Case S udies in The mal Enginee ing 33 (2022) 101928
A ailable online 15 Ma ch 2022
2214-157X/© 2022 The Au ho s. Published by Else ie L d. This is an open access a icle unde he CC BY-NC-ND license
(h p://c ea i ecommons.o g/licenses/by-nc-nd/4.0/).
Equi alen empe a u e p edic ion o conc e e- illed cold- o med
s eel (CF-CFS) buil -up column sec ions (pa A)
Rohola Rahna a d
*
, H´
elde D. C a ei o
**
, Rui A. Sim˜
oes, Aldina San iago
Uni e si y o Coimb a, ISISE, Depa men o Ci il Enginee ing, Coimb a, Po ugal
ARTICLE INFO
Keywo ds:
Composi e sec ion
CFS buil -Up
2D hea ans e analysis
Empi ical o mula ion
ABSTRACT
This s udy aims o p esen an empi ical o mula ion o p edic equi alen empe a u e o s eel
and conc e e componen s o he inno a i e conc e e- illed cold- o med s eel (CF-CFS) buil -up
column sec ions. This pape (pa A) p esen s a 2-dimensional (2D) ini e elemen modeling
echnique o p edic empe a u e e olu ion h ough he CF-CFS buil -up column sec ions. Hea
ans e analysis was unde aken conside ing exis ing models/da a o he mal p ope ies ( he -
mal conduc i i y and speci ic hea ) o conc e e and s eel as a unc ion o empe a u e. The
esul an hea emissi i y and he con ec i e hea coe icien we e de ined o desc ibe adia ion
and con ec ion. The esul s o ini e elemen modeling we e calib a ed agains expe imen al da a.
The esul s showed a good ag eemen wi h expe imen al da a o bo h s eel and conc e e em-
pe a u e e olu ion. The e o e, he 2D ini e elemen can accu a ely p edic he empe a u e o he
CF-CFS sec ions and can be used as a eliable ool o u he pa ame ic s udy.
1. In oduc ion
Due o i s supe io s uc u al pe o mance in a ious scena ios such as i e, conc e e- illed s eel ubes (CFST) a e widely u ilized in
mul i-s o y buildings. These s uc u al componen s ha e high s uc u al i e pe o mance. Recen ly s udies we e ca ied ou on
applying cold- o med s eel p o iles and ligh weigh conc e e ins ead o ho - olled and no mal conc e e [1,2]. The cold- o med s eel
p o iles ha e ad an ages o e ho - olled p o iles, such as less di icul y in anspo a ion, high s eng h- o-weigh a io, ease o
ab ica ion, less cons uc ion ime, abili y o gene a e a ious c oss-sec ion shapes [3–6]. Unde s anding he beha io o hese columns
subjec ed o acciden al i e ac ion is necessa y u he o enhance he i e pe o mance o such s uc u al membe s. In he las ew
decades, a g ea deal o expe imen al, compu a ional, and analy ical wo k has been done o be e unde s and he beha io o com-
posi e columns when subjec ed o i e [1-15]. Espinos e al. [8] nume ically compa ed he i e esis ance o conc e e- illed s eel ubula
composi e columns and conc e e- illed s eel ubula composi e columns wi h a s eel co e. They calib a ed hei nume ical modeling by
compa ing axial displacemen his o y o expe imen al specimens and nume ical simula ions. Mao e al. [9] in es iga ed he i e
esis ance o conc e e- illed s eel ubula composi e columns. They showed an excellen ag eemen be ween ini e elemen esul s and
expe imen al da a o he ou e su ace o he s eel ube. Howe e , ema kable di e ences we e seen be ween expe imen al and
nume ical esul s o p edic ing he conc e e co e empe a u e. Zhou e al. [10] in es iga ed he conc e e- illed hin-walled ci cula
s eel ubula columns using expe imen al es s and nume ical modeling. Thei ini e elemen modeling app oach showed an accep able
p edic ion. Meng e al. [11] in es iga ed he i e beha io o conc e e- illed s eel columns using expe imen al es s and nume ical
* Co esponding au ho .
** Co esponding au ho .
E-mail add esses: [email p o ec ed], [email p o ec ed] (R. Rahna a d), [email p o ec ed] (H.D. C a ei o).
Con en s lis s a ailable a ScienceDi ec
Case S udies in The mal Enginee ing
jou nal homepage: www.else ie .com/loca e/csi e
h ps://doi.o g/10.1016/j.csi e.2022.101928
Recei ed 22 Janua y 2022; Recei ed in e ised o m 26 Feb ua y 2022; Accep ed 8 Ma ch 2022
Case S udies in The mal Enginee ing 33 (2022) 101928
2
Fig. 1. Geome y de ails o he p o iles and composi e sec ions.
Fig. 2. a) s eel he mal conduc i i y, b) s eel speci ic hea [17,18]], c) conc e e he mal conduc i i y, and d) conc e e speci ic hea [19].
R. Rahna a d e al.
Case S udies in The mal Enginee ing 33 (2022) 101928
3
simula ion. They compa ed he expe imen al esul s wi h he co esponding nume ical model showing a ema kable disag eemen in
axial displacemen s and empe a u e e olu ion.
P io wo k by he au ho s [1,2] demons a ed he comp ession beha io o he CF-CFS column a bo h oom empe a u e and
inc eased empe a u es. E en hough ex ensi e expe imen al and nume ical in es iga ions in o he i e esis ance o composi e col-
umns ha e been ca ied ou , ad anced ools such as ini e elemen analysis a e s ill equi ed o de e mine he empe a u e dis ibu ion
in he c oss-sec ion and, he e o e, o de e mine he i e esis ance composi e columns. Mo eo e , he design p ocedu e o composi e
columns ollowing EN 1994-1-2 [16] is inco po a ed wi h ad anced hea ans e analysis. Mo eo e , he di icul y o EN 1994-1-2
[16] me hodologies (gene al me hod and simpli ied me hod (Annex H)) is o ob ain accu a e empe a u e dis ibu ion in s eel com-
ponen s and laye s o he conc e e sec ion. This pape p esen s a 2D modeling app oach as a e i ica ion ool o u u e s udies (pa B
o his s udy).
2. Fini e elemen modeling
2.1. Geome y de ails o he CF-CFS buil -up sec ions
Cold- o med s eel p o iles wi h c oss-sec ions in he shapes o C, U, and Σ we e used in his wo k as he nume ical models o his
in es iga ion. All o he p o iles ha e a pla e hickness o 1.5 mm. The CF-CFS composi e c oss-sec ions a e p esen ed in Fig. 1. The
es ed CF-CFS composi e sec ions we e ully desc ibed in [2].
2.2. The mal p ope ies
2.2.1. S eel
All p o iles we e made o S280GD +Z s uc u al s eel (nominal yield s eng h o 280 MPa and ul ima e ensile s eng h o 360
MPa). The he mal pa ame e s o his ma e ial ( he mal conduc i i y (λc) and speci ic hea (cp)) we e aken om he expe imen al
s udy pe o med by C a ei o e al. [17,18], whe e he T ansien Plane Sou ce echnique was used. The ob ained expe imen al esul s
a e displayed in Fig. 2a and b.
2.2.2. Conc e e
The he mal conduc i i y (λc) o he conc e e was de ined acco ding o he exp ession p esen ed by he EN1992-1-2 [19]; i in-
cludes lowe and uppe limi s de e mined by Eq. (2). In his s udy, an a e age be ween lowe and uppe limi s was conside ed o he
nume ical models. Fig. 2c depic s he uppe and lowe limi s and hei a e age he mal conduc i i y as a unc ion o empe a u e. The
speci ic hea (cp) was also de ined as a unc ion o empe a u e acco ding o he EN1992-1-2 [19] as shown in Fig. 2d. No e ha he
mois u e con en o 3% was assumed o he conc e e.
{λc=2−0.2451(θ
/
100
) + 0.0107(θ
/
100
)220 ◦C≤θ≤1200 ◦C(lowe limi )
λc=1.36 −0.136(θ
/
100
) + 0.0057(θ
/
100
)220 ◦C≤θ≤1200 ◦C(uppe limi )
(2)
2.3. Nume ical modeling
2D ansien hea ans e analyses we e conduc ed using Abaqus [20] o ob ain he he mal g adien wi hin he composi e
s eel-conc e e c oss-sec ion.
The adia ion and con ec ion we e de ined o simula e he ans e ing empe a u e om he i e o he ex e nal su ace o he
sec ions (Fig. 3), hence de e mining he bounda y condi ions o he hea ans e analysis. The i e’s empe a u e was de ined ac-
co ding o he u nace ai empe a u e based on an expe imen al s udy pe o med by Rahna a d e al. [2]. The esul an hea emis-
si i y o 0.23 was used o ep esen adia ion. A alue o 20 (W/m
2
K) was also used o he con ec i e hea coe icien [2]. The hea
esis ance a he in e ace can be desc ibed using he hea con ac conduc ance pa ame e . The 200 (W/m
2
K) hea con ac conduc-
ances we e de ined o s eel o conc e e con ac . S eel o s eel con ac conduc ances was de ined as 2000 (W/m
2
K). The ini ial ambien
empe a u e was de ined as 20 ◦C.
Mo eo e , physical cons an s such as absolu e ze o empe a u e and he S e an-Bol zmann cons an we e conside ed −273.15 ◦C
Fig. 3. Nume ical modeling.
R. Rahna a d e al.
Case S udies in The mal Enginee ing 33 (2022) 101928
4
and 5.67 ×10
−8
W/(m [2]⋅k [4]), espec i ely. Mo e in o ma ion ega ding he in e ac ion de ini ion is p esen ed in [2]. Fo he
meshing, DC2D4, a 4-node linea hea ans e quad ila e al om Abaqus [20] lib a y, was selec ed o bo h s eel and conc e e
componen s. No e ha he mesh size o conc e e and s eel was conside ed as 0.5 mm.
3. Ve i ica ion o empe a u e e olu ion
In his sec ion, he 2D modeling app oach is e i ied agains expe imen al esul s in [2]. The empe a u e s. ime o speci ic
posi ions on s eel su ace o 2D ini e elemen (cu en s udy) and bo h 3D ini e elemen modeling [2] and expe imen al es s [2] a e
plo ed in Fig. 4. No e ha he empe a u e e olu ion o he mid-heigh le el o he column om he expe imen al s udy [2] was
adop ed o compa ison pu poses. The nume ical esul s ob ained using he 2D hea ans e analysis a e in e y good ag eemen wi h
he expe imen al esul s. The cu en s udy’s 2D hea ans e analysis esul s we e consis en wi h hose om p e ious 3D hea
Fig. 4. Compa ison o expe imen al and ini e elemen esul s o empe a u e his o y on s eel su ace; a) R–2C+2U, b) S–2C+2U, c) R-2Ʃ+2U, d) S-2Ʃ+2U.
R. Rahna a d e al.
Case S udies in The mal Enginee ing 33 (2022) 101928
5
ans e in es iga ions [2]. As shown in Fig. 4a–c, he empe a u e on he s eel su ace o R–2C+2U and R-2Ʃ+2U c oss-sec ions had
lowe empe a u es on poin B (U-channel langes) han hei webs (poin A). This a ia ion is because poin B is loca ed in he web,
which is hinne (no o e lapping s eel pla es).
Fig. 4b shows he esul s o he squa e sec ion S–2C+2U. The ac ual empe a u es a ied, while i was assumed ha all su aces in
Fig. 4b would ha e he same empe a u e due o he sec ion’s squa e shape and equal hickness in poin s A and B. This di e ence in he
expe imen al esul s is because he u nace chambe is di ided in o wo sec ions. The e a e no elec ical esis ances in he a ea whe e
he wo chambe s link [2], which means ha he wo sides o he column we e somewha less exposed o hea adia ion. Fig. 4d shows a
close ag eemen be ween expe imen al esul s and he 2D hea ans e analysis o S-2+2U.
The conc e e co e empe a u e his o y cu es we e compa ed o he empe a u e cu es o he 2D hea ans e analysis, which a e
depic ed in Fig. 5. O e all, all con igu a ions we e ound in good ag eemen , esul ing in ini e elemen modeling ha is bo h accu a e
and eliable. The maximum conc e e co e empe a u es di e ence ob ained om expe imen al and nume ical 2D models is 6%, 9%,
1%, and 8% o R-2+2U, S-2+2U, R-2Ʃ+2U, and S-2Ʃ+2U. The modes di e ences in he empe a u e be ween he ini e elemen
models and he expe imen al specimens may be due o a ia ions in he mal p ope y alues. No e ha he mois u e con en o he
conc e e in ill was assumed uni o m h oughou he ini e elemen . In con as , he conc e e in ill in he c oss-cen e sec ion o he
Fig. 5. Compa ison o expe imen al and ini e elemen esul s o empe a u e his o y in he conc e e co e; a) R–2C+2U, b) S–2C+2U, c) R-2Ʃ+2U, d) S-2Ʃ+2U.
R. Rahna a d e al.

Case S udies in The mal Enginee ing 33 (2022) 101928
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expe imen al specimens may be highe han he mois u e con en o he conc e e in ill in he a ea adjacen o he s eel ube.
In sum, he 2D modeling echniques could p ecisely p edic he s eel empe a u e and he gene a ed he mal g adien in he
conc e e in ill.
4. Conclusions and u u e wo k
A 2D nume ical modeling o hea ans e analysis was de eloped o in es iga e he empe a u e e olu ion o composi e sec ions.
The composi e sec ions we e made o cold- o med s eel buil -up sec ions and illed wi h conc e e. The esul s o he 2D modeling
app oach showed a high accu acy agains expe imen al and 3D ini e elemen esul s in [2]. The 2D modeling app oach had he
ad an age o being less complex han he 3D app oach p esen ed by au ho s [2]. The e o e, he adop ed simula ion echniques will be
used in u u e pa ame ic s udies as a eliable e i ica ion ool o he de elopmen o empi ical o mula ions (pa B o his s udy)
capable o es ima ing he empe a u e e olu ion o s eel and conc e e pa s o he composi e sec ion o u u e applica ion wi h exis ing
s uc u al design me hodologies p esen ed in he EN 1994-1-2 [19].
CRediT au ho ship con ibu ion s a emen
Rohola Rahna a d: Nume ical modeling. Fo mula ion. Fo mal analysis and in e p e a ion o he esul s. W i ing he o iginal d a .
H´
elde D. C a ei o: Funding acquisi ion. Supe ision. Fo mal analysis and in e p e a ion o he esul s. W i ing – e iew, and edi ing.
Rui A. Sim˜
oes: Supe ision. W i ing – e iew, and edi ing. Aldina San iago: W i ing – e iew, and edi ing.
Decla a ion o compe ing in e es
The au ho s decla e ha hey ha e no known compe ing inancial in e es s o pe sonal ela ionships ha could ha e appea ed o
in luence he wo k epo ed in his pape .
Acknowledgmen s
This wo k is inanced by na ional unds h ough FCT - Founda ion o Science and Technology, unde g an ag eemen 2021.06528.
BD a ibu ed o he 1
s
au ho and unde he g an ag eemen 2020.03588.CEECIND a ibu ed o he 2
nd
au ho .
The au ho s g a e ully acknowledge he Po uguese Founda ion o Science and Technology (FCT) o i s suppo unde he
amewo k o he esea ch p ojec PTDC/ECI-EGC/31858/2017 - INNOCFSCONC - Inno a i e hyb id s uc u al solu ions using cold-
o med s eel and ligh weigh conc e e ", inanced by FEDER unds h ough he Compe i i i y Fac o s Ope a ional P og amme-
COMPETE and by na ional unds h ough FCT, and PCIF/AGT/0062/2018 – INTERFACESEGURA – Segu ança e Resiliˆ
encia ao Fogo
das Zonas e In e ace U bana-Flo es al, inanced by FCT h ough Na ional unds.
This wo k was pa ly inanced by FCT/MCTES h ough na ional unds (PIDDAC) unde he R&D Uni Ins i u e o Sus ainabili y and
Inno a ion in S uc u al Enginee ing (ISISE), unde e e ence UIDB/04029/2020.
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