Proceedings of the Annual Stability Conference

Structural Stability Research Council St. Louis, Missouri, April 16-20, 2013

Compression Members with Hollow Sections and Concentric Slotted Gusset Plates – Behavior and Recommended Design Model

H. Unterweger1, A. Taras2

Abstract In practical applications, compression members in trusses or bracing systems are often composed of hollow sections with slotted gusset plates on both ends. Either a bolted connection with splice plates on both sides or a welded connection are used to achieve a concentric configuration. In recent application cases, members of this type were designed with unusually long gusset plates at their ends, leading to reduced load bearing capacities. In the present paper, the load carrying behavior of such members is shown by means of realistic numerical calculations. The resulting compression member capacities are compared with the design models for flexural buckling as they are commonly employed in practice. It will be shown that these models significantly overestimate the compression member capacity – particularly in cases with low slenderness. Interestingly, imperfection forms similar to the second eigenmode often lead to the most critical design situation. The influence of residual stresses due to the welding of the gusset plate to the slotted hollow section is also studied in detail. On the basis of these numerical results, an improved engineering design recommendation for the practical verification of the gusset plate stability could be developed, which should be used in addition to the conventional member buckling verification. 1. Introduction and motivation for a comprehensive study Members in trusses as well as members of bracings are often designed with hollow sections (rectangular – RHS or circular – CHS) and slotted gusset plates on both ends. Either a bolted connection with splice plates on both sides or a welded connection are used to achieve a concentric configuration. Two typical examples are shown in Fig. 1.

1 Full Professor, Graz University of Technology, <h.unterweger@tugraz.at> 2 Assistant Professor, Graz University of Technology, <taras@tugraz.at>

19

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Figure

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e 1: Examples

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Figure 2:

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vation for aplates was

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for member j

a greater lend on a studth h, are giv

Studied RHS

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oints – welded

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for memberFig. 2b – a o cases are

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havior of core – to the a

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20

Within the literature, a lot of studies are available dealing with the load transfer from the gusset plate to the hollow section (e.g. Zhao R. (2009) and references there), however the focus is placed on tension applications, excluding buckling phenomena. In past detailing practice, the buckling resistance was sufficiently warranted by performing a buckling check for the hollow section itself, since the gusset plates were usually very short and had a negligible effect on the buckling length and/or were not the subject to significant second-order out of plane bending. However, more recent detailing practice led to free lengths L1 of the gusset plates that are significantly larger than old design tradition. As will be shown in the following, the limited cross-sectional bending capacity of the gusset plate can also lead to a significant reduction of the overall compression strength of the member. Only for very slender members a conventional buckling verification – even when taking account of the potentially increased buckling length due to the reduced bending stiffness in the joint region – is sufficient to guarantee structural safety. If, in addition to a long gusset plate, an eccentric joint configuration is chosen (e.g. directly bolted without splice plates) a further, significant reduction of the member compression capacity is observed. In this case design recommendations are given in Unterweger (2010). 2. Simplifications and parameter range of the study In order to study the load bearing capacity of hollow sections with slotted gusset plates on both ends, some simplifications were introduced, shown in Fig. 3. In this figure, the studied geometry with the chosen symbols and notations is presented as well. The two studied border cases for boundary conditions of the gusset plate are: - pinned (BC1) and, - fully clamped (BC2) ends, with rigid support out of plane (in both cases). In the study described here, squared hollow sections were analyzed, ignoring the fillets at the edges (b = h) and leading to the area A0, second moment of area Jz0 and radius of gyration rz0. However, the final results can be shown to also be valid for rectangular and circular hollow sections. The free length L1 of the gusset plate was varied between L1 = 1,0 · h ÷ 2,0 · h. The height of the gusset plate h1 was fixed with h1 = 1,3 · h, which is typical for practical applications. The slotted length Ls, which was chosen to be Ls = 1,75 · h, is of great significance and represents a minimum value: this length is at least necessary in order to utilize the full axial and bending capacity of the member at the end of the gusset plate, due to the load introduction from the gusset plate into the hollow section. This was also verified within the comprehensive FEM-study, which will be presented in section 4.

21

2.1 ReleThe bucplate (I1

Based oused in member

In pract Another÷ 0,10 i 2.2 LoadIn this swere tak

Figure 3: S

evant stiffneckling capac1 according t

on the assumEurope for

r respectivel

ice, A1 ~ A

r important s often valid

ding of the mstudy, only ken into acc

Sketch of studi

ess ratio I1/Icity of the mto Eq. 1) an

med geometr the stiffnely; A0 = are

A0 is often va

parameter id.

member constant ax

count, based

ied joint confi

I0 and membmember str

nd member (

try of the gess ratio I1/Iea of the mem

4,

alid leading

is the memb

xial compred on execut

iguration; geom

ber length rarongly depe(I0 = Iz0)

∙

gusset platesI0, Eq. (2) imber, A1 =

68 ∙ ∙

g to very sm

ber length r

ession forcetion toleranc

metry and ide

atio L1/L0 nds on the

s (h1 = 1,3 is valid (h =area of the

all stiffness

atio L1/L0. F

es are consices. The eff

alized bounda

stiffness ra

· h) and qu= depth andgusset plate

ratios of ab

For practica

idered. Geofect of resid

ary conditions

tio I1/I0 of t

uadratic RHd t = thickne)

bout I1/I0 ~ 0

al cases, L1/

ometric impdual stresses

the gusset

(1)

S-sections ness of the

(2)

0,01.

/L0 = 0,05

perfections s was also

22

studied,and gus 3. Buck 3.1 BuckDue to (length bendingused. Thbuckling2 repla

Figu The relathe well

In the lifactors (DimitroanalyticUnterwe For pracup in Fiare plott

in particulset plate.

kling verific

kling verificthe significL1), for th

g stiffness Iz

his is illustrg mode is re

aces Lcr,1 cal

ure 4: a.) First

ationship bel known Eq.

iterature, a i and ideaov (1953),

cal formulaeger, Taras

ctical applicig. 5. In theted for I = 0

ar those res

cation in pr

cation in praantly reduce buckling

z,0 over the wrated in Fig.elevant for tlculated with

t and b.) secon

etween effec. (3)

number of al buckling also found

s for the s(2011).

cations, all se figures, t

0,01 , 0,02 a

sidual stress

ractice and

actice ced bending

verificationwhole length. 4. For memthe ultimateh 1.

nd bifurcation

ctive length

analytic forloads Ncr,i

d in Petersestudied cas

the relevantthe paramet

and 0,04, cov

ses caused b

danger of o

stiffness ofn of the meh L0 – an inmbers with e buckling st

buckling mod

and ideal b

,∙ ∙

∙

rmulas for ai can be foen (1982)),ses (see Fig

t results forter I is equavering all pr

by the weld

overestima

f the gussetember out

ncreased effeslotted gusstrength of th

de shapes and t

uckling load

an iterative und (Pflüge, lead to vg. 4) are s

r the effectial to the stiffractical case

ded connect

tion of mem

t plate at thof plane – ective lengthset plates, she member,

the associated

d Ncr for ea

solution foer (1964)).

very unsafe summed up

ve length faffness ratio (es.

tion between

mber capac

he end of thbased on a

h Lcr = · Lsometimes t so that Lcr,2

d equivalent co

ch mode i is

or the effectSimplified results. Ap

p by the a

actors i are(I = I1/I0). T

n member

city

e member a constant L0 must be the second 2 based on

olumns

s given by

(3)

ive length solutions

ppropriate authors in

e summed The results

23

Figure

3.2 OveBefore section, bucklingover wh Fig. 6 shsimply order thincreasewell-kno

Makingstrengthlike the member

e 5: Factors i

erestimationall the detaa simplifi

g behavior hole length L

hows an altesupported m

heory, the ined deformatown second

use of theh of the mem

Eurocode (r as the one

i for the determm

of the buckails and resed examplewhen compL0).

ernative appmember. Banternal forcetion w depend-order elast

(elastic) mmber can b2012), givegiven by th

mination of bumember for, a.)

kling strengtsults of thee is shown,pared to a si

proach for thased on an ees at the relends on the tic amplifica

member capae determine

e formulas fohe buckling

uckling lengths) pinned ends

th of a mem comprehen, in order timply suppo

he calculatiequivalent ievant sectioactual load ation factor

⁄

acity in sectied analyticaor eequ that lcurves codi

s (1st and 2nd band b.) fixed e

ber with slonsive studyto emphasiorted const

on of the ulimperfection

on m (N = PP and the ifII in Eq. (4

ion m (max

ally from selead to the sfied in the s

buckling modeends

otted gusset are presenize the signtant-section

ltimate compn eequ and a

P, M = P · wdeal bucklin

4).

x = Fy), the uecond-order same comprsame standa

e) using the eq

plate nted in the nificant diffn member (s

pression strapplication w) are calcung load Pcr,

ultimate comtheory. Som

ression strenard.

quivalent

following ference in section Iz,0

rength of a of second

ulated. The using the

(4)

mpression me codes,

ngth of the

24

Figure 6: Compressive Strength of a column – alternative approach

Based on the second order theory approach in Fig. 6, it is now possible to show the utilization of the relevant gusset-plate section capacity in axis 1. In Fig. 7, a typical example of a hollow section member (RHS: h = b = 200, t = 10 mm) of length L0 = 8000 mm is shown. The member compression strength of Pn = 840 kN given in Fig. 7a is based on the proposed verification in Fig. 4, using the effective length factors 1 in Fig. 5 and the buckling curve a of the Eurocode (2012). The shape of the imperfections is based on the 1st buckling eigenmode (simplified in a sine-wave form) in Fig. 7a and on the 2nd mode (simplified, with eequ in section 1 of Fig. 7) in Fig. 7b. When the load is thus set equal to the theoretical resistance Pn = 840 kN, only the hollow member has sufficient section capacity. In the gusset plate section 1 – particularly for the imperfections based on the 2nd mode – the utilization factors UF1 are significantly higher than 1, and this even if the increased plastic section capacity is used (UF1,pl). This means that the compression strength based on the buckling verification of the member with increased, equivalent buckling length (see Fig. 4) significantly overestimates the buckling capacity of the member with slotted gusset plates, because the gusset plate section 1 (and not the mid-span cross-section of the HS member) determines the ultimate capacity, as well as the fact that imperfections based on the 2nd mode must also be considered.

25

Figure 7: Practical example of a hollow section member with slotted gusset plates; Reduced buckling strength due to

reduced section capacity in section 1 of the gusset plate 4. Simulation of the realistic load bearing behavior of members with slotted gusset plates The realistic load bearing behavior of members with slotted gusset plates, shown in Fig. 3, was studied in detail, based on numerical FEM-calculations.

h1=260 t1=28

b)

26

4.1 FEMThe numFEM-mwas choelementthe joinwelds bexecutiooutside element The bouof plane Within section In all cachosen, A0 · Fy were sel

4.2 LineFor eaclinear cathe selec

M-model merical calc

model at the osen. The gts with linea

nt region wabetween theon of butt wthe joint wa

ts.

undary conde.

the calculatRHS 200/20

alculations, with a yield= 1.786 kNlected.

Figu

ear bucklingh studied malculations, cted geomet

culations wemember en

gusset platear interpolatas modeled gusset plat

welds. The sas modeled

ditions in ax

tions memb00/10 mm w

a linear elad stress Fy =

N. An elastic

ure 8: FEM nu

g Analyses member, a

due to the tric imperfe

ere done witnd is showns were modtion functionusing shell te and mem

sealing plated using beam

xis I were b

ber lengths owithout fille

astic-ideal p= 235 N/mmc modulus o

umerical mode

linear buckfact that th

ections (1st a

th the Finiten. A combindeled using ns over the elements w

mber are noes (see Fig. m elements

based on the

of L0 = 4,8 ets (leading t

plastic materm². This leaof E = 210.0

el for the calcu

kling analyshe calculatedand 2nd mod

e Element Snation of vovolume ele

gusset platewith 20 elemot modeled

1, 3) were with a rigid

e studied ca

and 12 m to A0 = 760

rial behaviods to an ulti

000 N/mm²

ulation of the l

ses (LBA) wd buckling m

de studied).

Software ABolume, shelements withe thickness. ments for eain detail, imomitted. Th

d kinematic

ases, pinned

were consid00 mm², rz0 =

our without imate sectioand a Poiss

oad bearing ca

was performmodes also

BAQUS. In ll and beamh eight isopThe RHS-m

ach section mplying mehe rest of th

coupling to

or fully cla

dered with = 78 mm).

strain-hardeon capacity son’s ratio o

apacity

med prior toformed the

Fig. 8 the m elements parametric member in wall. The

eaning the he member o the shell

amped out

a member

ening was of N0,pl =

of = 0,3

o the non-e basis for

27

Fig. 9 shas well a The comcalculatoverestiintroducbending Based oincreasebasis of = h/5. Tused (ne

Figure

4.3 RealFor the plates, imperfe In a firselectedmaximuEN 109eigenmo

hows the firas fully clam

mparison oted using bimation by ction from tg stiffness pa

on a compree the – comf beam-theorThis leads toew paramete

9: Different b

listic comprcalculationa series ctions) was

st step, LBd for the impum value of 90-2 (2008) ode shapes.

rst and secomped ends o

f the ideal beam-theory

the latter.the gusset partially inef

ehensive stumputational -

retical metho an increaseer L1

*/L0).

buckling mode

ression loadn of realisticof GMNIAcarried out

BA-analysesperfection s

f the imperfenow used

ond bucklingof the gusse

buckling ly (Eq. (3) . This is uplate to the ffective, lead

udy by the a- free lengthhods such ased length L

es (FEM-Modeplate 2

d bearing bec compressiA-analyses t.

were perfoshape along

fection chosein Europe,

g modes foret plate.

oads Ncr,i bwith effec

understandamember, mding to an o

authors, it ih of the guss the one rep1

* = L1 + h/

el) for a memb260/28; L1 = 4

ehaviour ion strength(geometric

ormed. Theg the membeen with e0,m

which give

r a member

based on thctive length

able as a cmaking the f

verestimatio

is suggestedsset plate Lpresented by/5 if the effe

ber with L0 = 400 mm)

h values of c and mat

e calculateder. These sh

max = L0/750es measurem

with L0 = 8

he LBA anah factors oconsequencfirst portion on of Ncr,i.

d - for practL1 (used to dy Fig. 5 ) byective length

8 m (Profile R

the membeterial nonli

d eigenmodehapes were

0, based on tments that

000 mm an

alyses withof Fig. 5) e of the l of the RHS

tical applicadetermine Ny a distance h factors of

RHS 200/200/1

er with slottinear analy

es (1st and then scaled

the code of are relevan

nd pinned

h the ones shows a

local load S member

ations - to Ncr,i on the L1 = b/5

f Fig. 5 are

10; gusset

ted gusset yses with

2nd) were d, with the

execution nt for both

28

In additas well,

Figure 1

4.4 ImpaThe impweldingstressesyield strload cadistributultimatedeformaconservultimateThis effgeometr

tion, the effeleading to t

10: Realistic a

act of additpact of addig connection, a rather cress along thase T). Fitions in secte stresses 0

ation behavvative approe capacity offect will beric imperfec

fect of an inthe four diff

ssumptions of

ional residuitional residn between gonservativehe elementsig. 11 showtion A, B, C0 and u at

vior – with ach for the

of approxime considerection (factor

nclination anferent shape

f geometric imb.) E

ual stresses dual stressesgusset plate

e approach ws near the wews the resuC of the guss

top and botand witho

residual strmately 10 % ed in the der fequ).

ngle of max

es of imperf

mperfections, bEN ISO 13920

due to welds was also ste and the mwas selecteeld (simulatults for a mset plate arettom surface

out residual ress pattern

(609 kN inesign appro

x = 1/100 offection, sum

based on execu (1996)

ding tudied in th

member. Fored, leading ttion of the rmember wie plotted in Fe of the gus

stresses –was made,

nstead of 66oach in sec

f the gusset mmarized in F

utive codes; a.

his paper, dur the distribto residual

residual streith L0 = 40Fig. 11c (ressset plate). I

is presenteonly a mod

68 kN in Fition 5 in f

plate was cFig. 10.

.) EN 1090-2 (

ue to relevabution of thstresses reasses by a te000 mm. Tsidual stressIn Fig. 11b,ed. Althougderate decreig. 11) was form of an

considered

(2008) and

ance of the he residual aching the mperature

The stress ses E and , the load-gh a very ease of the

observed. increased

29

Figure 11

5. SuggBased oplates, tmodel, s 5.1 Desplate As showto the lim The mamemberat the e“realisti Startingin Fig. 1factor fI

e1,0 · fII) In additdescendincreaselinear) p

1: Load bearin

estion of a on the resuthe authors summed up

ign model fo

wn for the emited sectio

ain idea of tr with pinneend of the mic” behaviou

g from the ge12) increaseII that accou.

tion, the sding lines, les (due to adplastic and t

ng capacities aends (geome

design modlts of the Gdeveloped ain section 5

for compress

xample in Fon capacity

the design med ends. Thmember (seur, determin

eometric imes followingunts for the c

section capleading to dditional mothe (too low

and consideredtric imperfecti

del for pracGMNA-calca simple de5.2, will be

sive strength

Fig. 7, the cof the gusse

model, basee plot showection 1) wned by GMN

mperfection eg the elasticcorrect idea

pacity of threduced axoment MII =

w) linear-ela

d residual stresions based on

ctical applicculations fosign model shown in th

h considerin

ompressive et plate in it

ed on 2nd orws the deformwith increasiNIA-calcula

e1,0 at the mc 2nd order aal buckling l

he gusset plxial load ca= N · U3). Aastic cross-s

sses E for a mthe 1st bucklin

cation or the studie

for practicahe following

ng the limite

strength ofts cross-sect

rder theory,mation U3 (ing axial loations.

member end amplificationload Pcr, nea

late is alsoarrying capaAs border linsectional cap

member with Lng mode shap

ed memberal design. Thg.

ed section c

f the membetion 1.

, is summed(out-of-plan

oad N. The

in section 1n factor givarly up to th

representeacites N if nes the (toopacity curve

L0 = 4000 mme)

s with slotthe backgrou

capacity of th

er is often li

d up in Figne) in the gu

circles rep

, the deformven by Eq. (he ultimate l

ed in Fig. 1f the deformo high) fullyes for the re

m and pinned

ted gusset und of this

he gusset

imited due

g. 12 for a usset plate resent the

mation (U3 4), i.e. the load (U3 =

12 by the mation U3 y (i.e. non-ectangular

30

gusset plate section are shown. If a reduced plastic capacity curve – with a linear interaction between axial force and bending moment - is used for the gusset plate, the intersection point with the deformation curve (U3 = e1,0 · fII) gives the result of the design model (N/Npl,RHS = 0,28 in Fig. 12). This compressive strength is in good agreement with the real ultimate load of approximately N/Npl,RHS = 0,29, albeit the latter features higher deformations U3 = 20 mm.

Figure 12: Deformation and cross-sectional resistance at the relevant gusset plate section for pinned ends

This simple design model works for all types of geometrical imperfections (as described in Fig. 10) and for both buckling modes. It is worth mentioning that - for the deformation U3 based on

31

the simple elastic 2nd order amplification factor, the relevant ideal buckling load Ncr,i must always be considered. Table 1 summarized some additional examples. The results of the simple engineering design model (NEng.model) are compared with the FEM-calculations (NGMNIA). It can be seen that - for the eigenmode-affine imperfections, with equal amplitudes, see Fig. 10a- nearly in all cases the 2nd modes lead to the lower ultimate compressive strength. In the case of a member with clamped ends at the gusset plate (BC2 in Fig. 3), the design model is more complex due to the fact that the overall moment Mges caused by the deformation w1 at the member end must be splitted in two individual parts for the two relevant sections I and 1, see Fig. 13. Table 1: Load bearing capacities NR [kN] for the variation of geometric imperfection shapes only (based on Fig. 10);

RHS 100/200/10, t1 = 28, L1 = 400 mm

end support

length L0 [m]

Ncr,1 Ncr,2

eigenmode-affine; e0,max = L0/750 Gusset plate inclination e1,0

[mm] NGMNIA

[kN] NEng.model

[kN] e1,0

[mm] NGMNIA

[kN] NEng.model

[kN] BC 1 pinned

4,0 1.184 1527

4,51 5,33

670 707

680 (+1,5 %) 708 (+0,1 %)

4,0 4,0

697 772

707 (+1,4 %) 786 (+1,8 %)

8,0 954 1.313

4,45 10,6

611 514

615 (+0,7 %) 497 (-3,3 %)

4,0 4,0

646 726

633 (-2,0 %) 740 (+1,9 %)

12,0 595 1.213

2,78 14,6

497 430

497 (0 %) 412 (-4,2 %)

4,0 4,0

521 700

467 (-10,4 %) 1

716 (+2,3 %) BC 2 fully clamped

4,0 4.642 5.199

3,27 5,32

1.386 1.241

1.361 (-1,8 %) 1.217 (-2,0 %)

4,0 4,0

1.373 1.340

1.300 (-5,3 %) 1.313 (-2,0 %)

8,0 1.791 4.697

1,13 8,65

1.213 1.086

1.357 (+12 %) 1.012 (-6,8 %)

4,0 4,0

1.312 1.351

1.064 (-19 %) 1

1.302 (-3,6 %) 1. not relevant, because buckling of the member determined (section m)

The proposed design model for this cases focuses now on section I, because at this location a design verification of the welded connection is needed as well. The moment in section I can conservatively be estimated to amount to about 70 % of Mges, due to the fact that the simple engineering model underestimates the deformation w1 by using fII. In partial compensation of this error, it can be shown that at section I the full plastic section capacity can be utilized.

32

5.2 Sumslotted gSummincompres This de(particuagainst represenThe verAlternat(utilizatof the m Veri Con

buck For

incre Note

Veria) geom

e1,0 =

Figure 13: E

mmary of thegusset plateng up the ssion streng

sign model ularly, buck

axial comprntation of thrification otively, for tion factor e

member.

ification 1: bnventional bkling mode the calcula

eased lengthe: Verificat

internal f

ification 2: ametric impe= L1/100 ≥ 2

Engineering m

e suggested es

results of gth of memb

can be adaling curvesression forc

he design moof the mem

each verifequal to 1,0)

buckling chbuckling ch(L = 1 · L0

ation of theh L1

* = L1 +tion 1 checkforces (comp

additional verfection at t2 mm

model for the ca

design mod

section 4 bers with slo

apted to difs and toleraces Nd. For aodel all safe

mber contaification a m) – the mini

heck of the meck, based

0, see Fig. 5)e effective + h/5 shouldks the mempression + b

verification othe gusset p

alculation of th

del for the co

and 5.1, a otted gusset

fferent natioance requirea better undety factors ains two indmaximum imum of bo

member on an incr

) length fact

d be used mber in the bending) ex

of the sectioplate (section

he load bearin

ompression

design moplates is no

onal codes, ements) forderstandingare omitted.dividual chcompressio

oth gives the

reased effec

tor 1 using

region neaxceeding the

on capacity n 1)

ng capacity Nd

strength of

odel for thow available

which mayr column bof the prop

hecks - boton strength e resulting c

ctive buckli

g e.g. the g

ar midspan e section cap

of the gusse

d for fixed end

f members w

he calculatioe.

y have diffebuckling verosal, in the

th must becan be d

compression

ing length f

graphs in F

against secpacity

et plate

ds

with

on of the

erent rules rifications following

fulfilled. determined n capacity

for the 1st

Fig. 5, an

cond-order

33

Note: Based on execution codes EN 1090-2 (2008) and EN ISO 13920 (1996). Different imperfection amplitudes may be considered on the basis of other national or industry-specific tolerance requirements.

b) geometric equivalent imperfections at the gusset plate (section 1) e1,equ = fequ · e1,0 = 2.0 · e10 = 2.0 · L1/100 ≥ 4 mm Note: The factor fequ is a very conservative assumption, based on the study of the effects of

residual stresses due to welding of the connection between gusset plate and member.

c) verification pinned ends (BC1): (only reduced plastic section capacity available)

∙ , ∙,⁄ , , ∙ 1 , ,⁄ (5)

fully clamped ends (BC2):

0,7 ∙ ∙ , ∙,⁄ , , ∙ 1 , ,⁄ (6)

- End moment MI (basis for weld connection design)

0,7 ∙ ∙ , ∙,⁄ (7)

Note 1: - the ideal buckling load Ncr,1 for the 1st mode must always be used Note 2: - the plastic section capacity M1,pl,Rd and N1,pl,Rd of the gusset plate are defined (with

Fyd … design value of the yield stress), respectively:

, ,∙∙ ; , , ∙ ∙

References Zhao, R., Huang, R., Khoo, H.A., Cheng, J.J.R. (2009). “Parametric finite element study on slotted rectangular and

square HSS tension connections”. Journal of constructional steel research, 65 611-621. Unterweger, H. (2010). “Load bearing capacity of bracing members with almost centric joints”. Proceedings of Int.

conference stability and ductility of steel structures – SDSS, Rio de Janeiro, 603-610. Unterweger, H., Taras, A. (2011). “Hohlprofile mit beidseits zentrisch eingeschlitzten Knotenblechen –

Drucktragverhalten und Bemessungsvorschlag.” Stahlbau, Band 680, Heft 11, 839-851. Eurocode EN 1993-1-1 (2012). “Eurocode 3; Design of Steel Structures – Part 1-1: General rules and rules for

buildings.” Eurocode EN 1090-2 (2008). “Execution of steel structures and aluminium structures – Part 2: Technical

requirements for steel structures.” EN ISO 13920 (1996). “Welding – General tolerances for welded constructions – Dimensions for lengths and

angles, shape and position.” Petersen, Ch. (1982). “Statik und Stabilität der Baukonstruktionen”. Vieweg & Sohn, 2. Auflage. Pflüger, A. (1964). “Stabilitätsprobleme der Elastostatik”, Springer Verlag, 2. Auflage. Dimitrov, N. (1953). “Ermittlung konstanter Ersatz-Trägheitsmomente für Druckstäbe mit veränderlichen

Querschnitten”. Der Bauingenieur, 28, H6, 208-211.

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