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EUROPEAN STANDARD
NORME EUROPÉENNE
EUROPÄISCHE NORM
EN 199313
October 2006
ICS 91.010.30
Supersedes ENV 199313:1996
Incorporating corrigendum November 2009
English Version
Eurocode 3  Design of steel structures  Part 13: General rules  Supplementary rules for coldformed members and sheeting
Eurocode 3  Calcul des structures en acier  Partie 13: Règles générales  Règles supplémentaires pour les profilés et plaques à parois minces formés à froid 
Eurocode 3  Bemessung und Konstruktion von Stahlbauten  Teil 13: Allgemeine Regeln  Ergänzende Regeln für kaltgeformte dünnwandige Bauteile und Bleche 
This European Standard was approved by CEN on 16 January 2006.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration. Up–to–date lists and bibliographical references concerning such national standards 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 translation under the responsibility of a CEN member into its own language and notified to the Central Secretariat has the same status as the official versions.
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.
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© 2006 CEN All rights of exploitation in any form and by any means reserved worldwide for CEN national Members.
Ref. No. EN 199313:2006: E
1
Content
1 
Introduction 
5 

1.1 
Scope 
5 

1.2 
Normative references 
5 

1.3 
Terms and definitions 
6 

1.4 
Symbols 
7 

1.5 
Terminology and conventions for dimensions 
8 
2 
Basis of design 
11 
3 
Materials 
12 

3.1 
General 
12 

3.2 
Structural steel 
15 

3.3 
Connecting devices 
17 
4 
Durability 
17 
5 
Structural analysis 
18 

5.1 
Influence of rounded corners 
18 

5.2 
Geometrical proportions 
20 

5.3 
Structural modelling for analysis 
22 

5.4 
Flange curling 
22 

5.5 
Local and distortional buckling 
23 

5.6 
Plate buckling between fasteners 
41 
6 
Ultimate limit states 
41 

6.1 
Resistance of cross–sections 
41 

6.2 
Buckling resistance 
56 

6.3 
Bending and axial tension 
60 
7 
Serviceability limit states 
60 

7.1 
General 
60 

7.2 
Plastic deformation 
60 

7.3 
Deflections 
60 
8 
Design of joints 
61 

8.1 
General 
61 

8.2 
Splices and end connections of members subject to compression 
61 

8.3 
Connections with mechanical fasteners 
61 

8.4 
Spot welds 
68 

8.5 
Lap welds 
69 
9 
Design assisted by testing 
73 
10 
Special considerations for purlins, liner trays and sheetings 
74 

10.1 
Beams restrained by sheeting 
74 

10.2 
Liner trays restrained by sheeting 
92 

10.3 
Stressed skin design 
95 

10.4 
Perforated sheeting 
99 
Annex A [normative] – Testing procedures 
100 

A.1 
General 
100 

A.2 
Tests on profiled sheets and liner trays 
100 

A.3 
Tests on cold–formed members 
105 

A.4 
Tests on structures and portions of structures 
108 

A.5 
Tests on torsionally restrained beams 
110 

A.6 
Evaluation of test results 
114 2 
Annex B [informative] – Durability of fasteners 
119 
Annex C [informative] – Cross section constants for thin–walled cross sections 
121 

C.1 
Open cross sections 
121 

C.2 
Cross section constants for open cross section with branches 
123 

C.3 
Torsion constant and shear centre of cross section with closed part 
124 
Annex D [informative] – Mixed effective width/effective thickness method for outstand elements 
125 
Annex E [Informative] – Simplified design for purlins 
127 
3
Foreword
This European Standard EN 199313, Eurocode 3: Design of steel structures: Part 13 General rules –Supplementary rules for cold formed members and sheeting, 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 199313.
According to the CENCENELEC 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 199313
This standard gives alternative procedures, values and recommendations for classes with notes indicating where national choices may have to be made. Therefore the National Standard implementing EN 199313 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 199313 through clauses:
 – 2(3)P
 – 2(5)
 – 3.1(3) Note 1 and Note 2
 – 3.2.4(1)
 – 5.3(4)
 – 8.3(5)
 – 8.3(13), Table 8.1
 – 8.3(13), Table 8.2
 – 8.3(13), Table 8.3
 – 8.3(13), Table 8.4
 – 8.4(5)
 – 8.5.1(4)
 – 9(2)
 – 10.1.1(1)
 – 10.1.4.2(1)
 – A.1(1), NOTE 2
 – A.1(1), NOTE3
 – A.6.4(4)
 – E(1)
4
1 Introduction
1.1 Scope
 EN 199313 gives design requirements for coldformed members and sheeting. It applies to coldformed steel products made from coated or uncoated hot or cold rolled sheet or strip, that have been coldformed by such processes as coldrolled forming or pressbraking. It may also be used for the design of profiled steel sheeting for composite steel and concrete slabs at the construction stage, see EN 1994. The execution of steel structures made of coldformed members and sheeting is covered in EN 1090.
NOTE: The rules in this part complement the rules in other parts of EN 19931.
 Methods are also given for stressedskin design using steel sheeting as a structural diaphragm.
 This part does not apply to coldformed circular and rectangular structural hollow sections supplied to EN 10219, for which reference should be made to EN 199311 and EN 199318.
 EN 199313 gives methods for design by calculation and for design assisted by testing. The methods for design by calculation apply only within stated ranges of material properties and geometrical proportions for which sufficient experience and test evidence is available. These limitations do not apply to design assisted by testing.
 EN 199313 does not cover load arrangement for testing for loads during execution and maintenance.
 The calculation rules given in this standard are only valid if the tolerances of the cold formed members comply with EN 1090–2
1.2 Normative references
The following normative documents contain provisions which, through reference in this text, constitute provisions of this European Standard. For dated references, subsequent amendments to, or revisions of, any of these publications do not apply.
However, parties to agreements based on this European Standard are encouraged to investigate the possibility of applying the most recent editions of the normative documents indicated below. For undated references, the latest edition of the normative document referred to applies.
EN 1993 
Eurocode 3 – Design of steel structures 
Part 11 to part 112 
EN 10002 
Metallic materials  Tensile testing: 
Part 1: 
Method of test (at ambient temperature); 
EN 100251 
Hotrolled products of structural steels  Part 1: General delivery conditions; 
EN 100252 
Hotrolled products of structural steels  Part 2: Technical delivery conditions for nonalloy structural steels; 
EN 100253 
Hotrolled products of structural steels  Part 3: Technical delivery conditions for normalized / normalized rolled weldable fine grain structural steels; 
EN 100254 
Hotrolled products of structural steels  Part 4: Technical delivery conditions for thermomechanical rolled weldable fine grain structural steels; 
EN 100255 
Hotrolled products of structural steels  Part 5; Technical delivery conditions for structural steels with improved atmospheric corrosion resistance; 
EN 10143 
Continuously hotdip metal coated steel sheet and strip  Tolerances on dimensions and shape; 
EN 10149 
Hot rolled flat products made of high yield strength steels for coldforming: 
Part 2: 
Delivery conditions for normalized/normalized rolled steels; 
Part 3: 
Delivery conditions for thermomechanical rolled steels; 
EN 10204 
Metallic products. Types of inspection documents (includes amendment A 1:1995); 
EN 10268 
Coldrolled flat products made of high yield strength microalloyed steels for cold forming General delivery conditions; 5 
EN 10292 
Continuously hotclip coated strip and sheet of steels with higher yield strength for cold forming  Technical delivery conditions; 
EN 10326 
Continuously hotdip coated strip and sheet of structural steels  Technical delivery conditions; 
EN 10327 
Continuously hotdip coated strip and sheet of low carbon steels for cold forming  Technical delivery conditions; 
ENISO 129442 
Paints and vanishes. Corrosion protection of steel structures by protective paint systems. Part 2: Classification of environments (ISO 129442:1998); 
EN 10902 
Execution of steel structures and aluminium structures Part 2: Technical requirements for steel structures: 
EN 1994 
Eurocode 4: Design of composite steel and concrete structures; 
EN ISO 1478 
Tapping screws thread; 
EN ISO 1479 
Hexagon head tapping screws; 
EN ISO 2702 
Heattreated steel tapping screws  Mechanical properties; 
EN ISO 7049 
Cross recessed pan head tapping screws; 
EN ISO 10684 
Fasteners – hot deep galvanized coatings 
ISO 4997 
Cold reduced steel sheet of structural quality; 
EN 508–1 
Roofing products from metal sheet  Specification for selfsupporting products of steel, aluminium or stainless steel sheet  Part 1 : Steel; 
FEM 10.2.02 
Federation Européenne de la manutention, Secion X, Equipment et proceedes de stockage, FEM 10.2.02, The design of static steel pallet racking, Racking design code, April 2001 Version 1.02. 
1.3 Terms and definitions
Supplementary to EN 199311, for the purposes of this Part 13 of EN 1993, the following terms and definitions apply:
1.3.1
basic material
The flat sheet steel material out of which coldformed sections and profiled sheets are made by coldforming.
1.3.2
basic yield strength
The tensile yield strength of the basic material.
1.3.3
diaphragm action
Structural behaviour involving inplane shear in the sheeting.
1.3.4
liner tray
Profiled sheet with large lipped edge stiffeners, suitable for interlocking with adjacent liner trays to form a plane of ribbed sheeting that is capable of supporting a parallel plane of profiled sheeting spanning perpendicular to the span of the liner trays.
1.3.5
partial restraint
Restriction of the lateral or rotational movement, or the torsional or warping deformation, of a member or element, that increases its buckling resistance in a similar way to a spring support, but to a lesser extent than a rigid support.
6
1.3.6
relative slenderness
A normalized nondimensional_slenderness ratio.
1.3.7
restraint
Restriction of the lateral or rotational movement, or the torsional or warping deformation, of a member or element, that increases its buckling resistance to the same extent as a rigid support.
1.3.8
stressedskin design
A design method that allows for the contribution made by diaphragm action in the sheeting to the stiffness and strength of a structure.
1.3.9
support
A location at which a member is able to transfer forces or moments to a foundation, or to another member or other structural component.
1.3.10
nominal thickness
A target average thickness inclusive zinc and other metallic coating layers when present rolled and defined by the steel supplier (t_{nom} not including organic coatings).
1.3.11
steel core thickness
A nominal thickness minus zinc and other metallic coating layers (t_{cor}).
1.3.12
design thickness
the steel core thickness used in design by calculation according to 1.5.3(6) and 3.2.4.
1.4 Symbols
 In addition to those given in EN 199311, the following main symbols are used:
f_{y} 
yield strength 
f_{ya} 
average yield strength 
f_{yb} 
basic yield strength 
t 
design core thickness of steel material before cold forming, exclusive of metal and organic coating 
t_{nom} 
nominal sheet thickness after cold forming inclusive of zinc and other metallic coating not including organic coating 
t_{cor} 
the nominal thickness minus zinc and other metallic coating 
K 
spring stiffness for displacement 
C 
spring stiffness for rotation 
 Additional symbols are defined where they first occur.
 A symbol may have several meanings in this part.
7
1.5 Terminology and conventions for dimensions
1.5.1 Form of sections
 Coldformed members and profiled sheets have within the permitted tolerances a constant nominal thickness over their entire length and may have either a uniform cross section or a tapering cross section along their length.
 The crosssections of coldformed members and profiled sheets essentially comprise a number of plane elements joined by curved elements.
 Typical forms of sections for coldformed members are shown in figure 1.1.
NOTE: The calculation methods of this Part 13 of EN 1993 does not cover all the cases shown in figures 1.11.2.
Figure 1.1: Typical forms of sections for coldformed members
 Examples of crosssections for coldformed members and sheets are illustrated in figure 1.2.
NOTE: All rules in this Part 13 of EN 1993 relate to the main axis properties, which are defined by the main axes y  y and z  z for symmetrical sections and u  u and v  v for unsymmetrical sections as e.g. angles and Zedsections. In some cases the bending axis is imposed by connected structural elements whether the crosssection is symmetric or not.
8
Figure 1.2: Examples of coldformed members and profiled sheets
 Crosssections of coldformed members and sheets may either be unstiffened or incorporate longitudinal stiffeners in their webs or flanges, or in both.
1.5.2 Form of stiffeners
 Typical forms of stiffeners for coldformed members and sheets are shown in figure 1.3.
9
Figure 1.3: Typical forms of stiffeners for coldformed members and sheeting
 Longitudinal flange stiffeners may be either edge stiffeners or intermediate stiffeners.
 Typical edge stiffeners are shown in figure 1.4.
Figure 1.4: Typical edge stiffeners
 Typical intermediate longitudinal stiffeners are illustrated in figure 1.5.
Figure 1.5: Typical intermediate longitudinal stiffeners
1.5.3 Crosssection dimensions
 Overall dimensions of coldformed members and sheeting, including overall width b, overall height h, internal bend radius r and other external dimensions denoted by symbols without subscripts, such as a, c or d, are measured to the face of the material, unless stated otherwise, as illustrated in figure l .6.
10
Figure 1.6: Dimensions of typical crosssection
 Unless stated otherwise, the other crosssectional dimensions of coldformed members and sheeting, denoted by symbols with subscripts, such as b_{d}, h_{w} or s_{sw}, are measured either to the midline of the material or the midpoint of the corner.
 In the case of sloping elements, such as webs of trapezoidal profiled sheets, the slant height s is measured parallel to the slope. The slope is straight line between intersection points of flanges and web.
 The developed height of a web is measured along its midline, including any web stiffeners.
 The developed width of a flange is measured along its midline, including any intermediate stiffeners.
 The thickness t is a steel design thickness (the steel core thickness extracted minus tolerance if needed as specified in clause 3.2.4), if not otherwise stated.
1.5.4 Convention for member axes
 In general the conventions for members is as used in Part 11 of EN 1993, see Figure 1.7.
Figure 1.7: Axis convention
 For profiled sheets and liner trays the following axis convention is used:
  y  y axis parallel to the plane of sheeting;
  z  z axis perpendicular to the plane of sheeting.
2 Basis of design
 The design of cold formed members and sheeting should be in accordance with the general rules given in EN 1990 and EN 199311. For a general approach with FEmethods (or others) see EN 199315, Annex C.
 P Appropriate partial factors shall be adopted for ultimate limit states and serviceability limit states. 11
 P For verifications by calculation at ultimate limit states the partial factor γ_{M} shall be taken as follows:
  resistance of crosssections to excessive yielding including local and distortional buckling: γ_{M0}
  resistance of members and sheeting where failure is caused by global buckling: γ_{M1}
  resistance of net sections at fastener holes: γ_{M2}
NOTE: Numerical values for γ_{Mi} may be defined in the National Annex. The following numerical values are recommended for the use in buildings:
γ_{M0} = 1,00;
γ_{M1} = 1,00;
γ_{M2} = 1,25.
 For values of γ_{M} for resistance of connections, see Section 8.
 For verifications at serviceability limit states the partial factor γ_{M,ser} should be used.
NOTE: Numerical value for γ_{M,ser} may be defined in the National Annex. The following numerical value is recommended for the use in buildings:
γ_{M,ser} = 1,00.
 For the design of structures made of cold formed members and sheeting a distinction should be made between “structural classes” associated with failure consequences according to EN 1990 – Annex B defined as follows:
Structural Class I: Construction where coldformed members and sheeting are designed to contribute to the overall strength and stability of a structure;
Structural Class II: Construction where coldformed members and sheeting are designed to contribute to the strength and stability of individual structural elements;
Structural Class III: Construction where coldformed sheeting is used as an element that only transfers loads to the structure.
NOTE 1: During different construction stages different structural classes may be considered.
NOTE 2: For requirements for execution of sheeting see EN 1090.
3 Materials
3.1 General
 All steels used for coldformed members and profiled sheets should be suitable for coldforming and welding, if needed. Steels used for members and sheets to be galvanized should also be suitable for galvanizing.
 The nominal values of material properties given in this Section should be adopted as characteristic values in design calculations.
 This part of EN 1993 covers the design of cold formed members and profiles sheets fabricated from steel material conforming to the steel grades listed in table 3.1a.
12
Table 3.1a: Nominal values of basic yield strength f_{yb} and ultimate tensile strength f_{u}
Type of steel 
Standard 
Grade 
f_{yh} N/mm^{2} 
f_{u} N/mm^{2} 
Hot rolled products of nonalloy structural steels. Part 2: Technical delivery conditions for non alloy structural steels 
EN 10025: Part 2 
S 235 
235 
360 
S 275 
275 
430 
S 355 
355 
510 
Hotrolled products of structural steels. Part 3: Technical delivery conditions for normalized/normalized rolled weldable fine grain structural steels 
EN 10025: Part 3 
S 275 N 
275 
370 
S 355 N 
355 
470 
S 420 N 
420 
520 
S 460 N 
460 
550 
S 275 NL 
275 
370 
S 355 NL 
355 
470 
S 420 NL 
420 
520 
S 460 NL 
460 
550 
Hotrolled products of structural steels. Part 4: Technical delivery conditions for thermomechanical rolled weldable fine grain structural steels 
EN 10025: Part 4 
S 275 M 
275 
360 
S 355 M 
355 
450 
S 420 M 
420 
500 
S 460 M 
460 
530 
S 275 ML 
275 
360 
S 355 ML 
355 
450 
S 420 ML 
420 
500 
S 460 ML 
460 
530 
NOTE 1: For steel strip less than 3 mm thick conforming to EN 10025, if the width of the original strip is greater than or equal to 600 mm, the characteristic values may be given in the National Annex. Values equal to 0,9 times those given in Table 3.1 a are recommended.
NOTE 2: For other steel materials and products see the National Annex. Examples for steel grades that may conform to the requirements of this standard are given in Table 3.1b.
13
Table 3.1b: Nominal values of basic yield strength f_{yb} and ultimate tensile strength f_{u}
Type of steel 
Standard 
Grade 
f_{yb} N/mm^{2} 
f_{u} N/mm^{2} 
Cold reduced steel sheet of structural quality 
ISO 4997 
CR 220 
220 
300 
CR 250 
250 
330 
CR 320 
320 
400 
Continuous hot dip zinc coated carbon steel sheet of structural quality 
EN 10326 
S220GD+Z 
220 
300 
S250GD+Z 
250 
330 
S280GD+Z 
280 
360 
S320GD+Z 
320 
390 
S350GD+Z 
350 
420 
Hotrolled flat products made of high yield strength steels for cold forming. Part 2: Delivery conditions for thermomechanically rolled steels 
EN 10149: Part 2 
S 315 MC 
315 
390 
S 355 MC 
355 
430 
S 420 MC 
420 
480 
S 460 MC 
460 
520 
S 500 MC 
500 
550 
S 550 MC 
550 
600 
S 600 MC 
600 
650 
S 650 MC 
650 
700 
S 700 MC 
700 
750 

EN 10149: Part 3 
S 260 NC 
260 
370 
S 315 NC 
315 
430 
S 355 NC 
355 
470 
S 420 NC 
420 
530 
Coldrolled flat products made of high yield strength microalloyed steels for cold forming 
EN 10268 
H240LA 
240 
340 
H280LA 
280 
370 
H320LA 
320 
400 
H360LA 
360 
430 
H400LA 
400 
460 
Continuously hotdip coated strip and sheet of steels with higher yield strength for cold forming 
EN 10292 
H260LAD 
240 2) 
340 2) 
H300LAD 
280 2) 
370 2) 
H340LAD 
320 2) 
400 2) 
H380LAD 
360 2) 
430 2) 
H420LAD 
400 2) 
460 2) 
Continuously hotdipped zincaluminium (ZA) coated steel strip and sheet 
EN 10326 
S220GD+ZA 
220 
300 
S250GD+ZA 
250 
330 
S280GD+ZA 
280 
360 
S320GD+ZA 
320 
390 
S350GD+ZA 
350 
420 
Continuously hotdipped aluminiumzinc (AZ) coated steel strip and sheet 
EN 10326 
S220GD+AZ 
220 
300 
S250GD+AZ 
250 
330 
S280GD+AZ 
280 
360 
S320GD+AZ 
320 
390 
S350GD+AZ 
350 
420 
Continuously hotdipped zinc coated strip and sheet of mild steel for cold forming 
EN 10327 
DX51D+Z 
140 1) 
270 1) 
DX52D+Z 
140 1) 
270 1) 
DX53D+Z 
140 1) 
270 1) 
1) Minimum values of the yield strength and ultimate tensile strength are not given in the standard. For all steel grades a minimum value of 140 N/mm^{2} for yield strength and 270 N/mm^{2} for ultimate tensile strength may be assumed. 2) The yield strength values given in the names of the materials correspond to transversal tension. The values for longitudinal tension are given in the table. 
14
3.2 Structural steel
3.2.1 Material properties of base material
 The nominal values of yield strength f_{yb} or ultimate tensile strength f_{u} should be obtained
 either by adopting the values f_{y} = R_{eh} or R_{p0,2} and f_{u} = R_{m} direct from product standards, or
 by using the values given in Table 3.1 a and b
 by appropriate tests.
 Where the characteristic values are determined from tests, such tests should be carried out in accordance with EN 100021. The number of test coupons should be at least 5 and should be taken from a lot in following way:
 Coils:
 For a lot from one production (one pot of melted steel) at least one coupon per coil of 30% of the number of coils;
 For a lot from different productions at least one coupon per coil;
 Strips: At least one coupon per 2000 kg from one production.
The coupons should be taken at random from the concerned lot of steel and the orientation should be in the length of the structural element. The characteristic values should be determined on basis of a statistical evaluation in accordance with EN 1990 Annex D.
 It may be assumed that the properties of steel in compression are the same as those in tension.
 The ductility requirements should comply with 3.2.2 of EN 199311.
 The design values for material coefficients should be taken as given in 3.2.6 of EN 199311
 The material properties for elevated temperatures are given in EN 199312.
3.2.2 Material properties of cold formed sections and sheeting
 Where the yield strength is specified using the symbol f_{y} the average yield strength f_{ya} may be used if (4) to (8) apply. In other cases the basic yield strength f_{yb} should be used. Where the yield strength is specified using the symbol f_{yb} the basic yield strength f_{yb} should be used.
 The average yield strength f_{ya} of a crosssection due to cold working may be determined from the results of full size tests.
 Alternatively the increased average yield strength f_{ya} may be determined by calculation using:
where:
A_{g} 
is the gross crosssectional area; 
k 
is a numerical coefficient that depends on the type of forming as follows:
  k = 7 for roll forming;
  k = 5 for other methods of forming;

n 
is the number of 90° bends in the crosssection with an internal radius r ≤ 5t (fractions of 90° bends should be counted as fractions of n); 
t 
is the design core thickness of the steel material before coldforming, exclusive of metal and organic coatings, see 3.2.4. 
 The increased yield strength due to cold forming may be taken into account as follows:
15
  in axially loaded members in which the effective crosssectional area A_{eff} equals the gross area A_{g};
  in determining A_{eff} the yield strength f_{y} should be taken as f_{yb}.
 The average yield strength f_{ya} may be utilised in determining:
  the crosssection resistance of an axially loaded tension member;
  the crosssection resistance and the buckling resistance of an axially loaded compression member with a fully effective crosssection;
  the moment resistance of a crosssection with fully effective flanges.
 To determine the moment resistance of a crosssection with fully effective flanges, the crosssection may be subdivided into m nominal plane elements, such as flanges. Expression (3.1) may then be used to obtain values of increased yield strength f_{y,i} separately for each nominal plane element i, provided that:
where:
A_{g,i} 
is the gross crosssectional area of nominal plane element i, 
and when calculating the increased yield strength f_{y,i} using the expression (3.1) the bends on the edge of the nominal plane elements should be counted with the half their angle for each area A_{g,i}.
 The increase in yield strength due to cold forming should not be utilised for members that are subjected to heat treatment after forming at more than 580°C for more than one hour.
NOTE: For further information see EN 1090, Part 2.
 Special attention should be paid to the fact that some heat treatments (especially annealing) might induce a reduced yield strength lower than the basic yield strength f_{yb}.
NOTE: For welding in cold formed areas see also EN 199318.
3.2.3 Fracture toughness
 See EN 199311 and EN 1993110.
3.2.4 Thickness and thickness tolerances
 The provisions for design by calculation given in this Part 13 of EN 1993 may be used for steel within given ranges of core thickness f_{cor}.
NOTE: The ranges of core thickness t_{cor} for sheeting and members may be given in the National Annex. The following values are recommended:
  for sheeting and members: 0,45 mm ≤ t_{cor} ≤ 15 mm
  for connections: 0,45 mm ≤ t_{cor} ≤ 4 mm , see 8.1(2)
 Thicker or thinner material may also be used, provided that the load bearing resistance is determined by design assisted by testing. 16
 The steel core thickness t_{cor} should be used as design thickness, where
t = t_{cor} if tol≤ 5% …(3.3a)
With t_{cor} = t_{nom} − t_{metallic coalings} …(3.3c)
where tol is the minus tolerance in %.
NOTE: For the usual Z 275 zinc coating, t_{sinc} = 0.04 mm.
 For continuously hotdip metal coated members and sheeting supplied with negative tolerances less or equal to the “special tolerances (S)” given in EN 10143, the design thickness according to (3.3a) may be used. If the negative tolerance is beyond “special tolerance (S)” given in EN 10143 then the design thickness according to (3.3b) may be used.
 t_{nom} is the nominal sheet thickness after cold forming. It may be taken as the value to t_{nom} of the original sheet, if the calculative crosssectional areas before and after cold forming do not differ more than 2%; otherwise the notional dimensions should be changed.
3.3 Connecting devices
3.3.1 Bolt assemblies
 Bolts, nuts and washers should conform to the requirements given in EN 199318.
3.3.2 Other types of mechanical fastener
 Other types of mechanical fasteners as:
  selftapping screws as thread forming selftapping screws, thread cutting selftapping screws or selfdrilling selftapping screws,
  cartridgefired pins,
  blind rivets
may be used where they comply with the relevant European Product Specification.
 The characteristic shear resistance F_{v,Rk} and the characteristic minimum tension resistance F_{t,Rk} of the mechanical fasteners may be taken from the EN Product Standard or ETAG or ETA.
3.3.3 Welding consumables
 Welding consumables should conform to the requirements given in EN 199318.
4 Durability
 For basic requirements see section 4 of EN 199311.
NOTE: EN 10902, 9.3.1 lists the factors affecting execution that need to be specified during design.
 Special attention should be given to cases in which different materials are intended to act compositely, if these materials are such that electrochemical phenomena might produce conditions leading to corrosion.
NOTE 1: For corrosion resistance of fasteners for the environmental class following ENISO 129442 see Annex B.
NOTE 2: For roofing products see EN 5081.
NOTE 3: For other products see Part 11 of EN 1993.
NOTE 4: For hot dip galvanized fasteners see EN ISO 10684.
17
5 Structural analysis
5.1 Influence of rounded corners
 In crosssections with rounded corners, the notional flat widths b_{p} of the plane elements should be measured from the midpoints of the adjacent corner elements as indicated in figure 5.1.
 In crosssections with rounded corners, the calculation of section properties should be based upon the nominal geometry of the crosssection.
 Unless more appropriate methods are used to determine the section properties the following approximate procedure may be used. The influence of rounded corners on crosssection resistance may be neglected if the internal radius r ≤ 5t and r ≤ 0,10 b_{p} and the crosssection may be assumed to consist of plane elements with sharp corners (according to figure 5.2, note b_{p} for all flat plane elements, inclusive plane elements in tension). For crosssection stiffness properties the influence of rounded corners should always be taken into account.
18
Figure 5.1: Notional widths of plane cross section parts b_{p} allowing for corner radii
 The influence of rounded corners on section properties may be taken into account by reducing the properties calculated for an otherwise similar crosssection with sharp corners, see figure 5.2, using the following approximations:
A_{g} ≈ A_{g,sh}(1  δ) …(5.1a)
I_{g} ≈ I_{g,sh}(1  2δ) …(5.1b)
I_{w} ≈ I_{w,sh}(1  4δ) …(5.1c)
with:
19
where:
A_{g} 
is the area of the gross crosssection: 
A_{g,sh} 
is the value of A_{g} for a crosssection with sharp corners; 
b_{p,i} 
is the notional flat width of plane element i for a crosssection with sharp corners; 
I_{g} 
is the second moment of area of the gross crosssection; 
I_{g,sh} 
is the value of I_{g} for a crosssection with sharp corners; 
I_{w} 
is the warping constant of the gross crosssection; 
I_{w,sh} 
is the value of I_{w} for a crosssection with sharp corners; 
ϕ 
is the angle between two plane elements; 
m 
is the number of plane elements; 
n 
is the number of curved elements; 
r_{j} 
is the internal radius of curved element j. 
 The reductions given by expression (5.1) may also be applied in calculating the effective section properties A_{eff}, I_{y,eff}, I_{Z,eff} and I_{w,eff} , provided that the notional flat widths of the plane elements are measured to the points of intersection of their midlines.
Figure 5.2: Approximate allowance for rounded corners
 Where the internal radius r > 0,04 t E / f_{y} then the resistance of the crosssection should be determined by tests.
5.2 Geometrical proportions
 The provisions for design by calculation given in this Part 13 of EN 1993 should not be applied to crosssections outside the range of widthtothickness ratios b/t, h/t, c/t and d/t given in Table 5.1.
20
NOTE: These limits b/t, h/t, c/t and d/t given in table 5.1 may be assumed to represent the field for which sufficient experience and verification by testing is already available. Crosssections with larger widthtothickness ratios may also be used, provided that their resistance at ultimate limit states and their behaviour at serviceability limit stales are verified by testing and/or by calculations, where the results are confirmed by an appropriate number of tests.
Table 5.1: Maximum widthtothickness ratios
Element of crosssection 
Maximum value 

b/t ≤ 50 

b/t ≤ 60
c/t ≤50 

b/t ≤ 90
c/t ≤60
d/t ≤ 50 

b/t ≤ 500 

45° ≤ ϕ ≤90°
h/t ≤ 5OO sin ϕ 
 In order to provide sufficient stiffness and to avoid primary buckling of the stiffener itself, the sizes of stiffeners should be within the following ranges:
0,2 ≤ c / b ≤ 0,6 …(5.2a)
0,1 ≤ d / b ≤ 0,3 …(5.2b)
in which the dimensions b, c and d are as indicated in table 5.1. If c / b < 0,2 or d / b < 0,1 the lip should be ignored (c = 0 or d = 0).
NOTE 1: Where effective crosssection properties are determined by testing and by calculations, these limits do not apply.
NOTE 2: The lip measure c is perpendicular to the flange if the lip is not perpendicular to the flange.
NOTE 3: For FEmethods see Annex C of EN 199315.
21
5.3 Structural modelling for analysis
 Unless more appropriate models are used according to EN 199315 the elements of a crosssection may be modelled lor analysis as indicated in table 5.2.
 The mutual influence of multiple stiffeners should be taken into account.
 Imperfections related to flexural buckling and torsional flexural buckling should be taken from table 5.1 of EN 199311
NOTE: See also clause 5.3.4 of EN 199311.
 For imperfections related to lateral torsional buckling an initial bow imperfections e_{0} of the weak axis of the profile may be assumed without taking account at the same time an initial twist
NOTE: The magnitude of the imperfection may be taken from the National Annex. The values e_{0}/L = 1/600 for elastic analysis and e_{0}/L = 1/500 for plastic analysis are recommended for sections assigned to LTB buckling curve a taken from EN 199311, section 6.3.2.2.
Table 5.2: Modelling of elements of a crosssection
Type of element 
Model 
Type of element 
Model 




















5.4 Flange curling
 The effect on the loadbearing resistance of curling (i.e. inward curvature towards the neutral plane) of a very wide flange in a profile subjected to flexure, or of a flange in an arched profile subjected to flexure in which the concave side is in compression, should be taken into account unless such curling is less than 5% of the depth of the profile crosssection. If curling is larger, then the reduction in loadbearing resistance, for instance due to a decrease in the length of the lever arm for parts of the wide flanges, and to the possible effect of the bending of the webs should be taken into account.
NOTE: For liner trays this effect has been taken into account in 10.2.2.2.
22
 Calculation of the curling may be carried out as follows. The formulae apply to both compression and tensile flanges, both with and without stiffeners, but without closely spaced transversal stiffeners at flanges. For a profile which is straight prior to application of loading (see figure 5.3).
For an arched beam:
where:
u 
is bending of the flange towards the neutral axis (curling), see figure 5.3; 
b_{s} 
is one half the distance between webs in box and hat sections, or the width of the portion of flange projecting from the web, see figure 5.3; 
t 
is flange thickness; 
z 
is distance of flange under consideration from neutral axis; 
r 
is radius of curvature of arched beam; 
σ_{a} 
is mean stress in the flanges calculated with gross area. If the stress has been calculated over the effective crosssection, the mean stress is obtained by multiplying the stress for the effective crosssection by the ratio of the effective flange area to the gross flange area. 
Figure 5.3: Flange curling
5.5 Local and distortional buckling
5.5.1 General
 The effects of local and distortional buckling should be taken into account in determining the resistance and stiffness of coldformed members and sheeting.
 Local buckling effects may be accounted for by using effective crosssectional properties, calculated on the basis of the effective widths, see EN 199315.
 In determining resistance to local buckling, the yield strength f_{y} should be taken as f_{yb} when calculating effective widths of compressed elements in EN 199315.
NOTE: For resistance see 6.1.3(1).
 For serviceability verifications, the effective width of a compression element should be based on the compressive stress σ_{com,Ed,ser} in the element under the serviceability limit state loading.
 The distortional buckling for elements with edge or intermediate stiffeners as indicated in figure 5.4(d) are considered in Section 5.5.3.
23
Figure 5.4: Examples of distortional buckling modes
 The effects of distortional buckling should be allowed for in cases such as those indicated in figures 5.4(a), (b) and (c). In these cases the effects of distortional buckling should be determined performing linear (see 5.5.1(7)) or nonlinear buckling analysis (see EN 199315) using numerical methods or column stub tests.
 Unless the simplified procedure in 5.5.3 is used and where the elastic buckling stress is obtained from linear buckling analysis the following procedure may be applied:
 For the wavelength up to the nominal member length, calculate the elastic buckling stress and identify the corresponding buckling modes, see figure 5.5a.
 Calculate the effective width(s) according to 5.5.2 for locally buckled crosssection parts based on the minimum local buckling stress, see figure 5.5b.
 Calculate the reduced thickness (see 5.5.3.1(7)) of edge and intermediate stiffeners or other crosssection parts undergoing distortional buckling based on the minimum distortional buckling stress, see figure 5.5b.
 Calculate overall buckling resistance according to 6.2 (flexural, torsional or lateraltorsional buckling depending on buckling mode) for nominal member length and based on the effective crosssection from 2) and 3).
Figure 5.5a: Examples of elastic critical stress for various buckling modes as function of halvewave length and examples of buckling modes.
24
Figure 5.5b: Examples of elastic buckling load and buckling resistance as a function of member length
5.5.2 Plane elements without stiffeners
 The effective widths of unstiffened elements should be obtained from EN 199315 using the notional flat width b_{p} for by determining the reduction factors for plate buckling based on the plate slenderness .
 The notional flat width b_{p} of a plane element should be determined as specified in figure 5.1 of section 5.1.4. In the case of plane elements in a sloping webs, the appropriate slant height should be used.
NOTE: For outstands an alternative method for calculating effective widths is given in Annex D.
 In applying the method in EN 199315 the following procedure may be used:
 – The stress ratio Ψ, from tables 4.1 and 4.2 of EN 199315 used to determine the effective width of flanges of a section subject to stress gradient, may be based on gross section properties.
 – The stress ratio Ψ, from tables 4.1 and 4.2 of EN 1993–1 –5 used to determine the effective width of web, may be obtained using the effective area of compression flange and the gross area of the web.
 – The effective section properties may be refined by using the stress ratio Ψ based on the effective crosssection already found in place of the gross crosssection. The minimum steps in the iteration dealing with the stress gradient are two.
 – The simplified method given in 5.5.3.4 may be used in the case of webs of trapezoidal sheeting under stress gradient.
5.5.3 Plane elements with edge or intermediate stiffeners
5.5.3.1 General
 The design of compression elements with edge or intermediate stiffeners should be based on the assumption that the stiffener behaves as a compression member with continuous partial restraint, with a spring stiffness that depends on the boundary conditions and the flexural stiffness of the adjacent plane elements.
 The spring stiffness of a stiffener should be determined by applying an unit load per unit length u as illustrated in figure 5.6. The spring stiffness K per unit length may be determined from:
K = u/δ …(5.9)
where:
δ is the deflection of the stiffener due to the unit load u acting in the centroid (b_{1}) of the effective part of the crosssection.
25
Figure 5.6: Determination of spring stiffness
 In determining the values of the rotational spring stiffnesses C_{θ}, C_{θ,1} and C_{θ,2} from the geometry of the crosssection, account should be taken of the possible effects of other stiffeners that exist on the same element, or on any other element of the crosssection that is subject to compression.
 For an edge stiffener, the deflection δ should be obtained from:
with:
θ = u b_{p}/C_{θ}
26
 In the case of the edge stiffeners of lipped Csections and lipped Zsections, C_{θ} should be determined with the unit loads u applied as shown in figure 5.6(c). This results in the following expression for the spring stiffness K_{1} for the flange l:
where:
b_{1} 
is the distance from the webtoflange junction to the gravity center of the effective area of the edge stiffener (including effective part b_{e2} of the flange) of flange 1, see figure 5.6(a); 
b_{2} 
is the distance from the webtoflange junction to the gravity center of the effective area of the edge stiffener (including effective part of the flange) of flange 2; 
h_{w} 
is the web depth; 
k_{f} = 0 
if flange 2 is in tension (e.g. for beam in bending about the yy axis); 

if flange 2 is also in compression (e.g. for a beam in axial compression); 
k_{f} = 1 
for a symmetric section in compression. 
A_{S1} and A_{s2} 
is the effective area of the edge stiffener (including effective part b_{e2} of the flange, see figure 5.6(b)) of flange 1 and flange 2 respectively. 
 For an intermediate stiffener, as a conservative alternative the values of the rotational spring stiffnesses C_{θ,1}, and C_{θ,2} may be taken as equal to zero, and the deflection δ may be obtained from:
 The reduction factor χ _{d} for the distortional buckling resistance (flexural buckling of a stiffener) should be obtained from the relative slenderness from:
where:
where:
σ_{cr,s} is the elastic critical stress for the stiffener(s) from 5.5.3.2, 5.5.3.3 or 5.5.3.4.
 Alternatively, the elastic critical buckling stress σ_{cr,s} may be obtained from elastic first order buckling analysis using numerical methods (see 5.5.1 (7)).
 In the case of a plane element with an edge and intermediate stiffener(s) in the absence of a more accurate method the effect of the intermediate stiffener(s) may be neglected.
27
5.5.3.2 Plane elements with edge stiffeners
 The following procedure is applicable to an edge stiffener if the requirements in 5.2 are met and the angle between the stiffener and the plane element is between 45° and 135°.
Figure 5.7: Edge stiffeners
 The crosssection of an edge stiffener should be taken as comprising the effective portions of the stiffener, element c or elements c and d as shown in figure 5.7, plus the adjacent effective portion of the plane element b_{p}.
 The procedure, which is illustrated in figure 5.8, should be carried out in steps as follows:
 – Step 1: Obtain an initial effective crosssection for the stiffener using effective widths determined by assuming that the stiffener gives full restraint and that σ_{com,Ed} = f_{yb} / γ_{M0}, see (4) to (5);
 – Step 2: Use the initial effective crosssection of the stiffener to determine the reduction factor for distortional buckling (flexural buckling of a stiffener), allowing for the effects of the continuous spring restraint, see (6), (7) and (8);
 – Step 3: Optionally iterate to refine the value of the reduction factor for buckling of the stiffener, see (9) and (10).
 Initial values of the effective widths b_{e1} and b_{e2} shown in figure 5.7 should be determined from clause 5.5.2 by assuming that the plane element b_{p} is doubly supported, see table 4.1 in EN 199315. 28
 Initial values of the effective widths c_{eff} and d_{eff} shown in figure 5.7 should be obtained as follows:
 for a single edge fold stiffener:
c_{eff} = ρb_{p,c} …(5.13a)
with ρ obtained from 5.5.2, except using a value of the buckling factor k_{σ} given by the following:
 – if b_{p,c} / b_{p} ≤ 0,35:
k_{σ} = 0,5 …(5.13b)
 – if 0,35 < b_{p,c} / b_{p} ≤ 0,6:
 for a double edge fold stiffener:
C_{eff} = ρ b_{p,c} …(5.13d)
with ρ obtained from 5.5.2 with a buckling factor k_{σ} for a doubly supported element from table 4.1 in EN 199315
d_{eff} = ρ b_{p.d} …(5.13e)
with ρ obtained from 5.5.2 with a buckling factor k_{σ} for an outstand element from table 4.2 in EN 199315.
 The effective crosssectional area of the edge stiffener A_{s} should be obtained from:
A_{s} = t(b_{e2} + C_{eff}) or …(5.14a)
A_{s} = t(b_{e2} + C_{e1} + C_{e2} + d_{eff}) …(5.14b)
respectively.
NOTE: The rounded corners should be taken into account if needed, see 5.1.
 The elastic critical buckling stress σ_{cr,s} for an edge stiffener should be obtained from:
where:
K 
is the spring stiffness per unit length, see 5.5.3.1 (2). 
I_{s} 
is the effective second moment of area of the stiffener, taken as that of its effective area A_{s} about the centroidal axis a – a of its effective crosssection, see figure 5.7. 
 Alternatively, the elastic critical buckling stress σ_{cr,s} may be obtained from elastic first order buckling analyses using numerical methods, see 5.5.1(7).
 The reduction factor χ _{d} for the distortional buckling (flexural buckling of a stiffener) resistance of an edge stiffener should be obtained from the value of σ_{cr,s} using the method given in 5.5.3.1 (7).
29
Figure 5.8: Compression resistance of a flange with an edge stiffener
 If χ _{d} < 1 it may be refined iteratively, starting the iteration with modified values of ρ obtained using 5.5.2(1) with σ_{com,Ed,i} equal to χ _{d} f_{yb}/γ_{M0}, so that:
30
 The reduced effective area of the stiffener A_{s,red} allowing for flexural buckling should be taken as:
where
σ_{com,Ed} 
is compressive stress at the centreline of the stiffener calculated on the basis of the effective crosssection. 
 I n determining effective section properties, the reduced effective area A_{s,red} should be represented by using a reduced thickness t_{red} = t A_{s.red} / A_{s} for all the elements included in A_{s}.
5.5.3.3 Plane elements with intermediate stiffeners
 The following procedure is applicable to one or two equal intermediate stiffeners formed by grooves or bends provided that all plane elements are calculated according to 5.5.2.
 The crosssection of an intermediate stiffener should be taken as comprising the stiffener itself plus the adjacent effective portions of the adjacent plane elements b_{p,1} and b_{p,2} shown in figure 5.9.
 The procedure, which is illustrated in figure 5.10, should be carried out in steps as follows:
  Step 1: Obtain an initial effective crosssection for the stiffener using effective widths determined by assuming that the stiffener gives full restraint and that σ_{com,Ed} = fγ_{M0}, see (4) and (5);
  Step 2: Use the initial effective crosssection of the stiffener to determine the reduction factor for distortional buckling (flexural buckling of an intermediate stiffener), allowing for the effects of the continuous spring restraint, see (6), (7) and (8);
  Step 3: Optionally iterate to refine the value of the reduction factor for buckling of the stiffener, see (9) and (10).
 Initial values of the effective widths b_{1.e2} and b_{2.e1} shown in figure 5.9 should be determined from 5.5.2 by assuming that the plane elements b_{p,1} and b_{p,2} are doubly supported, see table 4.1 in EN 199315.
Figure 5.9: Intermediate stiffeners
 The effective crosssectional area of an intermediate stiffener A_{s} should be obtained from:
A_{s} = t(b_{1,e2} + b_{2,e1} + b_{s}) …(5.18)
in which the stiffener width b_{s} is as shown in figure 5.9.
31
NOTE: The rounded corners should be taken into account if needed, see 5.1.
 The critical buckling stress σ_{cr,s} for an intermediate stiffener should be obtained from:
where:
K 
is the spring stiffness per unit length, see 5.5.3.1(2). 
I_{s} 
is the effective second moment of area of the stiffener, taken as that of its effective area A_{s} about the centroidal axis a – a of its effective crosssection, see figure 5.9. 
 Alternatively, the elastic critical buckling stress σ_{cr,s} may be obtained from elastic first order buckling analyses using numerical methods, see 5.5.1(7).
 The reduction factor χ _{d} for the distortional buckling resistance (flexural buckling of an intermediate stiffener) should be obtained from the value of σ_{cr,s} using the method given in 5.5.3.1(7).
 If χ _{d} < 1 it may optionally be refined iteratively, starting the iteration with modified values of ρ obtained using 5.5.2(1) with σ_{com,Ed,i} equal to χ _{d}f_{yb}/γ_{M0}, so that:
 The reduced effective area of the stiffener A_{s,red} allowing for distortional buckling (flexural buckling of a stiffener) should be taken as:
where
σ_{com,Ed} is compressive stress at the centreline of the stiffener calculated on the basis of the effective crosssection.
 In determining effective section properties, the reduced effective area A_{s,red} should be represented by using a reduced thickness t_{red} = t A_{s,red} for all the elements included in A_{s}.
32
Figure 5.10: Compression resistance of a flange with an intermediate stiffener
33
5.5.3.4 Trapezoidal sheeting profiles with intermediate stiffeners
5.5.3.4.1 General
 This subclause 5.5.3.4 should be used for trapezoidal profiled sheets, in association with 5.5.3.3 for flanges with intermediate flange stiffeners and 5.5.3.3 for webs with intermediate stiffeners.
 Interaction between the buckling of intermediate flange stiffeners and intermediate web stiffeners should also be taken into account using the method given in 5.5.3.4.4.
5.5.3.4.2 Flanges with intermediate stiffeners
 If it is subject to uniform compression, the effective crosssection of a flange with intermediate stiffeners should be assumed to consist of the reduced effective areas A_{s,red} including two strips of width 0,5b_{eff} (or 15 t, see figure 5.11) adjacent to the stiffener.
 For one central flange stiffener, the elastic critical buckling stress σ_{cr,s} should be obtained from:
where:
b_{p} 
is the notional flat width of plane element shown in figure 5.11; 
b_{s} 
is the stiffener width, measured around the perimeter of the stiffener, see figure 5.11; 
A_{s}, I_{s} 
are the crosssection area and the second moment of area of the stiffener crosssection according to figure 5.11; 
k_{w} 
is a coefficient that allows for partial rotational restraint of the stiffened flange by the webs or other adjacent elements, see (5) and (6). For the calculation of the effective crosssection in axial compression the value k_{w} = 1,0. 
The equation 5.22 may be used for wide grooves provided that flat part of the stiffener is reduced due to local buckling and b_{p} in the equation 5.22 is replaced by the larger of b_{p} and 0,25(3b_{p} + b_{r}), see figure 5.11. Similar method is valid for flange with two or more wide grooves.
Figure 5.11: Compression flange with one, two or multiple stiffeners
34
 For two symmetrically placed flange stiffeners, the elastic critical buckling stress σ_{cr,s} should be obtained from:
with:
b_{e} = 2b_{p,1} + b _{p.2} + 2b_{s}
b_{1} = b_{p,1} + 0,5 b_{r}
where:
b_{p,1} 
is the notional flat width of an outer plane element, as shown in figure 5.11 ; 
b_{p,2} 
is the notional flat width of the central plane element, as shown in figure 5.11 ; 
b_{r} 
is the overall width of a stiffener, see figure 5.11; 
A_{s}, I_{s} 
are the crosssection area and the second moment of area of the stiffener crosssection according to figure 5.11. 
 For a multiple stiffened flange (three or more equal stiffeners) the effective area of the entire flange is
A_{eff} = ρb_{e}t …(5.23b)
where ρ is the reduction factor according to EN 199315, Annex E for the slenderness based on the elastic buckling stress
where:
I_{s} 
is the sum of the second moment of area of the stiffeners about the centroidal axis aa, neglecting the thickness terms bt^{3} 12 ; 
b_{o} 
is the width of the flange as shown in figure 5.11; 
b_{c} 
is the developed width of the flange as shown in figure 5.11. 
 The value of k_{w} may be calculated from the compression flange buckling wavelength l_{b} as follows:
  if 1_{b}/s_{w} ≥ 2:
k_{w} = k_{wo} …(5.24a)
  if 1_{b}/s_{w} < 2:
where:
s_{w} 
is the slant height of the web, see figure 5.1 (c). 
 Alternatively, the rotational restraint coefficient k_{w} may conservatively be taken as equal to 1,0 corresponding to a pinjointed condition. 35
 The values of l_{b} and k_{w0} may be determined from the following:
  for a compression flange with one intermediate stiffener:
with:
b_{d} = 2b_{p} + b_{s}
  for a compression flange with two intermediate stiffeners:
 The reduced effective area of the stiffener A_{s,red} allowing for distortional buckling (flexural buckling of an intermediate stiffener) should be taken as:
 If the webs are unstiffened, the reduction factor χ _{d} should be obtained directly from σ_{cr,s} using the method given in 5.5.3.1(7).
 If the webs are also stiffened, the reduction factor χ _{d} should be obtained using the method given in 5.5.3.1 (7), but with the modified elastic critical stress σ_{cr,mod} given in 5.5.3.4.4.
 In determining effective section properties, the reduced effective area A_{s,red} should be represented by using a reduced thickness t_{red} = t A_{s,red}/A_{s} for all the elements included in A_{s}.
 The effective section properties of the stiffeners at serviceability limit states should be based on the design thickness t.
5.5.3.4.3 Webs with up to two intermediate stiffeners
 The effective crosssection of the compression zone of a web (or other element of a crosssection that is subject to stress gradient) should be assumed to consist of the reduced effective areas A_{s,red} of up to two intermediate stiffeners, a strip adjacent to the compression flange and a strip adjacent to the centroidal axis of the effective crosssection, see figure 5.12.
 The effective crosssection of a web as shown in figure 5.12 should be taken to include:
 a strip of width s_{eff,l} adjacent to the compression flange;
 the reduced effective area A_{s,red} of each web stiffener, up to a maximum of two;
 a strip of width s_{eff,n} adjacent to the effective centroidal axis;
 the part of the web in tension.
36
Figure 5.12: Effective crosssections of webs of trapezoidal profiled sheets
 The effective areas of the stiffeners should be obtained from the following:
  for a single stiffener, or for the stiffener closer to the compression flange:
A_{sa}= t (S_{eff,2} + S_{eff,3} + S_{sa}) …(5.30)
  for a second stiffener:
A_{sb}= t (S_{eff,4} + S_{eff,5} + S_{sb}) …(5.31)
in which the dimensions S_{eff,1} to S_{eff,n} and S_{sa} and s_{sb} are as shown in figure 5.12.
 Initially the location of the effective centroidal axis should be based on the effective crosssections of the flanges but the gross crosssections of the webs. In this case the basic effective width S_{eff,0} should be obtained from:
where:
σ_{com,Ed} 
is the stress in the compression flange when the crosssection resistance is reached. 
 If the web is not fully effective, the dimensions S_{eff,1} to S_{eff,n} should be determined as follows:
S_{eff,1} = S_{eff,0} …(5.33a)
S_{eff,2} = (1 + 0,5h_{a}/e_{c})S_{eff,0} …(5.33b)
S_{eff,3} = [1 + 0,5(h_{a} + h_{sa})/e_{c}] S_{eff,0} …(5.33c)
S_{eff,4} = [1 + 0,5h_{b}/e_{c}) S_{eff,0} …(5.33d)
S_{eff,5} = [1 + 0,5(h_{b} + h_{sb})/e_{c}] S_{eff,0} …(5.33e)
S_{eff,n} = 1,5S_{eff,0} …(5.33f)
where:
e_{c} 
is the distance from the effective centroidal axis to the system line of the compression flange, see figure 5.12; 
and the dimensions h_{a},h_{b},h_{sa} and h_{sb} are as shown in figure 5.12.
37
 The dimensions S_{eff,1} to S_{eff,n} should initially be determined from (5) and then revised if the relevant plane element is fully effective, using the following:
  in an unstiffened web, if S_{eff,1} + S_{eff,n} ≥ s_{n} the entire web is effective, so revise as follows:
S_{eff,1} = 0,4s_{n} …(5.34a)
S_{eff,n} = 0,6S_{n} …(5.34b)
  in stiffened web, if S_{eff,1} + S_{eff,2} ≥ s_{a} the whole of s_{a} is effective, so revise as follows:
  in a web with one stiffener, if S_{eff,3} + S_{eff,n} ≥ s_{n} the whole of s_{n} is effective, so revise as follows:
  in a web with two stiffeners:
  if S_{eff,3} + S_{eff,4} ≥ s_{b} the whole of s_{b} is effective, so revise as follows:
  if S_{eff,5} + S_{eff,n} ≥ s_{n} the whole of s_{n} is effective, so revise as follows:
38
 For a single stiffener, or for the stiffener closer to the compression flange in webs with two stiffeners, the elastic critical buckling stress σ_{cr,sa} should be determined using:
in which S_{1} is given by the following:
  for a single stiffener:
s_{1} = 0,9(s_{a} + s_{sa} + s_{c}) …(5.39b)
  for the stiffener closer to the compression flange, in webs with two stiffeners:
s_{1} = s_{a} + s_{sa} + s_{b} + 0,5(s_{sb} + s_{c}) …(5.39c)
with:
s_{2} = s_{1} − s_{a} − 0,5s_{sa} …(5.39d)
where:
k_{f} 
is a coefficient that allows for partial rotational restraint of the stiffened web by the flanges; 
I_{s} 
is the second moment of area of a stiffener crosssection comprising the fold width s_{sa} and two adjacent strips, each of width S_{eff,1}, about its own centroidal axis parallel to the plane web elements, see figure 5.13. In calculating I_{s} the possible difference in slope between the plane web elements on either side of the stiffener may be neglected; 
s_{c} 
as defined in Figure 5.12. 
 In the absence of a more detailed investigation, the rotational restraint coefficient K_{f} may conservatively be taken as equal to 1,0 corresponding to a pinjointed condition.
Figure 5.13: Web stiffeners for trapezoidal profiled sheeting
 For a single stiffener in compression, or for the stiffener closer to the compression flange in webs with two stiffeners, the reduced effective area A_{sa,red} should be determined from:
39
 If the flanges are unstiffened, the reduction factor χ _{d} should be obtained directly from σ_{cr,sa} using the method given in 5.5.3.1(7).
 If the flanges are also stiffened, the reduction factor χ _{d} should be obtained using the method given in 5.5.3.1(7), but with the modified elastic critical stress σ_{cr,mod} given in 5.5.3.4.4.
 For a single stiffener in tension, the reduced effective area A_{sa,red} should be taken as equal to A_{sa}.
 For webs with two stiffeners, the reduced effective area A_{sb,red} for the second stiffener, should be taken as equal to A_{sb}.
 In determining effective section properties, the reduced effective area A_{sa,red} should be represented by using a reduced thickness t_{red} = χ _{d}t for all the elements included in A_{sa}.
 The effective section properties of the stiffeners at serviceability limit states should be based on the design thickness t.
 Optionally, the effective section properties may be refined iteratively by basing the location of the effective centroidal axis on the effective crosssections of the webs determined by the previous iteration and the effective crosssections of the flanges determined using the reduced thickness t_{red} for all the elements included in the flange stiffener areas A_{s}. This iteration should be based on an increased basic effective width S_{eff,0} obtained from:
5.5.3.4.4 Sheeting with flange stiffeners and web stiffeners
 In the case of sheeting with intermediate stiffeners in the flanges and in the webs, see figure 5.14, interaction between the flexural buckling of the flange stiffeners and the web stiffeners should be allowed for by using a modified elastic critical stress σ_{cr,mod} for both types of stiffeners, obtained from:
where:
σ_{cr,s} 
is the elastic critical stress for an intermediate flange stiffener, see 5.5.3.4.2(2) for a flange with a single stiffener or 5,5.3.4.2(3) for a flange with two stiffeners; 
σ_{cr,sa} 
is the elastic critical stress for a single web stiffener, or the stiffener closer to the compression flange in webs with two stiffeners, see 5.5.3.4.3(7); 
A_{s} 
is the effective crosssection area of an intermediate flange stiffener; 
A_{sa} 
is the effective crosssection area of an intermediate web stiffener; 
β_{s} 
= 1 − (h_{a} + 0,5 h_{m}) / e_{c} for a profile in bending; 
β_{s} 
= 1 for a profile in axial compression. 
40
Figure 5.14: Trapezoidal profiled sheeting with flange stiffeners and web stiffeners
5.6 Plate buckling between fasteners
 Plate buckling between fasteners should be checked for elements composed of plates and mechanical fasteners, see Table 3.3 of EN 199318.
6 Ultimate limit states
6.1 Resistance of crosssections
6.1.1 General
 Design assisted by testing may be used instead of design by calculation for any of these resistances.
NOTE: Design assisted by testing is particularly likely to be beneficial for crosssections with relatively high b_{p} / t ratios, e.g. in relation to inelastic behaviour, web crippling or shear lag.
 For design by calculation, the effects of local buckling should be taken into account by using effective section properties determined as specified in Section 5.5.
 The buckling resistance of members should be verified as specified in Section 6.2.
 In members with crosssections that are susceptible to crosssectional distortion, account should be taken of possible lateral buckling of compression flanges and lateral bending of flanges generally, see 5.5, and 10.1.
41
6.1.2 Axial tension
 The design resistance of a crosssection for uniform tension N_{t,Rd} should be determined from:
where:
A_{g} 
is the gross area of the crosssection; 
F_{n,Rd} 
is the netsection resistance from 8.4 for the appropriate type of mechanical fastener; 
f_{ya} 
is the average yield strength, see 3.2.2 . 
 The design resistance of an angle for uniform tension connected through one leg, or other types of section connected through outstands, should be determined as specified in EN 1993–1 –8, 3.10.3 .
6.1.3 Axial compression
 The design resistance of a crosssection for compression N_{c,Rd} should be determined from:
  if the effective area A_{eff} is less than the gross area A_{g} (section with reduction due to local and/or distortional buckling)
N_{c,Rd} = A_{eff}f_{yb} / γ_{M0} …(6.2)
  if the effective area A_{eff} is equal to the gross area A_{g} (section with no reduction due to local or distortional buckling)
where
A_{eff} 
is the effective area of the crosssection, obtained from Section 5.5 by assuming a uniform compressive stress equal to f_{yb}; 
f_{ya} 
is the average yield strength, see 3.2.2; 
fyb 
is the basic yield strength.; 
Text deleted
For plane elements
For stiffened elements
 The internal axial force in a member should be taken as acting at the centroid of its gross crosssection. This is a conservative assumption, but may be used without further analysis. Further analysis may give a more realistic situation of the internal forces for instance in case of uniformly buildingup of normal force in the compression element.
 The design compression resistance of a crosssection refers to the axial load acting at the centroid of its effective crosssection. If this does not coincide with the centroid of its gross crosssection, the shift e_{N} of the centroidal axes (see figure 6.1) should be taken into account, using the method given in 6.1.9. When the shift of the neutral axis gives a favourable result in the stress check, then that shift should be neglected only if the shift has been calculated at yield strength and not with the actual compressive stresses. 42
Figure 6.1: Effective crosssection under compression
6.1.4 Bending moment
6.1.4.1 Elastic and elasticplastic resistance with yielding at the compressed flange
 The design moment resistance of a crosssection for bending about one principal axis M_{c,Rd} is determined as follows (see figure 6.2):
  if the effective section modulus W_{eff} is less than the gross elastic section modulus W_{el}
M_{c,Rd} = W_{eff} f_{yb} / γ_{M0} …(6.4)
  if the effective section modulus W_{eff} is equal to the gross elastic section modulus W_{el}
where
The resulting bending moment resistance as a function of a decisive element is illustrated in the figure 6.2.
Figure 6.2: Bending moment resistance as a function of slenderness
43
 Expression (6.5) is applicable provided that the following conditions are satisfied:
 Bending moment is applied only about one principal axes of the crosssection;
 The member is not subject to torsion or to torsional, torsional flexural or lateraltorsional or distortional buckling;
 The angle ϕ between the web (see figure 6.5) and the flange is larger than 60°.
 If (2) is not fulfilled the following expression may be used:
M_{c,Rd} = W_{el}f_{ya} / γ_{M0} …(6.6)
 The effective section modulus W_{eff} should be based on an effective crosssection that is subject only to bending moment about the relevant principal axis, with a maximum stress σ_{max,Ed} equal to f_{yb} / γ_{M0}, allowing for the effects of local and distortional buckling as specified in Section 5.5. Where shear lag is relevant, allowance should also be made for its effects.
 The stress ratio Ψ = σ_{2} / σ_{1} used to determine the effective portions of the web may be obtained by using the effective area of the compression flange but the gross area of the web, see figure 6.3.
 If yielding occurs first at the compression edge of the crosssection, unless the conditions given in 6.1.4.2 are met the value of W_{eff} should be based on a linear distribution of stress across the crosssection.
 For biaxial bending the following criterion may be used:
where:
M_{y,Ed} 
is the bending moment about the major main axis; 
M_{Z,Ed} 
is the bending moment about the minor main axis; 
M_{cy,Rd} 
is the resistance of the crosssection if subject only to moment about the main y – y axis; 
M_{cz,Rd} 
is the resistance of the crosssection if subject only to moment about the main z – z axis. 
Figure 6.3: Effective crosssection for resistance to bending moments
 If redistribution of bending moments is assumed in the global analysis, it should be demonstrated from the results of tests in accordance with Section 9 that the provisions given in 7.2 are satisfied.
6.1.4.2 Elastic and elasticplastic resistance with yielding at the tension flange only
 Provided that bending moment is applied only about one principal axis of the crosssection, and provided that yielding occurs first at the tension edge, plastic reserves in the tension zone may be utilised without any strain limit until the maximum compressive stress σ_{com,Ed} reaches f_{yb} / γ_{M0}. In this clause only the bending case is considered. For axial load and bending the clause 6.1.8 or 6.1.9 should be applied.
 In this case, the effective partially plastic section modulus W_{pp.eff} should be based on a stress distribution that is bilinear in the tension zone but linear in the compression zone.
44
 In the absence of a more detailed analysis, the effective width b_{eff} of an element subject to stress gradient may be obtained using 5.5.2 by basing b_{c} on the bilinear stress distribution (see figure 6.4), by assuming Ψ = −1.
Figure 6.4: Measure b_{c} for determination of effective width
 If redistribution of bending moments is assumed in the global analysis, it should be demonstrated from the results of tests in accordance with Section 9 that the provisions given in 7.2 are satisfied.
6.1.4.3 Effects of shear lag
 The effects of shear lag should be taken into account according to EN 199315.
6.1.5 Shear force
 The design shear resistance V_{b,Rd} should be determined from:
where:
f_{bv} 
is the shear strength considering buckling according to Table 6.1; 
h_{w} 
is the web height between the midlines of the flanges, see figure 5.1(c); 
ϕ 
is the slope of the web relative to the flanges, see figure 6.5. 
Table 6.1: Shear buckling strength f_{bv}
Relative web slenderness 
Web without stiffening at the support 
Web with stiffening at the support ^{1)} 

0,58f_{yb} 
0,58f_{yb} 






^{1)} Stiffening at the support, such as cleats, arranged to prevent distortion of the web and designed to resist the support reaction. 
45
 The relative web slenderness should be obtained from die following:
  for webs without longitudinal stiffeners:
  for webs with longitudinal stiffeners. see figure 6.5:
with:
where:
I_{s} 
is the second moment of area of the individual longitudinal stiffener as defined in 5.5.3.4.3(7), about the axis a – a as indicated in figure 6.5; 
s_{d} 
is the total developed slant height of the web, as indicated in figure 6.5; 
s_{p} 
is the slant height of the largest plane element in the web, see figure 6.5; 
s_{w} 
is the slant height of the web, as shown in figure 6.5, between the midpoints of the corners, these points are the median points of the corners, see figure 5.1(c). 
Figure 6.5: Longitudinally stiffened web
6.1.6 Torsional moment
 Where loads are applied eccentric to the shear centre of the crosssection, the effects of torsion should be taken into account.
 The centroidal axis and shear centre and imposed rotation centre to be used in determining the effects of the torsional moment, should be taken as those of the gross crosssection.
 The direct stresses due to the axial force N_{Ed} and the bending moments M_{y,Ed} and M_{z,Ed} should be based on the respective effective crosssections used in 6.1.2 to 6.1.4. The shear stresses due to transverse shear forces, the shear stress due to uniform (St. Venant) torsion and the direct stresses and shear stresses due to warping, should all be based on the properties of the gross crosssection.
46
 In crosssections subject to torsion, the following conditions should be satisfied (average yield strength is allowed here, see 3.2.2):
σ_{tot,Ed} ≤ f_{ya} / γ_{M0} …(6.11a)
where:
σ_{tot,Ed} 
is the design total direct stress, calculated on the relevant effective crosssection; 
τ_{tot,Ed} 
is the design total shear stress, calculated on the gross crosssection. 
 The total direct stress σ_{tot,Ed} and the total shear stress τ_{tot,Ed} should by obtained from:
σ_{tot,Ed} = σ_{N,Ed} + σ_{My,Ed} + σ_{Mz,Ed} + σ_{w,Ed} …(6.12a)
τ_{tot,Ed} = τ_{Vy,Ed} + τ_{Vz,Ed} + τ_{t,Ed} + τ_{w,Ed} …(6.12b)
where:
σ_{My,Ed} 
is the design direct stress due to the bending moment M_{y,Ed} (using effective crosssection); 
σ_{Mz,Ed} 
is the design direct stress due to the bending moment M_{z,Ed} (using effective crosssection); 
σ_{N,Ed} 
is the design direct stress due to the axial force N_{Ed} (using effective crosssection); 
σ_{w,Ed} 
is the design direct stress due to warping (using gross crosssection); 
τ_{Vy,Ed} 
is the design shear stress due to the transverse shear force V_{y},_{Ed} (using gross crosssection); 
τ_{Vz,Ed} 
is the design shear stress due to the transverse shear force V_{Z,Ed} (using gross crosssection); 
τ_{t,Ed} 
is the design shear stress due to uniform (St. Venant) torsion (using gross crosssection); 
τ_{w,Ed} 
is the design shear stress due to warping (using gross crosssection). 
6.1.7 Local transverse forces
6.1.7.1 General
 P To avoid crushing, crippling or buckling in a web subject to a support reaction or other local transverse force applied through the flange, the transverse force F_{Ed} shall satisfy:
F_{Ed} ≤ R_{w,Rd} …(6.13)
where:
R_{w,Rd} 
is the local transverse resistance of the web. 
 The local transverse resistance of a web R_{w,Rd} should be obtained as follows:
 for an unstiffened web:
  for a crosssection with a single web: from 6.1.7.2;
  for any other case, including sheeting: from 6.1.7.3;
 for a stiffened web: from 6.1.7.4.
 Where the local load or support reaction is applied through a cleat that is arranged to prevent distortion of the web and is designed to resist the local transverse force, the local resistance of the web to the transverse force need not be considered.
 In beams with Ishaped crosssections built up from two channels, or with similar crosssections in which two components are interconnected through their webs, the connections between the webs should be located as close as practicable to the flanges of the beam.
47
6.1.7.2 Crosssections with a single unstiffened web
 For a crosssection with a single unstiffened web, see figure 6.6, the local transverse resistance of the web may be determined as specified in (2), provided that the crosssection satisfies the following criteria:
h_{w} / t ≤ 200 …(6.14a)
r / t ≤ 6 …(6.14b)
45° ≤ ϕ ≤ 90° …(6.14c)
where:
h_{w} 
is the web height between the midlines of the flanges; 
r 
is the internal radius of the corners; 
ϕ 
is the angle of the web relative to the flanges [degrees]. 
Figure 6.6: Examples of crosssections with a single web
 For crosssections that satisfy the criteria specified in (1), the local transverse resistance of a web R_{w,Rd} may be determined as shown if figure 6.7.
 The values of the coefficients k_{1} to k_{5} should be determined as follows:
k_{1} = 1,33 − 0,33 k
k_{2} = 1,15 − 0,15 r / t but k_{2} ≥ 0,50 and k_{2} ≤ 1,0
k_{3} = 0,7 + 0,3(ϕ / 90)^{2}
k_{4} = 1,22 − 0,22 k
k_{5} = 1,06 − 0,06 r / t but k_{5} ≤ 1,0
where:
k = f_{yb} / 228 [with f_{yb} in N/mm^{2}].
48
Figure 6.7a): Local loads and supports — crosssections with a single web
49
Figure 6.7b): Local loads and supports — crosssections with a single web
 If the web rotation is prevented either by suitable restraint or because of the section geometry (e.g. Ibeams, see fourth and fifth from the left in the figure 6.6) then the local transverse resistance of a web R_{w,Rd} may be determined as follows:
 for a single load or support reaction
 c < 1,5 h_{w} (near or at free end)
for a crosssection of stiffened and unstiffened flanges
 c > 1,5 h_{w} (far from free end)
for a crosssection of stiffened and unstiffened flanges
 for opposite loads or reactions
 c < 1,5 h_{w} (near or at free end)
50
for a crosssection of stiffened and unstiffened flanges
 c > 1,5 h_{w} (loads or reactions far from free end)
for a crosssection of stiffened and unstiffened flanges
Where the values of coefficients to k_{11} should be determined as follows:
= 1,49 − 0,53 k but ≥ 0,6
k_{6} = 0,88 − 0,12 t / 1,9
k_{7} = 1 + h_{w} /(t × 750) if s_{s} / t < 150; k_{7} = 1,20 if s_{s} / t > 150
k_{8} = 1 / k if s_{s} / t < 66,5 ; k_{8} = (1,10 − h_{w} / (t × 665)) / k if s_{s} / t > 66,5
k_{9} = 0,82 + 0,15 t /1,9
k_{10} = (0,98 − h_{w} /(t × 865)) / k
k_{11} = 0,64 + 0,31 t/1,9
where:
k =f_{yb}/ 228 [with f_{yb} in N/mm^{2}];
s_{s} 
is the nominal length of stiff bearing. 
In the case of two equal and opposite local transverse forces distributed over unequal bearing lengths, the smaller value of s_{s} should be used.
6.1.7.3 Crosssections with two or more unstiffened webs
 In crosssections with two or more webs, including sheeting, see figure 6.8, the local transverse resistance of an unstiffened web should be determined as specified in (2), provided that both of the following conditions are satisfied:
  the clear distance c from the bearing length for the support reaction or local load to a free end, see figure 6.9, is at least 40 mm;
  the crosssection satisfies the following criteria:
r / t ≤ 10 …(6.17a)
h_{w} / t ≤ 200 sin ϕ …(6.17b)
45° ≤ ϕ ≤ 90° …(6.17c)
where:
h_{w} 
is the web height between the midlines of the flanges; 
r 
is the internal radius of the corners; 
ϕ 
is the angle of the web relative to the flanges [degrees]. 
51
Figure 6.8: Examples of crosssections with two or more webs
 Where both of the conditions specified in (1) are satisfied, the local transverse resistance R_{w,Rd} per web of the crosssection should be determined from
where:
l_{a} 
is the effective bearing length for the relevant category, see (3); 
α 
is the coefficient for the relevant category, see (3). 
 The values of l_{a} and α should be obtained from (4) and (5) respectively. The maximum design value for l_{a} = 200 mm. When the support is a coldformed section with one web or round tube, for s_{s} should be taken a value of 10 mm. The relevant category (1 or 2) should be based on the clear distance e between the local load and the nearest support, or the clear distance c from the support reaction or local load to a free end, see figure 6.9.
 The value of the effective bearing length l_{a} should be obtained from the following:
 for Category 1: l_{a} = 10 mm …(6.19a)
 for Category 2:
  β_{v} ≤ 0,2: l_{a} = s_{s} …(6.19b)
  β_{v} ≥ 0,3: l_{a} = 10 mm …(6.19c)
  0,2 < β_{v} < 0,3:Interpolate linearly between the values of l_{a} for 0,2 and 0,3
with:
in which V_{Ed,1} and V_{Ed,2} are the absolute values of the transverse shear forces on each side of the local load or support reaction, and V_{Ed,1} ≥ V_{Ed,2} and s_{s} is the length of stiff bearing.
 The value of the coefficent α should be obtained from the following:
 for Category 1:
  for sheeting profiles: α = 0,075 …(6.20a)
  for liner trays and hat sections: α = 0,057 …(6.20b)
 for Category 2:
  for sheeting profiles: α = 0,15 …(6.20c)
  for liner trays and hat sections: α = 0,115 …(6.20d)
52
Figure 6.9: Local loads and supports —categories of crosssections with two or more webs
53
6.1.7.4 Stiffened webs
 The local transverse resistance of a stiffened web may be determined as specified in (2) for crosssections with longitudinal web stiffeners folded in such a way that the two folds in the web are on opposite sides of the system line of the web joining the points of intersection of the midline of the web with the midlines of the flanges, see figure 6.10, that satisfy the condition:
where:
e_{max} 
is the larger eccentricity of the folds relative to the system line of the web. 
 For crosssections with stiffened webs satisfying the conditions specified in (1), the local transverse resistance of a stiffened web may be determined by multiplying the corresponding value for a similar unstiffened web, obtained from 6.1.7.2 or 6.1.7.3 as appropriate, by the factor K_{a,s} given by:
K_{a,s} = 1,45 − 0,05 emax / t but K_{a,s} ≤ 0,95 + 35 000 t^{2} e_{min} / (b_{d}^{2} s_{p}) …(6.22)
where:
b_{d} 
is the developed width of the loaded flange, see figure 6.10; 
e_{min} 
is the smaller eccentricity of the folds relative to the system line of the web; 
s_{p} 
is the slant height of the plane web element nearest to the loaded flange, see figure 6.10. 
Figure 6.10: Stiffened webs
6.1.8 Combined tension and bending
 Crosssections subject to combined axial tension N_{Ed} and bending moments M_{y,Ed} and M_{z,Ed} should satisfy the criterion:
where:
N_{t,Rd} 
is the design resistance of a crosssection for uniform tension (6.1.2); 
M_{cy,Rd,ten} 
is the design moment resistance of a crosssection for maximum tensile stress if subject only to moment about the y – y axis (6.1.4); 
M_{cz,Rd,ten} 
is the design moment resistance of a crosssection for maximum tensile stress if subject only to moment about the z – z axis (6.1.4). 
54
 If M_{cy,Rd,com} ≤ M_{cy,Rd,ten} or M_{cz,Rd,com} ≤ M_{cz,Rd,ten} (where M_{cy,Rd,com} and M_{cz,Rd,com} are the moment resistances for the maximum compressive stress in a crosssection that is subject only to moment about the relevant axis), the following criterion should also be satisfied:
6.1.9 Combined compression and bending
 Crosssections subject to combined axial compression N_{Ed} and bending moments M_{y,Ed} and M_{z,Ed} should satisfy the criterion:
in which N_{c,Rd} is as defined in 6.1.3, M_{cy,Rd,com} and M_{cz,Rd,com} are as defined in 6.1.8.
 The additional moments ΔM_{y,Ed} and ΔM_{z,Ed} due to shifts of the centroidal axes should be taken as:
ΔM_{y,Ed} = N_{Ed}e_{Ny}
ΔM_{z,Ed} = N_{Ed}e_{Nz}
in which e_{Ny} and e_{Nz} are the shifts of yy and zz centroidal axis due to axial forces, see 6.1.3(3).
 If M_{cy,Rd,ten} ≤ M_{cy,Rd,com} or M_{cz,Rd,ten} ≤ M_{cy,Rd,com} the following criterion should also be satisfied:
in which M_{cy,Rd,ten}, M_{cz,Rd,ten} are as defined in 6.1.8.
6.1.10 Combined shear force, axial force and bending moment
 For crosssections subject to the combined action of an axial force N_{Ed}, a bending moment M_{Ed} and a shear force V_{Ed} no reduction due to shear force need not be done provided that V_{Ed} ≤ 0,5 V_{w,Rd}. If the shear force is larger than half of the shear force resistance then following equations should be satisfied:
where:
N_{Rd} 
is the design resistance of a crosssection for uniform tension or compression given in 6.1.2 or 6.1.3; 
M_{y,Rd} 
is the design moment resistance of the crosssection given in 6.1.4; 
V_{w,Rd} 
is the design shear resistance of the web given in 6.1.5(1); 
M_{f,Rd} 
is the moment of resistance of a crosssection consisting of the effective area of flanges only, see EN 199315; 
M_{pl,Rd} 
is the plastic moment of resistance of the crosssection, see EN 199315. 
For members and sheeting with more than one web V_{w,Rd} is the sum of the resistances of the webs. See also EN 199315.
55
6.1.11 Combined bending moment and local load or support reaction
 Crosssections subject to the combined action of a bending moment M_{Ed} and a transverse force due to a local load or support reaction F_{Ed} should satisfy the following:
M_{Ed} / M_{c,Rd} ≤ l …(6.28a)
F_{Ed} / R_{w,Rd} ≤ 1 …(6.28b)
where:
M_{c,Rd} 
is the moment resistance of the crosssection given in 6.1.4.1 (1); 
R_{w,Rd} 
is the appropriate value of the local transverse resistance of the web from 6.1.7. 
In equation (6.28c) the bending moment M_{Ed} may be calculated at the edge of the support. For members and sheeting with more than one web, R_{w,Rd} is the sum of the local transverse resistances of the individual webs.
6.2 Buckling resistance
6.2.1 General
 In members with crosssections that are susceptible to crosssectional distortion, account should be taken of possible lateral buckling of compression flanges and lateral bending of flanges generally.
 The effects of local and distortional buckling should be taken into account as specified in Section 5.5.
6.2.2 Flexural buckling
 The design buckling resistance N_{b,Rd} for flexural buckling should be obtained from EN 199311 using the appropriate buckling curve from table 6.3 according to the type of crosssection, axis of buckling and yield strength used, see (3).
 The buckling curve for a crosssection not included in table 6.3 may be obtained by analogy.
 The buckling resistance of a closed builtup crosssection should be determined using either:
  buckling curve b in association with the basic yield strength f_{yb} of the flat sheet material out of which the member is made by cold forming;
  buckling curve c in association with the average yield strength f_{ya} of the member after cold forming, determined as specified in 3.2.3, provided that A_{eff} = A_{g}.
6.2.3 Torsional buckling and torsionalflexural buckling
 For members with pointsymmetric open crosssections (e.g Zpurlin with equal flanges), account should be taken of the possibility that the resistance of the member to torsional buckling might be less than its resistance to flexural buckling.
 For members with monosymmetric open crosssections, see figure 6.12, account should be taken of the possibility that the resistance of the member to torsionalflexural buckling might be less than its resistance to flexural buckling.
 For members with nonsymmetric open crosssections, account should be taken of the possibility that the resistance of the member to either torsional or torsionalflexural buckling might be less than its resistance to flexural buckling.
 The design buckling resistance N_{b,Rd} for torsional or torsionalflexural buckling should be obtained from EN 1993–1 –1. 6.3.1.1 using the relevant buckling curve for buckling about the zz axis obtained from table 6.3.
56
Table 6.3: Appropriate buckling curve for various types of crosssection
Type of crosssection 
Buckling about axis 
Buckling curve 

if f_{yb} is used 
Any 
b 
if f_{ya} is used ^{*)} 
Any 
c 

y  y 
a 
z  z 
b 

Any 
b 

Any 
c 
^{*)} The average yield strength f_{ya} should not be used unless A_{eff} = A_{g} 
57
Figure 6.12: Monosymmetric crosssections crosssections susceptible to torsionalflexural buckling
 The elastic critical force N_{cr,T} for torsional buckling of simply supported beam should be determined from:
with:
i_{0}^{2} = i_{y}^{2} + i_{z}^{2} + y_{0}^{2} + z_{0}^{2} …(6.33b)
where:
G 
is the shear modulus; 
I_{t} 
is the torsion constant of the gross crosssection; 
I_{w} 
is the warping constant of the gross crosssection; 
i_{y} 
is the radius of gyration of the gross crosssection about the y – y axis; 
i_{y} 
is the radius of gyration of the gross crosssection about the z – z axis; 
l_{T} 
is the buckling length of the member for torsional buckling; 
y_{0}, z_{0} 
are the shear centre coordinates with respect to the centroid of the gross crosssection. 
 For doubly symmetric crosssections (e.g. y_{0} = z_{0} = 0), the elastic critical force N_{cr} should be determined from:
N_{cr} = N_{cr,i} …(6.34)
where N_{cr,i} should be determined as minimum from three values: N_{cr.y}, N_{cr,z}, N_{cr,T}.
58
 For crosssections that are symmetrical about the y  y axis (e.g. z_{0} = 0), the elastic critical force N_{er,TF} for torsionalflexural buckling should be determined from:
with:
Equation (6.35) is valid only if the torsional and flexural buckling lengths are equal l_{y} = l_{T}.
 The buckling length l_{T} for torsional or torsionalflexural buckling should be determined taking into account the degree of torsional and warping restraint at each end of the system length L_{T}.
 For practical connections at each end, the value of l_{T} / L_{T} may be taken as follows:
6.2.4 Lateraltorsional buckling of members subject to bending
 The design buckling resistance moment of a member that is susceptible to lateraltorsional buckling should be determined according to EN 199311, section 6.3.2.2 using the lateral buckling curve b.
 This method should not be used for the sections that have a significant angle between the principal axes of the effective crosssection, compared to those of the gross crosssection.
6.2.5 Bending and axial compression
 The interaction between axial force and bending moment may be obtained from a secondorder analysis of the member as specified in EN 199311, based on the properties of the effective crosssection obtained from Section 5.5. See also 5.3. 59
 As an alternative the interaction formula (6.36) may be used
where N_{b,Rd} is the design buckling resistance of a compression member according to 6.2.2 (flexural, torsional or torsionalflexural buckling) and M_{b,Rd} is the design bending moment resistance according to 6.2.4 and M_{Ed} includes the effects of shift of neutral axis, if relevant.
6.3 Bending and axial tension
 The interaction equations for compressive force in 6.2.5 are applicable.
7 Serviceability limit states
7.1 General
 The rules for serviceability limit states given in Section 7 of EN 199311 should also be applied to coldformed members and sheeting.
 The properties of the effective crosssection for serviceability limit states obtained from Section 5.1 should be used in all serviceability limit state calculations for coldformed members and sheeting.
 The second moment of area may be calculated alternatively by interpolation of gross crosssection and effective crosssection using the expression
where
I_{gr} 
is second moment of area of the gross crosssection; 
σ_{gr} 
is maximum compressive bending stress in the serviceability limit state, based on the gross crosssection (positive in formula); 
I(σ)_{eff} 
is the second moment of area of the effective crosssection with allowance for local buckling calculated for a maximum stress σ ≥ σ_{gr}, in which the maximum stress is the largest absolute value of stresses within the calculation length considered. 
 The effective second moment of area I_{eff} (or I_{fic}) may be taken as variable along the span. Alternatively a uniform value may be used, based on the maximum absolute span moment due to serviceability loading.
7.2 Plastic deformation
 In case of plastic global analysis the combination of support moment and support reaction at an internal support should not exceed 0,9 times the combined design resistance, determined using γ_{M,ser}, see section 2(5).
 The combined design resistance may be determined from 6.1.11, but using the effective crosssection for serviceability limit states and γ_{M,ser}.
7.3 Deflections
 The deflections may be calculated assuming elastic behaviour.
 The influence of slip in the connections (for example in the case of continuous beam systems with sleeves and overlaps) should be considered in the calculation of deflections, forces and moments.
60
8 Design of joints
8.1 General
 For design assumptions and requirements of joints see EN 199318.
 The following rules apply to core thickness t_{cor} ≥ 4 mm, not covered by EN 1993–1 –8.
8.2 Splices and end connections of members subject to compression
 Splices and end connections in members that are subject to compression, should either have at least the same resistance as the crosssection of the member, or be designed to resist an additional bending moment due to the secondorder effects within the member, in addition to the internal compressive force N_{Ed} and the internal moments M_{y,Ed} and M_{z,Ed} obtained from the global analysis.
 In the absence of a secondorder analysis of the member, this additional moment ΔM_{Ed} should be taken as acting about the crosssectional axis that gives the smallest value of the reduction factor χ for flexural buckling, see 6.2.2(1) , with a value determined from:
where:
A_{eff} 
is the effective area of the crosssection; 
a 
is the distance from the splice or end connection to the nearer point of contraflexure; 
l 
is the buckling length of the member between points of contraflexure, for buckling about the relevant axis; 
W_{eff} 
is the section modulus of the effective crosssection for bending about the relevant axis. 
Splices and end connections should be designed to resist an additional internal shear force
 Splices and end connections should be designed in such a way that load may be transmitted to the effective portions of the crosssection.
 If the constructional details at the ends of a member are such that the line of action of the internal axial force cannot be clearly identified, a suitable eccentricity should be assumed and the resulting moments should be taken into account in the design of the member, the end connections and the splice, if there is one.
8.3 Connections with mechanical fasteners
 Connections with mechanical fasteners should be compact in shape. The positions of the fasteners should be arranged to provide sufficient room for satisfactory assembly and maintenance.
NOTE: More information see Part 1–8 of EN 1993.
 The shear forces on individual mechanical fasteners in a connection may be assumed to be equal, provided that:
  the fasteners have sufficient ductility;
  shear is not the critical failure mode.
61
 For design by calculation the resistances of mechanical fasteners subject to predominantly static loads should be determined from:
  table 8.1 for blind rivets;
  table 8.2 for selftapping screws;
  table 8.3 for cartridge fired pins;
  table 8.4 for bolts.
NOTE: For determining the design resistance of mechanical fasteners by testing see 9(4).
 In tables 8.1 to 8.4 the meanings of the symbols should be taken as follows:
A 
the gross crosssectional area of a fastener; 
A_{s} 
the tensile stress area of a fastener; 
A_{net} 
the net crosssectional area of the connected part; 
β_{Lf} 
the reduction factor for long joints according to EN 199318; 
d 
the nominal diameter of the fastener; 
d_{0} 
the nominal diameter of the hole; 
d_{w} 
the diameter of the washer or the head of the fastener; 
e_{1} 
the end distance from the centre of the fastener to the adjacent end of the connected part, in the direction of load transfer, see figure 8.1; 
e2 
the edge distance from the centre of the fastener to the adjacent edge of the connected part, in the direction perpendicular to the direction of load transfer, see figure 8.1; 
f_{ub} 
the ultimate tensile strength of the fastener material; 
f_{u,sup} 
the ultimate tensile strength of the supporting member into which a screw is fixed; 
n 
the number of sheets that are fixed to the supporting member by the same screw or pin; 
n_{f} 
the number of mechanical fasteners in one connection; 
P_{1} 
the spacing centretocentre of fasteners in the direction of load transfer, see figure 8.1; 
p_{2} 
the spacing centretocentre of fasteners in the direction perpendicular to the direction of load transfer, see figure 8.1; 
t 
the thickness of the thinner connected part or sheet; 
t_{1} 
the thickness of the thicker connected part or sheet; 
t_{sup} 
the thickness of the supporting member into which a screw or a pin is fixed. 
 The partial factor γ_{M} for calculating the design resistances of mechanical fasteners should be taken as γ_{M2}:
NOTE: The value γ_{M2} may be given in the National Annex. The value γ_{M2} = 1,25 is recommended.
62
Figure 8.1: End distance, edge distance and spacings for fasteners and spot welds
 If the pullout resistance F_{0,Rd} of a fastener is smaller than its pullthrough resistance F_{p,Rd} the deformation capacity should be determined from tests.
 The pullthrough resistances given in tables 8.2 and 8.3 for selftapping screws and cartridge fired pins should be reduced if the fasteners are not located centrally in the troughs of the sheeting. If attachment is at a quarter point, the design resistance should be reduced to 0,9F_{p,Rd} and if there are fasteners at both quarter points, the resistance should be taken as 0,7F_{p,Rd} per fastener, see figure 8.2.
Figure 8.2: Reduction of pull through resistance due to the position of fasteners
 For a fastener loaded in combined shear and tension, provided that both F_{t,Rd} and F_{v,Rd} are determined by calculation on the basis of tables 8.1 to 8.4, the resistance of the fastener to combined shear and tension may be verified using:
 The gross section distortion may be neglected if the design resistance is obtained from tables 8.1 to 8.4, provided that the fastening is through a flange not more than 150 mm wide.
 The diameter of holes for screws should be in accordance with the manufacturer’s guidelines. These guidelines should be based on following criteria:
  the applied torque should be just higher than the threading torque;
  the applied torque should be lower than the thread stripping torque or headshearing torque;
  the threading torque should be smaller than 2/3 of the headshearing torque.
 For long joints a reduction factor β_{Lf} should be taken into account according to EN 199318, 3.8.
 The design rules for blind rivets are valid only if the diameter of the hole is not more than 0,1 mm larger than the diameter of the rivet.
 For the bolts M12 and M14 with the hole diameters 2 mm larger than the bolt diameter, reference is made to EN 199318.
63
Table 8.1: Design resistances for blind rivets ^{1)}
Rivets loaded in shear: 
Bearing resistance:
F_{b,Rd} = αf_{u} d t / γ_{M2} but F_{b,Rd} ≤ f_{u} e_{1} t / (1,2 γ_{M2})
In which α is given by the following:
  if t = t_{1}:
  if t_{1} ≥ 2,5t: α= 2,1
  if t < t_{1} < 2,5 t: obtain α by linear interpolation.
Netsection resistance:
F_{n,Rd} = A_{net}f_{u} / γ_{M2}
Shear resistance:
Shear resistance F_{v,Rd} to be determined by testing ^{*1)}and F_{v,Rd} = F_{v,Rk} / γ_{M2}

Conditions: ^{4)} F_{v,Rd} ≥ 1,2F_{b,Rd} / (n_{f} β_{Lf}) or F_{v,Rd} ≥ 1,2F_{n,Rd}

Rivets loaded in tension: ^{2)}

Pullthrough resistance: Pullthrough resistance F_{p,Rd} to be determined by testing ^{*1)}.
Pullout resistance: Not relevant for rivets.
Tension resistance: Tension resistance F_{t,Rd} to be determined by testing ^{*1)}

Conditions:
F_{t,Rd} ≥ ∑ F_{p,Rd}

Range of validity: ^{3)}

e_{1} ≥ 1,5d p_{1} ≥ 3d 2,6 mm ≤ d ≤ 6,4 mm
e_{2} ≥ 1,5d p_{2} ≥ 3d
f_{u} ≤ 550 N/mm^{2}

^{1)} In this table it is assumed that the thinnest sheet is next to the preformed head of the blind rivet.
^{2)} Blind rivets are not usually used in tension.
^{3)} Blind rivets may be used beyond this range of validity if the resistance is determined from the results of tests.
^{4)} The required conditions should be fulfilled when deformation capacity of the connection is needed. When these conditions are not fulfilled there should be proved that the needed deformation capacity will be provided by other parts of the structure.

NOTE:*^{1)} The National Annex may give further information on shear resistance of blind rivets loaded in shear and pullthrough resistance and tension resistance of blind rivets loaded in tension.

64
Table 8.2: Design resistances for selftapping screws^{1)}
Screws loaded in shear: 
Bearing resistance: 
F_{b.Rd} 
= 
αf_{u}dt/γ_{M2} 
In which α is given by the following: 
 if t = t_{1}: 

but 
α ≤ 2,1 
 if t_{1} ≥ 2,5t and t<1,0 mm: 

but 
α ≤ 2,1 
 if t_{1} ≥ 2,5t and t≥1,0 mm: 
α ≤ 2,1 


 if t < t_{1} < 2,5t: 
obtain α by linear interpolation. 
Netsection resistance: 
F_{n,Rd} 
= 
A_{net}f_{u}/γ_{M2} 
Shear resistance: 
Shear resistance F_{v,Rd} to be determined by testing ^{*2)} 

F_{v,Rd} 
= 
F_{v,Rk}/α_{M2} 
Conditions:^{4)} 
F_{v,Rd} ≥ 1,2 F_{b,Rd} 
or 
ƩF_{v,Rd} ≥ 1,2F_{n,Rd} 
Screws loaded in tension: 
Pullthrough resistaance:^{2)} 
 for static loads: 
F_{p,Rd} 
= 
d_{w}tf_{u}/γ_{M2} 
 for screws subject to wind loads and combination of wind loads and static loads: F_{p,Rd} = 0,5d_{w}tf_{u}/γ_{M2} 
Pullout resistance: 
If t_{sup}/s< 1: 
F_{o,Rd} 
= 
0,45dt_{sup}f_{u,sup}/γ_{M2}(s is the thread pitch) 
If t_{sup}/s< 1: 
F_{o,Rd} 
= 
0,65dt_{sup}f_{u,sup}/γ_{M2} 
Tension resistance: Tension resistance F_{t,Rd} to be determined by testing^{*2)}. 
Conditions:^{4)} 
F_{t.Rd} ≥ ƩF_{p.Rd} 
or 
F_{t.Rd} ≥ F_{o,Rd} 
Range of validity:^{3)} 
Generally: 
e_{1} ≥ 3d 
p_{1} ≥ 3d 
3,0 mm ≤ d ≤ 8,0 mm 

e_{2} ≥ 1,5d 
p_{2} ≥ 3d 

For tension: 
0,5 mm ≤ t ≤ 1,5 mm 
and 
t_{1} ≥ 0,9mm 
f_{u} ≤ 550 N/mm^{2} 
^{1)} In this table it is assumed that the thinnest sheet is next to the head of the screw.
^{2)} These values assume that the washer has sufficient rigidity to prevent it from being deformed appreciably or pulled over the head of the fastener.
^{3)} Selftapping screws may be used beyond this range of validity if the resistance is determined from the results of tests.
^{4)} The required conditions should be fulfilled when deformation capacity of the connection is needed. When these conditions are not fulfilled there should be proved that the needed deformation capacity will be provided by other parts of the structure.

Note:^{*2)} The National Annex may give further information on shear resistance of selftapping screws loaded in shear and tension resistance of selftapping screws loaded in tension. 
65
Table 8.3 Design resistances for cartridge fired pins
Pins loaded in shear: 
Bearing resistance: 
F_{b,Rd} = 3,2f_{u}dt/γ_{M2} 
Netsection resistance: 
F_{n,Rd} 
= 
A_{net}f_{u}/γ_{M2} 
Shear resistance: 
Shear resistance F_{v,Rd} to be determined by testing^{*3)} 

F_{v,Rd} 
= 
F_{v,Rk}/γ_{M2} 
Conditions:^{3)} F_{v,Rd} ≥ 1,5 Ʃ F_{b,Rd} or F_{v,Rd} ≥ 1,5 F_{n,Rd} 
Pins loaded in tension: 
Pullthrough resistance:^{1)} 
 for static loads: 
F_{p,Rd} 
= 
d_{w}tf_{u}/γ_{M2} 
 for wind loads and combination of wind loads and static loads: 
F_{p,Rd} 
= 
0,5d_{w}tf_{u}/γ_{M2} 
Pullout resistance: 
Pullout resistance F_{O,Rd} to be determined by testing^{*3)} 
Tension resistance: 
Tension resistance F_{t,Rd} to be determined by testing^{*3)} 
Conditions:^{3)} F_{o,Rd} ≥ Ʃ F_{p,Rd} or F_{t,Rd} ≥ Ʃ F_{o,Rd} 
Range of validity:^{2)} 
Generally 
e_{1} ≥ 4,5 d 
3,7 mm ≤ d ≤ 6,4 mm 

e_{2} ≥ 4,5 d 
for d = 3,7 mm: t_{sup} ≥ 4,0mm 

p_{1} ≥ 4,5 d 
for d = 4,5 mm: t_{sup} ≥ 6,0 mm 

p_{2} ≥ 4,5 d 
for d = 5,2 mm: t_{sup} ≥ 8,0 mm 

f_{u} ≤ 550 N/mm^{2} 

For tension: 
0,5 mm ≤ t ≤ 1,5 mm 
t_{sup} ≥ 6,0 mm 
^{1)} These values assume that the washer has sufficient rigidity to prevent if from being deformed appreciably or pulled over the head of the fastener.
^{2)} Cartridge fired pins may be used beyond this range of validity if the resistance is determined from the results of tests.
^{3)} The required conditions should be fulfilled when deformation capacity of the connection is needed. When these conditions are not fulfilled there should be proved that the needed deformation capacity will be provided by other parts of the structure.

NOTE:^{*3)} The National Annex may give further information on shear resistance of cartrige fired pins loaded in shear and pullout resistance and tension resistance of cartridge fired pins loaded in tension. 
66
Table 8.4: Design resistance for bolts
Bolts loaded in shear: 
Bearing resistance:^{2)} 
F_{b,Rd} = 2,5 α_{b} k_{t} f_{u} d t / γ_{M2} 
with α_{b} is the smallest of 1,0 or e_{1} / (3d) and 
k_{t} = (0,8t + 1,5)/2,5 for 0,75 mm ≤ t ≤ 1,25 mm; k_{t} = 1,0 for t > 1,25mm 
Netsection resistance: 
F_{n,Rd} 
= 
(1+3r(d_{o}/u − 0,3))A_{net}f_{u}/γ_{M2} but 
F_{n.Rd} ≤ A_{net}f_{u}/γ_{M2} 
with: 
r 
= 
[number of bolts at the crosssection]/[total number of bolts in the connection] 
u 
= 
2e_{2} but u ≤ p_{2} 
Shear resistance: 
 for strength grades 4.6,5.6 and 8.8: 
F_{v,Rd} = 0,6 f_{ub}A_{s}/γ_{M2} 
 for strength grades 4.8, 5.8, 6.8 and 10.9: 
F_{v,Rd} = 0,5f_{ub}A_{s} / γ_{M2} 
Conditions:^{3)} 
F_{v,Rd} ≥ 1,2 Ʃ F_{b,Rd} 
or 
ƩF_{v,Rd} ≥ 1,2 F_{n,Rd} 
Bolts loaded in tension: 
Pullthrough resistance: 
Pullthrough resistance F_{p,Rd} to be determined by testing^{*4)}. 
Pullout resistance: 
Not relevant for bolts. 
Tension resistance: 
F_{t,Rd} = 0,9f_{ub}A_{s}/γ_{M2} 
Conditions:^{3)} 
F_{t,Rd} ≥ ƩF_{p,Rd} 
Range of validity:^{1)} 
e_{1} ≥ 1, d_{o} 
p_{1} ≥ 3 d_{o} 
0,75 mm ≤ t > 3 mm 
Minimum bolt size: M6 
e_{2} ≥ 1,5 d_{o} 
p_{2} ≥ 3 d_{o} 

Strength grades: 4.6 − 10.9 
f_{u} ≤ 550 N/mm^{2} 
^{1)} Bolts may be used beyond this range of validity if the resistance is determined from the results of tests
^{2)} For thickness larger than or equal to 3mm the rules for bolts in EN 199318 should be used.
^{3)} The required conditions should be fulfilled when deformation capacity of the connection is needed. When these conditions are not fulfilled there should be proved that the needed deformation capacity will be provided by other parts of the structure.

Note:^{*4)} The National Annex may give further information on pullthrough resistance of bolts loaded in tension. 
67
8.4 Spot welds
 Spot welds may be used with asrolled or galvanized parent material up to 4,0 mm thick, provided that the thinner connected part is not more than 3,0 mm thick.
 Spot welds may be either resistance welded or fusion welded.
 The design resistance F_{v,Rd} of a spot weld loaded in shear should be determined using table 8.5.
 In table 8.5 the meanings of the symbols should be taken as follows:
A_{net} 
is the net crosssectional area of the connected part; 
n_{W} 
is the number of spot welds in one connection; 
t 
is the thickness of the thinner connected part or sheet [mm]; 
t_{1} 
is the thickness of the thicker connected part or sheet [mm]; 
and the end and edge distances e_{1} and e_{2} and the spacings p_{1} and p_{2} are as defined in 8.3(5).
 The partial factor γ_{M} for calculating the design resistances of spot welds should be taken as γ_{M2}.
NOTE: The National Annex may chose the value of γ_{M2}. The value γ_{M2} = 1,25 is recommended.
Table 8.5: Design resistances for spot weds
Spot welds loaded in shear: 
Tearing and bearing resistance: 
 if t ≤ t_{1} ≤ 2,5 t: 
[with t in mm] 
 if t_{1} < 2,5 t: 

End resistance: 
F_{e,Rd} = 1,4t e_{1}f_{u}/γ_{M2} 
Net section resistance: 
F_{n,Rd} = A_{net}f_{u}/γ_{M2} 
Shear resistance: 

Conditions: F_{v,Rd} ≥ 1,25 F_{tb,Rd} or F_{v,Rd} ≥ 1,25 F_{e,Rd} or ƩF_{v,Rd} ≥ 1,25 F_{n,Rd} 
Range of validity 
2d_{s} ≤ e_{1} ≤ 6d_{s} 
3d_{s} ≤ p_{1} ≤ 8d_{s} 
e_{2} ≤ 4d_{s}_{s} 
3d_{s} ≤ p_{2} ≤ 6d_{s} 
 The interface diameter d_{s}, of a spot weld should be determined from the following:
  for fusion welding: d_{s} = 0,5 _{t} + 5 mm …(8.3a)
  for resistance welding:
68
 The value of d_{s} actually produced by the welding procedure should be verified by shear tests in accordance with Section 9, using singlelap test specimens as shown in figure 8.3. The thickness t of the specimen should be the same as that used in practice.
Figure 8.3: Test specimen for shear tests of spot welds
8.5 Lap welds
8.5.1 General
 This clause 8.5 should be used for the design of arcwelded lap welds where the parent material is 4,0 mm thick or less. For thicker parent material, lap welds should be designed using EN 1993–1 –8.
 The weld size should be chosen such that the resistance of the connection is governed by the thickness of the connected part or sheet, rather than the weld.
 The requirement in (2) may be assumed to be satisfied if the throat size of the weld is at least equal to the thickness of the connected part or sheet.
 The partial factor γ_{M} for calculating the design resistances of lap welds should be taken as γ_{M2}
NOTE: The National Annex may give a choice of γ_{M2}. The value γ_{M2} = 1,25 is recommended.
8.5.2 Fillet welds
 The design resistance F_{w,Rd} of a filletwelded connection should be determined from the following:
  for a side fillet that is one of a pair of side fillets:
F_{w,Rd} = t L_{w,s}(0,9 – 0,45 L_{w,s}/b)f_{u} / γ_{M2} if L_{w,s}≤b …(8.4a)
F_{w,Rd} = 0,45tbf_{u} / γ_{M2} if L_{w,s} > …(8.4b)
  for an end fillet:
F_{w,Rd} = t L_{w,e}(1 – 0,3 L_{w,e} / b)f_{u} / γ_{M2} [for one weld and if L_{w,s} ≤ b] …(8.4c)
where:
b 
is the width of the connected part or sheet, see figure 8.4; 
L_{w,e} 
is the effective length of the end fillet weld, see figure 8.4; 
L_{w,s} 
is the effective length of a side fillet weld, see figure 8.4. 
69
Figure 8.4: Fillet welded lap connection
 If a combination of end fillets and side fillets is used in the same connection, its total resistance should be taken as equal to the sum of the resistances of the end fillets and the side fillets. The position of the centroid and realistic assumption of the distribution of forces should be taken into account.
 The effective length L_{w} of a fillet weld should be taken as the overall length of the fullsize fillet, including end returns. Provided that the weld is full size throughout this length, no reduction in effective length need be made for either the start or termination of the weld.
 Fillet welds with effective lengths less than 8 times the thickness of the thinner connected part should not be designed to transmit any forces.
8.5.3 Arc spot welds
 Arc spot welds should not be designed to transmit any forces other than in shear.
 Arc spot welds should not be used through connected parts or sheets with a total thickness ∑t of more than 4 mm.
 Arc spot welds should have an interface diameter d_{s}, of not less than 10 mm.
 If the connected part or sheet is less than 0,7 mm thick, a weld washer should be used, see figure 8.5.
 Arc spot welds should have adequate end and edge distances as given in the following:
 The minimum distance measured parallel to the direction of force transfer, from the centreline of an arc spot weld to the nearest edge of an adjacent weld or to the end of the connected part towards which the force is directed, should not be less than the value of e_{min} given by the following:
if f_{u} / f_{y} < 1,15
 The minimum distance from the centreline of a circular arc spot weld to the end or edge of the connected sheet should not be less than 1,5d_{w} where d_{w} is the visible diameter of the arc spot weld.
 The minimum clear distance between an elongated arc spot weld and the end of the sheet and between the weld and the edge of the sheet should not be less than 1.0d_{w}.
70
Figure 8.5: Arc spot weld with weld washer
 The design shear resistance F_{w,Rd} of a circular arc spot weld should be determined as follows:
F_{w,Rd} = (π/4)d_{s}^{2} × 0,625 f_{uw}/ γ_{M2} …(8.5a)
where:
f_{uw} 
is the ultimate tensile strength of the welding electrodes; 
but F_{w,Rd} should not be taken as more than the resistance given by the following:
  if d_{p} / ∑ t ≤ 18(420/f_{u})^{0,5} :
F_{w,Rd} = 1,5 d_{p} ∑ t / f_{u} / γ_{M2} …(8.5b)
  if 18 (420/f_{u})^{0,5} < d_{p} / ∑ t < 30 (420 / f_{u})0,5 :
F_{w,Rd} = 27 (420 /f_{u}) ^{0,5} (∑ t)^{2} f_{u} / γ_{M2} …(8.5c)
  if d_{p} / ∑ t ≥ 30(420/f_{u}) ^{0.5}
F_{w,Rd} = 0,9d_{p} ∑t f_{u} / γ_{M2} …(8.5d)
with d_{p} according to (8).
 The interface diameter d_{s} of an arc spot weld, see figure 8.6, should be obtained from:
d_{s} = 0,7d_{w} – 1,5 ∑ t but d_{s} ≥ 0,55 d_{w} …(8.6)
where:
d_{w} 
is the visible diameter of the arc spot weld, see figure 8.6. 
71
Figure 8.6: Arc spot welds
 The effective peripheral diameter d_{p} of an arc spot weld should be obtained as follows:
  for a single connected sheet or part of thickness t:
d_{p} = d_{w} – t …(8.7a)
  for multiple connected sheets or parts of total thickness ∑t.
d_{p} = d_{w} – 2 ∑t …(8.7b)
 The design shear resistance F_{w,Rd} of an elongated arc spot weld should be determined from:
F_{w,Rd} = [(π/4)d_{s}^{2} + L_{w}d_{s}] × 0,625f_{uw}/γ_{M2} …(8.8a)
but F_{w,Rd} should not be taken as more than the peripheral resistance given by:
F_{w,Rd} = (0,5 L_{w} + 1,67 d_{p}) ∑tf_{u}/ γ_{M2} …(8.8b)
where:
L_{w} 
is the length of the elongated arc spot weld, measured as shown in figure 8.7. 
72
Figure 8.7: Elongated arc spot weld
9 Design assisted by testing
 This Section 9 may be used to apply the principles for design assisted by testing given in EN 1990 and in Section 2.5. of EN 199311, with the additional specific requirements of coldformed members and sheeting.
 Testing should apply the principles given in Annex A.
NOTE 1: The National Annex may give further information on testing in addition to Annex A.
NOTE 2: Annex A gives standardised procedures for:
  tests on profiled sheets and liner trays;
  tests on coldformed members;
  tests on structures and portions of structures;
  tests on beams torsionally restrained by sheeting;
  evaluation of test results to determine design values.
 Tensile testing of steel should be carried out in accordance with EN 10002–1. Testing of other steel properties should be carried out in accordance with the relevant European Standards.
 Testing of fasteners and connections should be carried out in accordance with the relevant European Standard or International Standard.
NOTE: Pending availability of an appropriate European or International Standard, information on testing procedures for fasteners may be obtained from:
ECCS Publication No. 21 (1983): European recommendations for steel construction: the design and testing of connections in steel sheeting and sections;
ECCS Publication No. 42 (1983): European recommendations for steel construction: mechanical fasteners for use in steel sheeting and sections.
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10 Special considerations for purlins, liner trays and sheetings
10.1 Beams restrained by sheeting
10.1.1 General
 The provisions given in this clause 10.1 may be applied to beams (called purlins in this Section) of Z, C, ∑, U and Hat crosssection with h / t < 233, c / t ≤ 20 for single fold and d / t ≤ 20 for double edge fold.
NOTE: Other limits are possible if verified by tersting. The National Annex may give informations on tests. Standard tests as given in Annex A are recommended.
 These provisions may be used for structural systems of purlins with antisag bars, continuous, sleeved and overlapped systems.
 These provisions may also be applied to coldformed members used as side rails, floor beams and other similar types of beam that are similarly restrained by sheeting.
 Side rails may be designed on the basis that wind pressure has a similar effect on them to gravity loading on purlins, and that wind suction acts on them in a similar way to uplift loading on purlins.
 Full continuous lateral restraint may be supplied by trapezoidal steel sheeting or other profiled steel sheeting with sufficient stiffness, continuously connected to the flange of the purlin through the troughs of the sheets. The purlin at the connection to trapezoidal sheeting may be regarded as laterally restrained, if clause 10.1.1(6) is fulfilled. In other cases (for example, fastening through the crests of the sheets) the degree of restraint should either be validated by experience, or determined from tests.
NOTE: For tests see Annex A.
 If the trapezoidal sheeting is connected to a purlin and the condition expressed by the equation (1O.1a) is met, the purlin at the connection may be regarded as being laterally restrained in the plane of the sheeting:
where
S 
is the portion of the shear stiffness provided by the sheeting for the examined member connected to the sheeting at each rib (If the sheeting is connected to a purlin every second rib only, then S should be substituted by 0,20 S); 
I_{w} 
is the warping constant of the purlin; 
I_{t} 
is the torsion constant of the purlin; 
I_{z} 
is the second moment of area of the crosssection about the minor axis of the crosssection of the purlin; 
L 
is the span of the purlin; 
h 
is the height of the purlin. 
NOTE 1: The equation (10.1a) may also be used to determine the lateral stability of member flanges used in combination with other types of cladding than trapezoidal sheeting, provided that the connections are of suitable design.
NOTE 2: The shear stiffness 5 may be calculated using ECCS guidance (see NOTE in 9(4)) or determined by tests.
 Unless alternative support arrangements may be justified from the results of tests the purlin should have support details, such as cleats, that prevent rotation and lateral displacement at its supports. The effects of forces in the plane of the sheeting, that are transmitted to the supports of the purlin, should be taken into account in the design of the support details.
 The behaviour of a laterally restrained purlin should be modelled as outlined in figure 10.1. The connection of the purlin to the sheeting may be assumed to partially restrain the twisting of the purlin. This partial torsional restraint may be represented by a rotational spring with a spring stiffness CD. The stresses in the free flange, not directly connected to the sheeting, should then be calculated by superposing the effects of inplane bending and the effects of torsion, including lateral bending due to crosssectional distortion. The rotational restraint given by the sheeting should be determined following 10.1.5.
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 Where the free flange of a single span purlin is in compression under uplift loading, allowance should also be made for the amplification of the stresses due to torsion and distortion.
 The shear stiffness of trapezoidal sheeting connected to the purlin at each rib and connected in every side overlap may be calculated as
where t is the design thickness of sheeting, b_{roof} is the width of the roof, s is the distance between the purlins and h_{w} is the profile depth of sheeting. All dimensions are given in mm. For liner trays the shear stiffness is S_{v} times distance between purlins, where S_{v} is calculated according to 10.3.5(6).
10.1.2 Calculation methods
 Unless a second order analysis is carried out, the method given in 10.1.3 and 10.1.4 should be used to allow for the tendency of the free flange to move laterally (thus inducing additional stresses) by treating it as a beam subject to a lateral load q_{h,Ed}, see figure 10.1.
 For use in this method, the rotational spring should be replaced by an equivalent lateral linear spring of stiffness K. In determining K the effects of crosssectional distortion should also be allowed for. For this purpose, the free flange may be treated as a compression member subject to a nonuniform axial force, with a continuous lateral spring support of stiffness K.
 If the free flange of a purlin is in compression due to inplane bending (for example, due to uplift loading in a single span purlin), the resistance of the free flange to lateral buckling should also be verified.
 For a more precise calculation, a numerical analysis should be carried out, using values of the rotational spring stiffness C_{D} obtained from 10.1.5.2. Allowance should be made for the effects of an initial bow imperfection of (e_{0}) in the free flange, defined as in 5.3. The initial imperfection should be compatible with the shape of the relevant buckling mode, determined by the eigenvectors obtained from the elastic first order buckling analysis.
 A numerical analysis using the rotational spring stiffness CD obtained from 10.1.5.2 may also be used if lateral restraint is not supplied or if its effectiveness cannot be proved. When the numerical analysis is carried out, it should take into account the bending in two directions, torsional St Venant stiffness and warping stiffness about the imposed rotation axis.
 If a 2^{nd} order analysis is carried out, effective sections and stiffness, due to local buckling, should be taken into account.
NOTE: For a simplified design of purlins made of C, Z and ∑ cross sections see Annex E.
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Figure 10.1: Modelling laterally braced purlins rotationally restrained by sheeting
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10.1.3 Design criteria
10.1.3.1 Single span purlins
 For gravity loading, a single span purlin should satisfy the criteria for crosssection resistance given in 10.1.4.1. If it is subject to axial compression, it should also satisfy the criteria for stability of the free flange given in 10.1.4.2.
 For uplift loading, a single span purlin should satisfy the criteria for crosssection resistance given in 10.1.4.1 and the criteria for stability of the free flange given in 10.1.4.2.
10.1.3.2 Twospans continuous purlins with gravity load
 The moments due to gravity loading in a purlin that is physically continuous over two spans without overlaps or sleeves, may either be obtained by calculation or based on the results of tests.
 If the moments are calculated they should be determined using elastic global analysis. The purlin should satisfy the criteria for crosssection resistance given in 10.1.4.1. For the moment at the internal support, the criteria for stability of the free flange given in 10.1.4.2 should also be satisfied. For midsupport should be checked also for bending moment + support reaction (web crippling if cleats are not used) and for bending moment + shear forces depending on the case under consideration.
 Alternatively the moments may be determined using the results of tests in accordance with Section 9 and Annex A.5 on the momentrotation behaviour of the purlin over the internal support.
NOTE: Appropriate testing procedures are given in Annex A.
 The design value of the resistance moment at the supports M_{sup,Rd} for a given value of the load per unit length q_{Ed}, should be obtained from the intersection of two curves representing the design values of:
  the momentrotation characteristic at the support, obtained by testing in accordance with Section 9 and Annex A.5;
  the theoretical relationship between the support moment M_{sup,Ed} and the corresponding plastic hinge rotation ϕ_{Ed} in the purlin over the support.
To determine the final design value of the support moment M_{sup,Ed} allowance should be made for the effect of the lateral load in the free flange and/or the buckling stability of that free flange around the midsupport, which are not fully taken into account by the internal support test as given in clause A.5.2. If the free flange is physically continued at the support and if the distance between the support and the nearest antisag bar is larger than 0,5 s, the lateral load q_{h,Ed} according to 10.1.4.2 should be taken into account in verification of the resistance at midsupport. Alternatively, fullscale tests for two or multispan purlins may be used to determine the effect of the lateral load in the free flange and/or the buckling stability of that free flange around the midsupport.
 The span moments should then be calculated from the value of the support moment.
 The following expressions may be used for a purlin with two equal spans:
where:
I_{eff} 
is the effective second moment of area for the moment M_{spn,Ed}; 
L 
is the span; 
M_{spn,Ed} 
is the maximum moment in the span. 
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 The expressions for a purlin with two unequal spans, and for nonuniform loading (e.g. snow accumulation), and for other similar cases, the formulas (10.2a) and (10.2b) are not valid and appropriate analysis should be made for these cases.
 The maximum span moment M_{spn,Ed} in the purlin should satisfy the criteria for crosssection resistance given in 10.1.4.1. Alternatively the resistance moment in the span may be determined by testing. A single span test may be used with a span comparable to the distance between the points of contraflexure in the span.
10.1.3.3 Twospan continuous purlins with uplift loading
 The moments due to uplift loading in a purlin that is physically continuous over two spans without overlaps or sleeves, should be determined using elastic global analysis.
 The moment over the internal support should satisfy the criteria for crosssection resistance given in 10.1.4.1. Because the support reaction is a tensile force, no account need be taken of its interaction with the support moment. The midsupport should be checked also for ineraction of bending moment and shear forces.
 The moments in the spans should satisfy the criteria for stability of the free flange given in 10.1.4.2.
10.1.3.4 Purlins with semicontinuity given by overlaps or sleeves
 The moments in purlins in which continuity over two or more spans is given by overlaps or sleeves at internal supports, should be determined taking into account the effective section properties of the crosssection and the effects of the overlaps or sleeves.
 Tests may be carried out on the support details to determine:
  the flexural stiffness of the overlapped or sleeved part;
  the momentrotation characteristic for the overlapped or sleeved part. Note, that only when the failure occurs at the support with cleat or similar preventing lateral displacements at the support, then the plastic redistribution of bending moments may be used for sleeved and overlapped systems;
  the resistance of the overlapped or sleeved part to combined support reaction and moment;
  the resistance of the nonoverlapped unsleeved part to combined shear force and bending moment.
Alternatively the characteristics of the midsupport details may be determined by numerical methods if the design procedure is at least validated by a relevant numbers of tests.
 For gravity loading, the purlin should satisfy the following criteria:
  at internal supports, the resistance to combined support reaction and moment determined e.g. by calculation assisted by testing;
  near supports, the resistance to combined shear force and bending moment determined e.g. by calculation assisted by testing;
  in the spans, the criteria for crosssection resistance given in 10.1.4.1;
  if the purlin is subject to axial compression, the criteria for stability of the free flange given in 10.1.4.2.
 For uplift loading, the purlin should satisfy the following criteria:
  at internal supports, the resistance to combined support reaction and moment determined e.g. by calculation assisted by testing, taking into account the fact that the support reaction is a tensile force in this case;
  near supports, the resistance to combined shear force and bending moment determined e.g. by calculation assisted by testing;
  in the spans, the criteria for stability of the free flange given in 10.1.4.2;
  if the purlin is subjected to axial compression, the criteria for stability of the free flange is given in 10.1.4.2.
10.1.3.5 Serviceability criteria
 The serviceability criteria relevant to purlins should also be satisfied.
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10.1.4 Design resistance
10.1.4.1 Resistance of crosssections
 For a purlin subject to axial force and transverse load the resistance of the crosssection should be verified as indicated in figure 10.2 by superposing the stresses due to:
  the inplane bending moment M_{y,Ed};
  the axial force N_{Ed};
  an equivalent lateral load q_{h,Ed} acting on the free flange, due to torsion and lateral bending, see (3).
 The maximum stresses in the crosssection should satisfy the following:
  restrained flange:
  free flange:
where:
A_{eff} 
is the effective area of the crosssection for only uniform compression; 
f_{y} 
is the yield strength as defined in 3.2.1 (5); 
M_{fz,Ed} 
is the bending moment in the free flange due to the lateral load q_{h,Ed}, see formula (10.4); 
W_{eff,y} 
is the effective section modulus of the crosssection for only bending about the yy axis; 
W_{fz} 
is the gross elastic section modulus of the free flange plus the contributing part of the web for bending about the zz axis; unless a more sophisticated analysis is carried out the contributing part of the web may be taken equal to 1/5 of the web height from the point of webflange intersection in case of C and Zsections and 1/6 of the web height in case of ∑section, see Figure 10.2; 
and γ_{M} = γ_{M0} if Aeff = A_{g} or if W_{eff,y} = W_{e1,y} and N_{Ed} = 0, otherwise γ_{M} = γ_{M1}.
Figure 10.2: Superposition of stresses
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 The equivalent lateral load q_{h,Ed} acting on the free flange, due to torsion and lateral bending, should be obtained from:
q_{h,Ed} = k_{h} q_{Ed} …(10.4)
 The coefficient k_{h} should be obtained as indicated in figure 10.3 for common types of crosssection.
Figure 10.3: Conversion of torsion and lateral bending into an equivalent lateral load k_{h} q_{Ed}
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 The lateral bending moment M_{fz,Ed} may be determined from expression (10.5) except for a beam with the free flange in tension, where, due to positive influence of flange curling and second order effect moment M_{fz,Ed} may be taken equal to zero:
M_{fz,Ed} = k_{R} M_{0,fz,Ed} …(10.5)
where:
M_{0,fz,Ed} 
is 
the initial lateral bending moment in the free flange without any spring support; 
κ_{R} 
is 
a correction factor for the effective spring support. 
 The initial lateral bending moment in the free flange M_{0,fz,Ed} may be determined from table 10.1 for the critical locations in the span, at supports, at antisag bars and between antisag bars. The validity of the table 10.1 is limited to the range R ≤ 40.
 The correction factor κ_{R} for the relevant location and boundary conditions, may be determined from table 10.1 (or using the theory of beams on the elastic Winkler foundation), using the value of the coefficient R of the spring support given by:
where:
I_{fz} 
is the second moment of area of the gross crosssection of the free flange plus the contributing part of the web for bending about the zz axis, see 10.1.4.1(2); when numerical analysis is carried out, see 10.1.2(5); 
K 
is the lateral spring stiffness per unit length from 10.1.5.1; 
L_{a} 
is the distance between antisag bars, or if none are present, the span L of the purlin. 
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Table 10.1: Values of initial moment M_{0,fz,Ed} and correction factor κ_{R}
System 
Location 
M_{0,fz,Ed} 
κ_{R} 

m 



m 


e 



m 


e 


10.1.4.2 Buckling resistance of free flange
 If the free flange is in compression, its buckling resistance should be verified using:
in which χ_{LT} is the reduction factor for lateral torsional buckling (flexural buckling of the free flange).
NOTE: The use of the χ_{LT}value may be chosen in the National Annex. The use of EN 199311, 6.3.2.3 using buckling curve b (α_{LT} = 0,34 ; _{LT,0} =0,4 ; β= 0,75) is recommended for the relative slenderness _{fz} given in (2). In the case of an axial compression force N_{Ed}, when the reduction factor for buckling around the strong axis is smaller than the reduction factor for lateral flange buckling, e.g. in the case of many antisag bars, this failure mode should also be checked following clause 6.2.2 and 6.2.4.
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 The relative slenderness _{fz} for flexural buckling of the free flange should be determined from:
with:
where:
l_{fz} 
is the buckling length for the free flange from (3) to (7); 
i_{fz} 
is the radius of gyration of the gross crosssection of the free flange plus the contributing part of the web for bending about the zz axis, see 10.1.4.1 (2). 
 For gravity loading, provided that 0 ≤ R ≤ 200, the buckling length of the free flange for a variation of the compressive stress over the length L as shown in figure 10.4 may be obtained from:
where:
L_{a} 
is 
the distance between antisag bars, or if none are present, the span L of the purlin; 
R 
is 
as given in 10.1.4.1(7); 
and ƞ_{1} to ƞ_{4} are coefficients that depend on the number of antisag bars, as given in table 10.2a. The tables 10.2a and 10.2b are valid only for equal spans uniformly loaded beam systems without overlap or sleeve and with antisag bars that provide lateral rigid support for the free flange. The tables may be used for systems with sleeves and overlaps provided that the connection system may be considered as fully continuous. In other cases the buckling length should be determined by more appropriate calculations or, except cantilevers, the values of the table 10.2a for the case of 3 antisag bars per field may be used.
NOTE: Due to rotations in overlap or sleeve connection, the field moment may be much larger than without rotation which results also in longer buckling lengths in span. Neglecting the real moment distribution may lead to unsafe design.
Figure 10.4: Varying compressive stress in free flange for gravity load cases
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Table 10.2a: Coefficients ƞ_{i} for down load with 0,1, 2, 3, 4 antisag bars
Situation 
Anti sagbar Number 
ƞ_{1} 
ƞ_{2} 
ƞ_{3} 
ƞ_{4} 
End span 
0 
0.414 
1.72 
1.11 
0.178 
Intermediate span 
0.657 
8.17 
2.22 
0.107 
End span 
1 
0.515 
1.26 
0.868 
0.242 
Intermediate span 
0.596 
2.33 
1.15 
0.192 
End and intermediate span 
2 
0.596 
2.33 
1.15 
0.192 
End and intermediate span 
3 and 4 
0.694 
5.45 
1.27 
0.168 
Table 10.2b: Coefficients ƞ_{i} for uplift load with 0,1,2, 3, 4 antisag bars
Situation 
Anti sagbar Number 
ƞ_{1} 
ƞ_{2} 
ƞ_{3} 
ƞ_{4} 
Simple span 
0 
0.694 
5.45 
1.27 
0.168 
End span 
0.515 
1.26 
0.868 
0.242 
Intermediate span 
0.306 
0.232 
0.742 
0.279 
Simple and end spans 
1 
0.800 
6.75 
1.49 
0.155 
Intermediate span 
0.515 
1.26 
0.868 
0.242 
Simple span 
2 
0.902 
8.55 
2.18 
0.111 
End and intermediate spans 
0.800 
6.75 
1.49 
0.155 
Simple and end spans 
3 and 4 
0.902 
8.55 
2.18 
0.111 
intermediate span 
0.800 
6.75 
1.49 
0.155 
 For gravity loading, if there are more than three equally spaced antisag bars, and under conditions specified in (3), the buckling length need not be taken as greater than the value for two antisag bars, with L_{a} = L/3. This clause is valid only if there is no axial compressive force.
 If the compressive stress over the length L is almost constant, due to the application of a relatively large axial force, the buckling length should be determined using the values of ƞ_{i} from table 10.2a for the case shown as more than three antisag bars per span, but the actual spacing L_{a}.
 For uplift loading, when antisag bars are not used,_provided that 0 ≤ R_{0} ≤ 200, the buckling length of the free flange for variations of the compressive stress over the length L_{0} as shown in figure 10.5, may be obtained from:
with:
in which I_{fz} and K are as defined in 10.1.4.1(7). Alternatively, the buckling length of the free flange may be determined using the table 10.2b in combination with the equation given in 10.1.4.2(3).
 For uplift loading, if the free flange is effectively held in position laterally at intervals by antisag bars, the buckling length may conservatively be taken as that for a uniform moment, determined as in (5). The formula (10.9) may be applied under conditions specified in (3). If there are no appropriate calculations, reference should be made to (5) .
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Figure 10.5: Varying compressive stress in free flange for uplift cases
10.1.5 Rotational restraint given by the sheeting
10.1.5.1 Lateral spring stiffness
 The lateral spring support given to the free flange of the purlin by the sheeting should be modelled as a lateral spring acting at the free flange, see figure 10.1. The total lateral spring stiffness K per unit length should be determined from:
where:
K_{A} 
is 
the lateral stiffness corresponding to the rotational stiffness of the joint between the sheeting and the purlin; 
K_{B} 
is 
the lateral stiffness due to distortion of the crosssection of the purlin; 
K_{C} 
is 
the lateral stiffness due to the flexural stiffness of the sheeting. 
 Normally it may be assumed to be safe as well as acceptable to neglect 1/K_{C} because K_{C} is very large compared to K_{A} and K_{B}. The value of K should then be obtained from:
 The value of (1 / K_{A} + 1 / K_{B}) may be obtained either by testing or by calculation.
NOTE: Appropriate testing procedures are given in Annex A.
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 The lateral spring stiffness K per unit length may be determined by calculation using:
in which the dimension b_{mod} is determined as follows:
  for cases where the equivalent lateral force q_{h,Ed} bringing the purlin into contact with the sheeting at the purlin web:
b_{mod}= a
  for cases where the equivalent lateral force q_{h,Ed} bringing the purlin into contact with the sheeting at the tip of the purlin flange:
b_{mod}= 2a+b
where:
t 
is 
the thickness of the purlin; 
a 
is 
the distance from the sheettopurlin fastener to the purlin web, see figure 10.6; 
b 
is 
the width of the purlin flange connected to the sheeting, see figure 10.6; 
C_{D} 
is 
the total rotational spring stiffness from 10.1.5.2; 
h 
is 
the overall height of the purlin; 
h_{d} 
is 
the developed height of the purlin web, see figure 10.6. 
Figure 10.6: Purlin and attached sheeting
10.1.5.2 Rotational spring stiffness
 The rotational restraint given to the purlin by the sheeting that is connected to its top flange, should be modelled as a rotational spring acting at the top flange of the purlin, see figure 10.1. The total rotational spring stiffness C_{D} should be determined from:
where:
C_{D,A} 
is 
the rotational stiffness of the connection between the sheeting and the purlin; 
C_{D,C} 
is 
the rotational stiffness corresponding to the flexural stiffness of the sheeting. 
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 Generally C_{D,A} may be calculated as given in (5) and (7). Alternatively C_{D,A} may be obtained by testing, see (9).
 The value of C_{D,C} may be taken as the minimum value obtained from calculational models of the type shown in figure 10.7, taking account of the rotations of the adjacent purlins and the degree of continuity of the sheeting, using:
C_{D,C} = m/θ …(10.15)
where:
m 
is 
the applied moment per unit width of sheeting, applied as indicated in figure 10.7; 
θ 
is 
the resulting rotation, measured as indicated in figure 10.7 [radians). 
Figure 10.7: Model for calculating C_{D,C}
 Alternatively a conservative value of C_{D,C} may be obtained from:
in which k is a numerical coefficient, with values as follows:
 end, upper case of figure 10.7 
k = 2; 
 end, lower case of figure 10.7 
k = 3; 
 mid, upper case of figure 10.7 
k = 4; 
 mid, lower case of figure 10.7 
k = 6; 
where:
I_{eff} 
is 
the effective second moment of area per unit width of the sheeting; 
s 
is 
the spacing of the purlins. 
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 Provided that the sheettopurlin fasteners are positioned centrally on the flange of the purlin, the value of C_{D,A} for trapezoidal sheeting connected to the top flange of the purlin may be determined as follows (see table 10.3):
where
k_{ba} = (b_{a} / 100)^{2} 
if b_{a} < 125mm ; 
k_{ba} = 1,25(b_{a} / 100) 
if 125mm≤b_{a} <200mm ; 

k_{t} = (t_{nom} /0,75)^{1,1} 
if t_{nom} ≥0,75mm ; positive position; 
k_{t} = (t_{nom} /0,75)^{1,5} 
if t_{nom} ≥0,75mm ; negative position; 
k_{t} = (t_{nom} /0,75)^{1,5} 
if t_{nom} <0,75mm ; 

k_{bR} = 1,0 
if b_{R} ≤185mm ; 
k_{bR} = 185/b_{R} 
if b_{R} >185mm ; 
for gravity load:
k_{A} = 1,0 + (A – 1,0).0,08 
if t_{nom} =0,75mm ; positive position; 
k_{A} = 1,0 + (A – 1,0).0,16 
if t_{nom} =0,75mm ; negative position; 
k_{A} = 1,0 + (A – 1,0).0,095 
if t_{nom} =1,00mm ; positive position; 
k_{A} = 1,0 + (A – 1,0).0,095 
if t_{nom} =1,00mm ; negative position; 
  linear interpolation between t = 0,75 and t = 1,0mm is allowed
  for t < 0.75 mm the formula is not valid;
  for t > 1 mm, the formula needs to be used with t = 1 mm
for uplift load:
k_{A} = 1,0;
if b_{T} > b_{T,max}, otherwise k_{bT} = 1;
A[kN/m] ≤ 12kN/m load introduced from sheeting to beam;
where:
b_{a} 
is 
the width of the purlin flange [in mm]; 
b_{R} 
is 
the corrugation width [in mm]; 
b_{T} 
is 
the width of the sheeting flange through which it is fastened to the purlin; 
b_{T,max} 
is 
given in Table 10.3; 
C_{100} 
is 
a rotation coefficient, representing the value of C_{D,A} if b_{a} = 100 mm. 
 Provided that there is no insulation between the sheeting and the purlins, the value of the rotation coefficient C_{100} may be obtained from table 10.3.
88
 Alternatively C_{D,A} may be taken as equal to 130p [Nm/m/rad], where p is the number of sheettopurlin fasteners per metre length of purlin (but not more than one per rib of sheeting), provided that:
  the flange width b of the sheeting through which it is fastened does not exceed 120 mm;
  the nominal thickness t of the sheeting is at least 0,66 mm;
  the distance a or b  a between the centreline of the fastener and the centre of rotation of the purlin (depending on the direction of rotation), as shown in figure 10.6, is at least 25 mm.
 If the effects of crosssection distortion have to be taken into account, see 10.1.5.1, it may be assumed to be realistic to neglect C_{D,C}, because the spring stiffness is mainly influenced by the value of C_{D,A} and the crosssection distortion.
 Alternatively, values of C_{D,A} may be obtained from a combination of testing and calculation.
 If the value of (1 / K_{A} + 1 / K_{B}) is obtained by testing (in mm/N in accordance with A.5.3(3)), the values of C_{D,A}, for gravity loading and for uplift loading should be determined from:
in which b_{mod}, h and h_{d} are as defined in 10.1.5.1(4) and l_{A} is the modular width of tested sheeting and l_{B} is the length of tested beam.
NOTE: For testing see Annex A.5.3(3).
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Table 10.3: Rotation coefficient C_{100} for trapezoidal steel sheeting
Positioning of sheeting 
Sheet fastened through 
Pitch of fasteners 
Washer diameter [mm] 
C_{100} 
b_{T,max} 
Positive 1) 
Negative 1) 
Trough 
Crest 
e = b_{R} 
e = 2b_{R} 
[kNm/m] 
[mm] 
For gravity loading: 
X 

X 

X 

22 
5,2 
40 
X 

X 


X 
22 
3,1 
40 

X 

X 
X 

K_{a} 
10,0 
40 

X 

X 

X 
K_{a} 
5,2 
40 

X 
X 

X 

22 
3,1 
120 

X 
X 


X 
22 
2,0 
120 
For uplift loading: 
X 

X 

X 

16 
2,6 
40 
X 

X 


X 
16 
1,7 
40 
Key:
b_{R} 
is the corrugation width; 
b_{T} 
is the width of the sheeting flange through which it is fastened to the purlin. 

K_{a} indicates a steel saddle washer as shown below with t ≥ 0,75 mm

Sheet fastened:
  through the trough:
  through the crest:

The values in this table are valid for:
 
sheet fastener screws of diameter: 
ϕ = 6,3 mm; 
 
steel washers of thickness: 
t_{w} ≥ 1,0 mm. 

1) The position of sheeting in positive when the narrow flange is on the purlin and negative when the wide flange is on the purlin.

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10.1.6 Forces in sheet/purlin fasteners and reaction forces
 Fasteners fixing the sheeting to the purlin should be checked for a combination of shear force q_{s} e, perpendicular to the flange, and tension force q_{t} e where q_{s} and q_{t} may be calculated using table 10.4 and e is the pitch of the fasteners. Shear force due to stabilising effect, see EN199311, should be added to the shear force. Furthermore, shear force due to diaphragm action, acting parallel to the flange, should be vectorially added to q_{s}.
Table 10.4 Shear force and tensile force in fastener along the beam
Beam and loading 
Shear force per unite length q_{s} 
Tensile force per unit length q_{t} 
Zbeam, gravity loading 
(1 + ξ)k_{h}q_{Ed} , may be taken as 0 
0 
Zbeam, uplift loading 
(1 + ξ)(k_{h} – a / h)q_{Ed} 
 ξk_{h}q_{Ed}h / a  +q_{Ed} (a ≅ b / 2) 
Cbeam, gravity loading 
(1 – ξ)k_{h}q_{Ed} 
ξk_{h}q_{Ed} h / a 
Cbeam, uplift loading 
(1 – ξ)(k_{h} – a / h)q_{Ed} 
ξk_{h}q_{Ed} h /(b – a) + q_{Ed} 
 The fasteners fixing the purlins to the supports should be checked for the reaction force R_{w} in the plane of the web and the transverse reaction forces R_{1} and R_{2} in the plane of the flanges, see figure 10.8. Forces R_{1} and R_{2} may be calculated using table 10.5. Force R_{2} should also include loads parallel to the roof for sloped roofs. If R_{1} is positive there is no tension force on the fastener. R_{2} should be transferred from the sheeting to the top flange of the purlin and further on to the rafter (main beam) through the purlin/rafter connection (support cleat) or via special shear connectors or directly to the base or similar element. The reaction forces at an inner support of a continuous purlin may be taken as 2,2 times the values given in table 10.5.
NOTE: For sloped roofs the transversal loads to the purlins are the perpendicular (to the roof plane) components of the vertical loads and parallel components of the vertical loads are acting on the roof plane.
Figure 10.8: Reaction forces at support
Table 10.5 Reaction force at support for simply supported beam
Beam and loading 
Reaction force on bottom flange R_{1} 
Reaction force on top flange R_{2} 
Zbeam, gravity loading 
(1 – ς)k_{h}q_{Ed} L / 2 
(1 + ς)k_{h}q_{Ed} L / 2 
Zbeam, uplift loading 
– (1 – ς)k_{h}q_{Ed} L / 2 
– (1 + ς)k_{h}q_{Ed} L / 2 
Cbeam, gravity loading 
(1 – ς)k_{h}q_{Ed} L / 2 
– (1 – ς)k_{h}q_{Ed} L / 2 
Cbeam, uplift loading 
– (1 – ς)k_{h}q_{Ed} L / 2 
(1 – ς)k_{h}q_{Ed} L / 2 
 The factor ς may be taken as where K_{R} is the correction factor given in Table 10.1, and the factor ξ may be taken as ξ = 1,5 ς.
91
10.2 Liner trays restrained by sheeting
10.2.1 General
 Liner trays should be large channeltype sections, with two narrow flanges, two webs and one wide flange, generally as shown in figure 10.9. The two narrow flanges should be laterally restrained by attached profiled steel sheeting or by steel purlin or by similar component.
Figure 10.9: Typical geometry for liner trays
 The resistance of the webs of liner trays to shear forces and to local transverse forces should be obtained using 6.1.5 to 6.1.11, but using the value of M_{c,Rd} given by (3) or (4).
 The moment resistance M_{c,Rd} of a liner tray may be obtained using 10.2.2 provided that:
  the geometrical properties are within the range given in table 10.6;
  the depth h_{u} of the corrugations of the wide flange does not exceed h/8 , where h is the overall depth of the liner tray.
 Alternatively the moment resistance of a liner tray may be determined by testing provided that it is ensured that the local behaviour of the liner tray is not affected by the testing equipment.
NOTE: Appropriate testing procedures are given in annex A.
92
Table 10.6: Range of validity of 10.2.2
0,75 mm 
≤ 
t_{nom} 
≤ 
1,5 mm 
30 mm 
≤ 
b_{f} 
≤ 
60 mm 
60 mm 
≤ 
h 
≤ 
200 mm 
300 mm 
≤ 
b_{u} 
≤ 
600 mm 


I_{a} / b_{u} 
≤ 
10 mm^{4} / mm 


S_{1} 
≤ 
1000 mm 
10.2.2 Moment resistance
10.2.2.1 Wide flange in compression
 The moment resistance of a liner tray with its wide flange in compression should be determined using the stepbystep procedure outlined in figure 10.10 as follows:
  Step 1: Determine the effective areas of all compression elements of the crosssection, based on values of the stress ratio Ψ = σ_{2} / σ_{1} obtained using the effective widths of the compression flanges but the gross areas of the webs;
  Step 2: Find the centroid of the effective crosssection, then obtain the moment resistance M_{c,Rd}from:
M_{c,Rd} = 0,8 W_{eff,min} f_{yb} / γ_{M0} (10.19)
with:
W_{eff,min} = I_{y,eff} / z_{c} but W_{eff,min} ≤ I_{y,eff} / z_{t};
where z_{c} and z_{t} are as indicated in figure 10.10.
Figure 10.10: Determination of moment resistance — wide flange in compression
93
10.2.2.2 Wide flange in tension
 The moment resistance of a liner tray with its wide flange in tension should be determined using the stepbystep procedure outlined in figure 10.11 as follows:
  Step 1: Locate the centroid of the gross crosssection;
  Step 2: Obtain the effective width of the wide flange b_{u,eff,} allowing for possible flange curling, from:
where:
b_{u} 
the overall width of the wide flange; 
e_{0} 
the distance from the centroidal axis of the gross crosssection to the centroidal axis of the narrow flanges; 
h 
the overall depth of the liner tray; 
L 
the span of the liner tray; 
t_{eq} 
the equivalent thickness of the wide flange, given by:
t_{eq} = (12 I_{a} / b_{u})^{1/3}

I_{a} 
the second moment of area of the wide flange, about its own centroid, see figure 10.9. 
  Step 3: Determine the effective areas of all the compression elements, based on values of the stress ratio Ψ = σ_{2} / σ_{1} obtained using the effective widths of the flanges but the gross areas of the webs;
  Step 4: Find the centroid of the effective crosssection, then obtain the buckling resistance moment M_{b,Rd} using:
M_{b,Rd} = 0,8 β_{b} W_{eff,com}f_{yb} / γ_{M0} but M_{b,Rd} ≤ 0,8 W_{eff,t,}f_{yb} / γ_{M0} (10.21)
with:
W_{eff,com} = I_{y,eff} / z_{c}
W_{eff,t} = I_{y,eff} / z_{t}
in which the correlation factor β_{b} is given by the following:
where:
S_{1} 
is the longitudinal spacing of fasteners supplying lateral restraint to the narrow flanges, see figure 10.9 
 The effects of shear lag need not be considered if L / b_{u,eff} ≥ 25. Otherwise a reduced value of ρ should be determined as specified in 6.1.4.3.
94
Figure 10.11: Determination of moment resistance — wide flange in tension
 Flange curling need not be taken into account in determining deflections at serviceability limit slates.
 As a simplified alternative, the moment resistance of a liner tray with an unstiffened wide flange may be approximated by taking the same effective area for the wide flange in tension as for the two narrow flanges in compression combined.
10.3 Stressed skin design
10.3.1 General
 The interaction between structural members and sheeting panels that are designed to act together as parts of a combined structural system, may be allowed for as described in this clause 10.3.
 The provisions given in this clause should be applied only to sheet diaphragms that are made of steel.
 Diaphragms may be formed from profiled sheeting used as roof or wall cladding or for floors. They may also be formed from wall or roof structures based upon liner trays.
NOTE: Information on the verification of such diaphragms may be obtained from:
ECCS Publication No. 88 (1995): European recommendations for the application of metal sheeting acting as a diaphragm.
10.3.2 Diaphragm action
 In stressed skin design, advantage may be taken of the contribution that diaphragms of sheeting used as roofing, flooring or wall cladding make to the overall stiffness and strength of the structural frame, by means of their stiffness and strength in shear.
 Roofs and floors may be treated as deep plate girders extending throughout the length of a building, resisting transverse inplane loads and transmitting them to end gables, or to intermediate stiffened frames. The panel of sheeting may be treated as a web that resists inplane transverse loads in shear, with the edge members acting as flanges that resist axial tension and compression forces, see figures 10.12 and 10.13.
95
 Similarly, rectangular wall panels may be treated as bracing systems that act as shear diaphragms to resist inplane forces.
Figure 10.12: Stressed skin action in a flatroof building
10.3.3 Necessary conditions
 Methods of stressed skin design that utilize sheeting as an integral part of a structure, may be used only under the following conditions:
  the use made of the sheeting, in addition to its primary purpose, is limited to the formation of shear diaphragms to resist structural displacement in the plane of that sheeting;
  the diaphragms have longitudinal edge members to carry flange forces arising from diaphragm action;
  the diaphragm forces in the plane of a roof or floor are transmitted to the foundations by means of braced frames, further stressedskin diaphragms, or other methods of sway resistance;
  suitable structural connections are used to transmit diaphragm forces to the main steel framework and to join the edge members acting as flanges;
  the sheeting is treated as a structural component that cannot be removed without proper consideration;
  the project specification, including the calculations and drawings, draws attention to the fact that the building is designed to utilize stressed skin action;
  in sheeting with the corrugation oriented in the longitudinal direction of the roof the flange forces due to diaphragm action may be taken up by the sheeting.
 Stressed skin design may be used predominantly in lowrise buildings, or in the floors and facades of highrise buildings.
 Stressed skin diaphragms may be used predominantly to resist wind loads, snow loads and other loads that are applied through the sheeting itself. They may also be used to resist small transient loads, such as surge from light overhead cranes or hoists on runway beams, but may not be used to resist permanent external loads, such as those from plant.
96
Figure 10.13: Stressed skin action in a pitched roof building
10.3.4 Profiled steel sheet diaphragms
 In a profiled steel sheet diaphragm, see figure 10.14, both ends of the sheets should be attached to the supporting members by means of selftapping screws, cartridge fired pins, welding, bolts or other fasteners of a type that will not work loose in service, pull out, or fail in shear before causing tearing of the sheeting. All such fasteners should be fixed directly through the sheeting into the supporting member, for example through the troughs of profiled sheets, unless special measures are taken to ensure that the connections effectively transmit the forces assumed in the design.
 The seams between adjacent sheets should be fastened by rivets, selfdrilling screws, welds, or other fasteners of a type that will not work loose in service, pull out, or fail in shear before causing tearing of the sheeting. The spacing of such fasteners should not exceed 500 mm.
 The distances from all fasteners to the edges and ends of the sheets should be adequate to prevent premature tearing of the sheets.
 Small randomly arranged openings, up to 3% of the relevant area, may be introduced without special calculation, provided that the total number of fasteners is not reduced. Openings up to 15% of the relevant area (the area of the surface of the diaphragm taken into account for the calculations) may be introduced if justified by detailed calculations. Areas that contain larger openings should be split into smaller areas, each with full diaphragm action.
 All sheeting that also forms part of a stressedskin diaphragm should first be designed for its primary purpose in bending. To ensure that any deterioration of the sheeting would be apparent in bending before the resistance to stressed skin action is affected, it should then be verified that the shear stress due to diaphragm action does not exceed 0,25 f_{yb}/ γ_{M1}.
 The shear resistance of a stressedskin diaphragm should be based on the least tearing strength of the seam fasteners or the sheettomember fasteners parallel to the corrugations or, for diaphragms fastened only to longitudinal edge members, the end sheettomember fasteners. The calculated shear resistance for any other type of failure should exceed this minimum value by at least the following:
10.3.5 Steel liner tray diaphragms
 Liner trays used to form shear diaphragms should have stiffened wide flanges.
 Liner trays in shear diaphragms should be interconnected by seam fasteners through the web at a spacing e_{s} of not more than 300 mm by seam fasteners (normally blind rivets) located at a distance e_{u} from the wide flange of not more than 30 mm, all as shown in figure 10.15.
 An accurate evaluation of deflections due to fasteners may be made using a similar procedure to that for trapezoidal profiled sheeting.
 The shear flow T_{v,Ed} due to ultimate limit states design loads should not exceed T_{v,Rd} given by:
where:
I_{a} 
is the second moment of area of the wide flange about it own centroid, see figure 10.9; 
b_{u} 
is the overall width of the wide flange. 
Figure 10.15: Location of seam fasteners
98
 The shear flow T_{v,ser} due to serviceability design loads should not exceed T_{v,Cd} given by:
T_{v,Cd} = S_{v} / 375 (10.23)
where:
S_{v} 
is 
the shear stiffness of the diaphragm, per unit length of the span of the liner trays. 
 The shear stiffness S_{v} per unit length may be obtained from:
where:
L 
is 
the overall length of the shear diaphragm (in the direction of the span of the liner trays); 
b 
is 
the overall width of the shear diaphragm (b = Σ b_{u}); 
α 
is 
the stiffness factor. 
 The stiffness factor α may be conservatively be taken as equal to 2000 N/mm unless more accurate values are derived from tests.
10.4 Perforated sheeting
 Perforated sheeting with the holes arranged in the shape of equilateral triangles may be designed by calculation, provided that the rules for nonperforated sheeting are modified by introducing the effective thicknesses given below.
NOTE: These calculation rules tend to give rather conservative values. More economical solutions might be obtained from design assisted by testing, see Section 9.
 Provided that 0,2 ≤ d / a ≤ 0,9 gross section properties may be calculated using 5 , but replacing t by t_{a,eff} obtained from:
where:
d 
is the diameter of the perforations; 
a 
is the spacing between the centres of the perforations. 
 Provided that 0,2 ≤ d / a ≤ 0,9 effective section properties may be calculated using Section 5, but replacing t by t_{b,eff} obtained from:
 The resistance of a single web to local transverse forces may be calculated using 6.1 .7 , but replacing t by t_{c,eff} obtained from:
t_{c,eff} = t [1 (d / a)^{2} s _{per} / s _{w}]^{3/2} ...(10 27)
where:
s_{per} 
is 
the slant height of the perforated portion of the web; 
s_{w} 
is 
the total slant height of the web. 
99
Annex A – Testing procedures
[normative]
A.1 General
 This annex A gives appropriate standardized testing and evaluation procedures for a number of tests that are required in design.
NOTE 1: In the field of coldformed members and sheeting, many standard products arc commonly used for which design by calculation might not lead to economical solutions, so it is frequently desirable to use design assisted by testing.
NOTE 2: The National Annex may give further information on testing.
NOTE 3: The National Annex may give conversion factors for existing test results to be equivalent to the outcome of standardised tests according to this annex.
 This annex covers:
  tests on profiled sheets and liner trays, see A.2;
  tests on coldformed members, see A.3;
  tests on structures and portions of structures, see A.4;
  tests on torsionally restrained beams, see A.5;
  evaluation of test results to determine design values, see A.6.
A.2 Tests on profiled sheets and liner trays
A.2.1 General
 Although these test procedures are presented in terms of profiled sheets, similar test procedures based on the same principles may also be used for liner trays and other types of sheeting (e.g. sheeting mentioned in EN
 Loading may be applied through air bags or in a vacuum chamber or by steel or timber cross beams arranged to approximate uniformly distributed loading.
 To prevent spreading of corrugations, transverse ties or other appropriate test accessories such as timber blocks may be applied to the test specimen. Some examples are given in figure A.1.
Figure A.1: Examples of appropriate test accessories
100
 For uplift tests, the test setup should realistically simulate the behaviour of the sheeting under practical conditions. The type of connections between the sheet and the supports should be the same as in the connections to be used in practice.
 To give the results a wide range of applicability, hinged and roller supports should preferably be used, to avoid any influence of rotational restraint at the supports on the test results.
 It should be ensured that the direction of the loading remains perpendicular to the initial plane of the sheet throughout the test procedure.
 To eliminate the deformations of the supports, the deflections at both ends of the test specimen should also be measured.
 The test result should be taken as the maximum value of the loading applied to the specimen either coincident with failure or immediately prior to failure as appropriate.
A.2.2 Single span test
 A test setup equivalent to that shown in figure A.2 may be used to determine the midspan moment resistance (in the absence of shear force) and the effective flexural stiffness.
 The span should be chosen such that the test results represent the moment resistance of the sheet.
 The moment resistance should be determined from the test result.
 The flexural stiffness should be determined from a plot of the loaddeflection behaviour.
A.2.3 Double span test
 The test setup shown in figure A.3 may be used to determine the resistance of a sheet that is continuous over two or more spans to combinations of moment and shear at internal supports, and its resistance to combined moment and support reaction for a given support width.
 The loading should preferably be uniformly distributed (applied using an air bag or a vacuum chamber, for example).
 Alternatively any number of line loads (transverse to the span) may be used, arranged to produce internal moments and forces that are appropriate to represent the effects of uniformly distributed loading. Some examples of suitable arrangements are shown in figure A.4.
A.2.4 Internal support test
 As an alternative to A.2.3, the test setup shown in figure A.5 may be used to determine the resistance of a sheet that is continuous over two or more spans to combinations of moment and shear at internal supports, and its resistance to combined moment and support reaction for a given support width.
 The test span s used to represent the portion of the sheet between the points of contraflexure each side of the internal support, in a sheet continuous over two equal spans L may be obtained from:
s = 0,4 L ... (A.1)
 If plastic redistribution of the support moment is expected, the test span s should be reduced to represent the appropriate ratio of support moment to shear force.
101
Figure A.2: Test setup for single span tests
Figure A.3: Test setup for double span tests
102
Figure A.4: Examples of suitable arrangements of alternative line loads
 The width b_{B} of the beam used to apply the test load should be selected to represent the actual support width to be used in practice.
 Each test result may be used to represent the resistance to combined bending moment and support reaction (or shear force) for a given span and a given support width. To obtain information about the interaction of bending moment and support reaction, tests should be carried out for several different spans.
 Interpretation of test results, see A.5.2.3.
A.2.5 End support test
 The test setup shown in figure A.6 may be used to determine the shear resistance of a sheet at an end support.
 Separate tests should be carried out to determine the shear resistance of the sheet for different lengths u from the contact point at the inner edge of the end support, to the actual end of the sheet, see figure A.6.
NOTE: Value of maximum support reaction measured during a bending test may be used as a lower bound for section resistance to both shear and local transverse force.
103
Figure A.5: Test setup for internal support test
Figure A.6: Test setup for end support tests
104
A.3 Tests on coldformed members
A.3.1 General
 Each test specimen should be similar in all respects to the component or structure that it represents.
 The supporting devices used for tests should preferably provide end conditions that closely reproduce those supplied by the connections to be used in service. Where this cannot be achieved, less favourable end conditions that decrease the load carrying capacity or increase the flexibility should be used, as relevant.
 The devices used to apply the test loads should reproduce the way that the loads would be applied in service. It should be ensured that they do not offer more resistance to transverse deformations of the crosssection than would be available in the event of an overload in service. It should also be ensured that they do not localize the applied forces onto the lines of greatest resistance.
 If the given load combination includes forces on more than one line of action, each increment of the test loading should be applied proportionately to each of these forces.
 At each stage of the loading, the displacements or strains should be measured at one or more principal locations on the structure. Readings of displacements or strains should not be taken until the structure has completely stabilized after a load increment.
 Failure of a test specimen should be considered to have occurred in any of the following cases:
  at collapse or fracture;
  if a crack begins to spread in a vital part of the specimen;
  if the displacement is excessive.
 The test result should be taken as the maximum value of the loading applied to the specimen either coincident with failure or immediately prior to failure as appropriate.
 The accuracy of all measurements should be compatible with the magnitude of the measurement concerned and should in any case not exceed ± 1% of the value to be determined. The following magnitudes (in clause (9)) must also be fulfilled.
 The measurements of the crosssectional geometry of the test specimen should include:
  the overall dimensions (width, depth and length) to an accuracy of ± 1,0 mm;
  widths of plane elements of the crosssection to an accuracy of ± 1,0 mm;
  radii of bends to an accuracy of ± 1,0 mm;
  inclinations of plane elements to an accuracy of ±2,0°;
  angles between flat surfaces to an accuracy of ± 2,0°;
  locations and dimensions of intermediate stiffeners to an accuracy of ±1,0 mm;
  the thickness of the material to an accuracy of ±0,01 mm;
  accuracy of all measurements of the crosssection has to be taken as equal to maximum 0,5 % of the nominal values.
 All other relevant parameters should also be measured, such as:
  locations of components relative to each other;
  locations of fasteners;
  the values of torques etc. used to tighten fasteners.
105
A.3.2 Full crosssection compression tests
A.3.2.1 Stub column test
 Stub column tests may be used to allow for the effects of local buckling in thin gauge crosssections, by determining the value of the ratio β_{A} = A_{eef} / A_{g} and the location of the effective centroidal axis.
 If local buckling of the plane elements governs the resistance of the crosssection, the specimen should have a length of at least 3 times the width of the widest plate element.
 The lengths of specimens with perforated crosssections should include at least 5 pitches of the perforations, and should be such that the specimen is cut to length midway between two perforations.
 In the case of a crosssection with edge or intermediate stiffeners, it should be ensured that the length of the specimen is not less than the expected buckling lengths of the stiffeners.
 If the overall length of the specimen exceeds 20 times the least radius of gyration of its gross crosssection i_{min}, intermediate lateral restraints should be supplied at a spacing of not more than 20 i_{min}.
 Before testing, the tolerances of the crosssectional dimensions of the specimen should be checked to ensure that they are within the permitted deviations.
 The cut ends of the specimen should be flat, and should be perpendicular to its longitudinal axis.
 An axial compressive force should be applied to each end of the specimen through pressure pads at least 30 mm thick, that protrude at least 10 mm beyond the perimeter of the crosssection.
 The test specimen should be placed in the testing machine with a ball bearing at each end. There should be small drilled indentations in the pressure pads to receive the ball bearings. The ball bearings should be located in line with the centroid of the calculated effective crosssection. If the calculated location of this effective centroid proves not to be correct, it may be adjusted within the test series.
 In the case of open crosssections, possible springback may be corrected.
 Stub column tests may be used to determine the compression resistance of a crosssection. In interpreting the test results, the following parameters should be treated as variables:
  the thickness;
  the ratio b_{p} / t
 the ratio f_{u} / f_{yb};
  the ultimate strength f_{u} and the yield strength f_{yb};
  the location of the centroid of the effective crosssection;
  imperfections in the shape of the elements of the crosssection;
  the method of cold forming (for example increasing the yield strength by introducing a deformation that is subsequently removed).
A.3.2.2 Member buckling test
 Member buckling tests may be used to determine the resistance of compression members with thin gauge crosssections to overall buckling (including flexural buckling, torsional buckling and torsionalflexural buckling) and the interaction between local buckling and overall buckling.
 The method of carrying out the test should be generally as given for stub column tests in A.3.2.1.
 A series of tests on axially loaded specimens may be used to determine the appropriate buckling curve for a given type of crosssection and a given grade of steel, produced by a specific process. The values of relative slenderness to be tested and the minimum number of tests n at each value, should be as given in table A.1.
106
Table A.1: Relative slenderness values and numbers of tests

0,2 
0,5 
0,7 
1,0 
1,3 
1,6 
2,0 
3,0 
N 
3 
5 
5 
5 
5 
5 
5 
5 
 Similar tests may also be used to determine the effect of introducing intermediate restraints on the torsional buckling resistance of a member.
 For the interpretation of the test results the following parameters should be taken into account:
  the parameters listed for stub column tests in A.3.2.1(11);
  overall lack of straightness imperfections compared to standard production output, see (6);
  type of end or intermediate restraint (flexural, torsional or both).
 Overall lack of straighness may be taken into account as follows:
 Determine the elastic critical compression load of the member by an appropriate analysis with initial bow equal to test sample: F_{cr,bow,test}
 As a) but with an initial bow equal to the maximum allowed according to the product specification: F_{cr,bow,max,nom}
 Additional correction factor: F_{cr,bow,max,nom} / F_{cr,bow,test}
A.3.3 Full crosssection tension test
 This test may be used to determine the average yield strength f_{ya} of the crosssection.
 The specimen should have a length of at least 5 times the width of the widest plane element in the crosssection.
 The load should be applied through end supports that ensure a uniform stress distribution across the crosssection.
 The failure zone should occur at a distance from the end supports of not less than the width of the widest plane element in the crosssection.
A.3.4 Full crosssection bending test
 This test may be used to determine the moment resistance and rotation capacity of a crosssection.
 The specimen should have a length of at least 15 times its greatest transversal dimension. The spacing of lateral restraints to the compression flange should not be less than the spacing to be used in service.
 A pair of point loads should be applied to the specimen to produce a length under uniform bending moment at midspan of at least 0,2 × (span) but not more than 0,33 × (span). These loads should be applied through the shear centre of the crosssection. The section should be torsionally restrained at the load points. If necessary, local buckling of the specimen should be prevented at the points of load application, to ensure that failure occurs within the central portion of the span. The deflection should be measured at the load positions, at midspan and at the ends of the specimen.
107
 In interpreting the test results, the following parameters should be treated as variables:
  the thickness;
  the ratio b_{p} / t;
  the ratio f_{u} / f_{yb};
  the ultimate strength f_{u} and the yield strength f_{yb};
  differences between restraints used in the test and those available in service;
  the support conditions.
A.4 Tests on structures and portions of structures
A.4.1 Acceptance test
 This acceptance test may be used as a nondestructive test to confirm the structural performance of a structure or portion of a structure.
 The test load for an acceptance test should be taken as equal to the sum of:
  1,0 × (the actual selfweight present during the test);
  1,15 × (the remainder of the permanent load);
  1,25 × (the variable loads).
but need not be taken as more than the mean of the total ultimate limit state design load and the total serviceability limit state design load for the characteristic text deleted load combination.
 Before carrying out the acceptance test, preliminary bedding down loading (not exceeding the characteristic values of the loads) may optionally be applied, and then removed.
 The structure should first be loaded up to a load equal to the total characteristic load. Under this load it should demonstrate substantially elastic behaviour. On removal of this load the residual deflection should not exceed 20% of the maximum recorded. If these criteria are not satisfied this part of the test procedure should be repeat. In this repeat load cycle, the structure should demonstrate substantially linear behaviour up to the characteristic load and the residual deflection should not exceed 10% of the maximum recorded.
 During the acceptance test, the loads should be applied in a number of regular increments at regular time intervals and the principal deflections should be measured at each stage. When the deflections show significant nonlinearity, the load increments should be reduced.
 On the attainment of the acceptance test load, the load should be maintained for being no changes between a set of adjacent readings and deflection measurements should be taken to establish whether the structure is subject to any timedependent deformations, such as deformations of fasteners or deformations arising from creep in the zinc layer.
 Unloading should be completed in regular decrements, with deflection readings taken at each stage.
 The structure should prove capable of sustaining the acceptance test load, and there should be no significant local distortion or defects likely to render the structure unserviceable after the test.
A.4.2 Strength test
 This strength test may be used to confirm the calculated load carrying capacity of a structure or portion of a structure. Where a number of similar items are to be constructed to a common design and one or more prototypes have been submitted to and met all the requirements of this strength test, the others may be accepted without further testing provided that they are similar in all relevant respects to the prototypes.
 Before carrying out a strength test the specimen should first pass the acceptance test detailed in A.4.1.
108
 The load should then be increased in increments up to the strength test load and the principal deflections should be measured at each stage. The strength test load should be maintained for at least one hour and deflection measurements should be taken to establish whether the structure is subject to creep.
 Unloading should be completed in regular decrements with deflection readings taken at each stage.
 The total test load (including selfweight) for a strength test F_{str} should be determined from the total design load F_{Ed} specified for ultimate limit state verifications by calculation, using:
F_{str} = γ_{Mi} μ_{F} F_{Ed} ... (A.2)
in which μ_{F} is the load adjustment coefficient and γ_{Mi} is the partial coefficient of the ultimate limit state.
 The load adjustment coefficient μ_{F} should take account of variations in the load carrying capacity of the structure, or portion of a structure, due to the effects of variation in the material yield strength, local buckling, overall buckling and any other relevant parameters or considerations.
 Where a realistic assessment of the load carrying capacity of the structure, or portion of a structure, may be made using the provisions of this Part 13 of EN 1993 for design by calculation, or another proven method of analysis that takes account of all buckling effects, the load adjustment coefficient μ_{F} may be taken as equal to the ratio of (the value of the assessed load carrying capacity based on the averaged basic yield strength f_{ym}) compared to (the corresponding value based on the nominal basic yield strength f_{yb}).
 The value of f_{ym} should be determined from the measured basic strength f_{yb,obs} of the various components of the structure, or portion of a structure, with due regard to their relative importance.
 If realistic theoretical assessments of the load carrying capacity cannot be made, the load adjustment coefficient μ_{F} should be taken as equal to the resistance adjustment coefficient μ_{R} defined in A.6.2.
 Under the test load there should be no failure by buckling or rupture in any part of the specimen.
 On removal of the test load, the deflection should be reduced by at least 20%.
A.4.3 Prototype failure test
 A test to failure may be used to determine the real mode of failure and the true load carrying capacity of a structure or assembly. If the prototype is not required for use, it may optionally be used to obtain this additional information after completing the strength test described in A.4.2.
 Alternatively a test to failure may be carried out to determine the true design load carrying capacity from the ultimate test load. As the acceptance and strength test procedures should preferably be carried out first, an estimate should be made of the anticipated design load carrying capacity as a basis for such tests.
 Before carrying out a test to failure, the specimen should first pass the strength test described in A.4.2. Its estimated design load carrying capacity may then be adjusted based on its behaviour in the strength test.
 During a test to failure, the loading should first be applied in increments up to the strength test load. Subsequent load increments should then be based on an examination of the plot of the principal deflections.
 The ultimate load carrying capacity should be taken as the value of the test load at that point at which the structure or assembly is unable to sustain any further increase in load.
NOTE: At this point gross permanent distortion is likely to have occurred. In some cases gross deformation might define the test limit.
A.4.4 Calibration test
 A calibration test may be used to:
  verify load bearing behaviour relative to analytical design models;
  quantify parameters derived from design models, such as strength or stiffness of members or joints.
109
A.5 Tests on torsionally restrained beams
A.5.1 General
 These test procedures may be used for beams that are partially restrained against torsional displacement, by means of trapezoidal profiled steel sheeting or other suitable cladding.
 These procedures may be used for purlins, side rails, floor beams and other similar types of beams that have relevant restraint conditions.
A.5.2 Internal support test
A.5.2.1 Test setup
 The test setup shown in figure A.7 may be used to determine the resistance of a beam that is continuous over two or more spans, to combinations of bending moment and shear force at internal supports.
NOTE: The same test setup may be used for sleeved and overlap systems.
Figure A.7: Test setup for internal support tests
 The supports at A and E should be hinged and roller supports respectively. At these supports, rotation about the longitudinal axis of the beam may be prevented, for example by means of cleats.
 The method of applying the load at C should correspond with the method to be used in service.
NOTE: In many cases this will mean that lateral displacement of both flanges is prevented at C.
 The displacement measurements at points B and D located at a distance e from each support, see figure A.7, should be recorded to allow these displacements to be eliminated from the results analysis
 The test span s should be chosen to produce combinations of bending moment and shear force that represent those expected to occur in practical application under the design load for the relevant limit state.
 For double span beams of span L subject to uniformly distributed loads, the test span s should normally be taken as equal to 0,4 L. However, if plastic redistribution of the support moment is expected, the test span s should be reduced to represent the appropriate ratio of support moment to shear force.
A.5.2.2 Execution of tests
 In addition to the general rules for testing, the following specific aspects should be taken into account.
 Testing should continue beyond the peak load and the recording of the deflections should be continued either until the applied load has reduced to between 10% and 15% of its peak value or until the deflection has reached a value 6 times the maximum elastic displacement.
A.5.2.3 Interpretation of test results
 The actual measured test results R_{obs,i} should be adjusted as specified in A.6.2 to obtain adjusted values R_{adj,i} related to the nominal basic yield strength f_{yb} and design thickness t of the steel, see 3.2.4.
110
 For each value of the test span s the support reaction R should be taken as the mean of the adjusted values of the peak load F_{max} for that value of s . The corresponding value of the support moment M should then be determined from:
Generally the influence of the dead load should be added when calculating the value of moment M following the expression (A.3).
 The pairs of values of M and R for each value of s should be plotted as shown in figure A.8. Pairs of values for intermediate combinations of M and R may then be determined by linear interpolation.
Figure A.8: Relation between support moment M and support reaction R
 The net deflection at the point of load application C in figure A.7 should be obtained from the gross measured values by deducting the mean of the corresponding deflections measured at the points B and D located at a distance e from the support points A and E, see figure A.7.
 For each test the applied load should be plotted against the corresponding net deflection, see figure A.9. From this plot, the rotation θ should be obtained for a range of values of the applied load using:
where:
δ_{et} 
is 
the net deflection for a given load on the rising part of the curve, before F_{max}; 
δ_{pl} 
is 
the net deflection for the same load on the falling part of the curve, after F_{max}; 
δ_{lin} 
is 
the fictive net deflection for a given load, that would be obtained with a linear behaviour, see figure A.9; 
δ_{e} 
is 
the average deflection measured at a distance e from the support, see figure A.7; 
s 
is 
the test span; 
e 
is 
the distance between a deflection measurement point and a support, see figure A.7. 
111
The expression (A.4a) is used when analyses are done based on the effective crosssection. The expression (A.4b) is used when analyses are done based on the gross crosssection.
 The relationship between M and θ should then be plotted for each test at a given test span s corresponding to a given value of beam span L as shown in figure A.IO. The design M  θ characteristic for the moment resistance of the beam over an internal support should then be taken as equal to 0,9 times the mean value of M for all the tests corresponding to that value of the beam span L.
NOTE: Smaller value than 0,9 lor reduction should be used, if the fullscale tests are used to determine effect of lateral load and buckling of free flange around the midsupport, see 10.1.3.2(4).
Figure A.9: Relation between load F and net deflection δ
Figure A.10: Derivation of momentrotation (M  θ) characteristic
A.5.3 Determination of torsional restraint
 The test setup shown in figure A.1 1 may be used to determine the amount of torsional restraint given by adequately fastened sheeting or by another member perpendicular to the span of the beam.
112
 This test setup covers two different contributions to the total amount of restraint as follows:
 The lateral stiffness K_{A} per unit length corresponding to the rotational stiffness of the connection between the sheeting and the beam;
 The lateral stiffness K_{B} per unit length due to distortion of the crosssection of the purlin.
 The combined restraint per unit length may be determined from:
(1 / KA + 1 / KB) = δ / F ....(A.5)
where:
F 
is 
the load per unit length of the test specimen to produce a lateral deflection of h/10; 
h 
is 
the overall depth of the specimen; 
δ 
is 
the lateral displacement of the top flange in the direction of the load F. 
 In interpreting the test results, the following parameters should be treated as variables:
  the number of fasteners per unit length of the specimen;
  the type of fasteners;
  the flexural stiffness of the beam, relative to its thickness;
  the flexural stiffness of the bottom flange of the sheeting, relative to its thickness;
  the positions of the fasteners in the flange of the sheeting;
  the distance from the fasteners to the centre of rotation of the beam;
  the overall depth of the beam;
  the possible presence of insulation between the beam and the sheeting.
113
Figure A.11: Experimental determination of spring stiffness K_{A} and K_{B}
A.6 Evaluation of test results
A.6.1 General
 A specimen under test should be regarded as having failed if the applied test loads reach their maximum values, or if the gross deformations exceed specified limits.
 The gross deformations of members should generally satisfy:
δ ≤ L/50 ...(A.6)
ϕ ≤ 1/50 ...(A.7)
where:
δ 
is 
the maximum deflection of a beam of span L; 
ϕ 
is 
the sway angle of a structure. 
 In the testing of connections, or of components in which the examination of large deformations is necessary for accurate assessment (for example, in evaluating the momentrotation characteristics of sleeves), no limit need be placed on the gross deformation during the test.
114
 An appropriate margin of safety should be available between a ductile failure mode and possible brittle failure modes. As brittle failure modes do not usually appear in large scale tests, additional detail tests should be carried out where necessary.
NOTE: This is often the case for connections.
A.6.2 Adjustment of test results
 Test results should be appropriately adjusted to allow for variations between the actual measured properties of the test specimens and their nominal values.
 The actual measured basic yield strength f_{yb,obs} should not deviate by more than 25% from the nominal basic yield strength f_{yb} i.e. f_{yb,obs} ≥ 0,75 f_{yb}.
 The actual measured thickness t_{obs} should not exceed the nominal material thickness t_{nom} (see 3.2.4) by more than 12%.
 Adjustments should be made in respect of the actual measured values of the core material thickness t_{obs,cor} and the basic yield strength f_{yb,0bs} for all tests, except if values measured in tests are used to calibrate a design model then provisions of (5) need not be applied.
 The adjusted value R_{adj,i} of the test result for test i should be determined from the actual measured test result R_{obs,i} using:
R_{adj,i} = R_{obs,i} / μ_{R} ...(A.8)
in which μ_{R} is the adjustment coefficient:
 The exponent a for use in expression (A.9) should be obtained as follows:
 if f_{yb,obs} ≤ f_{yb}: α= 0
 if f_{yb,obs} > f_{yb}: α=1
For profiled sheets or liner trays in which compression elements have such large b_{p}/t ratios that local buckling is clearly the failure mode: α = 0,5.
115
 The exponent β for use in expression (A.9) should be obtained as follows:
  if t_{obs,cor} ≤ t_{cor}: β = l
  if t_{obs,cor} ≤ t_{cor}:
  for tests on profiled sheets or liner trays: β = 2
  for tests on members, structures or portions of structures:
  if b_{p}/t ≤ (b_{p}/t)_{lim}: β = l
  if b_{p}/t > 1,5(b_{p}/t)_{lim}: β= 2
  if (b_{p}/t)_{lim} < b_{p}/t < 1,5(b_{p}/t)_{lim}: obtain β by linear interpolation,
in which the limiting widthto thickness ratio (b_{p}/t)_{lim} given by:
where:
b_{p} 
is 
the national flat width of a plan element; 
k_{σ} 
is 
the relevant buckling factor from table 4.1 or 4.2 in En 199315; 
σ_{com,Ed} 
is 
the largest calculated compressive stress in the element, at the ultimate limit state. 
NOTE: In the case of available test report concerning sheet specimens with t_{obs,cor} / t_{cor} ≤ 1,06 readjustment of existing value not exceeding 1.02 times the R_{adj,i} value according to A.6.2 may be omitted.
For the adjustment of second moment of area, where linear behaviour is observed under the serviceability limit state loading, the exponents in the formula (A.9) should be taken as follows: α = 0,0 and β = 1,0.
A.6.3 Characteristic values
A.6.3.1 General
 Characteristic values may be determined statistically, provided that there are at least 4 test results.
NOTE: A larger number is generally preferable, particularly if the scatter is relatively wide.
 If the number of test results available is 3 or less, the method given in A.6.3.3 may be used.
 The characteristic minimum value should be determined using the following provisions. If the characteristic maximum value or the characteristic mean value is required, it should be determined by using appropriate adaptations of the provisions given for the characteristic minimum value.
 The characteristic value R_{k} determined on the basis of at least 4 tests may be obtained from:
R_{k} = R_{m} +/ k s ...(A.11)
where:
s 
is 
the standard deviation; 
k 
is 
the appropriate coefficient from table A.2; 
R_{m} 
is 
the mean value of the adjusted test results R_{adj}; 
The unfavourable sign “+” or “” should be adopted for given considered value.
NOTE: As general rule, for resistance characteristic value, the sign “” should be taken and e.g. for rotation characteristic value, both are to be considered.
116
 The standard deviation s may be determined using:
where:
R_{adj,i} 
is 
is the adjusted test result for test i; 
n 
is 
the number of tests. 
Table A.2: Values of the coefficient k
N 
4 
5 
6 
8 
10 
20 
30 
∞ 
k 
2,63 
2,33 
2,18 
2,00 
1,92 
1.76 
1,73 
1,64 
A.6.3.2 Characteristic values for families of tests
 A series of tests carried out on a number of otherwise similar structures, portions of structures, members, sheets or other structural components, in which one or more parameters is varied, may be treated as a single family of tests, provided that they all have the same failure mode. The parameters that are varied may include crosssectional dimensions, spans, thicknesses and material strengths.
 The characteristic resistances of the members of a family may be determined on the basis of a suitable design expression that relates the test results to all the relevant parameters. This design expression may either be based on the appropriate equations of structural mechanics, or determined on an empirical basis.
 The design expression should be modified to predict the mean measured resistance as accurately as practicable, by adjusting the coefficients to optimize the correlation.
NOTE: Information on this process is given Annex D of EN 1990.
 In order to calculate the standard deviation s each test result should first be normalized by dividing it by the corresponding value predicted by the design expression. If the design expression has been modified as specified in (3), the mean value of the normalized test results will be unity. The number of tests n should be taken as equal to the total number of tests in the family.
 For a family of at least four tests, the characteristic resistance R_{k} should then be obtained from expression (A.1 1) by taking R_{m} as equal to the value predicted by the design expression, and using the value of k from table A.2 corresponding to a value of n equal to the total number of tests in the family.
A.6.3.3 Characteristic values based on a small number of tests
 If only one test is carried out, then the characteristic resistance R_{k} corresponding to this test should be obtained from the adjusted test result R_{adj} using:
R_{k} = 0,9η_{k}R_{adj} .....(A.13)
in which η_{k} should be taken as follows, depending on the failure mode:
 yielding failure: 
η_{k} = 0,9; 
 gross deformation: 
η_{k} = 0,9; 
 local buckling: 
η_{k} = 0,8 ... 0,9 depending on effects on global behaviour in tests ; 
 overall instability: 
η_{k} = 0,7. 
117
 For a family of two or three tests, provided that each adjusted test result R_{adj,i} is within ± 10% of the mean value R_{m} of the adjusted test results, the characteristic resistance R_{k} should be obtained using:
R_{k} = η_{k}R_{m} ...(A. 14)
 The characteristic values of stiffness properties (such as flexural or rotational stiffness) may be taken as the mean value of at least two tests, provided that each test result is within ± 10% of the mean value.
 In the case of one single test the characteristic value of the stiffness is reduced by 0,95 for favourable value and increased by 1,05 for nonfavourable value.
A.6.4 Design values
 The design value of a resistance R_{d} should be derived from the corresponding characteristic value R_{k} determined by testing, using:
where:
γ_{M} 
is the partial factor for resistance; 
η 
is a conversion factor for differences in behaviour under test conditions and service conditions. 
 The appropriate value for η_{sys} should be determined in dependance of the modelling for testing.
 For sheeting and for other well defined standard testing procedures (including A.3.2.1 stub column tests, A.3.3 tension tests and A.3.4 bending tests) η_{sys} may be taken as equal to 1,0. For tests on torsionally restrained beams conformed to the section A.5, η_{sys} = 1,0 may also be taken.
 For other types of tests in which possible instability phenomena, or modes of behaviour, of structures or structural components might not be covered sufficiently by the tests, the value of η_{sys} should be assessed taking into account the actual testing conditions, in order to achieve the necessary reliability.
NOTE: The partial factor y_{M} may be given in the National Annex. It is recommended to use the γvalues as chosen in the design by calculation given in section 2 or section 8 of this part unless other values result from the use of Annex D of EN 1990.
A.6.5 Serviceability
 The provisions given in Section 7 should be satisfied.
118
Annex B – Durability of fasteners
[informative]
 In Construction Classes I, II and III table B.1 may be applied.
Table B.1: Fastener material with regard to corrosion environment (and sheeting material only for information). Only the risk of corrosion is considered. Classification of environment according to EN ISO 129442.
Classification of environment 
Sheet material 
Material of fastener 
Aluminium 
Electro galvanized steel. Coat thickness > 7μm 
Hotdip zinc coated steel^{b}. Coat thickness >45μm 
Stainless steel, case hardened. 1.4006^{d} 
Stainless steel. 1.4301 ^{d}1.4436^{d} 
Monet^{a} 
C1 
A, B,C D, E, S 
X X 
X X 
X X 
X X 
X X 
X X 
C2 
A C, D, E S 
X X X 
   
X X X 
X X X 
X X X 
X X X 
C3 
A C, E d s 
X X X  
    
X X X X 
 (X)^{C}  X 
X (X)^{C} (X)^{C} X 
X  X X 
C4 
A D E S 
X  X  
    
(X)^{C} X X X 
    
(X)^{C} (X)^{C} (X)^{C} X 
   X 
C5I 
A D^{f} S 
X   
   
 X  
   
(X)^{C} (X)^{C} X 
   
C5M 
A D^{f} S 
X   
   
 X  
   
(X)^{C} (X)^{C} X 
   
NOTE: Fastener of steel without coating may be used in corrosion classification class CI. 
A = 
Aluminium irrespective of surface finish 
B = 
Uncoated steel sheet 
C = 
Hotdip zinc coated (Z275) or aluzink coated (AZ150) steel sheet 
D = 
Hotdip zinc coated steel sheet + coating of paint or plastics 
E = 
Aluzink coated (AZ185) steel sheet 
S = 
Stainless steel 
x = 
Type of material recommended from the corrosion standpoint 
(X) = 
Type of material recommended from the corrosion standpoint under the specified condition only 

 = 
Type of material not recommended from the corrosion standpoint 
a 
Refers to rivets only 
b 
Refers to screws and nuts only 
c 
Insulating washer, of material resistant to ageing, between sheeting and fastener 
d 
Stainless steel EN 10088 
e 
Risk of discoloration. 
f 
Always cheek with sheet supplier 

 The environmental classification following ENISO 129442 is presented in table B.2.
119
Table B.2: Atmosphericcorrosivity categories according to EN ISO 129442 and examples of typical environments
Corrosivity category 
Corrosivity level 
Examples of typical environments in a temperate climate (informative)) 
Exterior 
Interior 
C1 
Very low 
 
Heated buildings with clean atmospheres, e. g. offices, shops, schools and hotels. 
C2 
Low 
Atmospheres with low level of pollution. Mostly rural areas 
Unheated buildings where condensation may occur, e. g. depots, sport halls. 
C3 
Medium 
Urban and industrial atmospheres, moderate sulphur dioxide pollution. Coastal areas with low salinity. 
Production rooms with high humidity and some air pollution, e. g. foodprocessing plants, laundries, breweries and dairies. 
C4 
High 
Industrial areas and coastal areas with moderate salinity. 
Chemical plants, swimming pools, coastal ship and boatyards. 
C5I 
Very high(industrial) 
Industrial areas with high humidity and aggressive atmosphere. 
Building or areas with almost permanent condensation and with high pollution. 
C5M 
Very high(marine) 
Coastal and offshore areas with high salinity. 
Building or areas with almost permanent condensation and with high pollution. 
120
Annex C – Cross section constants for thinwalled cross sections
[informative]
C.1 Open cross sections
 Divide the cross section into n parts. Number the parts 1 to n. Insert nodes between the parts. Number the nodes 0 to n.
Part i is then defined by nodes i  1 and i.
Give nodes, coordinates and (effective) thickness.
Figure C.1 Cross section nodes
Nodes and parts j = 0..n i = 1 ..n
Area of cross section parts
Cross section area n
First moment of area with respect to yaxis and coordinate for gravity centre
Second moment of area with respect to original yaxis and new yaxis through gravity centre
First moment of area with respect to zaxis and gravity centre
Second moment of area with respect to original zaxis and new zaxis through gravity centre
121
Product moment of area with respect of original y and zaxis and new axes through gravity centre
Principal axis
Sectorial coordinates
ω_{0} = 0 ω_{0}_{i} =y_{i1}.z_{i}  y_{i}.z_{i1} ω_{i} = ω_{i}1 + ω_{0}_{i}
Mean of sectorial coordinate
Sectorial constants
Shear centre
Warping constant
I_{w} = I _{ωω} + z_{sc} · I _{y ω} – y _{sc} · I _{z ω}
Torsion constants
122
Sectorial coordinate with respect to shear centre
ω_{sj} = ω_{j}  ω_{mean} + z_{sc}.(y_{j}  y_{gc})  y_{sc}.(z_{j}  z_{gc})
Maximum sectorial coordinate and warping modulus
Distance between shear centre and gravity centre
y_{s} = y_{sc}  y_{gc} z_{s} = z_{sc}  z_{gc}
Polar moment of area with respect to shear centre
I_{p} = I_{y} + I_{z} + A(y_{s}^{2} + z_{s}^{2}
Nonsymmetry factors Z_{j} and y_{j}
where the coordinates for the centre of the cross section parts with respect to shear center are
NOTE: z_{j} = 0 (y_{j} = 0) for cross sections with yaxis (zaxis) being axis of symmetry, see Figure C. 1.
C.2 Cross section constants for open cross section with branches
 In cross sections with branches, formulae in C.1 can be used. However, follow the branching back (with thickness t = 0) to the next part with thickness t ≠ 0 , see branch 3  4 5 and 6  7 in Figure C.2. A section with branches is a section with points where more than two parts are joined together.
Figure C.2 Nodes and parts in a cross section with branches
123
C.3 Torsion constant and shear centre of cross section with closed part
Figure C.3 Cross section with closed part
 For a symmetric or nonsymmetric cross section with a closed part, Figure C.3, the torsion constant is given by
where
124
Annex D – Mixed effective width/effective thickness method for outstand elements
[informative]
 This annex gives an alternative to the effective width method in 5.5.2 for outstand elements in compression. The effective area of the element is composed of the element thickness times an effective width b_{e0} and an effective thickness t_{eff} times the rest of the element width bp . See Table D. 1.
The slenderness parameter and reduction factor ρ is found in 5.5.2 for the buckling factor k_{σ} in Table D.1.
The stress relation factor Ψ in the buckling factor k_{σ} may be based on the stress distribution for the gross cross section.
 The resistance of the section should be based on elastic stress distribution over the section.
125
Table D.1: Outstand compression elements
Maximum compression at free longitudinal edge 
Stress distribution 
Effective width and thickness 
Buckling factor 

1 ≥ Ψ ≥ 0
b_{e0} = 0,42b_{p}
t_{eff} = (1,75≥  0,75)t

i ≥ Ψ ≥ 2


Ψ < 0
t_{eff} = (1,75ρ  0,75  0,15Ψ)t

 2 > Ψ ≥ 3
k_{σ} = 3,3(1+Ψ) + 1,25Ψ^{2}

Ψ < 3
k_{σ} = 0,29(1  Ψ)^{2}

Maximum compression at supported longitudinal edge 
Stress distribution 
Effective width and thickness 
Buckling factor 

1 > ψ > 0
b_{e0} = 0,42b_{p}
t_{eff} = (1,75ρ  0,75)t

1 > Ψ > 0


Ψ < 0
t_{eff} = (1,75ρ  0,75)t

0 ≥ Ψ ≥ 1
k_{σ} = 1,7  5Ψ + 17,1Ψ^{2}

Ψ < 1
k_{σ} = 5,98(1  Ψ)^{2}

126
Annex E – Simplified design for purlins
[Informative]
 Purlins with C, Z and Σcrosssections with or without additional stiffeners in web or flange may be designed due to (2) to (4) if the following conditions are fulfilled :
  the crosssection dimension are within the range of table E. 1;
  the purlins are horizontally restraint by trapezoidal sheeting where the horizontal restraint fulfill the conditions of the equation (10.1a);
  the purlins are restrained rotationally by trapezoidal sheeting and the conditions of table 10.3 are met.
  the purlins have equal spans and uniform loading
This method should not be used:
Table E.1: Limitations to be fulfilled if the simplified design method is used and other limits as in Table 5.1 and section 5.2
(the axis y and z are parallel respect rectangular to the top flange)
purlins 
t [mm] 
b/t 
h/t 
h/b 
c/t 
b/c 
L/h 

≥ 1,25 
≤ 55 
≤ 160 
≤ 3,43 
≤ 20 
≤ 4,0 
≥ 15 

≥ 1,25 
≤ 55 
≤ 160 
≤ 3,43 
≤ 20 
≤ 4,0 
≥ 15 
127
 The design value of the bending moment M_{Ed} should satisfy
where
and
W_{eff,y} 
is section modulus of the effective crosssection with regard to the yy axis; 
X_{LT} 
is reduction factor for lateral torsional buckling in dependency of due to 6.2.3, where α_{LT} is substituted by α_{LT,eff} ; 
and
and
α_{LT} 
is imperfection factor due to 6.2.3; 
W_{el,y} 
is section modulus of the gross crosssection with regard to the yy axis; 
k_{d} 
is coefficient for consideration of the non restraint part of the purlin according to equation (E.5) and table E.2; 
a_{1}, a_{2} 
coefficients from table E.2; 
L 
span of the purlin; 
h 
overall depth of the purlin. 
128
Table E.2: Coefficients a_{1}, a_{2} for equation (E.5)
System 
Zpurlins 
Cpurlins 
Σpurlins 
a_{1} 
a_{2} 
a_{1} 
a_{2} 
a_{1} 
a_{2} 
single span beam gravity load 
1.0 
0 
1.1 
0.002 
1.1 
0.002 
single span beam uplift load 
1.3 
0 
3.5 
0.050 
1.9 
0.020 
continuous beam gravity load 
1.0 
0 
1.6 
0.020 
1.6 
0.020 
continuous beam uplift load 
1.4 
0.010 
2.7 
0.040 
1.0 
0 
 The reduction factor χ_{LT} may be chosen by equation (E.6), if a single span beam under gravity load is present or if equation (E.7) is met
χ_{LT} = 1,0 0 0 0 0 ...(E.6)
where
M_{el,u} = W_{el,u} f_{y} 
elastic moment of the gross crosssection with regard to the major uu axis; ...(E.8) 
_{v} 
moment of inertia of the gross crosssection with regard to the minor vv axis: 
k_{υ} 
factor for considering the static system of the purlin due to table E.3. 
NOTE: For equal flanged Cpurlins and Σpurlins I_{v} = I_{z}, W_{u} = W_{y}, and M_{et,u} = M_{el,y}. Conventions used for cross section axes are shown in Figure 1.7 and section 1.5.4 .
Table E.3: Factors k_{υ}
Statical system 
Gravity load 
Uplift load 

 
0.210 
0.07 
0.029 
0.15 
0.066 
0.10 
0.053 
129
 The reduction factor χ_{LT} should be calculated according to 6.2.4 using and α_{LT,eff} in cases which are not met by (3). The elastic critical moment for lateraltorsional buckling M_{CT} may be calculated by the equation (E.9):
where
I_{t}^{*} 
is the fictitious St. Venant torsion constant considering the effective rotational restraint by equation (E. 10) and (E.11): 
I_{t} 
is St. Venant torsion constant of the purlin; 
C_{D,A},C_{D,C} 
rotational stiffnesses due to 10.1.5.2; 
C_{D,B} 
rotational stiffnesses due to distorsion of the crosssection of the purlin due to 10.1.5.1, C_{D,B} = K_{B} h^{2}, where h = depth of the purlin and K_{B} according to 10.1.5.1 ; 
k 
lateral torsional buckling coefficient due to table E.4. 
Table E.4: Lateral torsional buckling coefficients k for purlins restrained horizontally at the upper flange
Statical system 
Gravity load 
Uplift load 

∞ 
10.3 
17.7 
27.7 
12.2 
18.3 
14.6 
20.5 
130
131