Modelling o bol ed join s in i e
using he componen -based ini e elemen me hod
Ba uhan De 1 | F an išek Wald1 | Ma in Vild2
1 In oduc ion
The beha iou o he connec ions is equi ed o be accu-
a ely analysed o p edic he i e cha ac e is ics o a s uc-
u e. The s uc u al s eel connec ions a ele a ed empe -
a u e can be designed by expe imen al, cu e i ing,
analy ical and nume ical models. Expe imen al i e es s
a e qui e expensi e o ep esen he beha iou o each
ype o join s and he e a e size limi a ions o exis ing u -
naces o es he connec ions.
The analy ical modelling o componen s o connec ions a e
well de eloped o all connec o s, bol s, welds, ancho
bol s e c. EN 1993-1-8:2006 [1] s anda dised he equa-
ions o p edic he esis ance and s i ness o componen s
a ambien empe a u e. Fo i e design o s eel connec-
ions, EN 1993-1-2:2005 [2] p oposes educ ion ac o s
o ca bon s eel, bol s and welds.
Fini e elemen model is a gene al me hod commonly used
o connec ion analysis. The solid ini e elemen models
can simula e he beha iou o s eel connec ions a high
empe a u es. Howe e , he cos o simula ion ime and
s o age size make solid models imp ope o design s eel
connec ions in i e. Shell elemen s a e good al e na i es
o modelling o s eel connec ions.
The Componen based Fini e Elemen Me hod (CBFEM) is
a n me hod o analyse and design connec ions o s eel
s uc u es in i e. CBFEM model combines ad an ages o
gene al ini e elemen s me hod and s anda d me hod o
componen s [3]. I is able o model mos o join ypes and
p o ide s uc u al enginee s clea in o ma ion abou s ess
and s ain o indi idual componen s a ambien empe a-
u e. I is simple and as o p edic sa e esul s in ime
compa able o cu en solid ini e elemen models. Wald
e . al [4] p esen ed benchma k cases o i s alida ion and
e i ica ion o a ious s uc u al s eel join s and connec-
ions a ambien empe a u e. Each benchma k case
shows esul s om he analy ical model acco ding o de-
sign s anda ds ollowed by e e ences o labo a o y expe -
imen s, alida ed models, and nume ical expe imen s.
Howe e , he CBFEM is needed o be e i ied and alida ed
in o de o be su e i i is possible o use i o design s eel
connec ions a ele a ed empe a u e in i e.
The e i ica ion and alida ion p ocedu e a e an in eg al
pa o any ini e elemen analyses. The p ocedu e is
checking he so wa e and he use by designe . The e i-
ica ion and alida ion p ocedu e we e based on he p in-
ciples p oposed by Wald e al. [5]. Valida ion compa es
he analy ical and nume ical solu ion wi h he expe i-
men al da a whe eas, e i ica ion uses compa ison o
compu a ional solu ions wi h highly accu a e analy ical o
nume ical solu ion.
The pape p esen s he esul s o he e i ica ion and al-
ida ion o CBFEM o modelling o bol ed s eel join s a el-
e a ed empe a u es. I compa es he esul s o hand cal-
cula ions acco ding o EN1993-1-2:2005 wi h he esul s
o CBFEM [6]. Then, expe imen al s udies we e used o
alida e bol ed lap join s and T-s ubs models c ea ed in
shell model.
ORIGINAL ARTICLE
Abs ac
This pape p esen s a s udy using he componen -based ini e elemen me hod o
analyze he beha io bol ed join s in i e. The model was e i ied and alida ed on
analy ical and expe imen al esul s a ele a ed empe a u e. In his wo k, he pla es
a e modelled using shell elemen s and he bol is ep esen ed by non-linea sp ings.
The elemen s a e analyzed by geome ically and ma e ially nonlinea analysis wi h
impe ec ions (GMNIA). Consequen ly, he me hod used in his wo k can gi e ea-
sonable esul s o p edic he beha io o join s a ele a ed empe a u e. I is p e-
dic ing he esis ance and he s i ness o design o s eel s uc u e a ele a ed em-
pe a u e by 3D model wi h membe s ep esen ed by 1D o 2D elemen s.
Keywo ds
CBFEM, bol ed join s, i e, shell elemen , alida ion, e i ica ion.
Co espondence
Ba uhan De
Czech Technical Uni e si y in P a-
gue
Tháku o a 7
16629 P ague 6
Email: [email p o ec ed] .cz
1 Czech Technical Uni e si y, P a-
gue, Czech Republic
2 B no Uni e si y o Technology,
B no, Czech Republic
P oceedings
in ci il enginee ing
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use and dis ibu ion in any medium, p o ided he o iginal wo k is p ope ly ci ed, he use is non-comme cial and no modi ica ions o
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h ps://doi.o g/10.1002/cepa. 2485 wileyonlinelib a y.com/jou nal/cepa 2103
2 CBFEM
2.1 Gene al Desc ip ion
CBFEM model decomposes he whole join in o sepa a ed
componen s - s eel pla es, welds, bol s, ancho s and con-
c e e block. Each componen has i s own analysis model
[6]:
- 2D shell elemen s o s eel pla es
- Nonlinea sp ings o bol s and ancho s
- con ac elemen s be ween pla es in connec ions.
The model [6] pe o ms wo ypes o analysis: geome i-
cally linea analysis wi h ma e ial and con ac nonlinea i-
ies o s ess and s ain analysis and eigen alue analysis
o de e mine he possibili y o buckling.
2.2 Ma e ial Model and Elemen Types
The pla es in a e modelled wi h elas ic-plas ic ma e ial
wi h a nominal yielding pla eau slope as an-1 (E/1000) ac-
co ding o EN1993-1-5:2005 [7]. The ma e ial beha iou
is based on he on Mises yield c i e ion. A ele a ed em-
pe a u e, ma e ial deg ada ion o s eel pla es, bol s and
welds a e a ailable acco ding o EN 1993-1-2:2005 [2].
The CBFEM model uses 4-node quad angle shell elemen s
o model he pla es o s eel connec ions. E e y node con-
side s 6 deg ees o eedom ha a e 3 ansla ions and
o a ions. The s anda d penal y me hod is used o mod-
elling con ac be ween pla es. The penal y s i ness is con-
olled by a heu is ic algo i hm du ing he nonlinea i e a-
ion o ge a be e con e gence.
2.3 Failu e Types
In his s udy, bol ed lap join s and T-s ubs a e modelled
using CBFEM. The main ailu e modes o bol ed lap join s
a e bol s in shea and bea ing ailu e acco ding o he
s anda d EN 1993-1-8:2006 [1]. Th ee modes o collapse
a e conside ed: 1. mode wi h ull yielding o he lange, 2.
mode wi h wo yield lines by web and ac u e o he bol s,
and 3. mode o ac u e o he bol s.
The CBFEM model conduc s checks o he ollowing com-
ponen s:
- he plas ic s ain in pla es,
- he bol s esis ance in shea , ension, and a com-
bina ion o ension and shea ,
- he welds esis ance.
The model p opo ionally inc eases all load componen s
un il one o he included ailu es is no eached. S ain is
ecommended o be limi ed o 5 % in EN 1993-1-5. The
analysis s ops when he pla es each o 5% plas ic limi
s ain. Fu he mo e, he bol s and welds a e checked indi-
idually acco ding o EN1993-1-8:2006 and EN1993-1-
3:2005 o mulas. Fo bol ´s esis ance is expec ed maxi-
mum allowed plas ic s ain εlim as 25 % o elonga ion o
ac u e o bol acco ding o EN ISO 898-1 [8].
3 Ve i ica ion and Valida ion
The main componen s o bol ed join s a e bol s in ension
bol s in shea and pla e bea ing. The e o e, bol ed lap
join s and T-s ubs in ension we e chosen o e i ica ion
and alida ion. The expe imen al esul s we e aken om
ollowing s udies; bol ed lap join [9] and T-s ubs [10] o
alida ion o CBFEM. Indi idual componen s a e checked
acco ding o EN 1993-1-8:2006 [1] and CBFEM esul s
we e compa ed o e i ica ion.
3.1 Bol ed Lap Join s in Fi e
In he s udy [9], he nume ical and expe imen al s udy
we e ca ied ou on bol ed lap join s a ele a ed empe a-
u e. The co e and connec ed pla ed we e ab ica ed om
a single s eel pla e, g ade S355. The specimens we e
es ed a 3 di e en nominal empe a u e θ le els,
namely, a ambien empe a u e 20 °C and ele a ed ones
400 °C and 600 °C. The de ails o es specimen and he
model a e shown in Figu e 1. The hickness o inne and
co e pla es a e 8 mm and 16 mm, espec i ely.
Figu e 1. De ails and modelling o he bol ed lap join
The analy ical esis ance o es ed bol ed lap join s we e
p edic ed p e iously in acco dance wi h EN1993-1-
8:2006, conside ing he educ ion ac o s o ca bon s eel
and bol s a ele a ed empe a u es p esen ed in EN1993-
1-2:2005. To show he p edic ion o he CBFEM model, e-
sul s o he s udies a e plo ed in Figu e 2 compa ing e-
sis ances by CBFEM and analy ical model. The esul s
show ha he di e ence o he wo calcula ion me hods is
up o 10 %.
Figu e 2. Ve i ica ion o CBFEM model on analy ical one
– bol ed lap join
20°C
400°C
500°C
600°C
700°C
y = 0.9263x
R² = 0.9998
0
20
40
60
80
100
120
020 40 60 80 100 120 140
Resis ance by CBFEM [kN]
Resis ance by analy ical model [kN]
2104
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Figu e 2. shows a compa ison o he esis ance alues p e-
dic ed by he CBFEM and expe imen s a 20°C, 400°C and
600°C. The CBFEM model is in e y close ag eemen wi h
he expe imen al esul s.
Figu e 3. Valida ion o CBFEM model – bol ed lap join
The ailu e mode obse ed in expe imen s was bol s in
shea a each empe a u e le el. The CBFEM model ob-
ained he same ailu e mode as shown in Figu e 4. The
bol s eached o shea ul ima e capaci y be o e he 5 %
plas ic s ain occu s in he pla es.
Figu e 4. The plas ic s ain in bol ed lap join be o e he
bol ailu e in shea by CBFEM model a ele a ed empe -
a u e
3.2 T-s ubs in i e
Ba a a e . al [10] s udy expe imen ally he beha iou o
he welded T-s ub specimen exposed o s a ic loading, a
ambien and ele a ed empe a u es The s udy includs T-
s ub specimens wi h h ee di e en hicknesses o lange
(𝑡𝑓= 10 mm, 15 mm and 20 mm) a 20°C, 500°C and
600°C. M20 bol s, g ade 8.8 was used o as en T-s ub
specimens wi h he langes (𝑡𝑓= 10 mm and 15 mm), while
he 20 mm lange is connec ed using M24, g ade 10.9
bol s.
Figu e 5. De ails o he T-s ub specimens
The de ails o es specimens and impo an dimensions
a e shown in Figu e 5. The nominal alues o majo cha -
ac e is ics o specimens a e summa ised in Table 1.
Table 1 T-s ubs geome ical cha ac e is ics
Specimen
𝒕𝐩
𝒃𝐩
𝒉𝐩
c
n
m
FL-10
10
105
170
110
30
52.5
FL-15
15
105
170
110
30
52.5
FL-20
20
105
185
120
32.5
52.5
Fi e design esis ances e alua ed by CBFEM we e com-
pa ed wi h esul s o analy ical models including h ee di -
e en ailu e modes p oposed by EN 1993-1-8:2006 [1].
I can be seen ha e y good ag eemen obse ed be-
ween he CBFEM and analy ical esul s in Figu e 6. The
di e ence is o all hickness and empe a u e less han
11 %.
Figu e 6. Ve i ica ion o CBFEM model on componen
me hod - T-s ubs a ambien and ele a ed empe a u es
The compa ison o he i e esis ance o T-s ubs wi h di -
e en lange hickness a e shown g aphically o see he
di e ence be ween CBFEM esul s and es da a in Fig-
u e 7. CBFEM esul s is su icien ly conse a i e in e ms
o measu ed i e esis ance.
148.6
110.8
32.7
111.75 106.4
29.7
0
20
40
60
80
100
120
140
160
20 400 600
Resis ance [kN]
Tempe a u e [°C]
Expe imen
CBFEM
y = 0.9542x
R² = 0.9851
0
50
100
150
200
250
300
350
400
450
0100 200 300 400 500
Resis ance by CBFEM [kN]
Resis ance by analy ical models [kN]
2105
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Figu e 7. Valida ion o CBFEM model on expe imen s - T-
s ubs a ambien and ele a ed empe a u es
Ba a a e al. [10] s a ed ha he specimen wi h 15 mm o
lange hickness ailed due o he bol ac u e a 600°C.
The CBFEM check was also ended up due o he bol ac-
u e when he plas ic limi s ain eaches o only 0.7 % as
shown in Figu e 8.
Figu e 8. The plas ic s ain in T-s ub (15 mm) a 600°C
be o e he bol ailu e by CBFEM model
The 10 mm hickness o specimens a 500°C and 600°C,
he de elopmen o he plas ic hinges was i s ly obse ed
du ing he es s [10]. As indica ed in Figu e 9, he lange
eached o 5% plas ic limi s ain while he bol s s ill ha e
20% mo e capaci y o esis he load. Fu he mo e, simila
ailu e modes we e obse ed o he specimens wi h 20
mm hickness and CBFEM cap u ed he ailu e modes co -
ec ly.
Figu e 9. The limi ing plas ic s ain in T-s ub (10 mm) a
500°C by CBFEM model
4 Conclusion
The s udy p esen s CBFEM models o bol ed lap join and
T-s ub a di e en empe a u e le el. Design esis ances
a high empe a u es calcula ed by CBFEM a e compa ed
wi h esul s o analy ical model and expe imen s. To in-
es iga e he di e en componen s o s eel join s bol ed
lap join s and T-s ubs a e used o e i ica ion and alida-
ion o CBFEM model. Two di e en bol g ades a e s udied
in shea and ension a ele a ed empe a u es. The com-
pa ison o he esis ances ob ained by Eu ocode and
CBFEM indica ed ha he CBFEM p o ides sa e esis ance
alues a ele a ed empe a u es design enginee s. Since
he R-squa ed alues a e highe han 0.98 o bo h cases,
he CBFEM can be conside ed eliable me hod ins ead o
analy ical models o s uc u al i e designe s. Finally, he
CBFEM models a e alida ed by he expe imen al esul s.
The expe imen al esul s a e in e y close ag eemen wi h
he CBFEM esul s and he p edic ed ailu e mode closely
esembled ha obse ed in he expe imen s. I can be
concluded ha he CBFEM is well condi ioned o calcula e
he i e esis ance o bol ed join s.
Acknowledgemen
This esea ch is suppo ed by he g an o Czech Technical
Uni e si y in P ague SGS22/144/OHK1/3T/11.
Re e ences
[1] EN1993-1-8 (2006), Eu ocode 3: Design o s eel
s uc u es - Pa 1-8: Design o join s, CEN, B ussels.
[2] EN-1993-1-2 (2005), Eu ocode 3: Design o S eel
S uc u es, Pa 1.2, Gene al Rules, S uc u al Fi e
Design Eu opean Commi ee o S anda diza ion,
B ussels.
[3] Šaba ka, L.; Wald, F.; Kabeláč, J.; Kolaja, D.; Po-
spíšil, M. (2015) S uc u al Analysis and Design o
S eel Connec ions Using Componen -Based Fini e El-
emen Model. Jou nal o Ci il Enginee ing and A chi-
ec u e 9 895-901, doi: 10.17265/1934-
7359/2015.08.002.
0
50
100
150
200
250
300
350
400
450
500
510 15 20 25
Resis ance [kN]
Flange hickness [mm]
Expe imen
CBFEM
2106
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[4] Wald, F.; Šaba ka, L.; Baje , M.; Kozich M.; Vild M.;
Gulubia niko K.; Kabelac J.; Ku iko a M. (2021)
Componen -based Fini e Elemen Design o S eel
Connec ions, Czech Technical Uni e si y P ague,
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h ps://www.ideas a ica.com/suppo -cen e /gen-
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[7] EN1993-1-5 (2006), Eu ocode 3: Design o s eel
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u al elemen s, CEN, B ussels.
[8] EN ISO 898-1 (2013), Mechanical p ope ies o as-
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Bol s, sc ews and s uds wi h speci ied p ope y clas-
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