SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 23 | NUMBER: 1 | 2023 | JUNE
© 2023 VSB - TECHNICAL UNIVERSITY OF OSTRAVA FACULTY OF CIVIL ENGINEERING 12
ON DEVELOPMENT OF NUMERICAL RESISTANCE MODELS
OF THIN-WEB STEEL GIRDERS
Vi ali NADOLSKI 1, Jana MARKOVÁ 1, Vladisla PODYMAKO 2, Mi osla SÝKORA 1
1Depa men o S uc u al Reliabili y, Klokne Ins i u e, Czech Technical Uni e si y in P ague,
P ague, Czech Republic
2 Depa men o Building S uc u es, Bela usian Na ional Technical Uni e si y, Minsk, Bela us
Vi ali.Nado[email p o ec ed]; Jana.Ma ko a@c u .cz; V[email p o ec ed]m; Mi osla [email p o ec ed]
DOI: 10.35181/ ces-2023-0003
Abs ac . Thin-web s eel gi de s a e a ac i e o be used
because o hei e iciency in bending. Fo such gi de s,
he issue o ensu ing local buckling becomes e y ele an .
Calcula ion o mulas in mos cases a e complex and ha e
a limi ed scope o applica ion. The calcula ions based on
nume ical models make i possible o conside all he
speci ics o he designed elemen mo e uni e sally. The
a icle deals wi h he calcula ion o he buckling o he web
gi de unde he combina ion o pa ch and shea loading
by ini e elemen modelling. Nume ical models ha e been
c ea ed, and a compa a i e analysis wi h expe imen al
esul s has been ca ied ou . The p esen ed p inciples o
cons uc ing FE models (mesh size, ma e ial model, e c.)
a e ecommended o ollow when analysing he esis ance
and beha iou o beams wi h a hin web. Sensi i i y
analysis o he FE model wi h espec o he inpu
pa ame e s e ealed he mos impo an pa ame e s (yield
s eng h o s eel, web hickness, geome y), he unce ain y
o which needs o be aken in o accoun when c ea ing FE
models. The con e gence o he esul s suppo s he use o
he ini e elemen me hod in he design o s eel beams o
a quali a i e and quan i a i e assessmen o esis ance.
Howe e , u he de elopmen o uni ied p inciples o
c ea ing FE models and hei e i ica ion on a la ge
amoun o expe imen al da a is equi ed, as well as he
de e mina ion o pa ial ac o s conside ing he a iabili y
and unce ain ies in he ob ained esul s and speci ied
eliabili y le el.
Keywo ds
Web panel buckling, c i ical o ce, disc e iza ion, ini e
elemen me hod, impe ec ions, modelling, nume ical
model.
1. In oduc ion
Thin-web s eel beams a ac wi h hei e iciency when
subjec ed o bending. Howe e , he issue o ensu ing local
buckling becomes e y ele an o such beams. Many
heo e ical and expe imen al wo ks s udy he esis ance o
such beams, bu in mos cases, hey a e de o ed o he
in es iga ion o he beha iou o such elemen s unde he
in luence o indi idual o ce ac o s (load e ec s), such as
bending, shea , and pa ch loading. Ne e heless, in
p ac ice, he applica ion o a combined shea and pa ch
loading o beams wi h a hin web is o en encoun e ed. An
example o such a esis ance model is a s eel b idge gi de
in he p ocess o sliding (launch) on o suppo s o a c ane
gi de o an o e head c ane, in which he web o he c ane
gi de is no only locally loaded bu also subjec ed o a
shea o ce.
This combina ion o ac ions on welded I-beams wi h a
hin web was expe imen ally in es iga ed by Robe s T. M.
and Shahabian F. [1, 2], ollowed by B aun B. [3]. These
expe imen s showed a signi ican in e ac ion be ween
shea o ce and pa ch loading. As a esul , he in e ac ion
o mula and he modi ica ion o he educed s ess me hod
and he e ec i e wid h me hod desc ibed in EN 1993-1-5
unde combined loading we e p oposed [4, 5]. Howe e ,
he use o analy ical o mulas is limi ed by he complexi y
and a ea o which hey ha e been expe imen ally
con i med. As a ule, due o he complexi y o he
de o ma ion p ocess o a s eel beam aking in o accoun
he pos c i ical beha iou in he case o loss o local
buckling o he web, he models o ul ima e esis ance a e
conse a i e [6-8]. The use o nume ical me hods, in
pa icula he ini e elemen me hod, is e ec i e o
complex esis ance models. Acco ding o [4], nume ical
me hods may lead o a mo e accu a e desc ip ion o
beha iou and es ima es o ul ima e esis ance bu manuals
o speci ica ion o he pa ame e s o he models and
in e p e a ion o he esul s a e missing. The las decade
e ealed a g owing in e es in he use o compu e
(nume ical) models o he analysis o s uc u al
esis ance. While se e al s udies [9-14] showed a good
co espondence be ween expe imen s and FE models,
widely accep ed p inciples o c ea ing FE models a e
missing; his is an obs acle o hei p ac ical applica ions.
As a consequence, i is o in e es o analyse he beha iou
o s eel beams based on nume ical modelling and compa e
he esul s wi h expe imen s. The applica ion o FE models
in ol es h ee basic s eps:
 de elopmen and uni ica ion o p inciples and
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© 2023 VSB - TECHNICAL UNIVERSITY OF OSTRAVA FACULTY OF CIVIL ENGINEERING 13
pa ame e s o FE models – he main ocus o his
s udy,
 e alua ion o he accu acy o esul s based on
compa ison wi h expe imen al da a – discussed
b ie ly [15],
 de e mina ion o eliabili y pa ame e s such as
pa ial and sensi i i y ac o s [16].
The a icle p esen s an o e iew o he p inciples and
main pa ame e s o cons uc ing FE models (such as FE
mesh size, ma e ial model, e c.), as well as an analysis o
hei in luence on he esul o he FE model, based on
which ecommenda ions we e made on he me hods o
se ing and pa ame e alues o FE models o hin-web
s eel s uc u es. Sensi i i y analysis o he FE model o he
inpu pa ame e s (mechanical p ope ies o s eel,
geome ic dimensions) de e mined he se o pa ame e s
ha mos signi ican ly a ec he esul o he calcula ion
and o which u he esea ch is needed. Compa ison wi h
expe imen al da a shows he e iciency and accu acy o
calcula ions based on FE models.
2. FE Models
A p esen , nume ical modelling is o en used because o
he lack o he possibili y o ca ying ou a ull-scale
expe imen o o a pa ame ic s udy o he e ec s o
a ious pa ame e s. This makes i possible o e alua e he
ul ima e esis ance o comple ely new s uc u al solu ions
o which he e a e no calcula ion me hods (models). In
his wo k, nume ical modelling is done by he ini e
elemen me hod using he so wa e Abaqus. The c ea ion
and s udy o he accu acy o he applica ion o FE models
o ul ima e esis ance o hin-web welded beams is based
on he esul s o expe imen al s udies, which we e
published by Robe s T. M. and Shahabian F. [1] and
B aun B. [3]. The beams ma ked PG1-2 and PG4-2
om [1] and he beams SP600 and SP1200 om [3] a e
adop ed ( he o iginal designa ions a e kep in his s udy).
Schemes o he modelled ypes o beams a e p o ided in
Fig. 1.
In o de o elimina e possible in luence o expe imen al
e o , he es cases we e aken om di e en sou ces.
Since spacing o s i ene s is assumed o ha e a dominan
e ec on he beha io o he beams and in luences a ailu e
mode, he beams a e selec ed so as o conside di e en
cases o he a io o he s ep o he s i ene s а o he heigh
o he web, hw. Fo beams SP600 and SP1200 he dis ance
be ween he s i ene s is mo e han he heigh o he web,
and o beams PG1-2 and PG4-2 - less han hw.
FE models o he beams we e c ea ed om
measu emen s o he dimensions and mechanical
cha ac e is ics o he es ed beams. Table 1 p o ides he
geome ic pa ame e s and he mechanical p ope ies o he
s eel o he beam elemen s. The hickness o he s i ene s
and base pla es o he beams PG1-2 and PG4-2 a e 10
mm. Yield s eng h alues a e ob ained om a e aged
uniaxial ensile es da a o each beam ( h ee samples o
he web and wo o he langes). Ul ima e s eng h o s eel
was no measu ed in [1]. This alue is aken as equal o
u = 1.35 y acco ding o [17]. Due o he lack o da a,
gene ally accep ed alues a e conside ed o elas ic
modulus, E = 210 GPa, and Poisson's a io,

= 0.3.
(a)
(b)
Fig. 1: (a) Scheme o beams PG1-2 and PG4-2, (b) Scheme o beams
SP600 and SP1200.
S i ene s and base pla es o beams SP600 and SP1200
ha e he same wid h and hickness as he langes. Two es s
a e made om he same ba ch o s eel. Mechanical
p ope ies o s eel we e ob ained om he a e aged da a o
uniaxial ensile es s o specimens ( h ee es s each o
langes and webs). The elas ic modulus o he web is
equal o Ew = 177 GPa, and o he langes and s i ene s
is equal o E = 186 GPa. Poisson's a io is

= 0.3.
Tab.1: Geome ical pa ame e s and mechanical p ope ies o s eel
elemen s.
Beams SP600 SP1200 PG1-2 PG4-2
а, mm 2390 2390 600 500
hw, mm 600 1200 600 1000
w, mm 6 6 4.1 1.9
b
, mm 450 450 200 200
, mm 20 20 12.3 9.8
s
s, mm 200 200 50 50
y
w, MPa 383 383 339 247
uw, MPa 543 543 - -
y
, MPa 354 354 250 313
u
, MPa 519 519 - -
E
w, GPa 177 177 210 210
E
, GPa 186 186 210 210
SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 23 | NUMBER: 1 | 2023 | JUNE
© 2023 VSB - TECHNICAL UNIVERSITY OF OSTRAVA FACULTY OF CIVIL ENGINEERING 14
The s eng h and de o ma ion p ope ies o s eel
aken in o accoun by a s ess-s ain cu e ha e a dominan
e ec on he ul ima e esis ance o s eel s uc u es. The
esis ance o hin-web elemen s can be a ec ed by he
s ain ha dening o s eel as in he pla e, seconda y bending
s esses occu in addi ion o he p ima y s esses in he
memb ane. Conside ing he linea pa o ma e ial model
only may lead o he loss o bending s i ness o he pla es.
The ollowing ma e ial models we e conside ed in he
analysis o he obse ed e ec s: elas ic-plas ic wi hou
s ain ha dening, elas ic-plas ic wi h linea s ain
ha dening, and he quad ilinea ela ionship acco ding o
Swedish s anda d BSK07 [18] (Fig. 2).
Fig. 2: S ess-s ain cu e acco ding o BSK07.
Figu e 3 shows a compa ison o he load-displacemen
cu es o he SP600 and PG1-2 beams depending on he
selec ed ma e ial model. I can be seen ha a lowe alue
o he ul ima e load is eached in he s ess-s ain cu e
wi hou s ain ha dening. Howe e , he di e ence be ween
he esul s o he FE models is abou 1%, which
co esponds o he ac ha all ma e ial models apply o
sol e his p oblem. In he ollowing analysis, he
quad ilinea ela ionship acco ding o BSK07 is applied.
Fig. 3: Compa ison o load-displacemen cu es depending on selec ed
ma e ial model (а) Elas ic-plas ic wi hou s ain ha dening, (b)
Elas ic-plas ic wi h linea s ain ha dening, (c) Quad ilinea
ela ionship acco ding o BSK07, (d) Expe imen al da a.
The loading pla es a e modelled by he " igid" elemen .
The in e ac ion be ween he loading pla es and he op
lange is made h ough a «su ace- o-su ace» ype o
con ac wi h he p esence o ic ion. Loads a e applied as
s a ic loads, loading is pe o med by a concen a ed load
h ough he e e ence poin o he loading pla e. The
bounda y condi ions o he base pla es a e simply speci ied
as a pinned and olle suppo .
Disc e iza ion ( ini e elemen size) was pe o med by
he p elimina y analysis o he choice o he ini e elemen
size. Figu es 4 and 5 show he g aphs o he in luence o
he size o ini e-elemen on he alue o he c i ical
buckling o ce (Fc ) and he ul ima e o ce (Fu), aking in o
accoun geome ic and physical nonlinea i y o he SP600
and PG4-2 beams. As a esul , he mos op imal size om
he poin o iew o he solu ion accu acy and he use o
compu ing powe was adop ed a ini e elemen whose
dimensions a e i e beam web hicknesses (20 mm o he
PG1-2, 10 mm o he PG4-2, and 30 mm o beams SP600
and SP1200).
Fig. 4: Analysis o he ini e elemen size o he SP600 beam
Fig. 5: Analysis o he ini e elemen size o he PG4-2 beam.
In he manu ac u e and cons uc ion o eal s uc u es,
impe ec ions a e ine i able. In gene al, geome ic and
s uc u al impe ec ions a e dis inguished. Geome ic
impe ec ions include, o example, ini ial de lec ions,
cu a u es, eccen ici ies, and ole ances o de ia ions
om nominal geome ic alues. S uc u al impe ec ions
include, o example, esidual s esses caused by he
manu ac u ing p ocess.
Since he ampli ude and dis ibu ion o esidual
s esses signi ican ly depend on he manu ac u ing me hod
and he shape o he c oss-sec ion, he assignmen o hese
impe ec ions is di icul o au oma e, while he e is no
780.5
762.7
752.5
740.9
737.1
733.8
730.8
728.6
919.0
896.6
881.1
866.5
860.5
856.1
852.5
848.6
846
725
755
785
815
845
875
905
935
0 10203040506070
F [kN]
Fini e elemen size [mm]
Fc , FEA Fu, FEA Fu, exp
17.88
17.75
16.96
16.54
16.27
16.11
161.41
159.87
146.74
141.21
137.37
135.99
154
5
35
65
95
125
155
185
0 10203040506070
F [kN]
Fini e elemen size [mm]
F
c , FEA
F
u, FEA
F
u, exp
0
100
200
300
400
500
600
700
800
900
1000
0 4 8 12 16 20
F[kN]
[mm]
(a) (b) (c) (d)
SP600
0
50
100
150
200
250
300
350
400
450
500
02468
F [kN]
[mm]
PG1-2
SECTION BUILDING STRUCTURES & STRUCTURAL MECHANICS VOLUME: 23 | NUMBER: 1 | 2023 | JUNE
© 2023 VSB - TECHNICAL UNIVERSITY OF OSTRAVA FACULTY OF CIVIL ENGINEERING 15
enough expe imen al da a in which welding s esses we e
de e mined and hei e ec on he beha iou and esis ance
o he elemen was analyzed; he e o e, he use o
equi alen geome ic impe ec ions can be ecommended
o accoun o welding s esses. This app oach is used o
calcula e he s abili y o he common elemen s acco ding
o EN 1993-1-1 [4], a simila app oach is used o he
esis ance models unde conside a ion. The choice o his
app oach is also suppo ed by esea ch [19-21], in which
he insigni ican in luence o welding s esses is obse ed
on he esul s o calcula ions using FE models.
The mos di icul ask in speci ying impe ec ions is
choosing he shape, and ampli ude ( alue). Based on
ecommenda ions [22-26] wo op ions o aking in o
accoun impe ec ions a e conside ed – based on
eigen o ms o elas ic buckling and based on equi alen
geome ic impe ec ions (Eigenmode-a ine
impe ec ions and Manually de ined impe ec ions). The
shape o equi alen impe ec ions is assumed o be hal
sinusoidal wi h a de lec ion alue equal o min (а/200,
hw/200) [4], so ha o he beams SP600, PG1-2, PG4-2
he de lec ion was 3 mm, and o he beam SP1200 i was
6 mm.
The me hodology o impe ec ions modelling based on
eigen o ms o buckling is e y simple: i is necessa y o
pe o m a linea calcula ion o buckling o one model o
de e mine he eigen o ms o buckling, hen w i e down he
esul s o displacemen o i and use hem as he ini ial
impe ec ions o he second model o he same beam when
analysing i s geome ically and physically non-linea
wo k. The alue o impe ec ions is aken as equal o ha
o equi alen impe ec ions.
Figu e 6 shows a compa ison o he load-displacemen
cu es o he SP600 and PG1-2 beams depending on he
me hod o de ining impe ec ions, whe e i can be seen ha
he wo me hods apply o he ask a hand. The di e ence
be ween he esul s o he ul ima e load was app oxima ely
3%.
Fig. 6: Compa ison o load-displacemen cu es depending on he
me hod o de ining impe ec ions (a) Eigenmode impe ec ions,
(b) Manually de ined impe ec ions, (c) Expe imen al da a.
Common o all c oss-sec ional elemen s o nume ical
models is ha he dimensions a e la ge in wo di ec ions
and small in he hi d di ec ion. Thus, he geome y can be
idealised as an a e age su ace, which is hen subdi ided
in o shell elemen s. When calcula ing hin pla es, in
addi ion o he non-linea i y o he ma e ial, la ge
de o ma ions con ibu e o he occu ence o geome ically
non-linea e ec s. As he basic elemen o modelling he
sec ion o he beams, ou -node shell ini e elemen s wi h
a bilinea shape unc ion, deno ed as S4R, we e selec ed.
A solid wen y-node elemen , designa ed as C3D20R,
was selec ed o he compa a i e analysis, and simila FE
models we e c ea ed. Figu e 7 shows a compa ison o he
load-displacemen cu es o he S600 and PG1-2 beams
depending on he selec ed elemen ype. I can be seen
om he wo plo s ha he bes con e gence o he esul s
o he FE model wi h he expe imen al da a is achie ed
when using a solid FE. I was ound ha he di e ence
be ween he esul s o he ul ima e load be ween he FE
models was abou 2%. So i is mo e app op ia e o use he
shell S4R elemen , han an elemen o he solid C3D20R
ype, because modelling is mo e labo ious and mo e
compu ing powe is used.
Fig. 7: Compa ison o load-displacemen cu es depending on he
selec ed ini e elemen ype (a) Shell (b) Solid (c) Expe imen al
da a.
The ollowing pa ame e s a e aken o he basic FE
model apllied in he ollowing nume ical s udies:
 quad ilinea ela ionship acco ding o BSK07,
 mesh size equal o i e- imes web hickness (5 w),
 eigenmode impe ec ions and
 shell ype o ini e elemen s.
3. Resul s and Discussion
An impo an phase o he design based on FE models is
he sensi i i y analysis o he model o he alues o he
basic a iables (yield s eng h, elas ic modulus, web
hickness, impe ec ions, e c.) and model pa ame e s
(mesh size, ype o FE elemen , e c.) on he esul s (ou pu
0
100
200
300
400
500
600
700
800
900
1000
048121620
F[kN]
[mm]
(a) (b) (с)
SP600
0
50
100
150
200
250
300
350
400
450
500
02468
F [kN]
[mm]
PG1-2
0
100
200
300
400
500
600
700
800
900
1000
048121620
F[kN]
[mm]
(a) (b) (с)
SP600
0
50
100
150
200
250
300
350
400
450
500
02468
F [kN]
[mm]
PG1-2
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a iables) o he model [27]. I is necessa y o es ablish a
wha sca e o inpu da a he alidi y o he main
conclusions d awn om he modelling esul s is p ese ed.
Sensi i i y analysis should be pe o med aking in o
accoun he ac ual a iabili y o he a iables (inpu
pa ame e s). As a ule, i is mos co ec o conside
changes in he a iable ha accoun s o he mean alue
and he s anda d de ia ion. Howe e , o his pilo s udy, a
change o all a iables by plus o minus 10% is accep ed
o simpli ica ion.
When pe o ming a sensi i i y analysis o he
mechanical p ope ies o s eel, he yield s eng h,
ul ima e s eng h, and elas ic modulus alues ob ained
om expe imen al da a we e inc eased and dec eased by
10%. Fo example, he alue o he yield s eng h o he
SP600 beam a e an inc ease o 10% is: o he web yw =
422 MPa, and o he langes and s i ene s, y = 389 MPa.
Table 2 p esen s he esul s o he beam calcula ions
depending on he alue o he yield s eng h. This
pa ame e signi ican ly a ec s he alue o he ul ima e
load, bu he na u e o he de o ma ion emains unchanged.
Tab.2: Yield s eng h sensi i i y analysis.
Beams y F
exp, kN FFEA, kN Fexp /
FFEA
SP600
+10%
846
920 0.92
exp. 868 0.97
-10% 810 1.04
SP1200
+10%
1030
1086 0.94
exp. 1020 1.01
-10% 954 1.08
PG1-2
+10%
412
489 0.84
exp. 450 0.92
-10% 423 0.97
PG4-2
+10%
154
146 1.05
exp. 138 1.12
-10% 125 1.23
The alue o he ul ima e s eng h o he SP600 beam
a e an inc ease o 10% o he web is uw = 597 MPa, and
o he langes and he s i ene s - u = 571 MPa. This
pa ame e does no a ec he alue o he ul ima e load
wi h such a change.
The alue o he elas ic modulus o he SP600 beam
a e inc easing o he web is E = 194.6 GPa, and o
langes and s i ene s – E = 204.7 GPa. In Fig. 8, a
compa ison o he load-displacemen cu es o he SP600
beam is p esen ed depending on he alue o he elas ic
modulus. This pa ame e , wi h such a change, does no
signi ican ly a ec he alue o he maximum load, a
which he di e ence be ween he FE models is 3%. The
changes in he angle o inclina ion o he ini ial linea
sec ion o he cu es can be seen.
When pe o ming sensi i i y analysis o he
geome y o he FE models, he hickness o he web and
langes aken om expe imen al da a inc eased and
dec eased by 10%. The web hickness o he SP600 beam
a e an inc ease o 10% is 6.6 mm. In Fig. 9, you can see
a compa ison o he load-displacemen cu es o he
SP600 beam depending on he alue o he web hickness.
Table 3 shows he esul s o beam calcula ions a e
changing he hickness o he web. This pa ame e
signi ican ly a ec s he maximum load alue, bu he
na u e o he de o ma ion emains unchanged.
Fig. 8: Compa ison o he load-displacemen cu es depending on he
alue o he elas ic modulus (a) Basic FE model, (b) The alue
o he elas ic modulus a e an inc ease o 10%, (c) Expe imen al
da a.
Fig. 9: Compa ison o he load-displacemen cu es depending on he
alue o he web hickness (a) Basic FE model ( w = 6 mm), (b)
FE model ( w = 6.6 mm), (c) Expe imen al da a ( w = 6 mm).
Tab.3: Web hickness sensi i i y analysis.
Beam w Fexp, kN FFEA, kN Fexp / FFEA
SP600
exp.
846
868 0.97
+10% 1004 0.84
-10% 730 1.16
SP1200
exp.
1030
1020 1.01
+10% 1184 0.87
-10% 866 1.19
PG1-2
exp.
412
450 0.92
+10% 520 0.79
-10% 392 1.05
PG4-2
exp.
154
138 1.12
+10% 155 0.99
-10% 123 1.25
0
100
200
300
400
500
600
700
800
900
1000
0 4 8 12 16 20
F
[kN]
[mm
]
(a) (b) (с)
SP600
0
200
400
600
800
1000
1200
0 4 8 12 16 20
F
[kN]
[mm
]
(a) (b) (с)
SP600

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The hickness o he langes o he SP600 beam a e
an inc ease o 10% is 22 mm. Fig. 10 shows a compa ison
o he load-displacemen cu es o he SP600 beam
depending on he alue o he hickness o he langes. This
pa ame e , wi h such a change, does no signi ican ly a ec
he alue o he maximum load, a which he di e ence
be ween he wo models is abou 2% and he na u e o he
de o ma ion emains unchanged.
Fig. 10: Compa ison o he load-displacemen cu es depending on he
alue o he hickness o he langes (a) Basic FE model
( = 20 mm), (b) FE model ( = 22 mm), (c) Expe imen al da a
( = 20 mm).
Sensi i i y analysis o he ini ial impe ec ions was
pe o med o he i s and second eigen o ms and he
combina ion o eigen o ms. I can be no ed ha o hese
beams, he choice be ween he i s , second, and combined
eigen o ms o loss o s abili y does no signi ican ly a ec
he alue o he maximum load and he na u e o
de o ma ion. Table 4 p o ides he esul s o sensi i i y
analysis ocused on he e ec o he shape and magni ude
o equi alen impe ec ions on ul ima e model esis ance.
Tab.4: Sensi i i y o ul ima e model esis ance o ini ial impe ec ions.
Beam Eigen o ms Valu e,
mm Fexp, kN FFEA,
kN
Fexp/
FFEA
SP600
1- s 3
846
868 0.97
6 852 0.99
2- s
3 886 0.95
Comb. 3 882 0.96
SP1200
1- s 6
1030
1020 1.01
12 1014 1.02
2- s
6 1010 1.02
Comb. 6 1040 0.99
PG1-2
1- s 3
412
450 0.91
6 445 0.93
2- s
3 418 0.98
Comb. 3 418 0.98
PG4-2
1- s 2.5
154
138 1.11
5 137 1.12
2- s
2.5 123 1.25
Comb. 2.5 121 1.27
As a esul , FE models we e cons uc ed and da a we e
ob ained o compa ison wi h he esul s o he
expe imen s. G aphs o e ical mo emen o beams unde
he combined ac ion o local and shea o ces a e shown in
Fig.11. The esul s o he expe imen al and he FE models
a e summa ized in Tab. 5. The models showed close
nume ical con e gence wi h he expe imen al esul s.
Tab.5: Resul s o expe imen al da a and FE models
Beam
F
ex
p
.
,
kN
F
FEA., kN
F
ex
p
/
F
FEA
SP600 846 868 0.97
SP1200 1030 1020 1.01
PG1-2 412 450 0.92
PG4-2 154 137 1.12
Fig. 11: G aphs o he e ical mo emen o he beams unde he
combined ac ion o local and shea o ces (a) Basic FE model,
(b) Expe imen al da a.
The pu pose o his a icle is o apply a gene ic FE
model, and no o de elop he bes - alida ed model. In his
ligh , a di e ence o 10% may seem easonable. The main
easons o he di e ences be ween he FE models and
expe imen al da a may be he shape and magni ude o
impe ec ions. Mo eo e , also inaccu acies in
expe imen al measu emen s o yield s eng h, elas ic
modulus and web hickness may play a ole. Addi ional
assump ions and app oxima ions adop ed he e and
possibly a ec ing model p edic ions a e lis ed below:
 Only some mechanical p ope ies o s eel we e
speci ied In [1],, he e o e, he ensile s eng h is
assumed o be u = 1.35 y acco ding o [17], he
modulus o elas ici y and he Poisson's a io is
assumed o be E = 210 GPa and ν = 0.3.
 This s udy is limi ed ega ding a numbe o samples
0
100
200
300
400
500
600
700
800
900
1000
0 4 8 12 16 20
F
[kN]
[mm
]
(a) (b) (с)
SP600
0
50
100
150
200
250
300
350
400
450
500
0 2 4 6 8 10 12 14
F [kN]
[mm]
PG1-2
0
20
40
60
80
100
120
140
160
02468
F[kN]
[mm]
PG4-2
0
100
200
300
400
500
600
700
800
900
1000
0 4 8 12 16 20
F[kN]
[mm]
(a) (b)
SP600
0
200
400
600
800
1000
1200
0 8 16 24
F[kN]
[mm]
SP1200
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© 2023 VSB - TECHNICAL UNIVERSITY OF OSTRAVA FACULTY OF CIVIL ENGINEERING 18
o e i y he esul s. The ob ained indings hus
need o be e i ied by u he compa isons.
 Analysis co e s only h ee ma e ial models.
 No sensi i i y analysis wi h espec o he
eccen ici y o loading applica ion is made. I is
assumed ha his eccen ici y has a signi ican
e ec o a pa ch load; addi ional in es iga ions
based on measu emen s a e needed.
4. Conclusions
This a icle in es iga es he impo ance o selec ion o
pa ame e s o FE models, which should be conside ed
when assessing he esis ance o s eel elemen s wi h a
lexible hin web. The main pa ame e s a ec ing he esul
o modelling a hin-walled elemen include he selec ion o
he s ess-s ain cu e, speci ica ion o ma e ial p ope ies,
ype and size o he ini e elemen s, and shape and
magni ude o ini ial impe ec ions. A e analysing he
models o ma e ials, i is p oposed o use a quad ilinea
ela ionship wi h yielding and s ain ha dening. I appea s
ha a lowe alue o he ul ima e load is eached when he
load-displacemen cu e wi hou s ain ha dening is
applied. Howe e , he di e ence be ween he esul s o he
FE models may be e y small (abou 1% in he cases unde
in es iga ion). The analysis o he mesh size shows ha he
mos op imal size is abou i e web hicknesses o he
elemen . The use o solid elemen s does no lead o a
signi ican inc ease in he accu acy o he model; he e o e,
i is ecommended o use shell elemen s. The impe ec ions
a e ecommended o be based on he i s eigen o ms o
buckling.
The s udy indica es ha he ini e elemen me hod is
pe ec ly sui able o sol ing p oblems ela ed o he
s abili y o beam web unde combined load, makes i
possible o ake in o accoun a wide ange o ac o s and
alida e agains ull-scale expe imen al da a.
The sensi i i y analysis e eals ha domina ing is he
a iabili y o he hickness o he web (wi h a change o ±
10%, he load-bea ing capaci y changes by ± 16%) and he
s eng h o he yield (wi h a change o ± 10%, he load-
bea ing capaci y changes by ± 7%). These a iables should
hus be con olled du ing manu ac u ing and aken in o
accoun when calib a ing pa ial ac o s.
I should be no ed ha , in addi ion o esea ch in he
ield o he p inciples o cons uc ing FE models and hei
e i ica ion wi h expe imen al da a, i is necessa y o
de elop c i e ia o limi s a es and sa e y o ma o FE
applica ions [28].
5. Acknowledgemen s
This s udy has been suppo ed by he Technology Agency o he
Czech Republic unde G an CK03000125 and by he Minis y
o Educa ion, You h and Spo s o he Czech Republic unde
G an CZ.02.2.69/0.0/0.0/18_053/0016980.
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Abou Au ho s
Vi ali NADOLSKI was bo n in Minsk, Bela us. He
ecei ed his Ph.D. deg ee om B es S a e Technical
Uni e si y in 2015. His esea ch in e es s include
eliabili y analyses, design based on FEA, esis ance
models o s eel s uc u es.
Jana MARKOVÁ was bo n in P ague, Czech Republic.
She was appoin ed Associa e P o esso a Facul y o Ci il
Enginee ing, CTU in P ague in 2007. He esea ch
in e es s include basis o s uc u al design and assessmen
o exis ing s uc u es, s uc u al eliabili y, load modelling
wi h special ocus on clima ic ac ion e ec s, in es iga ions
o clima e change e ec s on s uc u al eliabili y, and
applica ions o p obabilis ic me hods in s uc u al design.
Vladisla PODYMAKO was bo n in Mogile , Bela us.
He ecei ed his M.Sc. om Bela usian Na ional Technical
Uni e si y in 2022. His esea ch in e es s include he
es ima ion o ul ima e esis ance o s eel s uc u es using
o Fini e Elemen Me hod o analysis.
Mi osla SÝKORA was bo n in České Budějo ice,
Czech Republic. He ecei ed his M.Sc. in 2001 and Ph.D.
in 2005 om he Facul y o Ci il Enginee ing, CTU in
P ague. In 2015 he ecei ed he academic deg ee o
Associa e P o esso a CTU in P ague. His esea ch
in e es s include a basis o s uc u al design, s uc u al
eliabili y, p obabilis ic op imisa ion, load modelling, isk
assessmen o echnical sys ems, and applica ions o
p obabilis ic me hods in s uc u al design.