Hyd o he mal pe o mance o wooden beam
on solid mason y wi h capilla y-ac i e
in e nal insula ion
Lukas Sukop1
*
, and Milan Os y1
1Vysoké učení echnické B ně, Fakul a s a ební, Ús a pozemního s a i els í, Ve eří 331,
60200 B no
Abs ac . Wi h he inc easing equi emen s o he ene gy
pe o mance o buildings, he e is a demand o in e nal
insula ion sys ems in buildings whe e i is no possible o
apply an ex e nal insula ion sys em o legisla i e easons.
Cu en ly, he e has been an upsu ge in he de elopmen o
di usion-open insula ion ma e ials whose p ope ies can
compensa e o he isks o damage o solid mason y walls
insula ed wi h adi ional di usion-closed in e nal insula ion
sys ems. The p ope ies o di usion-open sys ems a e al eady
well known. This pape ocuses on he simula ion o he
he mal mois u e beha iou o a de ail o a imbe beam
embedmen in a wall wi h capilla y ac i e he mal insula ion
in cold clima ic condi ions o Cen al Eu ope.
1 In oduc ion
In ecen yea s, he e has been an inc ease in ene gy pe o mance equi emen s o
buildings. One way o educe he ene gy pe o mance o a building is o imp o e he
he mal pe o mance o he building en elope. Typically, wall insula ion is ca ied
ou by means o an ex e nal insula ion sys em. This solu ion is gene ally conside ed
sa e and is commonly used in p ac ice. The e a e a la ge numbe o his o ic buildings
in Cen al Eu ope which can be conside ed as cul u al he i age. In o de o p ese e
aluable his o ic acades, he applica ion o an in e nal insula ion sys em is o en he
only way o imp o e he he mal pe o mance o solid mason y walls. The applica ion
o in e nal insula ion in his o ic buildings can educe hea ing ene gy consump ion by
30 % - 40 % [1]. In e nal insula ion sys ems a e one o he mos isky insula ion
me hods and signi ican ly al e he he mal and mois u e beha iou o he s uc u e.
*
Co esponding au ho : [email p o ec ed]
E3S Web o Con e ences 550, 01036 (2024)
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© The Au ho s, published by EDP Sciences. This is an open access a icle dis ibu ed unde he e ms o he C ea i e
Commons A ibu ion License 4.0 (h ps://c ea i ecommons.o g/licenses/by/4.0/).
In a la ge numbe o his o ic buildings in Eu ope, ceilings a e made up o imbe
beams suppo ed on solid b ickwo k. The du abili y and pe o mance o embedded
imbe elemen s a e la gely dependen on mois u e. The applica ion o an in e nal
insula ion sys em can expose he s uc u e and he embedded imbe elemen s o a
signi ican isk o mois u e damage [2-4]. These isks need o be p ope ly assessed
and he co ec insula ion s a egy selec ed. The isks o damage o he ends o imbe
beams can be educed by hea ing he imbe elemen s, o example wi h hea ing cables
o by applying ma e ials wi h highe he mal conduc i i y [5]. Wind-d i en ain is an
impo an sou ce o mois u e in mason y.
Mois u e ing ess in o he wall is in luenced by he ex e nal inish, mo e
speci ically he abili y o he ende o anspo mois u e. High WDR loads on he
pe ime e load-bea ing walls can lead o an inc ease in mois u e a he ends o he
imbe beams, po en ially damaging hem [6]. Mould can de elop which, amongs
o he hings due o he elease o spo es, can ad e sely a ec he indoo ai quali y
and pose heal h isks o he occupan s o he building. Ro leads o biological
decomposi ion o he wood and a ec s i s mechanical p ope ies. Walls wi h in e nal
insula ion should be p o ec ed agains he e ec s o WDR by app op ia e su ace
ea men o o he p o ec i e elemen s [7].
The ends o imbe beams can be p o ec ed om mois u e by aising hei
empe a u e, which inc eases he po en ial o d ying ou . A la ge numbe o s udies
dealing wi h imbe beams a e based on nume ical simula ions using 2D models. In a
s udy [8] i was shown ha he use o 2D models is app op ia e in assessing he isk
o mois u e damage o imbe beams o di e en ypes o cladding. 2D models we e
ound o be inapp op ia e when e alua ing he e ec i eness o ac i e hea ing o aise
he end empe a u e o a imbe beam. In he 2D models, he wid h o he imbe beam
is assumed o be he same as he wid h o he wall. In he case o he obse a ion o
he he mal and mois u e beha iou o he c i ical de ail, he 2D models show only
small de ia ions om he 3D models in empe a u e and mois u e con en . Fo ac i e
hea ing o he end o he wooden beam, he wid h plays an impo an ole. The eal
beam wid h is much smalle compa ed o he mason y wid h.
In his s udy, changes in he he mal mois u e beha iou o he end o he imbe
beam a se e al c i ical poin s a e p esen ed as a unc ion o he hickness o he
insula ion ma e ial. The modelled wall is insula ed wi h a di usion-open sys em wi h
capilla y-ac i e calcium silica e-based he mal insula ion. The model is simpli ied and
se es as a p epa a ion o a mo e de ailed analysis based on expe imen al
measu emen s and nume ical s udies. Ex e nal and in e nal su ace ea men s and he
e ec o wind-d i en ain a e neglec ed. The ex e io bounda y condi ions co espond
o he cold Eu opean clima e.
2 Me odology
The modelled wall co esponds o a ypical b ick wall o his o ical buildings in he
Czech Republic. The hickness o he wall is 440 mm. A wooden beam wi h a heigh
o 200 mm is placed in he mason y. The wid h o he wooden beam is no conside ed
due o he simpli ica ion o he model in o 2D. The leng h o he wooden beam is 150
mm behind he inne ace o he mason y. The imbe beam is placed in a 40 mm hick
ai pocke in bo h ho izon al and e ical di ec ions. The ai gap a ound he beam
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p e en s di ec con ac be ween he imbe and he mason y o p e en capilla y
anspo o mois u e in o he imbe beam.
The nume ical simula ion was pe o med using DELPHIN 6.1.5 so wa e [9].
Fou models o he wooden beam we e c ea ed. The i s model ( e e ence wall)
ep esen s he si ua ion wi hou he applica ion o he mal insula ion. Fo he
emaining 3 models, he applica ion o an in e nal insula ion sys em wi h capilla y
ac i e calcium silica e based he mal insula ion was conside ed. This he mal
insula ion has he abili y o edis ibu e mois u e owa ds he in e io . The o ma ion
o a condensa ion plane is assumed o occu a ound he adhesi e mo a , i.e. a he
con ac be ween he he mal insula ion and he b ickwo k. Models wi h in e nal
insula ion di e in he hickness o he he mal insula ion. The es ed he mal
insula ion hicknesses a e 50 mm, 100 mm and 200 mm. The adhesi e mo a
hickness is 10 mm. The obse ed c i ical poin s a ound he end o he imbe beam
(A, B, C) a e shown in Figu e 1. To obse e he changes in empe a u e and humidi y
pa e ns due o he applica ion o he insula ion sys em a he poin no a ec ed by he
cu a u e o he empe a u e and humidi y ield, poin s D, E, F we e de ined. In his
s udy, only he esul s o poin s A, B, C and D a e p esen ed.
Fo he ou e bounda y condi ions, clima e da a om he DELPHIN 6.1.5
da abase was used. This is he model yea o he ci y o Kassel, Ge many. The e ec
o he WDR has been neglec ed in he calcula ions. Indoo bounda y condi ions we e
also impo ed om he da abase in he p og am co esponding o he s anda d indoo
clima e acco ding o DIN 4108-3 o 2001. The indoo empe a u e is 20 °C and he
ela i e humidi y is 50 %. A wall wi hou in e nal insula ion has a hea ans e
coe icien alue o app oxima ely 1.467 W/m2K, a wall insula ed wi h 50 mm o
in e nal insula ion has 0.548 W/m2K, a wall wi h 100 mm o insula ion has 0.340
W/m2K and a wall wi h 200 mm o insula ion has a hea ans e coe icien alue o
0.194 W/m2K.
Fig. 1. Schema ic ep esen a ion o he compu a ional domain o a wooden beam placed on a
wall wi h in e nal insula ion wi h he s udy poin s ma ked.
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3 Resul s
3.1 Rela i e humidi y
In he esul s, one yea is p esen ed o all 4 models o wooden beam placemen wi h
and wi hou in e nal wall insula ion. The simula ion was se o 7 yea s o achie e a
quasi-s eady s a e. The quasi-s eady s a e was eached a e 5 yea s o simula ion.
Figu es 2- 5 ep esen he mois u e p o iles o each wall wi hou and wi h in e nal
he mal insula ion.
Fig. 2. Rela i e humidi y p o ile o a wall wi h an embedded wooden beam wi hou in e nal
insula ion.
Fig. 3. Rela i e humidi y p o ile o he wall wi h embedded wooden beam wi h 50 mm hick
in e nal insula ion.
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Figu es 3 - 5 show he changes in he mois u e beha iou o he s udied de ail.
Be ween he he mal insula ion and he mason y wall, he o ma ion o he assumed
condensa ion plane can be seen. The esul ing condensa e should be edis ibu ed by
he capilla y ac i e he mal insula ion owa ds he in e io . Fu he mo e, he e ec o
he in e nal insula ion on he inc ease o he ela i e humidi y in he a ea o he
ex e nal ace o he mason y is e iden . As he hickness o he he mal insula ion
Fig. 4. Rela i e humidi y p o ile o he wall wi h embedded wooden beam wi h 100 mm hick
in e nal insula ion.
Fig. 5. Rela i e humidi y p o ile o he wall wi h embedded wooden beam wi h 200 mm hick
in e nal insula ion.
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inc eases, he ela i e humidi y inc eases, especially in he a ea 5 cm om he ou e
ace o he mason y owa ds he in e io . This inc ease in humidi y could po en ially
inc ease he isk o damage o he ex e nal ace o he mason y due o eeze- haw
cycles. The igu es showing he ela i e humidi y p o iles show he e ec o he
educ ion in ela i e humidi y wi h he applica ion o capilla y ac i e in e nal
insula ion a ound he imbe beam.
Mo e de ailed esul s a e p esen ed in he ollowing g aphs. Figu e 5 shows he
ela i e humidi y p o ile a he pos ula ed c i ical poin A o e a pe iod o one yea .
The highes ela i e humidi y alue (78.3%) was obse ed o he uninsula ed wall.
The lowes RH alue (75,2 %) was obse ed o he wall wi h 200 mm hick he mal
insula ion. As he hickness o he he mal insula ion inc eases, he maximum RH
alues a poin A dec ease.
Figu e 6 shows he ela i e humidi y a he su ace o he imbe beam a he poin
o inse ion on he mason y. The lowes ela i e humidi y alue was eco ded o he
uninsula ed wall. Fo he insula ed walls, an inc ease in he maximum ela i e
humidi y alue was obse ed a poin B in all cases. The maximum RH alues o he
insula ed walls showed li le di e ence.
Fig. 5. Rela i e humidi y a assessmen poin A o a wall wi hou in e nal insula ion and wi h
in e nal insula ion hicknesses o 50 mm, 100 mm and 200 mm.
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Fig. 7. Rela i e humidi y a assessmen poin C o a wall wi hou in e nal insula ion and wi h
in e nal insula ion hicknesses o 50 mm, 100 mm and 200 mm.
Fig. 6. Rela i e humidi y a assessmen poin B o a wall wi hou in e nal insula ion and wi h
in e nal insula ion hicknesses o 50 mm, 100 mm and 200 mm.
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The ela i e humidi y a poin C (Fig. 7) shows a e y simila beha iou o poin
A. As a poin A, he maximum ela i e humidi y alue dec eased wi h inc easing
hickness o he he mal insula ion. Fo he uninsula ed wall, he maximum RH alue
was ound o be close o 80%. The lowes RH alue (75,01 %) was eco ded o he
model wi h 200 mm o he mal insula ion hickness. Figu e 8 shows he ela i e
humidi y on he inne su ace o he wall.
The highes ela i e humidi y alue was eco ded o he wall wi hou he mal
insula ion. Despi e he abili y o he capilla y ac i e he mal insula ion o edis ibu e
condensed mois u e in o he i e io , a dec ease in ela i e humidi y a he inne su ace
can be obse ed. As he hickness o he he mal insula ion inc eases, he ela i e
humidi y a he su ace dec eases and shows less a ia ion h oughou he yea . Wi h
inc easing hickness o he mal insula ion, in gene al, in all cases, smalle luc ua ions
in ela i e humidi y can be obse ed o e he yea .
Fig. 8. Rela i e humidi y a assessmen poin D o a wall wi hou in e nal insula ion and wi h
in e nal insula ion hicknesses o 50 mm, 100 mm and 200 mm.
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3.1 Tempe a u e
Figu es 9 - 12 show he empe a u e p o iles o he indi idual modelled walls. The
empe a u e p o iles show ha he applica ion o in e nal he mal insula ion esul s in
cooling o he mason y s uc u es. The empe a u e iso he ms a e shi ed owa ds he
in e io and he cooling e ec o he mason y is ampli ied wi h inc easing hickness
o he he mal insula ion.
Fig. 9. Tempe a u e p o ile o a wall wi h an embedded wooden beam wi hou in e nal
insula ion.
Fig. 10. Tempe a u e p o ile o he wall wi h embedded wooden beam wi h 50 mm hick
in e nal insula ion.
E3S Web o Con e ences 550, 01036 (2024)
Young Scien is 2024
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