Design of circular steel arches with hollow circular cross...

ARTICLE IN PRESS

Journal of Constructional Steel Research ( ) –www.elsevier.com/locate/jcsr

Design of circular steel arches with hollow circular cross-sectionsaccording to EC3

C.A. Dimopoulos, C.J. Gantes∗

Department of Civil Engineering, National Technical University of Athens, Greece

Received 10 June 2007; accepted 15 September 2007

Abstract

Design of either pin-ended or fixed circular steel arches with hollow circular cross-sections subjected to a uniformly distributed vertical loadalong the horizontal projection of the entire arch with the aid of the EC3 provisions is discussed. Appropriate modification factors are proposedthat should be included in EC3 interaction equations, to improve their accuracy for the design of such arches.c© 2007 Elsevier Ltd. All rights reserved.

Keywords: Design; Circular arches; Fixed; Pin-ended; EC3; Steel; Strength

1. Introduction

A great amount of work has been presented in the pastconcerning the behavior and the strength of arches. Timoshenkoand Gere [1] calculated the linear buckling load of circulararches under uniformly distributed radial and vertical loads.Geometrically nonlinear buckling loads and load–deflectioncurves for clamped arches have been given from Schreyerand Masur [2]. Accurate solutions and approximations forthe nonlinear symmetric and antisymmetric buckling of bothpin-ended and fixed shallow arches with arbitrary cross-section have been provided by Pi et al. [3]. The geometricallynonlinear buckling and postbuckling of elastic arches hasbeen thoroughly investigated by Pi and Trahair [4]. Pi andTrahair [5] using a finite element program for the nonlinearinelastic analysis, investigated the in-plane inelastic bucklingand strength of circular steel I-section arches. The effects ofinitial crookedness, rise-to-span ratio, residual stresses, anddead load to total load ratio on the in-plane inelastic stabilityof steel arches in uniform compression and in combinedcompression and bending were analyzed.

A great effort has also been directed towards the design ofsteel arches. Kuranishi and Yabuki [6] proposed design criteriafor parabolic steel arches that were expressed in terms of axial

∗ Corresponding author. Tel.: +30 210 7723440; fax: +30 210 7723442.E-mail address: [email protected] (C.J. Gantes).

force and bending moment at the quarter point, but were onlyvalid for slenderness ratio 0.5S/ i , where S is the length ofthe arch and i is the radius of gyration of the cross-sectionabout its major principal axis, in the range 50–150 and rise-to-span ratios f/L in the range 0.1–0.3. However, using theseactions for design seems doubtful because these are not alwaysthe maximum values. Verstappen et al. [7] proposed that thedesign rule for straight beam–columns from Dutch codes, canbe used for the check of the in-plane stability of pin-endedcircular arches. However, a linear interaction equation for astraight beam–column may be conservative because, amongothers, the favorable redistributions that take place in redundantarches after the first plastic hinge forms, is not taken intoaccount. Pi and Trahair [8] found that the design equation of theAustralian regulations for steel columns cannot be used directlyfor steel arches in uniform compression, nor can the designinteraction equations for steel beam–columns be used directlyfor steel arches under nonuniform compression and bending.Moreover, they proposed design equations for both uniformcompression and nonuniform compression and bending thatfollow the provisions for the design of straight members of theAustralian Steel Structures code. These proposed equations canbe used for both shallow and non-shallow arches and are validfor slenderness ratio 0.5S/ i in the range 10–170 and subtendedangles 2Θ in the range 10◦–180◦.

In Eurocode 3 no design provision is given for the designof steel arches. To the authors’ knowledge, no proposalhas been presented yet for the design of steel arches with

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Please cite this article in press as: Dimopoulos CA, Gantes CJ. Design of circular steel arches with hollow circular cross-sections according to EC3. Journal ofConstructional Steel Research (2008), doi:10.1016/j.jcsr.2007.09.009

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ARTICLE IN PRESS2 C.A. Dimopoulos, C.J. Gantes / Journal of Constructional Steel Research ( ) –

Fig. 1. Geometry, loading and cross-section.

the aid of Eurocode 3 provisions. This paper deals withthe design of either pinned or fixed circular steel archeswith hollow circular cross-sections, subjected to uniformlydistributed vertical load on the entire arch (Fig. 1), under theprovisions of EC3 concerning the design of uniform straightmembers in combined compression and bending. A modifiedinteraction equation that provides good lower bounds for thein-plane strength of both shallow and non-shallow steel archesis proposed.

2. Methodology

For the purposes of this paper, the nonlinear finite elementanalysis program, ADINA [9], has been used. A sufficientnumber of straight Hermite beam finite elements has beenused for the analysis of the circular arches accounting for theeffect of both geometric and material nonlinearities. For thesolution of the nonlinear system of equations, the well-knowndisplacement-control method (LDC) [9] is used in combinationwith the full Newton–Raphson procedure and the use of linesearches. An inelastic bilinear material with yield stress fy =

275 MPa, Young’s modulus E = 210 GPa, Poisson’s ratioν = 0.30, without any hardening, is used for the inelasticanalyses (Fig. 2). A hollow circular cross-section with a ratioof external diameter D to thickness t sufficiently small to avoidlocal buckling effects is used throughout this paper (Fig. 1). Itis assumed that the cross-section has no residual stresses. In theanalyses initial imperfections are taken into account, having theshape of the first antisymmetric eigenvector from a linearizedbuckling analysis (Fig. 3). The imperfection magnitude is equalto L/600, in accordance with the provisions of EC3 [10].

The behavioral characteristics of arches of this type underuniform vertical load have been discussed in [11]. Generallyspeaking, it was shown that the type of failure depends onthe geometrical and the cross-sectional characteristics. Whenarches are extremely shallow, they suffer no buckling. Howeverthey are likely to violate serviceability tolerances. Shallowarches suffer from elastic snap-through. In the other cases, thestrength of the arches is influenced by both the geometrical andthe material nonlinearity. It is possible, however, for very deeparches to evaluate their strength considering only the materialnonlinearity.

A large number of geometrically and materially nonlinearanalyses, including initial imperfection, was carried out in orderto capture the real, highly nonlinear, behavior of the arches and

Fig. 2. Material properties.

Fig. 3. Antisymmetric and symmetric eigenvectors.

to estimate their strength capacity. The results of these analyseswere used in order to propose, an appropriate interaction factorin the linear interaction equation of EC3 for straight members,in order to include all the nonlinearity effects. As a result, itis possible to check the carrying capacity of arches by simplysubstituting the maximum axial and bending moment forces,which need not be situated at the same cross-section, obtainedfrom a linear analysis.

3. EC3 linear interaction equation for beam–columnmembers

The in-plane linear interaction equation for beam–columnmembers with class 1 or 2 cross-sections in combinedcompression and bending that is provided in EC3 [12] is:

NEd

χyA fyγM1

+ kyyMy,EdWpl,y fyγM1

≤ φ. (1)

For the application of this equation for the case of archesNEd , My,Ed are taken as the design values of compressionand bending actions, which are the maximum values of theinternal actions appearing along the arch, not necessarily at thesame cross-section, A is the area of the cross-section, Wpl,y


ARTICLE IN PRESSC.A. Dimopoulos, C.J. Gantes / Journal of Constructional Steel Research ( ) – 3

is the plastic section modulus, fy is the yield stress, χy is areduction factor due to in-plane flexural buckling, kyy is aninteraction factor due to combined compression and bending.The expression on the left part of inequality (1), defined asthe utilization factor, should be bounded for design purposesby a maximum allowable value, denoted with φ, where φ = 1according to [12].

The reduction factor χy is obtained from

χy =1

Φ +

√[Φ2 − λ̄2

y

] (2)

where

Φ = 0.50[1 + α

(λ̄y − 0.20

)+ λ̄2

y

](3)

λ̄y =

√A fy

Ncr,y=

Lcr,y

iy

1λ1

(4)

λ1 = π

√E

fy(5)

Lcr,y is the equivalent buckling length. For in-plane buckling ofarches, this length can be taken as Lcr,y = γ S, where γ is afactor that takes the value 0.50 in the case of pin-ended archesand 0.35 in the case of fixed arches [13].

For a hot-rolled circular hollow section the “a” bucklingcurve is the appropriate one, so the imperfection factor α isequal to 0.21. The interaction factor kyy can be computed withtwo alternative, methods, outlined in Annexes A and B of Part1-1 of EC3 [12].

3.1. Method 1

According to method 1 [14], the interaction factor is:

kyy = CmyCmLTµy

1 −NEdNcr,y

1Cyy

. (6)

Since the in-plane strength of the arches is studied, λ̄0 = 0,where λ̄0 is a non-dimensional slenderness factor for lateral-torsional buckling due to uniform bending moment. This meansthat the flexural buckling factor Cmy = Cmy,0, the lateral-torsional buckling factor CmLT = 1 and the lateral-torsionalfactor bLT = 0.

For the computation of the above interaction factor thefollowing variables must first be computed.

Cmy,0 = 1 +

(π2 E Iy |δ|

L2cr

∣∣My,Ed∣∣ − 1

)NEd

Ncr,y(7)

Cyy = 1 +(wy − 1

) [(2 −

1.6wy

C2my λ̄max −

1.6wy

C2my λ̄

2max

)× n pl − bLT

]>

Wel,y

Wpl,y(8)

Ncr,y = π2 E Iy

L2cr,y

, µy =

1 −NEdNcr,y

1 − χyNEdNcr,y

,

wy =Wpl,y

Wel,y, n pl =

NEd

NRk/γM1

(9)

where Iy is the in-plane second moment of area of the cross-section, δ is the value of the vertical displacement of thecrown of the arch obtained from a linear analysis, My,Ed is themaximum bending moment, Wel,y and Wpl,y are the in-planeelastic and plastic section moduli, λ̄max = λ̄y , NRk = A fy .

The variable Cmy,0 depends on the bending diagram of thearch and is chosen to be equal to the expression of Eq. (7),because the corresponding bending diagram from [12] is similarand closer to the bending diagram exhibited by one-half of anarch, either fixed or pinned.

3.2. Method 2

The modification of this method for the case of arches liesin the appropriate computation of the factor Cmy , as explainednext. According to this method [15] the interaction factor is:

kyy = Cmy

(1 +

(λ̄y − 0.2

) NEd

χy NRk/γM1

)6 Cmy

(1 + 0.8

NEd

χy NRk/γM1

)(10)

where

Cmy =

0.2 + 0.8αs > 0.40, 0 6 αs 6 1,−1 6 ψ 6 10.1 − 0.8αs > 0.40, −1 6 αs < 0, 0 6 ψ 6 10.1 (1 − ψ)− 0.8αs > 0.40, −1 6 αs < 0,

−1 6 ψ < 0

(11)

αs = Ms/Mh,Ms is the bending moment at the quarter pointof the arch, γM1 = 1.00 is a partial factor,

Mh = max [|M (0)| , |M (S/2)|] and (12)

ψ =

{M (S/2) /M(0), |M (S/2)| < |M(0)|M(0)/M (S/2) , |M(0)| < |M (S/2)|

(13)

where M(0), M(S/2) are the bending moments that appear atthe support and the crown of the arch, respectively. For pin-ended arches the parameter ψ is always equal to zero becauseM(0) = 0. The corresponding parameter ψ for fixed arches isalways different from zero.

4. Use of EC3 linear interaction equation for straightbeam–column members for checking in-plane inelasticstability of circular arches

4.1. Pin-ended arches

A representative sample of two hundred and fifty two archeswere used to investigate the in-plane strength of pin-ended steelarches subjected to uniformly distributed vertical load along theentire arch. They were divided into 14 groups with slendernessratio 0.5S/ i in the range from 40 to 170 and the subtendedangle 2Θ in the range from 10◦ to 180◦.



Fig. 4. Load–displacement curve for a shallow pin-ended steel arch.

Fig. 5. Load–displacement curve for a deep pin-ended steel arch.

In Figs. 4 and 5 some typical load–displacement curvesfor the studied arches are given. On the horizontal axis thedimensionless vertical displacement vc/ f of the arch crown isplotted, where f is the height of the arch. The dimensionlessload q/qL B is plotted on the vertical axis, where qL B is thelinearized buckling load. These curves were obtained eitherthrough a geometrically nonlinear elastic analysis with initialimperfections (GNIA), or through a material and geometrynonlinear analysis with initial imperfections (GMNIA). Theequilibrium curve in Fig. 4 is representative of a shallow archcharacterized by snap-through buckling, while that in Fig. 5is representative of a deep arch characterized by materialfailure. The ultimate load, denoted as qGMNIA, is appliedin a subsequent linear elastic analysis in order to obtainthe maximum compression force and the maximum bendingmoment that are developed along the arch. These maximumvalues do not necessarily appear at the same cross-section andare the design values for the compression force and the bendingmoment that are encountered in the following linear interactionequations.

Fig. 6. Strength of pin-ended steel arches — method 1.

Fig. 7. Strength of pin-ended steel arches with λs/λT — method 1.

4.1.1. Method 1

In Figs. 6 and 7 the predictions of the interaction equation (1)with φ = 1 are given, and they are compared with thefinite element results. It is concluded that in most cases thepredictions of Eq. (1) are significantly conservative. In somecases of very shallow arches, the predictions are not on the safeside. So, it is seen that the interaction Eq. (1) is not adequateenough to be used for the design of pin-ended circular arches.

A modified interaction equation is proposed for the designof circular arches:

NEd

χyA fyγM1

+kyy

p1

My,EdWpl,y fyγM1

≤ φ. (14)

In Fig. 8 the three-dimensional graphs of p1 and p∗

1 aregiven. p∗

1 is the factor that results in φ = 1. p1 is anapproximation of the exact factor p∗

1 that is obtained usingthe optimization tools of Matlab [16], given by the following



Fig. 8. Graphic representation of factors p1 and p∗1 .

Fig. 9. Strength of pin-ended steel arches — modified method 1.

equation:

p1 =

0.661 + 0.125 (λs/λT )− 0.000155 (0.5S/ i)

− 0.000595 (λs/λT ) (0.5S/ i) ,15 6 λs/λT 6 50

4.10`n−1.59 (0.0681 (λs/λT )) ,

50 < λs/λT 6 140

(15)

where λs = S2/4i R, λT = (γ S/ i)√

fy/(π2 E

).

In Figs. 9 and 10, the strengths of steel arches using modifiedEq. (14) are given. It is verified that the modified Eq. (14)provides close to lower bound predictions of strength. Fordesign purposes it is suggested that the maximum allowablevalue of the utilization factor φ is taken equal to 0.90. Moreover,the modified Eq. (14) should be used for λs/λT > 15.

4.1.2. Method 2In Figs. 11 and 12 the predictions of the interaction Eq. (1)

with φ = 1 and the interaction factor calculated accordingto method 2 are given, and they are compared with the finite

Fig. 10. Strength of pin-ended steel arches with λs/λT — modified method 1.

Fig. 11. Strength of pin-ended steel arches — method 2.

element results. In contrast to the results of method 1, theseresults are in many cases not on the safe side. Thus, it isconcluded that neither interaction Eq. (1) using method 2 forthe determination of the interaction factor is appropriate to beused for the design of pin-ended circular arches.

A modified interaction equation is also proposed:

NEd

χyA fyγM1

+kyy

p2

My,EdWpl,y fyγM1

≤ φ. (16)

In Fig. 13 the three-dimensional graphs of p2 and p∗

2 aregiven. p∗

2 is that factor that results in φ = 1. p2 is anapproximation of the exact factor p∗

2 obtained by Matlab [16]and given by the following equation:

p2 =

0.704 + 0.0168 (λs/λT )− 0.00509 (0.5S/ i)+ 0.0000121 (λs/λT ) (0.5S/ i) ,15 6 λs/λT < 50

−0.065 + 0.00628 (λs/λT )+ 0.0191 (0.5S/ i)− 0.000138 (λs/λT ) (0.5S/ i) ,50 6 λs/λT 6 140.

(17)



Fig. 12. Strength of pin-ended steel arches with λs/λT — method 2.

Fig. 13. Graphic representation of factors p2 and p∗2 .

In Figs. 14 and 15, the strengths of steel arches usingmodified Eq. (16) are given. It is seen that the modified Eq.(16) provides sufficiently close to lower bound predictions. Fordesign purposes it is suggested that the maximum allowablevalue of the utilization factor φ is taken equal to 0.90 for15 6 λs/λT < 60 and 0.95 for λs/λT > 60.

4.2. Fixed arches

A representative sample of one hundred and ninety eightarches is used to investigate the in-plane strengths of fixedsteel arches subjected to uniformly distributed vertical loadalong the entire arch. They are divided into 11 groups with theslenderness ratio 0.5S/ i in the range from 40 to 170 and thesubtended angle 2Θ in the range from 10◦ to 180◦.

4.2.1. Method 1In Figs. 16 and 17 the predictions of the interaction Eq.

(1) with φ = 1, compared with the finite element results aregiven. It is concluded that in all cases the predictions of Eq.(1) are significantly conservative. Thus, it is observed that the

Fig. 14. Strength of pin-ended steel arches — modified method 2.

Fig. 15. Strength of pin-ended steel arches with λs/λT — modified method 2.

interaction Eq. (1) is not adequate to be used in the case of fixedcircular arches.

A modified interaction equation is proposed for the designof circular fixed steel arches:

NEd

χyA fyγM1

+kyy

f1

My,EdWpl,y fyγM1

≤ φ. (18)

In Fig. 18 the three-dimensional graphics of f1 and f ∗

1are given. f ∗

1 is the factor that results in φ = 1. f1 is anapproximation of the exact factor f ∗

1 obtained by Matlab andgiven by the following equation:

f1 =

0.168 + 0.0795 (λs/λT )+ 0.00955 (0.5S/ i)

− 0.000251 (λs/λT ) (0.5S/ i) ,20 6 λs/λT < 70

11.176 ln−1.906 (0.0807 (λs/λT )) ,

70 6 λs/λT < 195.

(19)

In Figs. 19 and 20, the strengths of fixed steel arches usingmodified Eq. (18) are given. It is verified that the modifiedEq. (18) provides close to lower bound predictions. For designpurposes it is suggested that the maximum allowable value of



Fig. 16. Strength of fixed steel arches — method 1.

Fig. 17. Strength of fixed steel arches with λs/λT — method 1.

Fig. 18. Graphic representation of factors f1 and f ∗1 .

the utilization factor φ be taken equal to 0.90 for 20 6 λs/λT <

195.

Fig. 19. Strength of fixed steel arches — modified method 1.

Fig. 20. Strength of fixed steel arches with λs/λT — modified method 1.

4.2.2. Method 2

In Figs. 21 and 22 the predictions of the interaction Eq. (1)with φ = 1 and the interaction factor calculated according tomethod 2, compared with the finite element results are given.In contrast to the results of method 1, these results are in thecase of small values of the ratio λs/λT not on the safe side.Furthermore, the results are generally less conservative than thecorresponding results of method 1.

A modified interaction equation is proposed for the designof circular arches:

NEd

χyA fyγM1

+kyy

f2

My,EdWpl,y fyγM1

≤ φ. (20)

In Fig. 23 the three-dimensional graphics of f2 and f ∗

2are given. f ∗

2 is that factor that results in φ = 1. f2 is anapproximation of the exact factor f ∗

2 obtained by Matlab and



Table 1Geometry, material and cross-sections of the three pinned example arches

θ (◦) R (m) S (m) fy (MPa) E (GPa) D (m) t (m) 0.5S/ i

P1 30 131.7145 68.9656 275 210 0.80 0.02 125P2 100 39.5144 68.9656 275 210 0.80 0.02 125P3 160 24.6965 68.9656 275 210 0.80 0.02 125

Fig. 21. Strength of fixed steel arches — method 2.

Fig. 22. Strength of fixed steel arches with λs/λT — method 2.

given by the following equation:

f2 =

0.195 + 0.0239 (λs/λT )+ 0.00101 (0.5S/ i)− 0.00013 (λs/λT ) (0.5S/ i) ,20 6 λs/λT < 70

0.230 + 0.00714 (λs/λT )+ 0.0102 (0.5S/ i)− 0.0000775 (λs/λT ) (0.5S/ i) ,70 6 λs/λT < 120

0.0344 + 0.00581 (λs/λT )+ 0.0131 (0.5S/ i)− 0.0000797 (λs/λT ) (0.5S/ i) ,120 6 λs/λT < 195.

(21)

Fig. 23. Graphic representation of factors f2 and f ∗2 .

Fig. 24. Strength of fixed steel arches — modified method 2.

In Figs. 24 and 25, the strengths of fixed steel arches usingmodified Eq. (20) are given also. It is seen that the modified Eq.(20) provides sufficient close to lower bound predictions. Fordesign purposes it is suggested that the maximum allowablevalue of the utilization factor φ be taken equal to 0.90 for20 6 λs/λT < 195.

5. Examples

For the demonstration of the validity of the two modifiedinteraction Eqs. (14) and (16), three pin-ended and threefixed arches with a variety of geometries and cross-sectionalcharacteristics, listed in Tables 1 and 2, respectively, have been



Table 2Geometry, material and cross-sections of the three fixed example arches

θ (◦) R (m) S (m) fy (MPa) E (GPa) D (m) t (m) 0.5S/ i

F1 30 131.7145 68.9656 275 210 0.80 0.02 125F1 100 39.5144 68.9656 275 210 0.80 0.02 125F1 170 23.2437 68.9656 275 210 0.80 0.02 125

Table 3Utilization factors for the three pinned example arches

Eq. (1) Method 1 Eq. (1) Method 2 Eq. (14) Eq. (16)

P1 1.1250 0.9069 1.0064 0.9610P2 1.2193 1.1185 0.9830 0.9835P3 1.1887 0.9627 1.0222 0.9672

Table 4Utilization factors for the three fixed example arches

Eq. (1) Method 1 Eq. (1) Method 2 Eq. (18) Eq. (20)

F1 1.6197 0.90 1.0561 1.0033F1 1.5087 1.0813 0.9658 0.9910F1 1.7147 0.9413 1.1344 0.9778

studied. The utilization factors presented in Table 3 show thatthe proposed Eqs. (14) and (16) provide improved accuracycompared to methods 1 and 2 of EC3 and could be used forthe design of pinned arches under the aforementioned loadingpattern. The same conclusions are drawn for fixed arches fromthe results presented in Table 4.

6. Conclusions

In this paper, an investigation of the effectiveness of thelinear interaction equation for straight beam–column membersaccording to the EC3 provisions for the design of circular steelarches subjected to a uniformly distributed load is carried out.Modified interaction equations for the design of such arches areproposed, making use of the two methods provided in EC3 forthe determination of the interaction factor kyy .

It has been concluded that the linear interaction equation forthe beam–column members provided by EC3 is not sufficientfor the design of circular steel arches. Particularly, usingmethod 1 for the determination of the interaction factor kyyleads, for the majority of arches, except some very shallowarches, to very conservative estimations. Using method 2 forthe determination of the interaction factor kyy may lead eitherto conservative or to unsafe estimations, depending on the case.

Thus, modified interaction equations are proposed for thedesign of both pin-ended and fixed circular steel arches.The linear interaction equation for beam–column members ismodified through a factor p1 for pin-ended arches ( f1 forfixed arches) when using method 1 for the determination ofthe interaction factor, or p2 ( f2) when using method 2 for thedetermination of the interaction factor. The proposed modifiedinteraction equations give sufficiently close to lower boundpredictions of strength.

Fig. 25. Strength of fixed steel arches with λs/λT — modified method 2.

References

[1] Timoshenko SP, Gere JM. Theory of elastic stability. 2nd ed. New York(NY): McGraw-Hill Book Co., Inc.; 1961.

[2] Schreyer HL, Masur EF. Buckling of shallow arches. In: Proceedingsof the American society of civil engineers. Journal of the EngineeringMechanics Division 1996;92(EM4).

[3] Pi YL, Bradford MA, Uy B. In-plane stability of arches. InternationalJournal of Solids and Structures 2002;39:105–25.

[4] Pi YL, Trahair NS. Nonlinear buckling and postbuckling of elastic arches.Engineering Structures 1998;20(7):571–9.

[5] Pi YL, Trahair NS. In-plane inelastic buckling and strengths of steelarches, ASCE. Journal of Structural Engineering 1996;122(7).

[6] Kuranishi S, Yabuki T. Some numerical estimation of the ultimate in-plane strength of two-hinged steel arches. Proceedings of JSCE 1979;287:155–8.

[7] Verstappen I, Snijger H, Bijlaard FSK, Steenbergen HMGM. Design rulesfor steel arches — in-plane stability. Journal of Constructional SteelResearch 1998;46(1–3):125–6.

[8] Pi YL, Trahair NS. In-plane buckling and design of steel arches. Journalof Structural Engineering 1999;125(11).

[9] ADINA System 8.3. Release notes. ADINA R & D Inc, 71 Elton Avenue,Watertown, MA 02472 USA. October 2005.

[10] European standard. Eurocode 3: Design of steel structures. Part 2: Steelbridges. Annex D [informative]. 2004. p. 91–100.

[11] Dimopoulos CA, Gantes CJ. Nonlinear in-plane behaviour of circularsteel arches with hollow circular cross-section. Journal of ConstructionalSteel Research [in press].

[12] Eurocode 3: Design of steel structures. Part 1-1: General rules and rulesfor buildings, prEN 1993-1-1. 2004.

[13] Pi YL, Trahair NS. In-plane inelastic buckling and strengths of steelarches. Journal of Structural Engineering 1996;122(7).

[14] Boissonnade N, Jaspart JP, Muzeau JP, Villette M. New interactionformulae for beam–columns in Eurocode 3: The French–Belgianapproach. Journal of Constructional Steel Research 2004;60:421–31.

[15] Greiner R, Lindner J. Interaction formulae for member subjected tobending and axial compression in EUROCODE 3-the method 2 approach.Journal of Constructional Steel Research 2006;62:757–70.

[16] MATLAB. Version 7 (R14), Copyright 1984-2004, The MathWorks Inc.


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