# SIST EN 1993-1-5:2007

(Main)## Eurocode 3 - Design of steel structures - Part 1-5: Plated structural elements

## Eurocode 3 - Design of steel structures - Part 1-5: Plated structural elements

(1) EN 1993-1-5 gives design requirements of stiffened and unstiffened plates which are subject to inplane

forces.

(2) Effects due to shear lag, in-plane load introduction and plate buckling for I-section girders and box

girders are covered. Also covered are plated structural components subject to in-plane loads as in tanks and

silos. The effects of out-of-plane loading are outside the scope of this document.

NOTE 1: The rules in this part complement the rules for class 1, 2, 3 and 4 sections, see EN 1993-1-1.

NOTE 2: For the design of slender plates which are subject to repeated direct stress and/or shear and also

fatigue due to out-of-plane bending of plate elements (breathing) see EN 1993-2 and EN 1993-6.

NOTE 3: For the effects of out-of-plane loading and for the combination of in-plane effects and out-of-plane

loading effects see EN 1993-2 and EN 1993-1-7.

NOTE 4: Single plate elements may be considered as flat where the curvature radius r satisfies:

t

a

r

2

3 (1.1)

where a is the panel width

t is the plate thickness

## Eurocode 3 - Bemessung und Konstruktion von Stahlbauten - Teil 1-5: Plattenförmige Bauteile

(1) EN 1993 1 5 enthält Regelungen für den Entwurf und die Berechnung von aus ebenen Blechen zusammengesetzten und in ihrer Ebene belasteten Bauteilen mit oder ohne Steifen.

(2) Diese Regelungen gelten für Blechträger mit I Querschnitt und Kastenträger, bei denen ungleichmäßige Spannungsverteilungen infolge Schubverzerrungen sowie Beulen unter Längsspannungen, Schub¬span¬nungen und Querlasten auftreten. Sie gelten auch für ebene Bleche aller anderen Bauteile, z. B. von Tankbauwerken und Silos, soweit Lasten und Beanspruchungen in der Ebene der Bauteile wirken. Die Wirkungen von Lasten quer zur Bauteilebene werden in EN 1993 1 5 nicht behandelt.

ANMERKUNG 1 Die Regelungen in EN 1993 1 5 ergänzen die Regelungen für Querschnitte der Querschnittsklassen 1, 2, 3 und 4, siehe EN 1993 1 1.

ANMERKUNG 2 Regelungen zu schlanken Platten mit wechselnden Längsspannungen und/oder Schubspannungen, die zu Ermüdung durch wechselnde Biegung aus der Plattenebene (Blechatmen) führen können, sind in EN 1993 2 und EN 1993 6 angegeben.

ANMERKUNG 3 Regelungen zur Wirkung von Lasten quer zur Plattenebene und zur Kombination von Lastwirkungen in der Ebene und aus der Ebene sind EN 1993 2 und EN 1993 1 7 zu entnehmen.

ANMERKUNG 4 Einzelne Blechfelder dürfen als eben angesehen werden, wenn für den Krümmungsradius r gilt:

(1.1)

Dabei ist

a die Blechfeldbreite;

t die Blechdicke.

## Eurocode 3 - Calcul des structures en acier - Partie 1-5: Plaques planes

(1) L'EN 1993-1-5 spécifie les exigences de calcul relatives aux plaques raidies et non raidies soumises a des charges dans le plan.

(2) Les effets du traînage de cisaillement, de l'application de charges dans le plan et du voilement des plaques pour les poutres en I a âme pleine et les poutres-caissons sont couverts. Les plaques planes soumises a des charges dans le plan telles que celles exercées dans les réservoirs et les silos, sont également couvertes. Les effets des charges hors du plan ne sont pas traités.

NOTE 1 Les regles définies dans la présente partie completent les regles applicables aux sections de classe 1, 2, 3 et 4 , voir EN 1993-1-1.

NOTE 2 Pour les plaques élancées sur lesquelles s'exercent des contraintes normales et/ou de cisaillement répétées et qui sont soumises a la fatigue due a la flexion hors plan de leurs éléments constitutifs (respiration), voir EN 1993-2 et EN 1993-6.

NOTE 3 Pour les effets des charges exercées hors du plan et pour la combinaison des effets desdites charges et des charges exercées dans le plan, voir EN 1993-2 et EN 1993-1-7.

NOTE 4 Les plaques simples peuvent etre considérées comme planes lorsque le rayon de courbure r satisfait :

(1.1)

ou

a est la largeur du panneau ;

t est l'épaisseur de la plaque.

## Evrokod 3: Projektiranje jeklenih konstrukcij - 1-5. del: Elementi pločevinaste konstrukcije

(1) Standard EN 1993-1-5 podaja zahteve za projektiranje utrjenih ali neutrjenih plošč, ki so podvržene silam v ravnini.

(2) Zajeti so učinki zaradi strižne podajnosti, nastanka obtežbe v ravnini in upogibanja plošče za I-nosilce in škatlaste nosilce. Zajeti so tudi prevlečeni sestavni deli konstrukcij, ki so podvrženi obtežbam v ravnini, kot so rezervoarji in silosi. Učinki obtežb zunaj ravnine niso zajeti v tem dokumentu.

OPOMBA 1: Pravila v tem delu dopolnjujejo pravila za prereze razreda 1, 2, 3 in 4, glej standard EN 1993-1-1.

OPOMBA 2: Za projektiranje vitkih plošč, ki so podvržene ponavljajočim se neposrednim napetostim in/ali strižnim napetostim in tudi utrujenosti zaradi upogibanja ploščatih elementov zunaj ravnine (dihanje), glej standarda EN 1993-2 in EN 1993-6.

OPOMBA 3: Za učinke obtežb zunaj ravnine in za kombinacijo učinkov v ravnini in učinkov obtežb zunaj ravnine glejte standarda EN 1993-2 in EN 1993-1-7.

OPOMBA 4: Posamezni ploščati elementi se lahko štejejo za ravne, ko polmer ukrivljenosti r izpolnjuje:

tar23 (1.1), pri čemer je a širina plošče, t je debelina plošče

### General Information

### RELATIONS

### Standards Content (sample)

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.Eurocode 3 - Design of steel structures - Part 1-5: Plated structural elementsNRQVWUXNFLMHEurocode 3 - Calcul des structures en acier - Partie 1-5: Plaques planesEurocode 3 - Bemessung und Konstruktion von Stahlbauten - Teil 1-5: Plattenförmige BauteileTa slovenski standard je istoveten z:EN 1993-1-5:2006SIST EN 1993-1-5:2007en91.080.10Kovinske konstrukcijeMetal structures91.010.30Technical aspectsICS:SIST ENV 1993-1-5:20011DGRPHãþDSLOVENSKI

STANDARDSIST EN 1993-1-5:200701-marec-2007EUROPEAN STANDARDNORME EUROPÉENNEEUROPÄISCHE NORMEN 1993-1-5October 2006ICS 91.010.30; 91.080.10Supersedes ENV 1993-1-5:1997

English VersionEurocode 3 - Design of steel structures - Part 1-5: Platedstructural elementsEurocode 3 - Calcul des structures en acier - Partie 1-5:Plaques planesEurocode 3 - Bemessung und konstruktion von Stahlbauten- Teil 1-5: PlattenbeulenThis European Standard was approved by CEN on 13 January 2006.CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this EuropeanStandard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such nationalstandards may be obtained on application to the Central Secretariat or to any CEN member.This European Standard exists in three official versions (English, French, German). A version in any other language made by translationunder the responsibility of a CEN member into its own language and notified to the Central Secretariat has the same status as the officialversions.CEN members are the national standards bodies of Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France,Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania,Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.EUROPEAN COMMITTEE FOR STANDARDIZATIONCOMITÉ EUROPÉEN DE NORMALISATIONEUROPÄISCHES KOMITEE FÜR NORMUNGManagement Centre: rue de Stassart, 36

B-1050 Brussels© 2006 CENAll rights of exploitation in any form and by any means reservedworldwide for CEN national Members.Ref. No. EN 1993-1-5:2006: E

EN 1993-1-5: 2006 (E)2 Content Page 1 Introduction 5 1.1 Scope 5 1.2 Normative references 5 1.3 Terms and definitions 5 1.4 Symbols 6 2 Basis of design and modelling 7 2.1 General 7 2.2 Effective width models for global analysis 7 2.3 Plate buckling effects on uniform members 7 2.4 Reduced stress method 8 2.5 Non uniform members 8 2.6 Members with corrugated webs 8 3 Shear lag in member design 9 3.1 General 9 3.2 Effectives width for elastic shear lag 9 3.3 Shear lag at the ultimate limit state 12 4 Plate buckling effects due to direct stresses at the ultimate limit state 13 4.1 General 13 4.2 Resistance to direct stresses 13 4.3 Effective cross section 13 4.4 Plate elements without longitudinal stiffeners 15 4.5 Stiffened plate elements with longitudinal stiffeners 18 4.6 Verification 21 5 Resistance to shear 21 5.1 Basis 21 5.2 Design resistance 22 5.3 Contribution from the web 22 5.4 Contribution from flanges 25 5.5 Verification 25 6 Resistance to transverse forces 25 6.1 Basis 25 6.2 Design resistance 26 6.3 Length of stiff bearing 26 6.4 Reduction factor cF for effective length for resistance 27 6.5 Effective loaded length 27 6.6 Verification 28 7 Interaction 28 7.1 Interaction between shear force, bending moment and axial force 28 7.2 Interaction between transverse force, bending moment and axial force 29 8 Flange induced buckling 29 9 Stiffeners and detailing 30 9.1 General 30 9.2 Direct stresses 30 9.3 Shear 34 9.4 Transverse loads 35 10 Reduced stress method 36 Annex A (informative) Calculation of critical stresses for stiffened plates 38

EN 1993-1-5: 2006 (E)3 Annex B (informative) Non uniform members

43 Annex C (informative) Finite Element Methods of Analysis (FEM) 45 Annex D (informative) Plate girders with corrugated webs 50 Annex E (normative) Alternative methods for determining effective cross sections 53

EN 1993-1-5: 2006 (E)4 Foreword

This European Standard EN 1993-1-5,, Eurocode 3: Design of steel structures Part 1.5: Plated structural elements, has been prepared by Technical Committee CEN/TC250 « Structural Eurocodes », the Secretariat of which is held by BSI. CEN/TC250 is responsible for all Structural Eurocodes.

This European Standard shall be given the status of a National Standard, either by publication of an identical text or by endorsement, at the latest by April 2007 and conflicting National Standards shall be withdrawn at latest by March 2010.

This Eurocode supersedes ENV 1993-1-5.According to the CEN-CENELEC Internal Regulations, the National Standard Organizations of the following countries are bound to implement this European Standard: Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.

National annex for EN 1993-1-5This standard gives alternative procedures, values and recommendations with notes indicating where national choices may have to be made. The National Standard implementing EN 1993-1-5 should have a National Annex containing all Nationally Determined Parameters to be used for the design of steel structures to be constructed in the relevant country.

National choice is allowed in EN 1993-1-5 through: – 2.2(5) – 3.3(1) – 4.3(6) – 5.1(2) – 6.4(2) – 8(2) – 9.1(1) – 9.2.1(9) – 10(1) – 10(5) – C.2(1) – C.5(2) – C.8(1) – C.9(3) – D.2.2(2)

EN 1993-1-5: 2006 (E)5 1 Introduction 1.1 Scope

(1) EN 1993-1-5 gives design requirements of stiffened and unstiffened plates which are subject to in-plane forces. (2) Effects due to shear lag, in-plane load introduction and plate buckling for I-section girders and box girders are covered. Also covered are plated structural components subject to in-plane loads as in tanks and silos. The effects of out-of-plane loading are outside the scope of this document.

NOTE 1:The rules in this part complement the rules for class 1, 2, 3 and 4 sections, see EN 1993-1-1.

NOTE 2:For the design of slender plates which are subject to repeated direct stress and/or shear and also fatigue due to out-of-plane bending of plate elements (breathing) see EN 1993-2 and EN 1993-6.

NOTE 3:For the effects of out-of-plane loading and for the combination of in-plane effects and out-of-plane loading effects see EN 1993-2 and EN 1993-1-7. NOTE 4:

Single plate elements may be considered as flat where the curvature radius r satisfies:

tar2³(1.1) where a is the panel width

t is the plate thickness 1.2 Normative references

(1) This European Standard incorporates, by dated or undated reference, provisions from other publications. These normative references are cited at the appropriate places in the text and the publications are listed hereafter. For dated references, subsequent amendments to or revisions of any of these publications apply to this European Standard only when incorporated in it by amendment or revision. For undated references the latest edition of the publication referred to applies. EN 1993-1-1 Eurocode 3 :Design of steel structures: Part 1-1: General rules and rules for buildings 1.3 Terms and definitions

For the purpose of this standard, the following terms and definitions apply: 1.3.1

elastic critical stress stress in a component at which the component becomes unstable when using small deflection elastic theory of a perfect structure 1.3.2

membrane stress stress at mid-plane of the plate 1.3.3gross cross-section the total cross-sectional area of a member but excluding discontinuous longitudinal stiffeners 1.3.4

effective cross-section and effective width the gross cross-section or width reduced for the effects of plate buckling or shear lag or both; to distinguish between their effects the word “effective” is clarified as follows: “effectivep“ denotes effects of plate buckling

EN 1993-1-5: 2006 (E)“effectives“ denotes effects of shear lag “effective“ denotes effects of plate buckling and shear lag 1.3.5

plated structure a structure built up from nominally flat plates which are connected together; the plates may be stiffened or unstiffened 1.3.6

stiffener a plate or section attached to a plate to resist buckling or to strengthen the plate; a stiffener is denoted:

– longitudinal if its direction is parallel to the member;– transverse if its direction is perpendicular to the member. 1.3.7

stiffened plate plate with transverse or longitudinal stiffeners or both 1.3.8

subpanel unstiffened plate portion surrounded by flanges and/or stiffeners 1.3.9

hybrid girder girder with flanges and web made of different steel grades; this standard assumes higher steel grade in flanges compared to webs 1.3.10

sign convention unless otherwise stated compression is taken as positive 1.4 Symbols

(1) In addition to those given in EN 1990 and EN 1993-1-1, the following symbols are used: As total area of all the longitudinal stiffeners of a stiffened plate; Ast gross cross sectional area of one transverse stiffener; Aeff

effective cross sectional area; Ac,eff effectivep cross sectional area; Ac,eff,loc effectivep cross sectional area for local buckling; a length of a stiffened or unstiffened plate; b width of a stiffened or unstiffened plate; bw clear width between welds;

beff effectives width for elastic shear lag; FEd design transverse force; hw clear web depth between flanges; Leff

effective length for resistance to transverse forces, see 6; Mf.Rddesign plastic moment of resistance of a cross-section consisting of the flanges only; Mpl.Rd design plastic moment of resistance of the cross-section (irrespective of cross-section class); MEd design bending moment; NEd design axial force; t thickness of the plate;

EN 1993-1-5: 2006 (E)7 VEd design shear force including shear from torque; Weff

effective elastic section modulus;

effectives width factor for elastic shear lag;

(2) Additional symbols are defined where they first occur.

2 Basis of design and modelling 2.1 General

(1)P The effects of shear lag and plate buckling shall be taken into account at the ultimate, serviceability or fatigue limit states. NOTE:

Partial factors gM0 and gM1 used in this part are defined for different applications in the National Annexes of EN 1993-1 to EN 1993-6. 2.2 Effective width models for global analysis

(1)P The effects of shear lag and of plate buckling on the stiffness of members and joints shall be taken into account in the global analysis. (2) The effects of shear lag of flanges in global analysis may be taken into account by the use of an effectives width. For simplicity this effectives width may be assumed to be uniform over the length of the span. (3) For each span of a member the effectives width of flanges should be taken as the lesser of the full width and L/8 per side of the web, where L is the span or twice the distance from the support to the end of a cantilever. (4) The effects of plate buckling in elastic global analysis may be taken into account by effectivep cross sectional areas of the elements in compression, see 4.3.

(5) For global analysis the effect of plate buckling on the stiffness may be ignored when the effectivep cross-sectional area of an element in compression is

larger than rlim times the gross cross-sectional area of the same element. NOTE 1:

The parameter rlim may be given in the National Annex. The value rlim = 0,5 is recommended.

NOTE 2:For determining the stiffness when (5) is not fulfilled, see Annex E. 2.3 Plate buckling effects on uniform members

(1) Effectivep width models for direct stresses, resistance models for shear buckling and buckling due to transverse loads as well as interactions between these models for determining the resistance of uniform members at the ultimate limit state may be used when the following conditions apply: – panels are rectangular and flanges are parallel;

– the diameter of any unstiffened open hole or cut out does not exceed 0,05b, where b is the width of the panel.

NOTE:The rules may apply to non rectangular panels provided the angle alimit (see Figure 2.1) is not greater than 10 degrees. If limit exceeds 10, panels may be assessed assuming it to be a rectangular panel based on the larger of b1 and b2 of the panel.

EN 1993-1-5: 2006 (E)Figure 2.1:

Definition of angle aaaa (2) For the calculation of stresses at the serviceability and fatigue limit state the effectives area may be used if the condition in 3.1 is fulfilled. For ultimate limit states the effective area according to 3.3 should be used with b replaced by bult. 2.4 Reduced stress method

(1) As an alternative to the use of the effectivep width models for direct stresses given in sections 4 to 7, the cross sections may be assumed to be class 3 sections provided that the stresses in each panel do not exceed the limits specified in section 10. NOTE:

The reduced stress method is analogous to the effectivep width method (see 2.3) for single plated elements. However, in verifying the stress limitations no load shedding has been assumed between the plated elements of the cross section. 2.5 Non uniform members

(1) Non uniform members (e.g. haunched members, non rectangular panels) or members with regular or irregular large openings may be analysed using Finite Element (FE) methods.

NOTE 1:See Annex B for non uniform members.

NOTE 2:

For FE-calculations see Annex C. 2.6 Members with corrugated webs

(1) For members with corrugated webs, the bending stiffness should be based on the flanges only and webs should be considered to transfer shear and transverse loads.

NOTE:For plate buckling resistance of flanges in compression and the shear resistance of webs see Annex D.

a a b 1 b 2EN 1993-1-5: 2006 (E)

9 3 Shear lag in member design 3.1 General

(1) Shear lag in flanges may be neglected if b0 < Le/50 where b0 is taken as the flange outstand or half the width of an internal element and Le is the length between points of zero bending moment, see 3.2.1(2).

(2) Where the above limit for b0 is exceeded the effects due to shear lag in flanges should be considered at serviceability and fatigue limit state verifications by the use of an effectives width according to 3.2.1 and a stress distribution according to 3.2.2. For the ultimate limit state verification an effective area according to 3.3 may be used. (3) Stresses due to patch loading in the web applied at the flange level should be determined from 3.2.3.

3.2 Effectives width for elastic shear lag 3.2.1 Effective width(1) The effectives width beff for shear lag under elastic conditions should be determined from:

beff =(3.1)

where the effectives factor

is given in Table 3.1.

This effective width may be relevant for serviceability and fatigue limit states.

(2) Provided adjacent spans do not differ more than 50% and any cantilever span is not larger than half the adjacent span the effective lengths Le may be determined from Figure 3.1. For all other cases Le should be taken as the distance between adjacent points of zero bending moment.

Figure 3.1:Effective length Le for continuous beam and distribution of effectives width

L LL L

/ 4L

/ 2L

/ 4 L

/ 4L

/ 2 L

/ 4L

= 0, 85 L

= 0 , 7 0L

0 , 2 5

) L

2 Lb

: b

: b

: b

: b b b b b b 1 1 11 11 1 11 1 eee e2 22222 222 2 203 3

EN 1993-1-5: 2006 (E) 10

1 for flange outstand 2 for internal flange 3 plate thickness t 4 stiffeners with =issAA

Figure 3.2:Notations for shear lag

Table 3.1:

Effectives width factor

Verification

– value

0,02

= 1,0 sagging bending 214,611kbb+== 0,02 <

0,70 hogging bending 226,1250010,611kkkbb+-+== sagging bending kbb9,511== > 0,70 hogging bending kbb6,812== all

end support 0 = (0,55 + 0,025 / ) 1, but 0 < 1 allCantilever

= 2 at support and at the end

= 0 b0 / Le

with

tbAs001+=a in which As is the area of all longitudinal stiffeners within the width b0 and other symbols are as defined in Figure 3.1 and Figure 3.2.

bb bb ef fe ff 0 04 1 23 C LEN 1993-1-5: 2006 (E)

11 3.2.2 Stress distribution due to shear lag (1) The distribution of longitudinal stresses across the flange plate due to shear lag should be obtained from Figure 3.3. bbyyb

bssssbb12(y)(y)effeff00b= 5

b0010b ()()()()4021212/120,025,1:20,0byy--+=-=>sssssbsb ()()4112/10:20,0byy-==£sssb

s1 is calculated with the effective width of the flange beffFigure 3.3:

Distribution of stresses due to shear lag 3.2.3 In-plane load effects (1) The elastic stress distribution in a stiffened or unstiffened plate due to the local introduction of in-plane forces (patch loads), see Figure 3.4, should be determined from:

()lstweffEdEdzatbF,,+=s(3.2) with: 21+=nszsbeeeff

wsttan1,878,01636,0+=

fsetss2+=

where ast,1 is the gross cross-sectional area of the stiffeners smeared over the length se. This may be taken, conservatively, as the area of the stiffeners divided by the spacing sst;

tw is the web thickness;z is the distance to flange.

NOTE:

The equation (3.2) is valid when sst/se £ 0,5; otherwise the contribution of stiffeners should be neglected.

EN 1993-1-5: 2006 (E) 121 stiffener 2 simplified stress distribution 3 actual stress distribution

Figure 3.4:

In-plane load introduction NOTE:

The above stress distribution may also be used for the fatigue verification.

3.3 Shear lag at the ultimate limit state

(1) At the ultimate limit state shear lag effects may be determined as follows: a) elastic shear lag effects as determined for serviceability and fatigue limit states, b) combined effects of shear lag and of plate buckling, c) elastic-plastic shear lag effects allowing for limited plastic strains.

NOTE 1:The National Annex may choose the method to be applied. Unless specified otherwise in EN 1993-2 to EN 1993-6, the method in NOTE 3 is recommended.

NOTE 2:The combined effects of plate buckling and shear lag may be taken into account by using Aeff as given by:

ulteffceffAAb,= (3.3) where Ac,eff is the effectivep area of the compression flange due to plate buckling (see 4.4 and 4.5);

bult is the effectives width factor for the effect of shear lag at the ultimate limit state, which may be taken as b determined from Table 3.1 with a0 replaced by

feffctbA0,*0=a(3.4)

tf is the flange thickness.

b s ss z F 1 :1 t t z , E dz , E d f w ef fs tef fs e1 s 2 3

EN 1993-1-5: 2006 (E)

13 NOTE 3:

Elastic-plastic shear lag effects allowing for limited plastic strains may be taken into account using Aeff as follows:

bbkeffceffceffAAA,,³= (3.5) where b and k are taken from Table 3.1.The expressions in NOTE 2 and NOTE 3 may also be applied for flanges in tension in which case Ac,eff should be replaced by the gross area of the tension flange.

4 Plate buckling effects due to direct stresses at the ultimate limit state 4.1 General

(1) This section gives rules to account for plate buckling effects from direct stresses at the ultimate limit state when the following criteria are met: a) The panels are rectangular and flanges are parallel or nearly parallel (see 2.3); b) Stiffeners, if any, are provided in the longitudinal or transverse direction or both; c) Open holes and cut outs are small (see 2.3); d) Members are of uniform cross section; e) No flange induced web buckling occurs. NOTE 1:

For compression flange buckling in the plane of the web see section 8.NOTE 2:

For stiffeners and detailing of plated members subject to plate buckling see section 9. 4.2 Resistance to direct stresses

(1) The resistance of plated members may be determined using the effective areas of plate elements in compression for class 4 sections using cross sectional data (Aeff, Ieff, Weff) for cross sectional verifications and member verifications for column buckling and lateral torsional buckling according to EN 1993-1-1.

(2)Effectivep areas should be determined on the basis of the linear strain distributions with the attainment of yield strain in the mid plane of the compression plate. 4.3 Effective cross section

(1) In calculating longitudinal stresses, account should be taken of the combined effect of shear lag and plate buckling using the effective areas given in 3.3.

(2) The effective cross sectional properties of members should be based on the effective areas of the compression elements and on the effectives area of the tension elements due to shear lag.

(3) The effective area Aeff should be determined assuming that the cross section is subject only to stresses due to uniform axial compression. For non-symmetrical cross sections the possible shift eN of the centroid of the effective area Aeff relative to the centre of gravity of the gross cross-section, see Figure 4.1, gives an additional moment which should be taken into account in the cross section verification using 4.6.

(4) The effective section modulus Weff should be determined assuming the cross section is subject only to bending stresses, see Figure 4.2. For biaxial bending effective section moduli should be determined about both main axes. NOTE:

As an alternative to 4.3(3) and (4) a single effective section may be determined from NEd and MEd acting simultaneously. The effects of eN should be taken into account as in 4.3(3). This requires an iterative procedure.

EN 1993-1-5: 2006 (E) 14 (5) The stress in a flange should be calculated using the elastic section modulus with reference to the mid- plane of the flange. (6) Hybrid girders may have flange material with yield strength fyf up to fh´fyw provided that:

a) the increase of flange stresses caused by yielding of the web is taken into account by limiting the stresses in the web to fyw ; b) fyf (rather than fyw) is used in determining the effective area of the web.

NOTE:The National Annex may specify the value fh. A value of fh = 2,0 is recommended.

(7)

The increase of deformations and of stresses at serviceability and fatigue limit states may be ignored for hybrid girders complying with 4.3(6) including the NOTE.

(8) For hybrid girders complying with 4.3(6) the stress range limit in EN 1993-1-9 may be taken as 1,5fyf.

Gross cross section Effective cross section G centroid of the gross cross section G´ centroid of the effective cross section 1 centroidal axis of the gross cross section 2 centroidal axis of the effective cross section 3 non effective zone Figure 4.1:

Class 4 cross-sections - axial forceGG´G´G112233

Gross cross section Effective cross section G centroid of the gross cross section G´ centroid of the effective cross section 1 centroidal axis of the gross cross section 2 centroidal axis of the effective cross section 3 non effective zone Figure 4.2:

Class 4 cross-sections - bending momentG1 23 3 GG´e N

EN 1993-1-5: 2006 (E)

15 4.4 Plate elements without longitudinal stiffeners

(1) The effectivep areas of flat compression elements should be obtained using Table 4.1 for internal elements and Table 4.2 for outstand elements. The effectivep area of the compression zone of a plate with the gross cross-sectional area Ac should be obtained from:

Ac,eff =(4.1) where

is the reduction factor for plate buckling.

(2) The reduction factor

may be taken as follows: – internal compression elements:

r = 1,0

for 673,0£pl

()0,13055,02£+-=pplylr for 673,0>pl

, where ()03³+y (4.2) – outstand compression elements:

r = 1,0

for 748,0£pl

0,1188,02£-=ppllr for 748,0>pl (4.3) where seslktbfcryp4,28/==

is the stress ratio determined in accordance with 4.4(3) and 4.4(4) b is the appropriate width to be taken as follows (for definitions, see Table 5.2 of EN 1993-1-1)

bw for webs;b for internal flange elements (except RHS);

b - 3 t for flanges of RHS;

c for outstand flanges;

h for equal-leg angles;

h for unequal-leg angles; k is the buckling factor corresponding to the stress ratio

and boundary conditions. For long plates k is given in Table 4.1 or Table 4.2 as appropriate; t is the thickness; cr is the elastic critical plate buckling stress see equation (A.1) in Annex A.1(2) and Table 4.1 and Table 4.2; []2/235mmNfy=e

(3) For flange elements of I-sections and box girders the stress ratio y used in Table 4.1 and Table 4.2 should be based on the properties of the gross cross-sectional area, due allowance being made for shear lag in the flanges if relevant. For web elements the stress ratio

used in Table 4.1 should be obtained using a stress distribution based on the effective area of the compression flange and the gross area of the web.

NOTE:If the stress distribution results from different stages of construction (as e.g. in a composite bridge) the stresses from the various stages may first be calculated with a cross section consisting of effective flanges and

EN 1993-1-5: 2006 (E) 16 gross web and these stresses are added together. This resulting stress distribution determines an effective web section that can be used for all stages to calculate the final stress distribution for stress analysis.

(4) Except as given in 4.4(5), the plate slenderness pl of an element may be replaced by:

0,,/MyEdcompredpfgsll=(4.4) where com,Ed is the maximum design compressive stress in the element determined using the effectivep area of the section caused by all simultaneous actions.

NOTE 1:The above procedure is conservative and requires an iterative calculation in which the stress ratio

(see Table 4.1 and Table 4.2) is determined at each step from the stresses calculated on the effectivep cross-section defined at the end of the previous step. NOTE 2:

See also alternative procedure in Annex E.(5) For the verification of the design buckling resistance of a class 4 member using 6.3.1, 6.3.2 or 6.3.4 of EN 1993-1-1, either the plate slenderness pl or redp,l with com,Ed based on second order analysis with global imperfections should be used. (6) For aspect ratios a/b < 1 a column type of buckling may occur and the check should be performed according to 4.5.4 using the reduction factor rc.

NOTE:This applies e.g. for flat elements between transverse stiffeners where plate buckling could be column-like and require a reduction factor rc close to cc as for column buckling, see Figure 4.3 a) and b). For plates with longitudinal stiffeners column type buckling may also occur for a/b ³ 1, see Figure 4.3 c).

a) column-like behaviour of plates without longitudinal supports b) column-like behaviour of an unstiffened plate with a small aspect ratio a

c) column-like behaviour of a longitudinally stiffened plate with a large aspect ratio a

Figure 4.3:Column-like behaviour

EN 1993-1-5: 2006 (E)

Table 4.1:

Internal compression elements Stress distribution (compression positive) Effectivep width beff

= 1:beff = `b

be1 = 0,5 beff

be2 = 0,5 beff

1 >

beff = `b

effebby-=521 be2 = beff - be1

< 0:

beff =

bc = `b / (1-)

be1 = 0,4 beff

be2 = 0,6 beff

= 2/1 1 1 >

> 0 0 0 >

> -1 -1 -1 >

> -3 Buckling factor k 4,0 8,2 / (1,05 + ) 7,81 7,81 - 6,29 + 9,782 23,9 5,98 (1 - )2

Table 4.2:Outstand compression elements Stress distribution (compression positive) Effectivep width beff

1 >beff =

< 0:

beff =

bc =

c / (1-)

= 2/1 1 0 -1 1

-3 Buckling factor k 0,43 0,57 0,85 0,57 - 0,21 + 0,072

1 >

beff =

< 0:

beff =

bc =

c / (1-)

= 2/1 1 1 >

> 0 0 0 >

> -1 -1 Buckling factor k 0,43 0,578 / ( + 0,34) 1,70 1,7 - 5 + 17,12 23,8

b s s 1 2b b e2e1b s s 1 2b b e2 e 1 b s s 1 2b bbbe2t e 1 c s s 21 b c ef f s s 21 b b b ef f t c s s 12b c e f f s s 12b c b b e f f t

EN 1993-1-5: 2006 (E) 18 4.5 Stiffened plate elements with longitudinal stiffeners 4.5.1 General (1) For plates with longitudinal stiffeners the effectivep areas from local buckling of the various subpanels between the stiffeners and the effectivep areas from the global buckling of the stiffened panel should be accounted for. (2) The effectivep section area of each subpanel should be determined by a reduction factor in accordance with 4.4 to account for local plate buckling. The stiffened plate with effectivep section areas for the stiffeners should be checked for global plate buckling (by modelling it as an equivalent orthotropic plate) and a reduction factor

should be determined for overall plate buckling.(3) The effectivep area of the compression zone of the stiffened plate should be taken as:

+=tbAAeffedgeloceffcceffc,,,,r(4.5) where Ac,eff,loc is the effectivep section areas of all the stiffeners and subpanels that are fully or partially in the compression zone except the effective parts supported by an adjacent plate element with the width bedge,eff, see example in Figure 4.4. (4) The area Ac,eff,loc should be obtained from:

tbAAlocccloceffsloceffc,,,,+=r(4.6) where c applies to the part of the stiffened panel width that is in compression except the parts bedge,eff, see Figure 4.4;

As,effis the sum of the effectivep sections according to 4.4 of all longitudinal stiffeners with gross area As located in the compression zone;

bc,locis the width of the compressed part of each subpanel;

loc

is the reduction factor from 4.4(2) for each subpanel.

Figure 4.4:

Stiffened plate under uniform compression NOTE:

For non-uniform compression see Figure A.1.

A c

b 1

b 2

b 3

2 1b

2 b 3

b 1

b 2

b 3

2 11 r b

2 33r b

Ac,eff,loc

2 22r b

2 1 1 , , 1 r b b eff edge =

eff edge b ,, 3

2 22 r b

EN 1993-1-5: 2006 (E)

(5) In determining the reduction factor c for overall buckling, the reduction factor for column-type buckling, which is more severe than the reduction factor than for plate buckling, should be considered.

(6) Interpolation should be carried out in accordance with 4.5.4(1) between the reduction factor

for plate buckling and the reduction factor c for column buckling to determine rc see 4.5.4.

(7) The reduction of the compressed area Ac,eff,loc through c may be taken as a uniform reduction across the whole cross section. (8) If shear lag is relevant (see 3.3), the effective cross-sectional area Ac,eff

**...**

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