o es ing and modeling o he beha io
o wooden s ai s and s ai join s. The nume ically de e mined esul s in [
13
] showed he
sui abili y and necessi y o idealize he cons uc ion (Figu e 2) in ques ion by he nume ic
s a ic model in mo e de ail and wi h highe accu acy.
Buildings 2023, 13, x FOR PEER REVIEW 2 o 16
enginee ing esea ch, which is con i med by a ange o ecen scien i ic publica ions [7–
12] an example o expe imen al loading o s ai cases is gi en a Figu e 1.
A combina ion o he abo emen ioned me hods o e i ica ion o s ai case s a ic
bea ing capaci y, i.e., a nume ical analysis wi h ull-scale expe imen s, was used by Pěnčík
e al. in [7] o analysis o he beha io o p e ab ica ed wooden s ai cases wi h one-sided
suspended s ai s made om Sco s pine (Pinus syl es is L.), by La ický e al. in hei anal-
ysis o a p e ab ica ed winde wooden s ai case wi h cen al s inge made om Sco s
pine (Pinus syl es is L.) [13], and by Pouse e in [14] o es ing and modeling o he be-
ha io o wooden s ai s and s ai join s. The nume ically de e mined esul s in [13]
showed he sui abili y and necessi y o idealize he cons uc ion (Figu e 2) in ques ion by
he nume ic s a ic model in mo e de ail and wi h highe accu acy.
(a) (b)
Figu e 1. (a) P o o ypes o wooden s ai case du ing s a ic load es , ull-scale expe imen [7]; (b) 3D
wooden s ai case FEA model [7].
(a) (b)
Figu e 2. (a) P o o ypes o wooden s ep du ing s a ic load es , semi-scale expe imen [13]; (b) 3D
wooden s ep FEA model [13].
Acco ding o Sachs e al. [15], apa om he s ai case s uc u e s a ic load, i is nec-
essa y o pay a en ion o ib a ions caused by people walking, i.e., dynamic e ec s on he
s uc u e. The assessmen o he e ec o he p esence o people on dynamic beha io o
s eel s ai cases was published by Cappellini e al. in [16], whe e a me hodology o quan-
i ica ion o modal pa ame e changes due o he p esence o passi e people on a na ow
s uc u e was applied. Dynamic es s can be conside ed as an ad anced le el o a s uc u e
analysis, which is p eceded by a s a ic load es , a ull-scale expe imen , and a nume ic
simula ion [17,18].
In cons uc ions, he mos equen ly used s ai cases a e monoli hic ein o ced con-
c e e s ai cases. In o de o speed up he cons uc ion p ocess and emo e he we p ocess,
p e ab ica ed s ai cases [19] a e cu en ly used mo e o en han monoli hic s ai cases.
They a e made om s eel, conc e e, o wood. In Eu opean Union coun ies, he
Figu e 2.
(
a
) P o o ypes o wooden s ep du ing s a ic load es , semi-scale expe imen [
13
]; (
b
) 3D
wooden s ep FEA model [13].
Acco ding o Sachs e al. [
15
], apa om he s ai case s uc u e s a ic load, i is
necessa y o pay a en ion o ib a ions caused by people walking, i.e., dynamic e ec s on
he s uc u e. The assessmen o he e ec o he p esence o people on dynamic beha io
o s eel s ai cases was published by Cappellini e al. in [
16
], whe e a me hodology o
quan i ica ion o modal pa ame e changes due o he p esence o passi e people on a
na ow s uc u e was applied. Dynamic es s can be conside ed as an ad anced le el o a
s uc u e analysis, which is p eceded by a s a ic load es , a ull-scale expe imen , and a
nume ic simula ion [17,18].
In cons uc ions, he mos equen ly used s ai cases a e monoli hic ein o ced conc e e
s ai cases. In o de o speed up he cons uc ion p ocess and emo e he we p ocess,
p e ab ica ed s ai cases [
19
] a e cu en ly used mo e o en han monoli hic s ai cases. They
a e made om s eel, conc e e, o wood. In Eu opean Union coun ies, he equi emen s o
hese ypes o s ai cases a e de ined in acco dance wi h Eu ocode 1: Ac ions on s uc u es
Buildings 2023,13, 704 3 o 16
- Pa 1-1: Gene al ac ions - Densi ies, sel -weigh , imposed loads o buildings [
20
] and
ETAG 008: P e ab ica ed S ai Ki s [21].
A p ojec o he Technological Agency o he Czech Republic TH04020263 es ed he
po en ial o use cemen ibe boa ds (CFBs) o building cons uc ions. CFBs ha e had
a long his o y o applica ion in ci il enginee ing, and he mos commonly used CFBs
a e p oduced by Ha schek echnology [
22
], which is based on he p inciple o a machine
o p oduc ion o ca dboa d [
23
]. CFBs usually p oduced by his echnology a e used in
he o m o acade panels [
24
–
26
] oo ing [
27
,
28
], shu e ing [
29
,
30
], o in e io acous ic
iles [
31
]; in all hese cases, hin boa ds up o a hickness o 12 mm a e used. Po en ial
applica ion a eas o CFBs a e in e io s ai case s uc u es.
The Ha schek me hod [
22
] p oduc ion p ocess includes c ea ion o so-called monoboa ds
wi h hickness o up o 6 mm by laye ing hin cemen ibe laye s on an accumula ion cylin-
de . CFBs a e made by g adual laye ing o monoboa ds and subsequen comp ession by
a hyd aulic p ess. Applying p essu e leads o wa e emo al as well as o in e connec ion
o monoboa ds in o a single body. By applying he men ioned p oduc ion p ocess, i is
possible o make a CFB wi h a inal limi ing hickness o up o 40 mm. Howe e , his
limi ing hickness o en causes spon aneous delamina ion o indi idual monoboa ds. Based
on long- e m es s [
32
], i was decided o use boa ds wi h he maximum hickness o 30 mm,
in o de o u he de elop he use o CFBs. Nei he spon aneous delamina ion, no hei
de o ma ion, no su ace damage occu s wi h hose boa ds du ing ma u ing.
The publica ion [
32
] claims ha s eng h and oughness in he di ec ion pe pendicula
o he ibe o ien a ion (pe pendicula o p oduc ion di ec ion, also e e ed o as pa allel
o he boa d mid-plane—di ec ions x and z in Figu e 3) a e highe han in he case when
he boa d is loaded pe pendicula o he boa d mid-plane (di ec ion y in Figu e 3). In [
33
],
mic os uc u al aniso opy was con i med, which is he di ec cause o he men ioned
mac oscopic mechanic beha io . This ac appea s o be bene icial o he o e all load-
bea ing capaci y o he main suppo ing elemen — he s inge . The esul s and cou se
o he ull-scale expe imen and nume ic simula ion a e p esen ed by he au ho s in his
publica ion, which desc ibes he same cemen ibe boa ds (CFBs) ein o ced wi h cellulose
ibe s o c ea ing he segmen s inge s ai case as hose desc ibed by Nespˇešnýe al.
in [32].
Buildings 2023, 13, x FOR PEER REVIEW 3 o 16
equi emen s o hese ypes o s ai cases a e de ined in acco dance wi h Eu ocode 1: Ac-
ions on s uc u es - Pa 1-1: Gene al ac ions - Densi ies, sel -weigh , imposed loads o
buildings [20] and ETAG 008: P e ab ica ed S ai Ki s [21].
A p ojec o he Technological Agency o he Czech Republic TH04020263 es ed he
po en ial o use cemen ibe boa ds (CFBs) o building cons uc ions. CFBs ha e had a
long his o y o applica ion in ci il enginee ing, and he mos commonly used CFBs a e
p oduced by Ha schek echnology [22], which is based on he p inciple o a machine o
p oduc ion o ca dboa d [23]. CFBs usually p oduced by his echnology a e used in he
o m o acade panels [24–26] oo ing [27,28], shu e ing [29,30], o in e io acous ic iles
[31]; in all hese cases, hin boa ds up o a hickness o 12 mm a e used. Po en ial applica-
ion a eas o CFBs a e in e io s ai case s uc u es.
The Ha schek me hod [22] p oduc ion p ocess includes c ea ion o so-called mono-
boa ds wi h hickness o up o 6 mm by laye ing hin cemen ibe laye s on an accumu-
la ion cylinde . CFBs a e made by g adual laye ing o monoboa ds and subsequen com-
p ession by a hyd aulic p ess. Applying p essu e leads o wa e emo al as well as o
in e connec ion o monoboa ds in o a single body. By applying he men ioned p oduc ion
p ocess, i is possible o make a CFB wi h a inal limi ing hickness o up o 40 mm. How-
e e , his limi ing hickness o en causes spon aneous delamina ion o indi idual mono-
boa ds. Based on long- e m es s [32], i was decided o use boa ds wi h he maximum
hickness o 30 mm, in o de o u he de elop he use o CFBs. Nei he spon aneous
delamina ion, no hei de o ma ion, no su ace damage occu s wi h hose boa ds du ing
ma u ing.
The publica ion [32] claims ha s eng h and oughness in he di ec ion pe pendicu-
la o he ibe o ien a ion (pe pendicula o p oduc ion di ec ion, also e e ed o as pa -
allel o he boa d mid-plane—di ec ions x and z in Figu e 3) a e highe han in he case
when he boa d is loaded pe pendicula o he boa d mid-plane (di ec ion y in Figu e 3).
In [33], mic os uc u al aniso opy was con i med, which is he di ec cause o he men-
ioned mac oscopic mechanic beha io . This ac appea s o be bene icial o he o e all
load-bea ing capaci y o he main suppo ing elemen — he s inge . The esul s and
cou se o he ull-scale expe imen and nume ic simula ion a e p esen ed by he au ho s
in his publica ion, which desc ibes he same cemen ibe boa ds (CFBs) ein o ced wi h
cellulose ibe s o c ea ing he segmen s inge s ai case as hose desc ibed by Nespěšný
e al. in [32].
(a) (b)
Figu e 3. (a) Cemen ibe boa d o ien a ion by di ec ion o p oduc ion wi h de ini ion o coo dina e
sys em [x, y, z]; (b) o ien a ion o s inge om cemen ibe boa ds.
In e es in p e ab ica ion in he scien i ic communi y was a i s peak in he 1990s.
Along wi h he de elopmen o new ma e ials and echnologies, p e ab ica ion has been
imp o ed o e he yea s [34]. The ad an ages o p e ab ica ed cons uc ions a e summa-
ized in [35], whe e he au ho s men ion, in pa icula , inc eased wo k p oduc i i y, e i-
ciency in quali y con ol, educ ion o cons uc ion cos s, sho ened pe iod o wo k, and
las , bu no leas , au oma ion. The applica ion o p e ab ica ed s uc u es is s ill cu en ,
which is also con i med by he publica ion [36], which e alua es he li e cycle (LCA) o
p e ab ica ed empo a y cons uc ion in China. In he compa a i e LCA calcula ions, he
Figu e 3.
(
a
) Cemen ibe boa d o ien a ion by di ec ion o p oduc ion wi h de ini ion o coo dina e
sys em [x, y, z]; (b) o ien a ion o s inge om cemen ibe boa ds.
In e es in p e ab ica ion in he scien i ic communi y was a i s peak in he 1990s. Along
wi h he de elopmen o new ma e ials and echnologies, p e ab ica ion has been imp o ed
o e he yea s [
34
]. The ad an ages o p e ab ica ed cons uc ions a e summa ized in [
35
],
whe e he au ho s men ion, in pa icula , inc eased wo k p oduc i i y, e iciency in quali y
con ol, educ ion o cons uc ion cos s, sho ened pe iod o wo k, and las , bu no leas ,
au oma ion. The applica ion o p e ab ica ed s uc u es is s ill cu en , which is also
con i med by he publica ion [
36
], which e alua es he li e cycle (LCA) o p e ab ica ed
empo a y cons uc ion in China. In he compa a i e LCA calcula ions, he au ho s ook
in o accoun he use o p e ab ica ed s ai cases and also poin ed o he ecological bene i .
The de elopmen o he use o globally a ailable ibe cemen boa d ma e ial can be
conside ed inno a i e and p omising o he u he de elopmen o p e ab ica ed s ai s.
Buildings 2023,13, 704 4 o 16
2. Ma e ials and Me hods
Wi hin he s udy, a eal s ai case acco ding o he equi emen s o s anda d ˇ
CSN 73
4130 [
2
] was p oduced and es ed wi h he use o a ull-scale expe imen (in 1:1 scale). The
s ai case was assembled om cemen ibe boa d segmen s ein o ced wi h o ganic cellulose
ibe s. I is a g oup o cemen ibe boa ds wi h a high cemen con en and lowe con en o
he p ima y ein o cing ibe om cellulose, i.e., “low ibe con en ” [
37
]. The ing edien
used o p oduc ion o cemen ibe boa d is cemen wi h he main componen s being
Po land clinke (
≈
84.5 w . %, speci ica ion in Table 1), cellulose (
≈
8 w . %), expanded
pea li e (
≈
7 w . %), and polyp opylene ibe (
≈
0.5 w . %). The aw ma e ials used in
p oduc ion can be seen in he de ailed analysis o he b oken sample in Figu e 4.
Table 1. Physico-chemical composi ion o cemen .
Densi y
[g/cm3]
SiO2
[%]
Al2O3
[%]
Fe2O3
[%]
CaO
[%]
MgO
[%]
Sul a e
Con en
[%]
K2O
[%]
Na2O
[%]
Cl
Con en
[%]
Na2O
ek .
[%]
Loss on
Igni ion
[%]
Insoluble
Residue
CEM I
42.5 R 3.11 20.86 4.87 2.52 67.48 2.25 3.12 0.60 0.10 0.069 0.50 3.41 1.10
Buildings 2023, 13, x FOR PEER REVIEW 4 o 16
au ho s ook in o accoun he use o p e ab ica ed s ai cases and also poin ed o he eco-
logical bene i . The de elopmen o he use o globally a ailable ibe cemen boa d ma e-
ial can be conside ed inno a i e and p omising o he u he de elopmen o p e ab i-
ca ed s ai s.
2. Ma e ials and Me hods
Wi hin he s udy, a eal s ai case acco ding o he equi emen s o s anda d ČSN 73
4130 [2] was p oduced and es ed wi h he use o a ull-scale expe imen (in 1:1 scale). The
s ai case was assembled om cemen ibe boa d segmen s ein o ced wi h o ganic cellu-
lose ibe s. I is a g oup o cemen ibe boa ds wi h a high cemen con en and lowe
con en o he p ima y ein o cing ibe om cellulose, i.e., “low ibe con en ” [37]. The
ing edien used o p oduc ion o cemen ibe boa d is cemen wi h he main componen s
being Po land clinke (≈84.5 w . %, speci ica ion in Table 1), cellulose (≈8 w . %), ex-
panded pea li e (≈7 w . %), and polyp opylene ibe (≈0.5 w . %). The aw ma e ials used
in p oduc ion can be seen in he de ailed analysis o he b oken sample in Figu e 4.
Table 1. Physico-chemical composi ion o cemen .
Densi y
[g/cm
3
]
SiO
2
[%]
Al
2
O
3
[%]
Fe
2
O
3
[%]
CaO
[%]
MgO
[%]
Sul a e
Con en
[%]
K
2
O
[%]
Na
2
O
[%]
Cl
Con en
[%]
Na
2
O
ek .
[%]
Loss on
Igni ion
[%]
Insoluble
Residue
CEM I
42.5 R 3.11 20.86 4.87 2.52 67.48 2.25 3.12 0.60 0.10 0.069 0.50 3.41 1.10
Rega ding he use o cemen ibe boa ds o building cons uc ion, i is o en neces-
sa y o combine a angemen s o ma e ial, i.e., some elemen s a e loaded as slab elemen s
(⊥), e.g., ead, while some s uc u e elemen s a e loaded as wall elemen s (||), e.g.,
s inge . The e o e, be o e designing and p oducing he s ai case s uc u e, mechanical
p ope y de e mina ion was pe o med, as desc ibed by Nespěšný e al. in [32], and he
a e age alues de e mined by ou -poin bending a e shown in Table 2. The speci ic ac-
u e ene gy and ac u e oughness alues we e de e mined acco ding o Ka ihaloo [38].
F om he esul s o he expe imen , i can be seen ha he bigges di e ence be ween he
pa allel o boa d mid-plane and pe pendicula o boa d mid-plane a ian s is in he
s eng h in simple comp ession and simple ension.
Figu e 4. De ail o used ibe cemen boa d, ensile ailu e.
Table 2. O e iew o expe imen ally de e mined mechanical p ope ies o cemen ibe boa ds wi h
cellulose ibe s [N/mm
2
].
A e age Values a Loading MO
E
MOR
c
G
*
F
K
Ic
Pa allel o boa d mid-plane (||) 14,213.15 21.73 56.01 10.13 270.96 1.82
Pe pendicula o boa d mid-plane (⊥) 14,175.54 21.84 67.71 2.16 435.74 1.91
Figu e 4. De ail o used ibe cemen boa d, ensile ailu e.
Rega ding he use o cemen ibe boa ds o building cons uc ion, i is o en necessa y
o combine a angemen s o ma e ial, i.e., some elemen s a e loaded as slab elemen s (
⊥
),
e.g., ead, while some s uc u e elemen s a e loaded as wall elemen s (||), e.g., s inge .
The e o e, be o e designing and p oducing he s ai case s uc u e, mechanical p ope y
de e mina ion was pe o med, as desc ibed by Nespˇešnýe al. in [
32
], and he a e age
alues de e mined by ou -poin bending a e shown in Table 2. The speci ic ac u e ene gy
and ac u e oughness alues we e de e mined acco ding o Ka ihaloo [
38
]. F om he
esul s o he expe imen , i can be seen ha he bigges di e ence be ween he pa allel
o boa d mid-plane and pe pendicula o boa d mid-plane a ian s is in he s eng h in
simple comp ession and simple ension.
Table 2.
O e iew o expe imen ally de e mined mechanical p ope ies o cemen ibe boa ds wi h
cellulose ibe s [N/mm2].
A e age Values a Loading MOE MOR c G*FKIc
Pa allel o boa d mid-plane (||) 14,213.15 21.73 56.01 10.13 270.96 1.82
Pe pendicula o boa d mid-plane (
⊥
)
14,175.54 21.84 67.71 2.16 435.74 1.91
MOE is an elas ici y modulus in MPa, MOR is modulus o up u e in MPa,
c
is comp essi e s eng h in MPa and
is ensile s eng h in MPa; G*Fis speci ic ac u e ene gy in J·m−2;KIc is ac u e oughness in MPa·m1/2.
Buildings 2023,13, 704 5 o 16
2.1. P elimina y Nume ical Analysis o he S ai case
The CFB ma e ial p oduced by he Ha schek me hod can be classi ied as a quasi-
b i le ma e ial, simila o conc e e. Rega ding analyses o CFBs wi h he me hod o ini e
elemen s, i is possible o use se e al app oaches o geome ic modeling and ma e ial
beha io modeling based on he ype and pu pose o he pe o med analysis. I is possible
o use specialized p og ams o analyzing quasi-b i le ma e ials, e.g., ATENA so wa e.
The analyses wo k wi h nonlinea beha io in e ms o ma e ial and geome y, and he
analyses may also include he e ec o cons uc ion nonlinea i y. When using he ATENA
p og am, which includes specially designed algo i hms o modeling beha io o a quasi-
b i le ma e ial om a no damage s a e up o a comple e ailu e s a e, based on a cohesion
c ack model, i is possible o use a ma e ial model SBETA [
39
], and i s p ocess is desc ibed
in Figu e 5. Acco ding o [
33
], CFB ma e ial can be cha ac e ized as a ma e ial wi h
mic os uc u al aniso opy. Howe e , idealiza ion o CFB beha io modeling can be used
o calcula ions.
Buildings 2023, 13, x FOR PEER REVIEW 5 o 16
MOE is an elas ici y modulus in MPa, MOR is modulus o up u e in MPa, c is comp essi e s eng h
in MPa and is ensile s eng h in MPa; G*F is speci ic ac u e ene gy in J·m−2; KIc is ac u e ough-
ness in MPa·m1/2.
2.1. P elimina y Nume ical Analysis o he S ai case
The CFB ma e ial p oduced by he Ha schek me hod can be classi ied as a quasi-
b i le ma e ial, simila o conc e e. Rega ding analyses o CFBs wi h he me hod o ini e
elemen s, i is possible o use se e al app oaches o geome ic modeling and ma e ial be-
ha io modeling based on he ype and pu pose o he pe o med analysis. I is possible
o use specialized p og ams o analyzing quasi-b i le ma e ials, e.g., ATENA so wa e.
The analyses wo k wi h nonlinea beha io in e ms o ma e ial and geome y, and he
analyses may also include he e ec o cons uc ion nonlinea i y. When using he ATENA
p og am, which includes specially designed algo i hms o modeling beha io o a quasi-
b i le ma e ial om a no damage s a e up o a comple e ailu e s a e, based on a cohesion
c ack model, i is possible o use a ma e ial model SBETA [39], and i s p ocess is desc ibed
in Figu e 5. Acco ding o [33], CFB ma e ial can be cha ac e ized as a ma e ial wi h mic o-
s uc u al aniso opy. Howe e , idealiza ion o CFB beha io modeling can be used o
calcula ions.
The cemen ibe boa d’s nonlinea esponse unde biaxial s ess is explained
h ough wo pa ame e s: he e ec i e s ess 𝜎
and he equi alen uniaxial s ain 𝜀
(Figu e 5). Gene ally, he e ec i e s ess is a p ima y s ess. To elimina e he Poisson e ec
unde plane s ess, an equi alen uniaxial s ain is used.
𝜀 =



, (1)
By assuming ha he nonlinea i y, which ep esen s damage, is solely caused by he
go e ning s ess 𝜎, he equi alen uniaxial s ain can be de ined as he s ain ha would
be gene a ed by he s ess 𝜎 in a uniaxial es wi h a modulus 𝐸 linked o di ec ion i.
Figu e 5. (a) Failu e c i e ion o he 2-axial s ess s a e case; (b) SBETA ma e ial model wi h ma e ial
ailu e in ension.
The unloading p ocess in ension and also in comp ession ollows a s aigh line back
o he o igin, as demons a ed by poin s A and B in Figu e 5. Fo his eason, he ela ion-
ship be ween e ec i e s ess 𝜎
 and equi alen uniaxial s ain 𝜀 is in luenced by he
Figu e 5.
(
a
) Failu e c i e ion o he 2-axial s ess s a e case; (
b
) SBETA ma e ial model wi h ma e ial
ailu e in ension.
The cemen ibe boa d’s nonlinea esponse unde biaxial s ess is explained h ough
wo pa ame e s: he e ec i e s ess
σe
c
and he equi alen uniaxial s ain
εeq
(Figu e 5).
Gene ally, he e ec i e s ess is a p ima y s ess. To elimina e he Poisson e ec unde
plane s ess, an equi alen uniaxial s ain is used.
εeq =
σci
MOEci
, (1)
By assuming ha he nonlinea i y, which ep esen s damage, is solely caused by he
go e ning s ess
σci
, he equi alen uniaxial s ain can be de ined as he s ain ha would
be gene a ed by he s ess σci in a uniaxial es wi h a modulus Eci linked o di ec ion i.
The unloading p ocess in ension and also in comp ession ollows a s aigh line
back o he o igin, as demons a ed by poin s A and B in Figu e 5. Fo his eason, he
ela ionship be ween e ec i e s ess
σe
c
and equi alen uniaxial s ain
εeq
is in luenced by
he load his o y. I he equi alen uniaxial s ain inc emen changes sign, he unloading
s age changes o loading s age. The loading p ocess ollows a s aigh line back o poin

Buildings 2023,13, 704 6 o 16
A o B, a e which he loading p ocess will con inue. The maximum comp ession and
ension s ess alues
σ0e
c
and
σ0e
a e compu ed based on he biaxial s ess s a e. The e o e,
he equi alen uniaxial s ess–s ain law e lec s he biaxial s ess s a e.
When p oducing CFBs by he Ha schek p ocess, he o a ion o p oduc ion olle s
causes he ein o cing ibe s o o ien a e along he p oduc ion di ec ion. In addi ion, a CFB
is made by laye ing monoboa ds and hei subsequen comp ession in o a single body. This
p oduc ion p ocess clea ly de ines he longi udinal di ec ion z, which is iden ical o he
dominan o ien a ion o ein o cing ibe s, o di ec ion o p oduc ion and di ec ions x and
y, espec i ely (Figu e 3). The design o he dimensions o he s ai load-bea ing elemen s,
i.e., 20 mm hick eads and 40 mm hick ead suppo s ( om wo 20 mm hick slabs)
wi h 30 mm hick slabs, was e i ied by nume ical analysis using he ATENA so wa e o
nonlinea analyses o s uc u es wi h use o he SBETA ma e ial model men ioned abo e
(Figu e 6), aking in o accoun he expe imen ally de e mined CFB p ope ies lis ed in
Table 2. The model case does no ake in o accoun he epea ed loading o he s uc u e
and he occu ence o pe manen de o ma ions.
Buildings 2023, 13, x FOR PEER REVIEW 6 o 16
load his o y. I he equi alen uniaxial s ain inc emen changes sign, he unloading s age
changes o loading s age. The loading p ocess ollows a s aigh line back o poin A o B,
a e which he loading p ocess will con inue. The maximum comp ession and ension
s ess alues 𝜎′
 and 𝜎′
 a e compu ed based on he biaxial s ess s a e. The e o e, he
equi alen uniaxial s ess–s ain law e lec s he biaxial s ess s a e.
When p oducing CFBs by he Ha schek p ocess, he o a ion o p oduc ion olle s
causes he ein o cing ibe s o o ien a e along he p oduc ion di ec ion. In addi ion, a CFB
is made by laye ing monoboa ds and hei subsequen comp ession in o a single body.
This p oduc ion p ocess clea ly de ines he longi udinal di ec ion z, which is iden ical o
he dominan o ien a ion o ein o cing ibe s, o di ec ion o p oduc ion and di ec ions x
and y, espec i ely (Figu e 3). The design o he dimensions o he s ai load-bea ing ele-
men s, i.e., 20 mm hick eads and 40 mm hick ead suppo s ( om wo 20 mm hick
slabs) wi h 30 mm hick slabs, was e i ied by nume ical analysis using he ATENA so -
wa e o nonlinea analyses o s uc u es wi h use o he SBETA ma e ial model men-
ioned abo e (Figu e 6), aking in o accoun he expe imen ally de e mined CFB p ope -
ies lis ed in Table 2. The model case does no ake in o accoun he epea ed loading o
he s uc u e and he occu ence o pe manen de o ma ions.
A quad ila e al compu a ional mesh model wi h a compu a ional side size o 10 mm
was chosen as he mac o elemen . The maximum numbe o i e a ions in one compu a-
ional s ep was se o 80. The New on–Raphson [39] compu a ional me hod was used, in
which he ollowing se o nonlinea equa ions is ob ained by applying he concep o s ep-
by-s ep analysis:
𝐾󰇡𝑝󰇢Δ𝑝 = 𝑞−
𝑓
(𝑝), (2)
whe e 𝑞 is he ec o o o al applied join loads, 𝑓(𝑝) is he ec o o in e nal join o ces,
Δ𝑝 is he de o ma ion inc emen due o loading inc emen , p a e he de o ma ions o he
s uc u e p io o load inc emen , 𝐾󰇡𝑝󰇢 is he s i ness ma ix, ela ing loading inc e-
men s o de o ma ion inc emen s.
The po ion on he igh side o Equa ion (2) deno es he o ces ha exis ou side o
equilib ium du ing he load inc emen . This means i ep esen s he o e all load le el a -
e he load inc emen is applied, minus he in e nal o ces ha we e p esen a he end o
he p e ious load s ep. Typically, he s i ness ma ix is dependen on s ain, meaning i
is a unc ion o p. Howe e , i is gene ally igno ed du ing he load inc emen o p ese e
linea i y. Ins ead, he s i ness ma ix is calcula ed based on he alue o p ela ed o he
le el be o e he load inc emen .
Th ee measu ing poin s we e selec ed on he s uc u e o eco d he e ical displace-
men s ( e e ed o as po _2, po _3, and po _4 in he expe imen as shown in Figu e 7.
Figu e 6. (a) De ail o s ai case s uc u e du ing load es (uppe pa ); (b) de ail o he s ai case
s uc u e du ing he load es (lowe pa ); (c) model o he cons uc ion o an in e io s ai case made
Figu e 6.
(
a
) De ail o s ai case s uc u e du ing load es (uppe pa ); (
b
) de ail o he s ai case
s uc u e du ing he load es (lowe pa ); (
c
) model o he cons uc ion o an in e io s ai case
made o ibe cemen boa ds in ATENA so wa e; (
d
) localiza ion o c ack ini ia ion on he s ai case
s uc u e in nume ical simula ion; (
e
) ac ual ailu e o he s ai case wi h c ack ma king, ac ual load
on he s uc u e 9.25 kN/m2.
A quad ila e al compu a ional mesh model wi h a compu a ional side size o 10 mm
was chosen as he mac o elemen . The maximum numbe o i e a ions in one compu a ional
s ep was se o 80. The New on–Raphson [
39
] compu a ional me hod was used, in which
he ollowing se o nonlinea equa ions is ob ained by applying he concep o s ep-by-s ep
analysis:
Kp∆p=q− p, (2)
whe e qis he ec o o o al applied join loads, pis he ec o o in e nal join o ces,
∆p
is he de o ma ion inc emen due o loading inc emen , pa e he de o ma ions o he
s uc u e p io o load inc emen ,
Kp
is he s i ness ma ix, ela ing loading inc emen s
o de o ma ion inc emen s.
The po ion on he igh side o Equa ion (2) deno es he o ces ha exis ou side o
equilib ium du ing he load inc emen . This means i ep esen s he o e all load le el a e
he load inc emen is applied, minus he in e nal o ces ha we e p esen a he end o
he p e ious load s ep. Typically, he s i ness ma ix is dependen on s ain, meaning i
is a unc ion o p. Howe e , i is gene ally igno ed du ing he load inc emen o p ese e
Buildings 2023,13, 704 7 o 16
linea i y. Ins ead, he s i ness ma ix is calcula ed based on he alue o p ela ed o he
le el be o e he load inc emen .
Th ee measu ing poin s we e selec ed on he s uc u e o eco d he e ical displace-
men s ( e e ed o as po _2, po _3, and po _4 in he expe imen as shown in Figu e 7.
Buildings 2023, 13, x FOR PEER REVIEW 7 o 16
o ibe cemen boa ds in ATENA so wa e; (d) localiza ion o c ack ini ia ion on he s ai case s uc-
u e in nume ical simula ion; (e) ac ual ailu e o he s ai case wi h c ack ma king, ac ual load on
he s uc u e 9.25 kN/m2.
Figu e 7. Cons uc ion scheme o segmen s inge s ai case o s ai case s uc u e (A is s inge
pa , B–D is s ep suppo )— op, s ai case c oss sec ion—le , on iew— igh .
The loading o he s uc u e in he nume ical simula ion was ca ied ou in s eps as
planned in he expe imen al load es . The a angemen o he load es was iden ical o
he bounda y condi ions in he p oposed expe imen . Possible ho izon al displacemen a
he base o he s ai case was conside ed, while ho izon al and e ical displacemen s a
he uppe pa o he s uc u e we e a oided o nume ical simula ion pu poses (Figu e
6). In nume ical simula ion a a load o in ensi y 3.0 kN/m
2
, he e was no loss o s abili y.
A his load, he e ical displacemen a po _3 was 1.819 mm. The collapse o he s uc u e
occu ed a a load o in ensi y o 7.35 kN/m
2
. Be o e he loss o s abili y, he e ical dis-
placemen was 4.096 mm.
2.2. P oduc ion and Assembly o One-A m S inge S ai case
The s ai case was designed as segmen ed, s inge , s aigh , wi h 9 s eps, wi h con-
s uc ion heigh o 1500 mm, wi h s ai case a m wid h o 900 mm, and s ai case a m incli-
na ion o 30.76°. Wi h i s dimensions, he designed s ai case co esponded wi h he com-
mon U-shaped s inge s ai case wi h 2 ou side s inge s in amily houses; he design was
based on s ai case equa ion 2h + b = l
s
, whe e h is he heigh o a s ai case s ep in mm, b is
he wid h o a s ai case s ep in mm, and l
s
is he leng h o an a e age human s ep in mm.
In he case o he designed s ai case, he conside ed a e age human s ep leng h was as-
sumed o be equal o 630 mm. Fo ma e ial sa ings, he op imized cu ing plan in Figu e
4 was designed in such way ha he amoun o was e du ing he segmen cu ing was
minimized. Indi idual s ai case segmen s we e manually cu by a plunge saw om la ge
cemen ibe boa ds ein o ced by o ganic cellulose ibe s wi h dimensions o 3000 × 1200
mm and hickness o 20 mm and 30 mm.
Segmen s A–D in Figu e 7 we e used o build he s ai case. The s ai case was assem-
bled sys ema ically as shown in Figu e 8a–g. The i s s ep (a) included clamping o wo
segmen s (A) om which he s inge was made using F-shaped hea y du y ba clamps.
Subsequen ly, (b) measu ing and d illing o holes o sc ews in segmen s (B, C, and D)
and (c) measu ing and d illing o holes o sc ews in s inge s (A) we e ca ied ou . In he
nex s ep, (d) s ep suppo s (B, C, and D) we e i ed by sc ews o s inge s (A). In he las
s ep, (e) and ( ) holes we e p ed illed o i ing s eps (E) o s ep suppo s (B, C, and D).
All join s in he s ai case s uc u e we e i ed by sc ews. Conc e e HILTI HUS3-C 6 and
Figu e 7.
Cons uc ion scheme o segmen s inge s ai case o s ai case s uc u e (A is s inge pa ,
B–D is s ep suppo )— op, s ai case c oss sec ion—le , on iew— igh .
The loading o he s uc u e in he nume ical simula ion was ca ied ou in s eps as
planned in he expe imen al load es . The a angemen o he load es was iden ical o
he bounda y condi ions in he p oposed expe imen . Possible ho izon al displacemen a
he base o he s ai case was conside ed, while ho izon al and e ical displacemen s a he
uppe pa o he s uc u e we e a oided o nume ical simula ion pu poses (Figu e 6). In
nume ical simula ion a a load o in ensi y 3.0 kN/m
2
, he e was no loss o s abili y. A
his load, he e ical displacemen a po _3 was 1.819 mm. The collapse o he s uc u e
occu ed a a load o in ensi y o 7.35 kN/m
2
. Be o e he loss o s abili y, he e ical
displacemen was 4.096 mm.
2.2. P oduc ion and Assembly o One-A m S inge S ai case
The s ai case was designed as segmen ed, s inge , s aigh , wi h 9 s eps, wi h cons uc-
ion heigh o 1500 mm, wi h s ai case a m wid h o 900 mm, and s ai case a m inclina ion
o 30.76
◦
. Wi h i s dimensions, he designed s ai case co esponded wi h he common
U-shaped s inge s ai case wi h 2 ou side s inge s in amily houses; he design was based
on s ai case equa ion 2h+b=l
s
, whe e h is he heigh o a s ai case s ep in mm, bis he
wid h o a s ai case s ep in mm, and l
s
is he leng h o an a e age human s ep in mm. In
he case o he designed s ai case, he conside ed a e age human s ep leng h was assumed
o be equal o 630 mm. Fo ma e ial sa ings, he op imized cu ing plan in Figu e 4was
designed in such way ha he amoun o was e du ing he segmen cu ing was minimized.
Indi idual s ai case segmen s we e manually cu by a plunge saw om la ge cemen ibe
boa ds ein o ced by o ganic cellulose ibe s wi h dimensions o 3000
×
1200 mm and
hickness o 20 mm and 30 mm.
Buildings 2023,13, 704 8 o 16
Segmen s A–D in Figu e 7we e used o build he s ai case. The s ai case was assem-
bled sys ema ically as shown in Figu e 8a–g. The i s s ep (a) included clamping o wo
segmen s (A) om which he s inge was made using F-shaped hea y du y ba clamps.
Subsequen ly, (b) measu ing and d illing o holes o sc ews in segmen s (B, C, and D)
and (c) measu ing and d illing o holes o sc ews in s inge s (A) we e ca ied ou . In he
nex s ep, (d) s ep suppo s (B, C, and D) we e i ed by sc ews o s inge s (A). In he las
s ep, (e) and ( ) holes we e p ed illed o i ing s eps (E) o s ep suppo s (B, C, and D). All
join s in he s ai case s uc u e we e i ed by sc ews. Conc e e HILTI HUS3-C 6 and HILTI
HUS3-P 6 sc ews we e used o i ing connec ions. Fo s inge segmen s (A) and s ep
suppo s (B, C, and D), la head hea y du y gal anized sc ews (min. 5
µ
m) wi h leng h
o 60 mm and diame e o 6 mm made om ca bon s eel we e used. Fo sc ew join s o
s eps, sc ews om he same ma e ial wi h a di e en leng h o 40 mm wi h coun e sunk
head we e used. Pho o documen a ion o he whole p oduc ion p ocedu e is shown in
Figu e 8a– . The assembled s ai case was hen pu in o a designed and new-build es ing
polygon o es ing in e io s ai cases made om CLT panels Figu e 8g and was subjec ed
o load es s.
Buildings 2023, 13, x FOR PEER REVIEW 8 o 16
HILTI HUS3-P 6 sc ews we e used o i ing connec ions. Fo s inge segmen s (A) and
s ep suppo s (B, C, and D), la head hea y du y gal anized sc ews (min. 5 µm) wi h
leng h o 60 mm and diame e o 6 mm made om ca bon s eel we e used. Fo sc ew join s
o s eps, sc ews om he same ma e ial wi h a di e en leng h o 40 mm wi h coun e sunk
head we e used. Pho o documen a ion o he whole p oduc ion p ocedu e is shown in
Figu e 8a– . The assembled s ai case was hen pu in o a designed and new-build es ing
polygon o es ing in e io s ai cases made om CLT panels Figu e 8g and was subjec ed
o load es s.
Figu e 8. Assembly o in e io s ai case made om cemen ibe boa ds. (a) Clamping o wo seg-
men s o s inge ; (b) measu ing and d illing o holes o sc ews in s ep suppo s; (c) measu ing and
d illing o holes o sc ews in s inge s; (d) sc ewing s ep suppo s; (e) d illing o holes o sc ews
in ead; ( ) g adual sc ewing o ead; (g) ins alla ion o he s ai case s uc u e in he es polygon.
2.3. P epa a ion and P ocedu e o S a ic Load Tes s
Expe imen al es ing was pe o med o e i y s ai case bea ing capaci y unde load-
ing de ined by s anda d Eu ocode 1: Ac ions on s uc u es - Pa 1-1: Gene al ac ions -
Densi ies, sel -weigh , imposed loads o buildings [20]. Rega ding s a ics, he load es
was pe o med unde he leas a o able condi ions. The s ai case was designed as a
simply suppo ed beam made by 2 s inge s wi h ixed join s in he uppe pa , whe e he
join s we e made wi h 4 s eel gal anized L-ba s wi h a g oo e o 65 × 90/90 wi h h eaded
ods wi h diame e o 10 mm unning h ough s eps, and he mo able suppo was simu-
la ed by a s eel od wi h diame e o 10 mm, as shown in Figu e 9. Two eigh -channel
swi chboa ds we e used o con inual eco ding o e ical displacemen s o he s ai case
s uc u e Uy,i [mm] in ime du ing he expe imen al es s, and he eco ding speed du ing
he load es was 2 Hz. Ve ical displacemen Uy,i o nine measu ing poin s (po _1 o po _9)
was moni o ed by nine po en iome ic mo ion senso s. Du ing he s ai case loading, he
alues o e ical displacemen Uy,I in 1/3, in 1/2, and in 2/3 o he s inge span we e ec-
o ded (Figu e 7). An indi idual senso was placed in he middle o he i h s ep (Figu e
9).
Figu e 8.
Assembly o in e io s ai case made om cemen ibe boa ds. (
a
) Clamping o wo
segmen s o s inge ; (
b
) measu ing and d illing o holes o sc ews in s ep suppo s; (
c
) measu ing
and d illing o holes o sc ews in s inge s; (
d
) sc ewing s ep suppo s; (
e
) d illing o holes o sc ews
in ead; ( ) g adual sc ewing o ead; (g) ins alla ion o he s ai case s uc u e in he es polygon.
2.3. P epa a ion and P ocedu e o S a ic Load Tes s
Expe imen al es ing was pe o med o e i y s ai case bea ing capaci y unde loading
de ined by s anda d Eu ocode 1: Ac ions on s uc u es-Pa 1-1: Gene al ac ions - Densi ies,
sel -weigh , imposed loads o buildings [
20
]. Rega ding s a ics, he load es was pe o med
unde he leas a o able condi ions. The s ai case was designed as a simply suppo ed
beam made by 2 s inge s wi h ixed join s in he uppe pa , whe e he join s we e made
wi h 4 s eel gal anized L-ba s wi h a g oo e o 65
×
90/90 wi h h eaded ods wi h diame e
o 10 mm unning h ough s eps, and he mo able suppo was simula ed by a s eel od
wi h diame e o 10 mm, as shown in Figu e 9. Two eigh -channel swi chboa ds we e used
o con inual eco ding o e ical displacemen s o he s ai case s uc u e U
y,i
[mm] in
ime du ing he expe imen al es s, and he eco ding speed du ing he load es was 2 Hz.
Ve ical displacemen U
y,i
o nine measu ing poin s (po _1 o po _9) was moni o ed by
nine po en iome ic mo ion senso s. Du ing he s ai case loading, he alues o e ical
displacemen U
y,I
in 1/3, in 1/2, and in 2/3 o he s inge span we e eco ded (Figu e 7).
An indi idual senso was placed in he middle o he i h s ep (Figu e 9).
Buildings 2023,13, 704 9 o 16
Buildings 2023, 13, x FOR PEER REVIEW 9 o 16
Figu e 9. P epa a ion o expe imen , in e io s ai case s uc u e be o e loading.
S ai case loading was applied by loading boxes made om OSB boa ds wi hou bo -
oms wi h app oxima e weigh mb = 10.5 kg. The eason o using boxes wi hou bo oms
was o ue modeling o he e ec o con inuous loading on a s ai case s ep. Loading
bags, whose weigh co esponded wi h he loading o indi idual loading phases mb,2 =
35 kg, mb,3 = 30 kg, mb,4 = 22.68 kg, mb,5 = 15.12 kg, we e placed in loading boxes. All loading
bags we e illed wi h pebbles o ac ion 2/4 mm. The o de o placing loading boxes No.
1 o No. 9 was de e mined on he basis o an op imized calcula ion. The aim was o place
loading boxes and loading bags in such an o de ha he cou se o he bending momen
by he applied loading became as simila o he cou se o he bending momen by he
con inuous uni o m loading as possible. The e o e, loading o indi idual s ai case s eps
was pe o med in he o de o 7 h, 2nd, 6 h, 3 d, 8 h, 1s , 5 h, 4 h, 9 h, and load emo al
o he s uc u e was pe o med in he e e se o de . The o de o loading and load e-
mo al is shown in Figu e 7.
The s a ic load es was di ided in o wo phases—loading and load emo al (Figu e
10). The loading and load emo al cycle was pe o med h ee imes. A b eak o 15 minu es
occu ed be ween indi idual phases and be ween indi idual loading s eps, i.e., 1.0 × Vk,
1.3 × Vk, and 1.5 × Vk, whe e Vk is su ace cha ac e is ic alue o e ical uni o m su ace
load o s ai s acco ding o 3.0 kN/m2 de ined acco ding o [20], wi h espec o he na-
ional annex. The b eak was ca ied ou in o de o s abilize he s ai case s uc u e and o
s abilize e ical displacemen s Uy, and o moni o he s uc u e elaxa ion o e ime. The
s ai case was loaded in wo loading cycles ha included moni o ing o he s uc u e e -
ical displacemen Uy and subsequen ly he load was applied up o he s uc u e collapse.
The i s and second loading we e pe o med acco ding o he scheme: Gk → 1.0 × Vk →
1.3 × Vk → 1.5 × Vk → 1.3 × Vk → 1.0 × Vk → Gk, whe e Gk is he cha ac e is ic weigh o he
s uc u e. In he las measu emen , he s uc u e was loaded up o eaching he ul ima e
up u e limi acco ding o he scheme: Gk → 1.0 × Vk → 1.3 × Vk → 1.5 × Vk → g adual
inc ease in loading in mul iples o 0.2 × Vk up o he loss o s abili y, when he s uc u e
collapsed. An o e iew o loading o indi idual s ai case s eps and an o e iew o load-
ing o he whole s uc u e a e desc ibed in Table 3.
Figu e 9. P epa a ion o expe imen , in e io s ai case s uc u e be o e loading.
S ai case loading was applied by loading boxes made om OSB boa ds wi hou
bo oms wi h app oxima e weigh m
b
= 10.5 kg. The eason o using boxes wi hou
bo oms was o ue modeling o he e ec o con inuous loading on a s ai case s ep.
Loading bags, whose weigh co esponded wi h he loading o indi idual loading phases
m
b,2
= 35 kg, m
b,3
= 30 kg, m
b,4
= 22.68 kg, m
b,5
= 15.12 kg, we e placed in loading boxes.
All loading bags we e illed wi h pebbles o ac ion 2/4 mm. The o de o placing loading
boxes No. 1 o No. 9 was de e mined on he basis o an op imized calcula ion. The aim was
o place loading boxes and loading bags in such an o de ha he cou se o he bending
momen by he applied loading became as simila o he cou se o he bending momen by
he con inuous uni o m loading as possible. The e o e, loading o indi idual s ai case s eps
was pe o med in he o de o 7 h, 2nd, 6 h, 3 d, 8 h, 1s , 5 h, 4 h, 9 h, and load emo al o
he s uc u e was pe o med in he e e se o de . The o de o loading and load emo al is
shown in Figu e 7.
The s a ic load es was di ided in o wo phases—loading and load emo al (Figu e 10).
The loading and load emo al cycle was pe o med h ee imes. A b eak o 15 minu es
occu ed be ween indi idual phases and be ween indi idual loading s eps, i.e.,
1.0 ×Vk
,
1.3
×
V
k
, and 1.5
×
V
k
, whe e V
k
is su ace cha ac e is ic alue o e ical uni o m su ace
load o s ai s acco ding o 3.0 kN/m
2
de ined acco ding o [
20
], wi h espec o he
na ional annex. The b eak was ca ied ou in o de o s abilize he s ai case s uc u e and o
s abilize e ical displacemen s U
y
, and o moni o he s uc u e elaxa ion o e ime. The
s ai case was loaded in wo loading cycles ha included moni o ing o he s uc u e e ical
displacemen U
y
and subsequen ly he load was applied up o he s uc u e collapse. The
i s and second loading we e pe o med acco ding o he scheme: G
k→
1.0
×
V
k→
1.3
×
V
k→
1.5
×
V
k→
1.3
×
V
k→
1.0
×
V
k→
G
k
, whe e G
k
is he cha ac e is ic weigh o
he s uc u e. In he las measu emen , he s uc u e was loaded up o eaching he ul ima e
up u e limi acco ding o he scheme: G
k→
1.0
×
V
k→
1.3
×
V
k→
1.5
×
V
k→
g adual
inc ease in loading in mul iples o 0.2
×
V
k
up o he loss o s abili y, when he s uc u e
collapsed. An o e iew o loading o indi idual s ai case s eps and an o e iew o loading
o he whole s uc u e a e desc ibed in Table 3.
Buildings 2023,13, 704 16 o 16
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Disclaime /Publishe ’s No e:
The s a emen s, opinions and da a con ained in all publica ions a e solely hose o he indi idual
au ho (s) and con ibu o (s) and no o MDPI and/o he edi o (s). MDPI and/o he edi o (s) disclaim esponsibili y o any inju y o
people o p ope y esul ing om any ideas, me hods, ins uc ions o p oduc s e e ed o in he con en .