ds 412 e-2001

Danish Standards Association

DS 412

Code of Practice for the structural use of steel

Norm for

stlkonstruktioner

(3.1)

titelblad412.1.korr. 22/11/01 10:08 Side 1

Licens kbt af: Vesta Wind System A/S

Descriptors:steel structures, corrosion protection, fatigue subjected steel structures

DS 412 E:2001

KbenhavnDS projekt: 47983ICS 91.080.10

National forewordThe prefix in the reference number of this publication is DS which means that the pub-lication has the status of Danish Standard.Degree of correspondence of this publication:IDT with DS 412:1998 in Danish.In case of doubt with regard to the correctness of the translation into English, the Danishlanguage version should be consulted.This publication replaces: DS 412 E:1984.


Translation of DS 412:1998

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0 Preface 1 0.1 Approval of the code 1 0.2 Interim provisions 2 0.3 Construction products 2

1 Introduction 3 1.1 General 3 1.2 Scope 4 1.3 Definitions 5 1.4 Symbols 9

2 Preliminary investigations 14

3 Materials 15 3.1 General 15 3.2 Materials for welded structures 16 3.3 Materials for non-welded structures 21 3.4 Filler metals 21 3.5 Bolt materials 21 3.6 Bearings 21

4 Actions 22 4.1 Thermal actions 22

5 Safety 23 5.1 Limit states 23 5.2 The partial safety factor method 24

6 Design and analysis 28 6.1 General 28 6.2 Calculation of internal forces and moments 31 6.3 Analysis of cross-sections 32 6.4 Buckling resistance of members 48 6.5 Welded connections 60 6.6 Bolted connections 66 6.7 Bearings 74 6.8 Structures subjected fatigue 76 7 Fabrication 84 7.1 General 84 7.2 Geometrical imperfections 84



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7.3 Welded connections 85 7.4 Bolted connections 87 7.5 Structures subjected to fatigue 89 7.6 Protective treatment 90

8 Inspection 92 8.1 General 92 8.2 Materials 92 8.3 Welded connections 94 8.4 Bolted connections of category A 96 8.5 Bolted connections of categories B and C 96 8.6 Structures subjected to fatigue 97 8.7 Testing 99 8.8 Test loading 99

9 Fire design 100

9.1 General 100

9.2 Material properties 100

9.3 Determination of the temperature curve 103

9.4 Verification of structural resistance 105

10 Associated standards 108

11 Preparation of the code 111

Annex A Design against brittle fracture 114

A.1 Controlling parameters 114

A.2 Design 116

Annex B Fatigue curves 118

B.1 Fatigue expressions 118

B.2 Tables with construction details 118

Annex C Material properties of steel at elevated temperatures 137 Subject index 139


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0 Preface (1) The structural design codes are: DS 409 Code of Practice for the Safety of Structures DS 410 Code of Practice for Actions for the Design of Structures DS 411 Code of Practice for the Structural Use of Concrete DS 412 Code of Practice for the Structural Use of Steel DS 413 Code of Practice for the Structural Use of Timber DS 414 Code of Practice for the Structural Use of Masonry DS 415 Code of Practice for Foundation Engineering DS 419 Code of Practice for the Structural Use of Aluminium DS 420 Code of Practice for the Structural Use of Lightweight Concrete DS 446 Code of Practice for the Structural Use of Thin-Plate Steel Structures DS 451 Code of Practice for Design and Construction of Composite Structures forming a coherent, consistent set of codes based on DS 409 and DS 410. DS 409-415 have been updated as described in chapter 11 of the individual codes. DS 419, DS 420, DS 446 and DS 451 are being revised and will be published at a later date.

(2) The Pan-European Eurocodes that have been in preparation for a number of years are now close to completion. The Danish Standards Association, however, is of the opinion that it has been necessary to update the set of Danish codes of practice to adapt them to the Eurocodes, since there is still some uncertainty with regard to the time when the Eurocodes will be ready to replace the national codes. It is likely, however, that the present set of codes will be the last with national application only. The code text has been divided into chapters (e.g. chapter 7), sections (e.g. section 7.2) and paragraphs (e.g. paragraph 7.2.1 or 7.2.1.1). Each chapter, section or paragraph is composed of a number of clauses that are either normative or informative. The passages are consecutively numbered within each chapter, section or paragraph with a number in parenthesis. For code text, i.e. normative text (Principles) the parenthesis is followed by a P, while informative text (Application rules) has no letter, but is printed in smaller types. Tables and figures are provided with numbers identical with the number of the chapter, section or paragraph from which reference is made to the table or figure. In case of more tables or figures, the numbers are provided with lower-case letters (e.g. table 3.2b). Tables and figures in informative text are preceded by a V (e.g. figure V5.4).

0.1 Approval of the code

(1)P The code is approved as a Danish Standard. It replaces DS 412, 2nd edition, 1983. The code is related to DS 409, 2nd edition 1998 and DS 410, 4th edition 1998 and shall only be applied in connection with these editions.



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0.2 Interim provisions

(1)P The following applies to DS 409, 410, 411, 412, 413, 414 and 415: For an interim period, from the publication of the first, revised structural design codes up to one year after publication of all the above-mentioned, revised structural codes, both the previous and the new editions will be in force.

During this period, design of structures in accordance with the previous as well as the new editions is allowable, however an entire project shall be in accordance with either the previous or the new editions. After expiration of the interim period, only the new editions apply.

(2)P On their publication, DS 419, 420, 446 and 451 will have a corre-sponding interim period of one year. In the period up to the publication of these codes, they shall be used together with DS 409, 1st edition 1982 and DS 410, 3rd edition 1982, notwithstanding that the other structures are con-structed in accordance with the updated structural codes.

(3)P The code has been prepared on the assumption that the Construc-tion Products Directive is fully operational, i.e. the related, harmoinzed stan-dards with corresponding conformity certification systems are available.

0.3 Construction Products (1) Under paragraphs 30-36 in the European Union Treaty, construction products from other EU member states and EEA member states complying with the requirements of technical standards or specifications at the same level as the Danish standards can be marketed.

Jacob E. Holmblad Jrgen S. Steenfelt Manager of DS Chairman of Codes of Practice Committee



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1 Introduction 1.1 General

(1)P A steel structure is in conformity with the structural design codes of the Danish Standards Association when it satisfies the requirements of DS 409 Code of Practice for the Safety of Structures and DS 410 Code of Prac-tice for Actions for the Design of Structures.

(2)P The codes contain requirements whose purpose is to ensure the adequate safety and performance of load-bearing structures, including build-ings where the soil acts as a load or a load-bearing element.

(3)P A code of practice is a standard, which for a predefined area lists a number of requirements aiming to ensure a proper technical quality level. A code of practice is submitted to public approval ensuring widespread accep-tance of its contents.

To the greatest possible extent the codified requirements are performance-based and based on knowledge of technical sciences. Generally, the code does not prescribe requirements for methods of design and construction or physical elements. In the code text, references to Danish or international standards, e.g. concerning material qualities and test methods may be given.

(4)P The codes apply to structures within the normal field of experience. There may be structures where failure will have disastrous consequences, and for such structures the requirements cannot be assumed to give adequate safety. Within the scope of the codes, special cases not covered by the codes may occur. An evaluation of whether or not a particular case is covered by the codes shall always be made.

(5)P To facilitate the use of the codes they are supplemented by applica-tion rules among other things giving examples of how the requirements of the codes may be satisfied. The application rules shall not be considered as codified requirements.



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(6) Application rules can be distinguished from the code text (principles) by the typography as shown here and as mentioned in chapter 0, Preface.

(7)P The rules and provisions of the codes shall be assessed and applied in accordance with the purpose of the codes with due consideration to the development within their field of application. It is therefore assumed that the users of the code have the necessary technical knowledge.

(8)P The code text does not contain references to laws, instructions or circulars etc. Such references may in exceptional cases appear in the applica-tion rules. It is assumed that users of the code have the necessary knowledge of legal and other external rules significant to the practical application of the codes.

(9)P Deviation from the requirements of the codes is permitted when the soundness of such deviation can be substantiated.

(10)P Questions as to the interpretation of the codes are to be settled by the Planning Committee for Steel and Aluminium, PLU-11 of the Danish Standards Association.

1.2 Scope

(1)P The code applies to load-bearing steel structures in buildings, bridges etc. For structures of a special design and structures for which spe-cial requirements are made, the provisions of the present code will not form an adequate basis.

(2) The present code alone does not form an adequate basis for the design and analysis of e.g. nuclear power plants, extremely tall buildings, offshore struc-tures, storage tanks, thin-plate structures, composite structures, and pressurized plants. The code applies to such structures only to the extent where the special codes for these areas refer to the provisions in the present code.

(3) Codes for special areas are: DS 417 Welded storage tanks DS 446 Thin-plate structures



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DS 449 Pile supported offshore steel structures DS 451 Composite structures DS 458 Pressurized plants

(4) To a large extent the principles and equations of the present code are identical with those of Eurocode 3, particularly ENV 1993-1-1 (including ENV 1993-1-1/A1) and DS/ENV 1993-1-2. However, generally DS 412 does not address the subjects as thor-oughly as Eurocode 3. In a number of cases the principles have been changed or modified compared to Eurocode 3. This fact should be considered if Eurocode 3 is used as a back-ground document for elaboration of the methods of the present code. In particular it should be noted that the safety system applied in Eurocode 3 is different from that in DS 412.

1.3 Definitions

Action parameter The total number of actions (cycles) assumed to occur in the design life.

Bearing-type connection Connection where the forces between the connected parts are expected to be transferred by bending and shear action of bolts.

Bearing-type slip-resistant connection Connection that in analysis of the resistance is considered a bearing-type connection, but which in analysis of serviceability properties is considered a slip-resistant connection.

Block shear failure Failure in a plate in connection with a bolt group subjected to shear. Due to the failure, part of a plate containing a group of bolts will be disconnected along lines passing through the bolt holes in the shear sides and in the tensile side of the bolt group, cf. figure 6.6.11.

Bolting through packings Bolt arrangement in a connection subjected to shear where one or more packings are inserted between the plates to be connected.



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Buckling length For a given compressed member the length of a corresponding simply sup-ported member with the same elastic buckling resistance as the given one.

Characteristic fatigue strength The fatigue strength determined as the 2.3-percentile of the results of tests with the actual structural member.

Characteristic fatigue life The fatigue parameter corresponding to the characteristic action and charac-teristic fatigue strengths.

Crippling Buckling failure of the web in a profile caused by compression due to a concentrated action applied to the flange in the plane of the web.

Design fatigue life The fatigue life corresponding to design action and design fatigue strengths.

Design fatigue strength Characteristic fatigue strength divided by the appropriate partial safety fac-tor.

Ductility The property of a structural member or connection that fracture will only occur after large plastic strains.

Fatigue action Variable action of such a magnitude, frequency and duration that fatigue phenomena control the resistance of the structure.

Fatigue life



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The fatigue life of a structural member corresponding to a specific stress range is the number of actions of constant magnitude that under the given circumstances only just results in fatigue failure.

Fatigue strength The fatigue strength of a structural member corresponding to a specific number of cycles is the stress range of constant width that under the given circumstances only just results in failure by fatigue.

Fire insulation Method for protection of steel against unacceptable heating during fire.

Fire insulation system The complete system comprising fire insulation, fasteners, surface coating etc. for protection of steel against unacceptable heating during fire.

Fire isolation Material for protection of steel against unacceptable heating during fire.

Flange induced buckling Stability failure of a compressed flange in a section where the web is so slender that it cannot support the flange against buckling into the section.

Fracture toughness General designation for a number of parameters describing the fracture toughness: elongation at failure, necking, impact strength, fracture mechani-cal parameters etc. Often, for a given type of fracture only one of the above parameters for ductility will be relevant.

Lifetime The period of time for which the structure will be able to resist the actions occurring until failure due to fatigue. The fatigue life can be used as a meas-ure of the lifetime.



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Post-critical capacity The resistance of a cross-section or a member, which is not achieved until buckling of compressed plate elements has taken place.

Preloaded bolt (high-strength friction grip bolt) Bolt with large width across the flat in which a well-defined considerable prestress has been produced by preloading.

Prying force Additional force in tensioned bolts in an end plate joint or similar connec-tion, associated with the contact pressure, which develops between the pro-jecting elements due to the deformation of the plates.

Segregation zones In a rolled steel specimen zones with particularly large content of impurities and certain alloy components such as carbon.

Service life The period of time for which a structure subjected to fatigue is assumed or required to be in use.

Slip-resistant connection Connection where the forces between the connected elements are assumed to be transferred fully or partly by friction provided by compression of the structural elements by means of preloaded bolts or the like.

Static action Action of such low frequency that fatigue of the structural material or the connections will not be critical for the resistance of the structure.

Stress range The difference between the maximum and minimum stress of one cycle, tensile stresses being considered positive and compressive stresses negative.



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Stress-range spectrum Diagram showing the stress variation during the service life of the structure.

Stress ratio The ratio between minimum and maximum stress, tensile stresses being considered positive and compressive stresses negative.

Throat section The section parallel to the longitudinal direction of a weld which fully or partly placed through the weld has minimum width.

1.4 Symbols 1.4.1 Main symbols A cross-sectional area a relative share of area, weld thickness b width c width, calculation factor, heat capacity d diameter, depth, thickness E slope of stress-strain curve for steel, modulus of elasticity e bolt distance F force, error size factor f strength G shear modulus h height, coefficient of heat transfer K fracture toughness k moment correction factor, factor, auxiliary factor L span l length, span M moment m number, relative moment utilisation N axial force n number, number of load cycles, relative axial force utilisation p spacing of bolts, spacing of holes q uniformly distributed action R structural resistance r radius s distance, length



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t thickness, time V shear force, volume W section modulus thermal coefficient of linear expansion, ratio, imperfection

factor, calculation factor, auxiliary factor factor for equivalent constant moment, correlation factor,

stress ratio, auxiliary factor partial safety factor auxiliary factor, deflection coefficient, strain, absorption coefficient temperature factor relative slenderness ratio, coefficient of linear expansion,

thermal conductivity coefficient of friction, auxiliary factor Poissons ratio unit mass, Winter-factor axial stress, Stefan Boltzmanns constant shear stress auxiliary factor slenderness reduction factor (edge) stress ratio

1.4.2 Subscripts a steel b post-critical, bearing, bolt c compression zone, compression com compression cr critical according to theory of elasticity d design ded deduction e effective eff effective el elastic eq equivalent f dependent on action, flange



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fat fatigue g fire compartment i penetration LT lateral-torsional buckling M moment m material dependent mat material max maximum min minimum n nominal, lower net net p preloading, proportionality pl plastic Q transverse action q transverse action R resistance red reduced S internal force s column, distributed, friction ser serviceability state t tension u ultimate v stress range, shear resistance w web, welding y related to the y-axis, yield z related to the z-axis temperature end moments

1.4.3 Characteristic and design values (1)P Subscript d for design values is solely applied to the symbols fy, fu, E, , fat, fat, and nfat.



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(2)P In general, all values stated in the code text and equations shall be considered design values, unless the context or the text itself expressively states that they shall be considered characteristic values.

1.4.4 Conventions for coordinate axes (1)P In the present code the following convention for coordinate axes is applied:

x-axis: axis in the longitudinal direction of the member y-axis: generally: cross-sectional axis parallel to the

flanges for angle sections: cross-sectional axis parallel to the

shorter leg z-axis: generally: cross-sectional axis perpendicular

to the flanges for angle sections: cross-sectional axis perpendicular

to the shorter leg u-axis: major (strong) axis where it does not coincide with the y-

axis v-axis: minor (weak) axis where it does not coincide with the z-

axis

Reference is also made to figure 1.4.4.



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Figure 1.4.4 Convention for cross-sectional axes



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2 Preliminary investigations Generally, no special preliminary investigations are necessary in connection with steel structures.



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3 Materials 3.1 General

(1)P Materials with well-defined resistance properties corresponding to those assumed to verify the resistance of the structure shall be applied.

3.1.1 Material groups (1)P Distinction is made between 5 groups of materials covered by the code:

I Ordinary hot-rolled structural steel meeting the require-ments in EN 10025 or similar. Hot-rolled fine-grain steel with designations S275 and S355 meeting the requirements in DS/EN 10113-2 or DS/EN 10113-3 or similar.

II Hot-rolled fine-grain steel with the designations S420 and S460 meeting the requirements in DS/EN 10113-2 or DS/EN 10113-3 or similar.

III High strength steel in the quenched and tempered condi-tions that meet the requirements in DS/EN 10137-2 or similar. Distinction is made between the subgroups: a) S460 Q b) other quenched and tempered steel

IV Carbon steel meeting the requirements for E-steel in DS/EN 10025 or similar.

V Cast iron.

3.1.2 Characteristic material parameters

(1)P The characteristic ultimate tensile strength of the material fu and the characteristic tensile yield strength fy is taken as the 5-percentile of the ulti-mate tensile strength and the upper tensile yield strength, respectively. The compressive yield strength of the steel is assumed to be equal to the tensile yield strength.

(2) Conformity with the requirement that the 5-percentile should be applied to tensile strength and upper tensile yield stress may be assumed by applying the values of the lower tensile strength and the upper tensile yield stress, respectively, as stated in the standards specified for the different material groups in 3.1.1.



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(3)P The characteristic fatigue strength fat is taken as the 2.3-percentile of the results of fatigue tests.

(4) For all material groups the following characteristic material coefficients are used:

modulus of elasticity: E = 0,21 106 MPa shear modulus G = E/2 (1 +) unit mass = 7.85 103 kg/m3 Poissons ratio = 0.3 linear coefficient of thermal expansion = 12 10-6 oC-1

(5) For characteristic material parameters and material constants at elevated tem-peratures, see paragraphs 9.2.1 and 9.2.2.

3.1.3 Imperfections (1)P The material shall be free from surface imperfections and corrosion due to rust of degree D (pitting) in accordance with ISO 8501-1 and cracks, lamination, dents, etc. which are adverse to the fabrication, application and structural resistance.

(2) For definition of surface imperfections, reference is made to DS/EN 10163.

(3) Assessment of imperfections in the material may also include requirements for the appearance of the structure.

3.2 Materials for welded structures 3.2.1 Applicable material groups (1)P For welded structures, materials of groups I and II are permitted. Further, materials of groups III and V are permitted if the soundness hereof is justified. The codified requirements regarding execution and control of welded structures are adequate for materials of groups I and II only.

3.2.2 Safety against brittle fracture (1)P The material shall have adequate fracture toughness to prevent brittle fracture and similar fractures in the structure with the required safety.



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Consideration shall be given to the risks of impairing the fracture toughness during manufacture and erection due to cold-work, welding and other manufacturing processes, as well as to the pos-sibility of weakening the material during service due to fatigue and corrosion.

(2)P In principle, verification for the safety against brittle frac-ture can be made by fracture mechanics. For materials of groups I, II and IIIa with metal thickness not exceeding 150 mm, however, it is permissible to base the safety entirely on the use of steel with the required fracture toughness measured by impact resistance testing using Charpy-V test specimens according to DS/EN 10045.

(3)P Materials loaded in through-thickness direction shall have the properties necessary to prevent lamellar tearing.

(4) In addition to fracture toughness of the material the risk of brittle fracture is dependent on:

the lowest service temperature to which the material is exposed stress level strain rate material thickness effect on properties due to cold-work, etc. geometrical defects of the material

(5) Lowest service temperature should be determined according to table V3.2.2a. For structures, which are artificially cooled, the lowest service temperature is determined as the lowest temperature to which the structure can be exposed during service.



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Table V3.2.2a Lowest service temperature

type of structure lowest service temperature [oC]

outdoor structures (exclusive of Greenland) indoor structure, effective heating (residences, etc.) indoor structure, moderate heating (storerooms, etc.)

10 +10 0

(6) For materials of groups I and II which are suited for cold working not includ-ing, however, materials according to DS/EN 10113-3 the reduction of the fracture toughness due to cold-working can be counteracted by performing a normalisation after the cold-working. As an alternative, a direct verification can be made to show that the material after cold-working and the resulting ageing fulfils the requirements of the code with regard to fracture toughness. For materials of groups I, II and IIIa the influence of the cold-working can be taken into consideration by assuming an equivalent material thickness in the assessment of the fracture toughness in accordance with figure V3.2.2.a. For round steel a value 0.85 times the diameter of the round steel is used as the "true material thickness". Cutting gives rise to cold-work which for properly maintained shears is about 10 % for materials of group I with a thickness not exceeding 10 mm. Materials of the other material groups should only be cut if the suitability is verified by testing of the cut material.

(7) In annex A a general method for evaluating the safety against brittle fracture is given. For structures of materials in groups I, II and IIIa subjected to a static or slow action (selfweight, floor action, snow load, action from vehicles, wind and wave action, uplift, etc.), the safety against brittle fracture may be assumed to be documented if the equivalent metal thickness does not exceed the values in table V3.2.2b.

(8) For structures, which are subjected to impact action (explosion, vertical action on air raid shelters, action due to impacts etc.) and for structures with large stress concen-trations, the safety against brittle fracture can be verified according to the procedure in annex A.



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Figure V3.2.2a Equivalent material thickness for cold-working

3.2.3 Special provisions for grading of structural steel (1)P It is permissible to use steel of groups I, and II as structural steel of a desired strength and quality class, if tests are carried out to prove that the steel satisfies the testing requirements for the actual grade. However, the form of treatment of the steel, e.g. non-normalised, normalised or thermo-mechanical treatment cannot be changed by the upgrading. Tests shall be carried out for each individual plate, profile, etc.



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3.3 Materials for non-welded structures

(1)P For materials for non-welded structures it is permissible to take into account that non-welded structures have a relatively high resistance against brittle fracture.

3.4 Filler metals

(1)P Filler metals and welding procedures shall be adjusted to the parent metal. With regard to strength and toughness the welds shall at least correspond to the structural materials. If two members with different thickness are welded together the weld shall at least satisfy the requirements for the material of the thinner member. The fracture toughness shall be chosen to correspond to the stronger of the structural steels being welded together.

(2) An adequate fracture toughness can be achieved by choosing welding proce-dures and filler metals resulting in weld metals with an impact resistance that at least corresponds to the grade of the steel.

3.5 Bolt materials

(1)P For bolts, materials conforming with DS/EN 20898-1 and 2 or materials of groups I, II, III or IV shall be used.

(2) In 6.6.1 and 6.6.2 it is specified which bolt strength classes are permissible for the different categories of bolted connections.

3.6 Bearings

(1)P Materials of the groups I, II, III, IV and V can be used for bearings. For materials of group IV the suitability of the products used shall be veri-fied in particular to ensure adequate toughness of the internal material mem-bers and an adequate depth of hardening.



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4 Actions 4.1 Thermal actions

(1)P I addition to the possible changes of air temperatures stated in DS 410, outdoor structures or structural steel members shall be considered sub-ject to a possible non-uniform thermal action by the influx of sunlight.

(2) The influx of sunlight can be assumed to imply a maximum increase of tem-perature of 25 C relative to the air temperature. Depending on the conditions for the influx, the heat capacity of the structure and other aspects of the structural design, the increase in temperature due to the influx of sunlight may imply a uniform increase addi-tional to the air temperature and a non-uniform distribution of temperature on the separate parts of the structure.



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5 Safety 5.1 Limit states (1) Further to the examples given in DS 409 the following ultimate limit states may be relevant for steel structures:

limited slip. Limited slip may occur if the forces to be transferred after a pos-sible initial slip may be transferred by other structural members. Slip in slip-resistant connections is an example of limited slip.

alternating yielding. Alternating yielding may result in material failure after relatively few cycles (low cycle fatigue).

(2) Further to the examples given in DS 409 the following serviceability limit states may be relevant for steel structures:

initial buckling. It may be required to limit the utilisation of the post-critical capacity by considering initial buckling a serviceability limit state, cf. 6.3.3 (5).

slip in bearing-type slip-resistant connections. In bearing-type slip-resistant connections, the friction ensures against slip in the serviceability limit state whereas the ultimate capacity of the connection is based on bearing and bending of the bolts.

alternating yielding. As an alternative to considering alternating yielding an ultimate limit state it may be required that alternating yielding does not oc-cur in the serviceability limit state.

(3) For beams the following limits for the maximum deflections due to variable action exclusive of any dynamic factor may serve as a guide for acceptable deflections.

floors l/400 roofs and external walls l/400

where: l is the span of simply supported and continuous beams, and twice the cantile-

ver of cantilevered structures The values apply to primary as well as secondary members, but in analyses only the deflection of the actual member shall be considered.

(4) For columns the following values for the maximum deflection of the column top due to variable action may serve as a guide for acceptable deflections:

frames in buildings without cranes h/150 columns in single-storey framed buildings h/300 columns in multi-storey framed buildings for each storey h/300 for the total height he/500



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where h is the height of the individual column he is the total height of the building

(5) In the assessment of deflections the structure can be assumed subject to only one variable action at a time.

(6) In the assessment of deflections account shall be taken of eventual one-off yielding at the serviceability state and of eventual slip in bolted connections.

5.2 The partial safety factor method 5.2.1 Accidental action (1) For steel framed structures in buildings compliance with the requirements in action combinations 3.1 and 3.2 may be assumed if the following constructional require-ments are fulfilled:

the primary connections of the structure should be able to transfer an ade-quate tensile force in the longitudinal direction of the connected members. Compliance with this requirement may be assumed for conventional welded connections, bolted fishplate connections and bolted connections with tie panels, since the tensile capacity of these types of connections is of the same magnitude as the shear capacity. For primary connections, where the beams have been placed on brackets welded to the columns and where the horizontal position of the beams has been secured by restraining bolts or otherwise, the requirement may be assumed to be fulfilled if the restraining elements can sustain a force in the longitudinal direction of the beam, which is at least 20 kN/m of the loaded width measured perpendicular to the longitudinal direc-tion of the beam

the connections should be ductile in the structure at least one extra wind bracing system should be arranged.

5.2.2 Design material parameters (1)P For analysis of ultimate limit states the partial safety factors for materials, m , have been determined as a product of 6 factors: m = 0 1 2 3 4 5

in accordance with DS 409 unless otherwise stated.



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(2)P In analyses of ultimate limit states the partial safety factor m for materials of groups I, II, III, and IV depends on the safety class and material control class of individual structures or structural members as follows:

5017.1 =m for yield strength yf modulus of elasticity E

coefficient of friction (for category C connections)

5030.1 =m for coefficient of friction (unlimited slip possible)

5043.1 =m for ultimate strength uf fatigue strength fat

The factor 0 depends on the safety class and is stated in table 5.2.2a. The factor 5 depends on the material control class and is stated in table 5.2.2b.

Table 5.2.2a - 0 dependent on the safety class

safety class low normal high 0.9 1.0 1.1

Table 5.2.2b - 5 dependent on the material control class

material group material parameters material control class according to 8.2.1 (1)P

strict normal

I, II, and III yield strength yf ultimate strength fu modulus of elasticity E fatigue strength, fat , however, not for welded connections

0.95 1.0

fatigue strength fat of 1.0 1.0



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welded connections coefficient of friction

IV all material parameters

(3)P For materials of group V the same value of the partial safety factor m as for materials of group IV is applied, however, the material parameters referring to the tensile resistance are taken corresponding to the larger stan-dard deviation of the properties.

(4) For materials of group V, subjected to tensile action, the larger standard deviation of the material parameters may be taken into account by increasing m for uy ff , and fat by 30 %.

(5) The partial safety factor m in (2)P has been produced as follows, cf. DS 409: 9.01 = corresponding to ductile failure with surplus capacity for yield

strength, modulus of elasticity (stability failure) and coefficient of friction (category C connections)

0.11 = corresponding to ductile failure without surplus capacity for co-efficient of friction (unlimited slip possible)

1.11 = corresponding to brittle fracture for tensile strength and fatigue strength

3.12 = corresponding to a coefficient of variation less than 5 % for all material properties

0.13 = corresponding to normal accuracy of the calculation model 0.14 = corresponding to normal safety for the determination of the mate-

rial parameters.

(6)P 0.1=m is applied in analyses of serviceability limit states.

5.2.3 Structures subjected to fatigue (1)P The structural resistance of structures subjected to fatigue is gener-ally evaluated on the basis of actions corresponding to the service life of the structure. For the partial safety factor m of material parameters the value given in 5.2.2 (2) is applied. For partial safety factors for actions f in ac-cordance with DS 409 is applied.

(2)P As an alternative the structural resistance may be assessed on the basis of actions corresponding to shorter time intervals using the same val-



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ues of the partial safety factors as above. This will require that the structure is inspected between these time intervals, cf. 8.6 (1)P. If this alternative method is used, however, an additional assessment of the structural resistance shall be made on the basis of actions corresponding to the service life, using partial safety factors corresponding to the serviceabil-ity limit state (action combination 1) for actions as well as material parame-ters.

5.2.4 Testing (1)P The structural resistance of a structure, a structural member or a structural connection may be determined by tests, see 8.7. In the assessment of the structural resistance the partial safety factor m may in this case be reduced by 10 %.



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6 Design and Analysis 6.1 General 6.1.1 Scope of the methods of the code (1)P The equations and methods of the code may be assumed to apply directly to materials in groups I, II, and IIIa. For other material groups the application of the equations and methods shall be evaluated for each indi-vidual case.

6.1.2 Static action and fatigue action (1)P Structures subject to static action shall comply with the require-ments of 6.1 - 6.7. Structures subject to fatigue action shall furthermore comply with the requirements of 6.8.

(2) A structure designed for static action will in most cases be sufficiently safe against fatigue failure provided one of the following conditions is fulfilled:

mffatnv / or

3

,

6 36102

mfeqv

n

where v is the maximum stress range occurring fatn is the lower bound to the fatigue strength at constant stress range. On the

safe side, fatn may be taken as 26 MPa n is the number of load cycles eqv, is the equivalent constant stress range in MPa for the load cycle value

6102 , cf. 6.8.3 (4) mf is the partial safety factor with regard to the fatigue strength of the

material.

(3) Examples of structures, which may normally be assumed to be subject to static action, are building structures, overhead transmission masts, and hydraulic engineering structures.

(4) Examples of structures, which should normally be assumed to be subject to fatigue, are masts and chimneys apt to oscillate due to wind action as well as bridges and crane structures.



29

6.1.3 Stress-strain curve for the material (1)P In analyses of buckling resistance the decreasing slope of the stress-strain curve above the limit of proportionality shall be considered. In other cases a linear elastic stress-strain curve up to the yield stress can be assumed.

(2)P If plastic design methods are applied, the material shall fulfil the following requirements:

the ratio between the minimum tensile strength and the mini-mum yield strength shall normally not be less than 1.2

the elongation at fracture as measured on the length 065.5 A , where 0A is the sectional area of the unloaded member, shall be at least 15 %

the strain corresponding to the tensile strength shall be larger than or equal to 20 times the strain corresponding to the yield strength.

(3) The design methods for analysis of buckling resistance as stated in the applica-tion rules of section 6.4 include considerations of the curve of the stress-strain decreasing slope above the limit of proportionality.

(4) Materials of groups I, II, and IIIa are assumed to fulfil the requirements for application of plastic design methods.

6.1.4 Tension perpendicular to the surface (1)P In the design of a structure it shall be taken into account that struc-tural steel has reduced mechanical properties perpendicular to the material surface when lamination, micro-lamination and segregation occur.

(2)P Lamination: Structural members subject to tension perpendicular to the plate surface shall not be laminated, cf. 8.2.4.

(3)P Micro-lamination: The tensile stress at the middle of the plate per-pendicular to the surface of the plate, determined on the assumption that the outer force distributes uniformly at an angle of 45, shall not exceed ydf21 ,



30

unless it is verified that the mechanical properties of the material in the through-thickness direction are adequate, cf. 8.2.4.

(4)P Segregation: In the segregation zones of rimmed steel the tensile stress perpendicular to the surface of the profile shall not exceed ydf21 .

6.1.5 Distribution of forces in connections (1)P In connections the internal forces may be assumed to be sustained in the most favourable way provided that

the action on the elements of the connection forms a system which is in equilibrium with the internal forces due to the ex-ternal action

the structural resistance of the individual elements of the con-nection is at least equal to the assumed action

the deformation of the elements of the connection correspond-ing to the assumed action does not exceed the deformation ca-pacity of the elements

the deformations assumed in a design model based on the yield line theory are based on physically possible rotations of rigid components

the assumed force distribution in the connection is realistic in consideration of the relative stiffness in the connection.

(2)P Residual stresses, and stresses due to tightening of fasteners and due to accuracy of fit-up in the connection need not normally be allowed for.

(3) In 6.5.5 and 6.6.8, examples of welded and bolted connections are given, where the requirements in (1)P have not been fulfilled.

6.1.6 Direct transmission of forces in splices (1)P Direct transmission of the forces through the abutting surfaces in a splice may be assumed when the contact faces of the members to be spliced are accurately prepared, cf. 7.2, and it is ensured that they maintain direct contact after splicing. If the compression force is transmitted partly directly



31

and partly through welds or bolted connections of categories B or C these shall be able to transmit at least 25 % of the compression force. Bolted con-nections of category A shall not be assumed capable of transmitting com-pression forces in a connection with direct transmission of force.

(2)P A connection with direct transmission of compression forces shall be adequately secured against transverse displacement even if the connec-tion according to the calaulation model is not subjected to transverse forces. The connection shall be able to transmit a force of at least 5 % of the com-pression force as shear irrespective of friction.

6.2 Calculation of internal forces and moments

6.2.1 Consideration of structural deformation (1)P A global analysis can be accomplished by

a 1st order analysis neglecting structural deformation due to the action. A 1st order analysis can be used for non-sway structures as well as for structures where deformations are indirectly taken into account.

a 2nd order analysis taking account of structural deformations due to the action. A 2nd order analysis can be used for all struc-tures.

6.2.2 Analysis according to the theory of elasticity (1)P For a global elastic analysis a linear elastic stress-strain relation with the modulus of elasticity dE up to the yield strength ydf can be assumed. This applies to both 1st and 2nd order analyses.

(2)P The analysis shall take due account of the reduction, if any, of the stiffness and structural resistance of the members due to local buckling from axial compression and moment.

(3)P Global elastic analysis combined with plastic analysis of the cross-sections is permitted.



32

6.2.3 Analysis according to the theory of plasticity (1)P For global plastic analysis the elements shall have sufficient rotation capacity in areas of plastic hinges to allow development of the hinges, cf. 6.3.2. Special requirements apply to the slenderness of structural members with plastic hinges subject to moment as well as compression.

(2)P If global plastic analysis is applied, the member deflections shall be controlled in the transverse direction in areas with plastic hinges.

6.2.4 Consideration of imperfections (1)P The global analysis of internal forces and the analysis of global non-sway bracing systems shall take account of geometrical imperfections re-lated to the joint configuration. For sway structures the analysis shall also take account of imperfections related to the individual structural members.

6.3 Analysis of cross-sections 6.3.1 Sectional properties (1)P The gross area of a cross-section is determined on the basis of the cross-section without holes and local contractions but with deductions for larger openings.

(2)P The net area of a cross-section is determined as the gross area with deduction for holes, contractions and openings.

(3)P Deduction for holes dedA is determined on the basis of the section straight or staggered through the structural member which results in the largest deduction according to the expression:

= )4/(20 ptstdAded where 0d is the hole diameter t is the material thickness s is the spacing of two successive holes in the section measured

in the direction of the force



33

p is the spacing of the same holes measured perpendicular to the direction of the force, cf. figure 6.3.1

The summation in the equation includes all holes and all spacings between the holes in the actual section. The value )4/(2 pts shall not exceed st6.0 for any distance.

For a cross-section with holes in more than one plane, p is measured in the unfolded plane of the cross-section, cf. figure 6.3.1.

Figure 6.3.1 Deduction for holes

6.3.2 Resistance of cross-sections

(1)P The cross-sections shall have such proportions that their rotation capacity, structural resistance and stiffness correspond to the assumptions made for the global analysis. The analysis shall take due account of any reduction of the structural resistance and stiffness of the cross section from local buckling due to axial compression and moment.

(2) As a means to decide whether the proportions of a given cross-section are such that it can be used elastically without any reduction due to local buckling, whether the cross-section can be used plastically, and further whether it can form plastic hinges with sufficient rotation capacity, the following classification may be used:

Class 1 cross-section (plastic cross-section): The cross-section provides sufficient rota-tion capacity for the structure to form plastic hinges in the member.

Class 2 cross-section (compact cross-section): The cross-section can develop full plastic-ity (yielding to the neutral axis), but cannot ensure sufficient rotation capacity of the member.



34

Class 3 cross-section (semi-compact cross-section:) The cross-section can be utilised for yielding in the extreme fibres, but cannot develop plasticity because of local buckling in the compressed parts of the memner. Class 4 cross-section (slender cross-section): The cross-section cannot be utilised for yielding in the extreme fibres, without the introduction of local buckling in the com-pressed parts of the member.

(3) In table V6.3.2a upper limits of the width-to-thickness ratio for compressed parts of the member corresponding to classes 1,2 and 3 are specified. Cross-sectional members, which do not meet the requirements for class 3 cross-sections, are referred to class 4.

For equal leg angles with the leg width c and the leg thickness ft the limit for the width-to-thickness ratio for class 3 cross-section is: 15/ ftc

For unequal leg angles with leg widths h and b and leg thickness ft the limit for the width-to-thickness ratio for class 3 cross-sections is the most restrictive of 15/ fth and 5.11)2/()( + ftbh . For circular hollow sections with outer diameter d and wall thickness t the limit value of the diameter-to-thickness ratio is 250/ td for class 1, 270/ td for class 2, and

290/ td for class 3 cross sections.

In the above limit values, is defined as in table V6.3.2a.

(4) The classification for a given cross-section is normally taken as the class indi-cated by the highest classified (less favourable) member of the cross-section.

(5) In table V6.3.2b recommended upper-bound values are stated for the width-to-thickness ratio for class 4 cross-sections.

Table V6.3.2b Recommended upper-bound values of width-to-thickness ratio for class 4 cross-sections outstand compression element

internal compression element

web

60/ ftc 2350/ ftb

2350/ wtd

See table V6.3.2a for symbols.



35

Table V6.3.2.a Maximum width-to-thickness ratios for compression elements in class 1, 2, and 3 cross-section

In the table 5.0)/235( yf= . k is the buckling coefficient. Compressive stresses are considered positive.



36

6.3.3 Post-critical structural strength of cross-section (1)P For class 4 cross-sections in structural members subject to static ac-tion where buckling initiates at a compression stress level lower than the yield stress it is allowed to utilise the post-critical structural strength of the cross-section.



37

Table V6.3.3 Effective width of plane compression elements



38

(2) The post-critical structural resistance of a cross-section can be utilised by bas-ing the analysis on yielding in the extreme fibres of the effective cross-section. In the effective cross-section the width of the plane compression elements is replaced by their effective width.

(3) The effective width of a plane compression member can be determined by table V6.3.3. In the table is a factor determined by Winters formula: 1= for 673.0

2/)22.0( = for 673.0> is the relative slenderness ratio of the compression member determined by:

ktbf

cr

yd

4.28/

==

The last term of the equation assumes the same partial safety factor for yf and E as is the case in 5.2.2.

In the equation ydf is the yield stress of the material. Instead of ydf it is permissible to use

the highest compressive stress calculated, com , based on the effective width of all the compression elements concerned. Normally, this results in an iterative computational procedure. However, by analysis of com-pressed members according to 6.4.2, lateral-torsional buckling according to 6.4.3 and bending and axial compression according to 6.4.4, ydf should be applied. If ydcom f


39

For determination of the effective width of a web, in table V6.3.3 can be determined on the basis of the effective width of the compression flange and the gross area of the web and tension flange.

(4) For circular hollow sections a post-critical structural resistance must not be assumed.

(5) Utilisation of the post-critical structural resistance may in some cases result in visible buckles in the normal serviceability state of the structure. Depending on the type of the structure it may therefore be required to limit the utilisation of the post-critical structural resistance. This may be achieved e.g. by considering initial buckling a service-ability limit state. Also, refer to the recommended upper-bound values of width-to-thickness ratios for class 4 cross-sections in table V6.3.2b. Care should be taken to ensure that the width-to-thickness ratio of the web is sufficiently low to prevent flange induced buckling, cf. 6.4.6.

(6) The axial stress b corresponding to initial buckling of a compression element with normal initial stresses due to welding and rolling can be determined by the expres-sion:

1/ =ydb f for 8.0

)8.0(8.01/ = ydb f for 0.8 1.25<

2/1/ =ydb f for


40

the plastic resistance where the cross-section is capable of and allowed to develop yielding over the entire cross-section after initiation of yielding

the elastic resistance where the stress in the cross-section can (only just) reach the yield limit, but where yielding cannot de-velop any further or is not allowed to develop any further. For pure tension and compression the elastic resistance is equal to the plastic resistance

the post-critical resistance where buckling occurs in com-pressed elements before the stress reaches the yield limit, but the buckling is allowed to develop until yielding is reached in the boundary zones of the cross-sectional parts.

6.3.6 Alternating yielding (1)P If alternating yielding occurs in a cross-section, a special analysis of structural resistance allowing for material failure shall be carried out, or it shall be verified that alternating yielding does not occur in the serviceability limit state.

6.3.7 Tension (1)P For a cross-section in a structural member subjected to tension it shall be verified that the tension does not exceed:

the elastic resistance of the gross cross-section, and 90 % of the ultimate capacity of the net cross-section through

holes.

(2)P For bolted connections of category C the tensile action must not exceed the elastic resistance of the net cross-section through bolt holes. In this case it is normally assumed that 30 % of the load transferred by a bolt is transferred ahead of the section through the bolt hole.

(3) The requirements for a cross-section in a member subjected to tension can be expressed by:

RtS NN ,



41

where

ydRt AfN =, for gross cross-sections

,0.9t R net udN A f= for net cross-sections

ydnetRt fAN =, for net cross-sections through bolt holes in connections in category C A is the area of the gross cross-section netA is the area of the net cross-section.

6.3.8 Compression (1)P For a cross-section in a structural member subjected to compression it shall be verified that the compression does not exceed:

the elastic resistance or the post-critical resistance of the gross cross-section depending on the relevant type of failure, cf. 6.3.5 and

90% of the ultimate resistance of the net cross-section through oversize holes and slotted holes.

(2) The requirements for a cross-section in a structural member subjected to com-pression can be expressed by:

RcS NN , where ydRc AfN =, for gross cross-sections of classes 1, 2 and 3 ydeffRc fAN =, for gross cross-sections of class 4 udnetRc fAN 9.0, = for net cross sections through oversize holes and slotted

holes A is the area of the gross cross-section effA is the area of the effective cross-section netA is the area of the net cross-section

6.3.8 Bending (1)P For a cross-section in a member subjected to bending it shall be verified that the moment does not exceed:

the plastic resistance, the elastic resistance, or the post-critical resistance of the gross cross-section depending on the relevant type of failure, cf. 6.3.5. and



42

90 % of the ultimate resistance of the net cross-section through holes. The net cross-section is determined on the basis of the gross cross-section with deduction for holes in tensile parts of the cross-section and oversize holes and slotted holes in com-pressed parts of the cross-section.

(2)P For bolted connections of category C the moment must not exceed the elastic moment resistance of the net cross-section through bolt holes. In this case it is normally assumed that 30 % of the action transferred by a bolt is transferred ahead of the section through the bolt hole.

(3) The requirements for a cross-section in a member subject to bending can be expressed by:

RcS MM ,

where

ydplRc fWM =, for gross cross-sections in classes 1 and 2 ydelRc fWM =, for gross cross-sections in class 3 ydeffRc fWM =, for gross cross-sections in class 4 udnetRc fWM 9.0, = for net cross-sections through bolt holes in tensile parts

of the cross-sections and oversize holes and slotted holes in compressed parts

ydnetRc fWM =, for net cross-sections through bolt holes in category C connections

plW is the plastic section modulus elW is the elastic section modulus effW is the section modulus of the effective cross-section netW is the section modulus of the net cross-section

6.3.10 Shear (1)P For a cross-section in a member subject to shear it shall be verified that the shear force does not exceed:

the plastic shear resistance or the post-critical shear resistance of the gross shear cross-section depending on the relevant type of failure, and



43

the ultimate shear resistance of the net shear cross-section. In analysis of the block shear resistance of bolt groups with cate-gory C bolts, however, the plastic shear resistance, cf. 6.6.11(1)P.

(2)P The post-critical shear resistance shall only be utilised in members subject to static action. If the post-critical resistance is utilised, the web shall be provided with bat-tens over the supports.

(3) The requirements for a cross-section in a member subject to shear can be ex-pressed by:

RS VV

where

)3/( ydvR fAV = for gross shear cross-sections in a web with a relative slenderness ratio of 8.0w

)3/(, udnetvR fAV = for net shear cross-section

)3/(, ydnetvR fAV = for net shear cross-section by analysis of block shear

resistance of bolt groups with category C bolts bwR tdV = for cross section in web with a relative slenderness

ratio of 8.0>w vA is the gross shear cross-sectional area netvA , is the net shear cross-sectional area d is the depth of the web wt is the thickness of the web b is the post-critical shear strength, cf. (5) w is the relative slenderness ratio.

With the partial safety factors used in 5.2.2, 8.0=w for an unstiffened shear member corresponds to 69/ =wtd . For , reference is made to table V6.3.2a.

(4) The gross shear area vA may be taken as: wth04.1 for rolled I-, H-, and channel sections wtd for welded I-, H-, and channel sections tdm2 for circular hollow sections



44

th2 for rectangular hollow sections A for solid rectangular and circular cross-sections where h is the total depth of the section t is the wall thickness of the hollow section md is the mean diameter of the hollow section A is the cross-sectional area.

The net shear area is determined on the basis of the gross shear area with deduction for holes as stated in 6.3.1 (3)P.

(5) The post-critical shear strength can be determined by

( )[ ] 3/8.0625.01 ydwb f= for 2.18.0 < w [ ]( )3//9.0 ydwb f = for w


45

ceed half the axial plastic capacity of the web or one quarter of the axial plastic capacity of the entire cross-section, if the latter is smaller.

(2)P Where the elastic resistance is the relevant type of resistance a lin-ear stress distribution over the cross-section shall be assumed in the analysis.

(3)P Where the post-critical resistance is the relevant type of resistance it is permissible to assume development of the buckling to the point of yielding in the extreme fibres of the cross-sectional part. Any contribution due to displacement of the neutral axis shall be added to the moment.

(4) The requirements for a cross-section subjected to combined bending and axial force can be expressed by

12 + plpl mn for class 1 and 2 cross-sections, massive rectan-gular cross-sections

1)5.01( + amn plpl for class 1 and 2 cross-sections, rolled or welded 1plm I-, H-, and channel sections, bending around the

y-axis 1

,,++ elzelyel mmn for class 3 cross-sections

1,,

++ effzeffyeff mmn for class 4 cross-sections where RcS MMm ,/= is the relative moment utilisation regarding the

actual type of failure RtS NNn ,/= (or RcS NN ,/ ) is the relative axial force utilisation regarding the

actual type of failure AbtAa f /)2( = but 5.0 is the relative web proportion of the area.

The interaction expressions above are shown in figure V6.3.11.



46

Figure V6.3.11 Member capacity by combined moment and axial force

6.3.12 Influence from moment, shear and axial force (1)P If the shear force does not exceed half the shear resistance of the cross-section, the entire cross-section can be considered efficient by verifica-tion of the bending and axial force resistance. If the actual shear force ex-ceeds half the shear resistance of the cross-section, reduced bending and axial force resistance shall be assumed.

(2)P By combined moment, shear, and axial force the resistance of the cross-section can be considered adequate if the part of the cross-section, which is not included in the shear area can solely transfer the bending mo-ment and axial force, and the shear area can solely transfer the shear force.

(3) If the actual shear force exceeds half the shear resistance, the resistance of the cross-section can be considered adequate with regard to combined bending, shear, and axial force by the expression:



47

1m

2)12( = v where RS MMm /= is the relative moment utilisation RM the moment resistance of the entire cross-section reduced

for possible axial force according to the expressions in 6.3.11(4)

is the fraction of the moment resistance which relates to the shear area

5.0/ >= RS VVv is the relative shear force utilisation.

The expression is shown in figure V6.3.12.

Figure V6.3.12 Member capacity by combined bending, shear and axial force



48

6.4 Buckling resistance of members 6.4.1 General (1)P By analysis of members subjected to compression as a result of applied axial force or moment due account shall be taken of the influence of the deflections, of residual stresses from the manufacturing process and of geometrical imperfections.

6.4.2 Central axial compression (1)P Compressed members shall be controlled for flexural buckling as well as for torsional and/or flexural-torsional buckling.

(2)P The slenderness ratio ils / of a compressed member subjected to forces due to the action on the structure must not exceed 200. sl is the buck-ling length and i is the radius of gyration appropriate for the actual bending direction. For a class 4 cross-section the radius of gyration for the effective cross-section shall be applied. The slenderness ratio ils / of a purely bracing member subjected to secon-dary compression forces must not exceed 250.

(3) The buckling resistance of a member subjected to central axial compression can be verified by the expression:

ydRbS AfNN = ,

22

1

+= but 1

( )2)2.0(15.0 ++= where is the reduction factor A is the cross-sectional area. For class 4 cross-section the area of the effec-

tive cross-section should be applied, the slenderness ratios being deter-mined on the basis of the yield stress

is an imperfection factor is the relative slenderness ratio. The relative slenderness ratio is determined by



49

cr

yd

NAf

05.1=

where crN is the critical buckling action according to the theory of elasticity (the

Euler force) regarding flexural or flexural-torsional buckling. For class 4 cross-section crN should be determined on the basis of the gors cross-section.

The factor 1.05 aims at an increased safety for slender columns.

By flexural buckling the following expression can be used for the relative slenderness ratio:

4.89/ ils

=

where sl is the buckling length of the compression member i is the appropriate radius of gyration of the cross-section regarding the buck-

ling direction is a relative material parameter, cf. table V6.3.2a.

The expression assumes the same partial safety factor for fy and E as is the case in 5.2.2. A distinction between five buckling cases (buckling curves) 0a , a, b, c, and d is made as stated in table V6.4.2.

For the five cases the imperfection factor is

= 0.13 for column curve 0a = 0.21 for column curve a = 0.34 for column curve b = 0.49 for column curve c = 0.76 for column curve d

The reduction factor is illustrated in figure V6.4.2.

(4) The equations in (3) include considerations of a geometrical imperfection corresponding to an initial deflection of the member of 1/1000 of the buckling length. If the initial deflection exceeds this limit, the expression in 6.4.4 for bending and axial compression should be applied, taking only the moment resulting from the part of the initial deflection, which exceeds 1/1000 of the buckling length into consideration.



50

Figure V6.4.2 Reduction factor



51

Table V6.4.2 The buckling cases a0, a, b, c, and d



52

6.4.3 Lateral-torsional buckling (1)P The structural resistance of beams subjected to lateral-torsional buckling shall be verified.

(2) The structural resistance regarding lateral-torsional buckling can be verified by the expression:

ydLTRbS fWMM = ,

For the lateral-torsional buckling factor LT the expression for in 6.4.2(3) should be applied where

5.0)/(05.1 cryd MWf= is the relative slenderness ratio. The factor 1.05 covers the requirement for greater safety for slender beams

21.0= for rolled members 49.0= for welded members

Here crM is the critical lateral-torsional bending moment ac-

cording to theory of elasticity. W is taken as

plW for class 1 and 2 cross-sections elW for class 3 cross-sections effW for class 4 cross-sections, effW being determined on

the basis of the slenderness ratio corresponding to the yield stress.

For 4.0 , verification of the lateral-torsional buckling resistance is not required.

6.4.4 Bending and axial compression 1(P) Members subjected to combined bending and axial compression and eccentrically loaded compression members shall be analysed for the same conditions as members subjected to central axial compression, see 6.4.2.

Further, the analysis shall take account of the actual bending moments, in-cluding additional moments from the axial force due to the deflection of the member.



53

(2) For compressed members subjected to biaxial bending the structural strength can be verified by the interaction expression:

1max ++ zzyy mkmkn

where )/(max ydS AfNn = is the relative axial force utilisation regarding

the most critical direction of deflection )/(and ydSzy WfMmm = are the relative moment utilisations regarding

bending about the y and z axis, respectively yyy nk = 1 but 5.1yk are moment correction factors with regard to zzz nk = 1 but 5.1zk the y and z axis respectively, where

90.0but)42( += is an auxiliary coefficient regarding the ap-propriate axis, and

M is a factor for equivalent constant moment, cf. table V 6.4.4.

W is taken as

plW for class 1 and 2 cross-sections elW for class 3 cross-sections effW for class 4 cross-sections, effW being determined

on the basis of the slenderness ratio correspond-ing to the yield stress.

is taken as elelpl WWW /)( for class 1 and 2 cross-sections 0 for class 3 and 4 cross-sections.

For SM the maximum actual moment in the member is applied. In cases of biaxial bend-ing the moment with regard to the two axes is applied separately for each axis.

For class 4 cross-sections any additional moment originating from the displacement of the neutral axis in the effective cross-section should be added to SM .

It should be noted that a stress analysis of the cross-section of the member according to 6.3.11 may sometimes govern the dimensions.

(3) For compressed members subjected to lateral action and for which lateral-torsional buckling may occur, it should further be verified that

1)/( ++ zzLTyLTz mkmkn

where 0.1but1 = LTzLTLT knk



54

90.0but15.015.0,

= LTLTMzLT LT is the lateral-torsional buckling reduction factor according to 6.4.3 (2).

The other symbols are analogous to the symbols in 6.4.4.(2).



55

Table V 6.4.4 Equivalent uniform moment factor M



56

6.4.5 Crushing and crippling (1)P For an unstiffened web loaded in the web plane by a transverse action transmitted through a flange, the structural resistance regarding yield-ing in the throat zone (crushing) and/or local buckling of the web (crippling) shall be verified.

(2) Conservatively, verifying the structural resistance in consideration of crushing the transverse action can be assumed distributed at an angle of 45 through solid flange material to the throat zone. Distribution through packings should not be considered.

(3) The structural resistance RsR , of an I- or channel section regarding crippling can be verified by the expression:

2,

0.5 3f w sS s R w d ydw f

t t sF R t E f

t t d

= +

where SF is the transverse action fw tt , is the thickness of web and flange respectively d is the depth of the web ss is the distribution length for the lateral action determined as stated

above with regard to yielding in the throat zone. dss / should not exceed 0.2

For materials of grade S460 the factor 0.5 on the right-hand side of the equation may be replaced by 0.6.

(4) For a combination of transverse action and moment the following interaction expression should further be verified

5.1//,,

+ RcSRsS MMRF

6.4.6 Flange induced buckling (1)P For a compressed flange it shall be verified that buckling of the flange in the plane of the web will not occur.

(2) Flange induced buckling may occur if the web is too slender to prevent the compressed flange from intruding on the web.



57

For a straight member having the web depth d and thickness tw the structural resistance regarding flange induced buckling can be considered verified by the expression:

fcw

yd

d

w AA

fEk

t

d

where wA is the area of the web ckA is the area of the compressed flange ydf is the yield stress of the compressed flange k is a factor equal to 0.30 for class 1 flanges 0.40 for class 2 flanges 0.55 for class 3 and 4 flanges.

6.4.7 Special conditions for bracing members in triangulated struc-tures

(1)P Analysis of bracing members in triangulated structures or in built-up compression members shall include the effect of the moments at the member ends.

For determination of the buckling length the stiffness of the restraint at the ends of the bracing members shall be considered.

(2) By evaluation of the effect of moments at members the capability of the chord members to absorb structural eccentricities at the member ends as well as moments due to deformations of the initial joint configuration and transverse action, if any, on the chord members should be considered. Further, the capacity of the member connection to trans-fer moments shall be considered.

(3) By evaluation of the stiffness of the connections at the member ends the bend-ing and torsional stiffness of the chord member as well as simultaneous utilisation of the chord and brancing member regarding yielding should be considered. Further, account may be taken of the effect of any tensile bracing members connected to the same joint as the compressed member as well as any other bracing planes restraining the chord member against torsion. Finally, the stiffness of the connection of the bracing members should be considered.

(4) For chord members the buckling length may normally be assumed to be equal to the node distance.



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For web members of V or N-geometry the buckling length can normally be taken as a value in the interval 0.7 to 1.0 times the node distance.

(5) For compressed bracing members of angular sections with at least two bolts in each end connection and with sufficient end restraint of the chord members, the eccen-tricities and end restraints may be taken into account by introducing a fictitious slender-ness eff determined by: 7.00 +=eff

where is the relative slenderness corresponding to the buckling length equal to

the system length 0 is 0.35 for buckling about the v axis is 0.50 for buckling about the y axis and the z axis.

(6) For compressed bracing members of angular sections with one bolt in each end connection and for angular sections with two or more bolts in each end connection, but with insufficient end restraint, the structural resistance should be taken as equal to 80 % of the resistance of an angular section with two bolts in each end connection and with sufficient end restraint in the chord members.

6.4.8 Restraint of compressed members (1)P In order that a compressed member or a flange may be assumed to be restrained against buckling at certain points, the support system must provide sufficient strength and stiffness to comply with the structural strength requirement.

(2) Analysis of a lattice or frame system restraining one or more compressed mem-bers may be performed in accordance with the simple method stated below.

The restraining system is designed for an equivalent evenly distributed action over the entire length acting in the direction of deflection of the restrained member or flange as well as any external actions.

For restraining a single compressed member or flange the equivalent and equally distrib-uted load q is taken as

LNq 50/= for 2500/Lq

LNq 60/)1( += for 2500/Lq >



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For restraining several compressed members or flanges the equivalent and equally dis-tributed load q is taken as

+= LkNq r 60/)2.0( for 2500/Lq += LkNq r 60/)( for 2500/Lq > where N is the axial force in the member or the flange. For a flange N is equal to

the moment of the member divided by the total depth of the member L is the span of the restraining system q is the deflection of the restraining system due to q and external actions, if

any is taken as 500 Lq / but not less than 0.2 rk is taken as

5.0)/12.0( rn+ , but not exceeding 1.0 rn is the number of members or flange plates to be restrained.

6.4.9 Built-up compression members (1)P For a built-up compression member consisting of two or more main components mutually connected at intervals, e.g. by lacings or tie panels, to form a single compound member, adequate structural safety regarding buck-ling of the member as a whole as well as buckling of the chord elements - or, where this is important, a combination of the two phenomena - shall be documented. The analysis shall include consideration of the stiffness of the internal connections.

(2)P The analysis of the chord elements of the built-up member shall consider the increase of the chord force due to the deflection of the built-up member due to transverse action or eccentric axial action, if any.

It shall be verified that the internal connections of the built-up member have sufficient strength to comply with the requirements for safety against failure with regard to the structural resistance of the member as a whole.

If the internal connections are designed as lacings in which considerable forces are introduced due to bending stiffness and changes in lengths these forces shall also be considered.

Any purely stiffening members are also designed according to these rules.



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(3) The analysis of the internal connections of the built-up member can be based on the assumption that in addition to the shear force from any external actions the elements are subjected to a force equal to 2.5 % of the axial force in the built-up member. This force is assumed to be effective in the plane concerned and perpendicular to the built-up member. It is assumed that the initial deflection of the built-up member does not exceed 1/500 of the length.

6.5 Welded connections 6.5.1 General (1)P The provisions of this section apply to materials of groups I, II and IIIa. For materials of group IIIa the rules will ensure adequate structural resistance but not necessarily adequate ductility. As for the other material groups, acceptable alternative provisions shall be used or the strength of the connections shall be determined by tests.

(2) Apart from material groups I and II it is not always possible to obtain strength and toughness in weld metal and heat affected zones which are at least equal to the prop-erties of the parent metal. Therefore, special calculation models should be used.

6.5.2 Calculation of welds (1)P Welds are incorporated as part of the structure and shall be calcu-lated accordingly. For safety evaluation the same rules as for the total struc-ture apply, cf. chapter 5.

(2) The resistance of a weld subjected to static action may be verified by an analy-sis where the forces transmitted by the weld are resolved into components parallel with and perpendicular to the longitudinal direction of the weld and perpendicular to and in the throat section. On the assumption that the stresses due to the forces on the weld are evenly distributed over the throat section, the resistance may be assumed to be verified subject to fulfilment of both of the following expressions:

2 2 290 0 90 03( ) ud

w

fc + +

udfc090 where

90 is the axial stress in the throat section



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0 is the shear stress in the throat section parallel with the longitudinal direction of the weld

90 is the shear stress in the throat section perpendicular to the longitudinal direction of the weld

0c is a strength reduction factor taking account of the quality of the weld and the extent of the inspection

udf is the tensile strength of the weakest material of the connection w is a correlation factor.

0 , which is acting on sections perpendicular to the longitudinal direction of the weld, has been disregarded in the above expressions. This can be justified by considering the theory of plasticity. The stress components are illustrated in figure V6.5.2.

The strength reduction factor 0c is shown in table V6.5.2a corresponding to the weld classes defined in 7.3.4 (2). For full penetration butt welds the correlation factor w is taken as 1.0. For fillet welds

w is stated in table V6.5.2b.

Figure V6.5.2 Stress components in welds

(3) As a conservative simplification the expressions in (2) may be replaced by the resistance expression



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af

cFw

udS 30

where SF is the resulting external force per unit length of the weld irrespective of

the force direction a is the weld thickness.

Table V6.5.2a Strength reduction factor 0c

weld class I II III 1.0 0.9 0.7

Table V6.5.2b Correlation factor w for fillet welds strength class correlation factor w DS/EN 10025: S235 S275 S355

0.8 0.85 0.9

DS/EN 10113: S275 S355

0.8 0.9

DS/EN 10113 and DS/EN 10137: S420 S460

1.0 1.0

6.5.3 Thickness and length of welds (1)P Normally the weld thickness a may be assumed to be equal to the nominal weld thickness na . However, for butt welds with partial penetra-tion a shall never be taken greater than corresponding to the actual penetra-tion. For machine made fillet welds, the weld thickness may be taken as

3/2 in aaa +=

where ia is the penetration, cf. figure 6.5.3a.



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However, a shall never be taken greater than corresponding to full penetra-tion welds. It is a condition for incorporating ia in the design that its value can be verified by tests.

Figure 6.5.3a Nominal weld thickness and penetration

(2)P For submerged arc welding na may be increased by 20 % of na , however, not exceeding 2 mm, without testing,.

(3)P The weld length is the nominal weld length with deduction for end craters, if any. The length of an end crater is assumed to be equal to na .

(4) For butt welds and fillet welds na is defined as shown in figure V6.5.3b. A full penetration butt weld is defined as a butt weld that has complete penetration and fusion of weld and parent material throughout the thickness of the joint, cf. figure V6.5.3b 1 5. A partial penetration butt weld is defined as a butt weld that has a penetration, which is less than the full thickness of the parent metal, cf. figure V6.5.3b - 6.



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Figure V6.5.3b Nominal weld thickness for welds

6.5.4 Minimum and maximum dimensions of fillet welds

(1)P Fillet welds assumed capable of transmitting force shall not be shorter than 6a and in any case not shorter than 40 mm.

The thickness of fillet welds shall not be less than a = 3mm.

(2) The significance and magnitude of weld stresses in fillet welds are increased with the thickness of the welds. Therefore, the thickness of fillet welds shall not be greater than necessary, and the thickness shall not exceed 20 mm unless the propriety hereof can be documented.

6.5.5 Distribution of forces in welded connections (1)P The conditions in 6.1.5 for assuming the internal forces in a connec-tion to be transmitted most favourably does not apply to long welds sub-jected to shear at a lap joint or at a similar concentrated action. At such a



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connection a weld shall at most be assumed to be fully loaded over a weld length l = 150 a, where a is the weld thickness.

(2) For central transmission of a force in a connection consisting of longitudinal and transverse welds the resistance of the connection when subjected to static action is calculated as the sum of the resistance of the individual welds.

6.5.6 Unsymmetrical welds (1)P In the analysis of unsymmetrical welds as shown in figures 6.5.5a and b the eccentricities due to the lack of symmetry sha

ds 412 e-2001

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