Review of plate buckling rules in EN 1993-1-5

228 © Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Steel Construction 2 (2009), No. 4

EN 1993-1-5 provides harmonized European design rules for plated struc-tures. It is a step forward in the harmonization process, but like all the Eu-rocodes it includes many options for national choices, in terms of para-meters and also methods, which leads to quite different results. Actually,there are four different methods for dealing with buckling problems. Onepurpose of this paper is to illustrate differences by way of examples andalso to suggest topics for studies intended to improve the design rulesand bring them closer together. The revision of EN 1993-1-5 is due to takeplace around 2014 and there is ample time for performing research pro-jects that can form the basis for the new version. Examples of such topicsare the recalibration of buckling curves, reviewing the interaction checksand the verification format of the reduced stress method.

1 Introduction

EN 1993-1-5 [1] provides design rules for plated structureswith the main focus on girders for which plate bucklinginfluences the behaviour, so-called class 4 sections. How -ever, the code also provides some design rules applicableto all types of cross-section, e.g. rules for shear lag andpatch loading. It represents a big step forward in the har-monization of European design standards but due to dif-ferent traditions there are still several openings for na-tional choices. It was developed between 2000 and 2004by a project team chaired by the first author and in whichProfessor Gerhard Sedlacek was a prominent member. Heand his team in Aachen made substantial contributions tothe standard, including providing Dr. Christian Müller,RWTH, as technical secretary. Following normal CENprocedures it would soon be time to revise EN 1993-1-5,but that has been postponed until around 2014, which means that there are several years available for finding improvements and the purpose of this paper is to indicateissues that need further studies. Several of the proposalsare quite substantial tasks suitable for PhD projects andhopefully someone will be attracted to them.

Since EN 1993-1-5 was finalized, new findings havebecome available through research projects and some willbe presented here. This paper is aimed at researchers orexperienced engineers and basic concepts are assumed tobe familiar. The content may also be of interest for writingNational Annexes. Notation follows that of EN 1993-1-5

but abbreviations are used where there is no risk of mis -understanding.

2 Effective width method

The effective width method for describing the effects ofplate buckling due to direct stress is presented in section 4of EN 1993-1-5. However, to cover other buckling phenom-ena and detailing it also relies on sections 5 to 9. This is aset of rules that covers common structures such as I-gird-ers and box girders. The effective width method describesthe effects of plate buckling due to direct stress by reducingthe actual area to an effective area for each plate that issubject to local buckling and in the case of longitudinallystiffened plates also due global plate buckling. The resis-tance of the cross-section is given by a linear stress distrib-ution with the maximum stress equal to the yield strength.It is a basic assumption of the effective width method thatthe yield strength can be reached in a corner of the cross-section or at a supported edge. This assumption is mostlyvalid and has been proven in hundreds of tests, but it mayrequire some restrictions on web slenderness in order toavoid flange-induced buckling and the breakdown of cor-ners between plates forming a small angle.

One objection to the effective width method may bethat a plate in compression may show a sharp drop in re-sistance after the maximum load has been passed. Thismay be correct for an isolated plate, but if the plate is con-nected to other plates that have not reached their yieldstrength, the strains will be controlled by these other plates.This means that the strains will be elastic and small andthe drop in the resistance of the plate that has buckled willbe small until the other plates reach their yield strength.

2.1 Buckling of plates loaded in uniform compression

For the basic case, a plate with hinged edges under uni-form compression, the effective width is given by the Win-ter formula:

(1)

This formula results in a safe estimate of the resistance forplates with small residual stresses but may overestimate theresistance for plates with high residual stresses. This was dis-

bbeff p

p

= =−

ρλ

λ

0 222

.

Review of plate buckling rules in EN 1993-1-5Dedicated to Emeritus Professor Dr.-Ing. Dr. h.c. Gerhard Sedlacek on the occasion of his 70th birthday

Bernt Johansson Milan Veljkovic*

Articles

Received 31 July 2009, accepted 4 September 2009 * Corresponding author: [email protected]

DOI: 10.1002/stco.200910031

229Steel Construction 2 (2009), No. 4

B. Johansson/M. Veljkovic · Review of plate buckling rules in EN 1993-1-5

cussed in the EN 1993-1-5 project team and the conclusionwas that it was mainly a problem of small test specimens inwhich the relation between weld area and plate area waslarge compared to that of full-size structures. Since then,more tests have been added to the database and the ten-dency is clear: specimens with large welds have a resistancelower than (1), see Fig. 1 from [2]. The tests, except thosefrom the literature, were carried out on square boxes of high-strength steel (fy = 420–1100 MPa) and had welds in the cor-ners equal to the plate thickness. Some previous studies haveshown a higher relative resist ance for high-strength steel butthis study shows that there is no such difference, which is adisappointment. The proposal in [2] is to use the formula:

(2)

where

φ = 0.5[1 + αp(λp – λp0) + λp]

with

αp = 0.5 and λp0 = 0.6.

The expression has been proposed by Müller [11] andbeen introduced in Annex B of EN 1993-1-5. In [2] it isapplied to plates with large welds with a shorter plateauand larger imperfection factor. The curve is shown in Fig-ure 1 and it has been calibrated to make a safe estimate ofthe test result.

The question of the influence of the weld size is wortha closer look, which, even if not common with large welds,may be relevant and should therefore be covered. The posi-tive effect would be that such rules would discourageoverdesign of the welds. It is also worth mentioning thatthere are no indications that the rules for webs in bendingoverestimate the effective width.

2.2 Interaction between shear and bending

There are several studies that show that interaction be -tween shear and bending is very weak. The design rules in

ρφ φ λ

=+ −

≤1 1 02

p

.

section 7.1 of EN 1993-1-5 reflect this fact. The interac-tion formula uses the plastic bending resistance as a ref-erence for all cross-section classes and the influence ofthe shear force has been reduced compared to the origi-nal model of Basler [3]. The interaction formula is actu-ally the same as the one in EN 1993-1-1 for plastic resis-tance except that the shear buckling resistance is used in-stead of the plastic shear resistance. Further, there is arule that the interaction need not be checked closer thanhw/2 to an internal support (actually only valid for webswithout longitudinal stiffeners). This latter rule is basedon a judgement that the shear buckling is not critical for atransverse load that is applied close to a support. This islikely to be correct for shear force only, but here there isalso a bending moment with a quite steep gradient. That

Fig. 1. Results from stubcolumn tests on squarewelded based on [2]

Fig. 2. Interaction between moment and shear force, girderswith longitudinal stiffeners [4]

230 Steel Construction 2 (2009), No. 4


means that the bending moment has dropped off signifi-cantly in the design section compared to the maximumvalue. The consequence is that the interaction formulararely governs. It would be worth a study to check this in-teraction in order to simplify the rules or even to omit thecheck completely for certain cases. Fig. 2 shows test re-sults for girders with longitudinal stiffeners [4] evaluatedwith maximum moment and shear and normalized withthe respective resistances based on Swedish design ruleswhich are very similar to EN 1993. It is an indication thatit is sufficient to check the moment and shear resistanceswithout interaction. Further, the Swedish design codeBSK [5] neglects the interaction between shear and bend-ing for class 1 cross-sections. This is consistent with testresults and can be justified by utilizing the strain harden-ing of the material.

3 Reduced stress method3.1 General

The reduced stress method is general and it is able to dealwith complex states of stress including biaxial direct stressand shear stress. For an isolated plate with longitudinal di-rect stress or shear stress, it results in the same resistance asthe effective width method. For combined states of stress,the reduced stress method uses a criterion similar to thevon Mises yield criterion. It has the merit of being generalbut it yields results very different from the interaction for-mulae discussed in section 2.2 above.

The reduced stress method calculates the bucklingstrength expressed as a stress in each individual plate andthe resistance of the cross-section is given by the platewith the lowest strength at a junction between two plates.What this means is that no redistribution of stresses is uti-lized, which is a very conservative approach. The practicalconsequence is that the slenderness of each plate has tobe limited such that the buckling strength is close to theyield strength for economic reasons. This is usuallyachieved by providing the girder with stiffeners, which isunfortunate because longitudinal stiffeners are expensive.Actually, it was shown in [6] that for a composite I-girderbridge the depth had to be over 4 m before it becamecheaper to add longitudinal stiffeners. It was designed us-ing the effective width method, but if it had been designedwith the reduced stress method, longitudinal stiffenerswould have been needed at a depth of about 2.5 m.

Improvements to the reduced stress method havebeen discussed in the commentary to EN 1993-1-5 [7] andin a recent paper from RWTH [8]. One suggestion is to al-low redistribution of stresses such that different plateshave different stress distributions according to theirstrengths. As stated in section 2 above, this would be safe.A modification to the strength criterion is suggested in [8]for the interaction between bending and shear, and theproposal shows that it is possible to bring the methodscloser to each other.

3.2 Example: Biaxial compression

For simplicity, this discussion will be limited to biaxial stress;shear stress is excluded. Further, it is assumed that γM1 =1.0 in order to simplify the formulae.

In brief, the reduced stress method uses load ampli-fiers αult, which is the yield strength divided by the equiva-lent stress according to von Mises yield criterion, and αcr,which is a factor for the actual stresses, to reach the criti-cal level according to elastic plate buckling theory. Theseare used to define a slenderness parameter:

(3)

This slenderness parameter is used for defining reductionfactors for buckling ρx and ρz according to section 4.5.4(1)of EN 1993-1-5. The formula gives an interpolation be-tween plate-like behaviour and column-like behaviour.The verification of the resistance (without partial factors) iscarried out with the following expression in which σx andσz are the applied stresses:

(4)

If the plate is stocky (ρx = ρz = 1), the expression coincideswith the von Mises yield criterion. However, we would ex-pect another type of interaction for slender plates. For instance, the interaction is linear for critical stresses if thebuckling modes coincide.

An alternative procedure for checking this interac-tion is found in [9], developed by Professor TorstenHöglund at KTH, Stockholm, for shell instability. The fullversion also covers shear and the influence of tension aswell as compression. Here, the description is limited to bi-axial compression. The verification is similar to (4) and isas follows:

(5)

where k = 2–3ρxρz

The coefficient k changes the shape of the interactioncurve such that for slender plates it becomes more linear,

σρ

σρ

σρ

σρ

x

x y

z

z y

x

x y

z

z yf fk

f f

⎛

⎝⎜

⎞

⎠⎟ +

⎛

⎝⎜

⎞

⎠⎟ + ≤

2 2

1

σρ

σρ

σρ

σρ

x

x y

z

z y

x

x y

z

z yf f f f

⎛

⎝⎜

⎞

⎠⎟ +

⎛

⎝⎜

⎞

⎠⎟ − ≤

2 2

1

λαα

= ult

cr

Fig. 3. Interaction curve for biaxial buckling according to [8]



see Fig. 3 in which X = σx/(ρxfy) and Z = σz/(ρzfy). In thismethod the reduction factors ρx and ρz are calculated in-dependently in contrast to expression (4) in which theyare calculated for the combined state of stress.

In order to quantify this we consider a square platewith hinged edges according to Fig. 4. Firstly, it is loadedwith uniform longitudinal stresses σx and its propertiesare such that σcrx = fy/2 leading to λ = 1.41 and ρx = 0.597.Now set σx = 0.597fy, meaning that resistance is fully uti-lized, and then add σz = σx/2. Following section 10 it endsup in a utilization (square root of (10.5)) of 1.09 or, inother words, by adding σz the plate has become over-loaded by 9 %. This is a quite small effect and a FE simu-lation reveals that the utilization is 1.38 when σz is added.The interaction formula in (5) in this case has k = 0.93 andresults in a utilization of 1.31, which is fairly close to thecomputer simulation but on the unconservative side.Fig. 4 also shows a full comparison between (5) and theFE simulation for this plate, indicating that (5) has to beadjusted somewhat in order to be safe. This is just one ex-ample and a thorough study is needed before an improvedmethod can be pro posed. The study in [8] is a good start-ing point but it needs to be calibrated for several cases.

4 Method in Annex B

Annex B presents a method for dealing with plate buckl -ing of non-uniform members. It is based on the reducedstress method and uses the same definition of the slen-derness parameter λp, see expression (3). As this is calcu-lated for the total stress field, there may be a need formodifying the buckling curves and Annex B presents aset of curves with a new format (2). It is, however, reason-able to require that they should produce the same resultsas the rules for elementary cases in sections 4 and 5 whenapplied to such cases. This leads to the suggestion for aproject to recalibrate all the buckling curves to create asingle format. This would preferably be carried out basedon critical stresses considering the continuity betweenthe different plates of the cross-section. Such criticalstresses can easily be calcu lated with the EBPlate soft-ware which can be downloaded free of charge [10]. Itwould then be safe to use such critical stresses in design,and if hinged conditions are used as a simplification itwould be conservative.

5 Design by FEM

Annex C of EN 1993-1-5 describes a method for applyingFEM to the design of plated structures. In principle, it isgeneral and can be applied to any kind of structure, but ithas only been calibrated against simple structural elements.It is suggested that more systematic calibrations should bemade against test results. The method will not be describedin detail here but an example is presented in section 7.3and further information can be found in [7] and [11].

6 Patch loading

The rules for patch loading are to be found in section 6 ofEN 1993-1-5 and are fairly new. They use the same proce-dure for finding the resistance as for other buckling phe-

Fig. 5. Computer simulation of patch loading, load deforma-tion curve (top) and stress distribution in the web (bottom) [13]

Fig. 4. Square plate with hinged edgesloaded in biaxial compression σcrx = fy/2



nomena, which is a step forward. There is, however, a dif-ference between the patch loading rules and other platebuckling rules, which was pointed out in [12]. The patchloading curve is much lower than other plate bucklingcurves. The problem is that the plastic resistance for patchloading is not well defined because the resistance in-creases gradually with the deformation, see Fig. 5 [13].The upper diagram in Fig. 5 shows the load as a functionof the shortening of the web from a computer simulation.The solid line in lower diagram in the figure indicates thestress distribution in the web. The blue dashed line is thestress block assumed in EN 1993-1-5, which correspondsto a fairly high plastic resistance, and the red dashed lineshows the stress distribution proposed in [13], which corre-sponds to the red dot on the curve in the upper diagram.This corresponds to a smaller plastic resistance and a re-calibration of the buckling curve led to an expressionmore in line with other plate buckling phenomena, seeFig. 6. The curve is according to (2) with αp = 0.43 and λp0= 0.65 but without the limitation less than 1.0. Actually,the curve rises as high as 1.4 for very stocky plates andfrom the test results it can be seen that it is safe. The in-crease in resistance is caused by strain hardening and re-distribution of stresses.

The critical load used for defining the slenderness forpatch loading is a rather rough estimate for the case thatrotation of the flange is assumed to be prevented at thepoint of load application. This is the case for most testsand also for most applications. However, this assumptionis worth some consideration in the recalibration of thebuckling curves suggested in section 4.

7 Example of application

I-girders are the most common type of plated structureand the girder shown in Fig. 7 will be used as an exampleof the application of the various design rules. The cross-section is class 3 close to the limit between 3 and 4. Thisexample has been chosen in order to make the compari-son between the methods fair. A class 4 section would bevery unfavourable for the reduced stress method.

7.1 Effective width method

The cross-section is fully effective. Verification of the bend-ing resistance is checked at midspan:

MEd = 3500 kNmMRd = 3540 kNmMEd/MRd = 0.99

Note that the bending resistance should be calculated withthe section modulus referred to the centroid of the flange.

The shear buckling resistance is verified at a cross-section hw/2 = 0.5 m from the support and the stiffenersfulfil the rigidity requirements.

VEd =1260 kNVRd = 1320 kNVEd/VRd = 0.95

It should also be shown that the maximum shear does notexceed the plastic shear resistance at the support and thatis also fulfilled.

In this example the load is relatively high and a checkof the web‘s resistance to transverse forces may be required.However, the rules in EN 1993-1-5 section 6 are not applic-able. The interaction is likely to be weak, see section 7.3,but possibly worth examining.

7.2 Reduced stress method

The verification of the web at midspan requires the deter-mination of the load multipliers for yielding αult and forelastic plate buckling of the web αcr. At the top edge of theweb σx = 348 MPa and σz = 28 MPa, which results in αult =1.06. An assumption of the boundary conditions of the webhas to be made in order to determine αcr. EN 1993-1-5

Fig. 6. Proposed new buckling curve for patch loading andtest results [13]

Table 1. Verification of the web according to section 10 ofEN 1993-1-5

1 2 3 4

αcrx 1.30 –

α crz 1.30 –

αcr 0.80 1.10 1.10

λ (10.2) 1.06 0.98 0.98

ρx 0.78 0.90 0.79

ρz 0.45 0.55 0.74

utilization 1.18 1.02 1.20

Fig. 7. I-girder used as example, steel grade S 355, compressionflange supported laterally



does not state explicitly that hinged conditions should beused but the design buckling resistances for longitudinalstress and shear have been evaluated from tests on girderswith flanges but assuming hinged conditions for the webfor defining its slenderness. If those design rules are usedtogether with critical stresses considering the restraint fromthe flanges, the result will be unconservative. We thereforeassume hinged conditions for the web. The results areshown in column 2 of Table 1. The critical stresses havebeen calculated using kσx = 23.9 and kσz = 2. The latter fig-ure is an approximation for a column buckling from thestress distribution in the transverse direction. The load am-plifier for the combined stresses has been calculated usingexpression (10.6) in EN 1993-1-5 and the slenderness para-meter according to expression (10.2). For the longitudinalstresses it is obviously a case of plate-like behaviour andexpression (4.2) of EN 1993-1-5 has been used for ρx. Forthe transverse stresses it is a clear case of column-like be-haviour (no change in the critical stress if the stiffeners atthe support are removed) and expression (6.49) ofEN 1993-1-1 with α = 0.49 has been used for ρz. Finally, theutilization has been calculated as the square root of ex-pression (10.5) of EN 1993-1-5. From column 2 in Table 1it can be seen that this method produces a load that is 18 %higher than the resistance, which is not correct.

Using EBPlate with the actual longitudinal and trans-verse stresses acting simultaneously gives αcr = 1.10 insteadof 0.80 according to expression (10.6). This difference isprobably caused by the big difference between the bucklingdeformations for longitudinal stress with buckling over alength of 0.5 m and the buckling deformation for thetransverse stress with an almost cylindrical buckle alongthe whole girder. The results are shown in column 3 ofTable 1 and the resistance is more reasonable, only 3 %lower than in section 7.1.

The method in Annex B is quite similar to the reducedstress method and the difference is the buckling curves.Using the curves for welded girders gives the results shownin column 4 of Table 1. Note that ρz is substantially higherthan in column 3 because Annex B does not mention col-umn-like behaviour. The great surprise is that now theplate becomes weaker. The load is now 20 % higher thanthe resistance. This is another example that shows theneed to revise the verification format of section 10, butthis is not the only problem that has to be fixed in order toget the resistance right, assuming that section 7.3 gives usthe right answer.

Assuming that column-like behaviour is relevant, thereis a problem with the resistance given by curve c accordingto Table 6.2 of EN 1993-1-1. This cannot be correct for aplate, which has very small residual stresses. The plateaushould be longer and the imperfection factor should besmaller. An indication in this direction can be found inTable 9.1 of EN 1994-2, which specifies maximum dis-tances between connectors of composite plates. The limitfor class 3 corresponds to λ = 0.44. Furthermore, the stressgradient in the transverse direction is quite steep and thegoverning cross-section is not at the edge where σz is max-imum. A remedy may be to apply the idea in sec-tion 6.3.4.2(7) of EN 1993-2 and to perform the bucklingverification at a cross-section 0.25hw from that with maxi-mum stress.

7.3 Design by FEM

The procedure according to Annex C of EN 1993-1-5 isapplied. The software Abacus is used and the model isbuilt up with type S4R shell elements – four-node shell el-ements for general application and very suitable for thinplates. Thin plates have a thickness less than 1/15 of acharacteristic length on the surface of the shell, such as thedistance between supports or the wavelength of a signifi-cant eigenmode [4]. The material behaviour is bilineartype c) as shown in Fig. C.2 of EN 1993-1-5. Imperfectionsare introduced as eigenmodes scaled to a maximum am-

Fig. 8. Second buckling mode, which produced the lowestresistance

Fig. 9. Deformation at failure

Fig. 10. Load deflection curves with initial deformationsfrom the first five eigenmodes



plitude of b/200 = 5 mm. The first eigenmode is an almostcylindrical buckle corresponding to buckling caused bythe transverse stresses. The following eigenmodes were morewavy or mixed. The five first eigenmodes were used as im-perfections in separate runs with results according to Fig. 10.The results differ only slightly, 4 % between the lowest andhighest resistance. The second eigenmode, shown in Fig. 8,produced the lowest resistance, 299 kN/m, correspondingto a utilization of 0.94. As long as the eigenmodes lead tothe same failure mode it is not so important as to whichform is used. The deformation at failure is shown in Fig. 9and the failure mode is web buckling followed by flangebuckling. This estimate of the resistance is likely to be thebest and taking it as a reference the effective widthmethod results in 95 % , the best application of section 10a figure of 92 % and Annex B 78 %. This is all on the safeside but may be a bit too widely spread for a simple case.

8 Conclusions

The present edition of EN 1993-1-5 specifies four methodsfor the design of plated structures and they are in someways inconsistent. The rules are safe or even conservativefor normal girders but in odd cases they may be unconser-vative. The following conclusions in the form of sugges -tions for studies are drawn from this review:– The buckling curves should be recalibrated against testresults and computer simulations to create a single mathe-matical format. This should preferably be carried out usingcritical stresses considering the continuity between theplates because they can be easily calculated with tools likeEBPlate.– The interaction between moment and shear in section 7of EN 1993-1-5 should be reviewed. The question is: Forwhich cases, if ever, is it needed?– The reduced stress method in section 10 of EN 1993-1-5should in the first place be so improved such that it allowsre distribution of stresses between plates. Further, Annex Bshould be merged with section 10. Finally, the verificationformat should be reviewed because the present one onlyworks for stocky plates.– The patch loading rules should be changed in line withthe suggestion in [12] and possibly also extended to covercontinuous loads. The possible interaction with flange-in-duced buckling should be investigated.

References

[1] Eurocode 3 Design of steel structures. Part 1-5 Plated struc-tures, EN 1993-1-5:2006.

[2] Clarin, M.: Plate Buckling Resistance. Patch Loading ofLongitudinally Stiffened Webs and Local Buckling. Doctoralthesis 2007:31, Lulea University of Technology, 2007, ISRN-LTU-DT-07Ú31–SE.

[3] Basler, K.: Strength of plate girders under combined bendingand shear, ASCE Journal, St 7, October 1961.

[4] Höglund, T.: Strength of Steel and Aluminium Plate Girders –Shear Buckling and Overall Web Buckling of Plane and Trapezoidal webs. Comparisons with Tests. Royal Institute ofTechnology, Dept of Structural Engineering, technical report1995:4, Steel structures.

[5] BSK Swedish design rules for steel structures. Boverket1999. ISBN 91-7147-527-3.

[6] COMBRI+ Final report of RFCS project Valorisation ofKnowledge for Competitive Steel and Composite BridgesCOMBRI+.

[7] Johansson, B., Maquoi, R., Sedlacek, G., Müller, C., Beg, D.:Commentary and worked examples to EN 1993-1-5-Platedstructural elements, EUR 22898 EN – 2007, October 2007.

[8] Naumes, J., Feldmann, M., Sedlacek, G.: Gemeinsame Grund-lagen von Methode 1 (wirksame Breiten) und Methode 2 (Beul-spannungsbegrenzung) beim Plattenbeulnachweis nach Euro-code 3 – Teil 1-5. Stahlbau 78 (2009), No. 3, pp. 139–147.

[9] Samuelsson, L., Eggwertz, S. (Eds.): Shell Stability Hand-book. London: Elsevier Applied Science, 1992.

[10] EBPlate http://www.cticm.eu/spip.php?article45 [11] Johansson, B., Veljkovic, M.: Steel Plated Structures. Pro-

gress in Structural Engineering and Materials, Vol. 3, No. 1,January–March 2001, pp. 13–27.

[12] Müller, C.: Zum Nachweis ebener Tragwerke aus Stahl ge-gen seitliches Ausweichen. Aachen: Shaker-Verlag, 2003.

[13] Gozzi, J.: Patch loading resistance of plated girders – Ulti-mate and serviceability limit state. Doctoral Thesis 2007:30,Lulea University of Technology, 2007, ISRN: LTU-DT-07/30-SE.

[14] Documentation for ABAQUS v. 6.8 software, © DassaultSystèmes, 2008.

Keywords: plate buckling; effective width; reduced stress me-thod; patch loading; FEM

Authors:Prof. Dr. Bernt Johansson and Prof. Dr. Milan Veljkovic, LuleaUniversityof Technology, F-Huset, 97187-Lulea, Sweden

Review of plate buckling rules in EN 1993-1-5

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