Bsi bs en 01994 1 1 2004 (2005)

1.5.2.6 Composite slab a slab in which profiled steel sheets are used initially as permanent shuttering and subsequently combine structurally with the hardened concrete and act as tensil

General

Scope

Eurocode 4 governs the design of composite structures and components in buildings and civil engineering projects, ensuring adherence to safety and serviceability standards It aligns with the design and verification principles outlined in EN 1990, which serves as the foundation for structural design.

(2) Eurocode 4 is concerned only with requirements for resistance, serviceability, durability and fire resistance of composite structures Other requirements, e.g concerning thermal or sound insulation, are not considered

(3) Eurocode 4 is intended to be used in conjunction with:

EN 1990 Eurocode: Basis of structural design

EN 1991 Eurocode 1: Actions on structures

ENs, hENs, ETAGs and ETAs for construction products relevant for composite structures

EN 1090 Execution of steel structures and aluminium structures

EN 13670 Execution of concrete structures

EN 1992 Eurocode 2: Design of concrete structures

EN 1993 Eurocode 3: Design of steel structures

EN 1998 Eurocode 8: Design of structures for earthquake resistance, when composite structures are built in seismic regions

(4) Eurocode 4 is subdivided in various parts:

Part 1-1: General rules and rules for buildings

1.1.2 Scope of Part 1-1 of Eurocode 4

(1) Part 1-1 of Eurocode 4 gives a general basis for the design of composite structures together with specific rules for buildings

(2) The following subjects are dealt with in Part 1-1:

Section 8: Composite joints in frames for buildings

Section 9: Composite slabs with profiled steel sheeting for buildings

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Normative references

This European standard incorporates provisions from various normative documents, which are referenced throughout the text For dated references, any amendments or revisions made after the publication date do not apply However, it is advisable for parties involved in agreements based on this standard to consider using the most recent editions of the referenced normative documents In the case of undated references, the latest edition of the cited normative document is applicable.

EN 1090-2 1 Execution of steel structures and aluminium structures - Technical rules for the execution of steel structures

EN 1990: 2002 Basis of structural design

EN 1992-1-1 1 Eurocode 2: Design of concrete structures: General rules and rules for buildings

EN 1993-1-1 1 Eurocode 3: Design of steel structures: General rules and rules for buildings

EN 1993-1-3 1 Eurocode 3: Design of steel structures: Cold-formed thin gauge members and sheeting

EN 1993-1-5 1 Eurocode 3: Design of steel structures: Plated structural elements

EN 1993-1-8 1 Eurocode 3: Design of steel structures: Design of joints

EN 1993-1-9 1 Eurocode 3: Design of steel structures: Fatigue strength of steel structures

EN 10025-1: 2002 Hot-rolled products of structural steels: General delivery conditions

EN 10025-2: 2002 Hot-rolled products of structural steels: Technical delivery conditions for non-alloy structural steels

EN 10025-3: 2002 Hot-rolled products of structural steels: Technical delivery conditions for normalized/normalized rolled weldable fine grain structural steels

EN 10025-4: 2002 Hot-rolled products of structural steels: Technical delivery conditions for thermomechanical rolled weldable fine grain structural steels

EN 10025-5: 2002 Hot-rolled products of structural steels: Technical delivery conditions for structural steels with improved atmospheric corrosion resistance

EN 10025-6: 2002 Hot-rolled products of structural steels: Technical delivery conditions for flat products of high yield strength structural steels in the quenched and tempered condition

EN 10147: 2000 Continuously hot-dip zinc coated structural steels strip and sheet: Technical delivery conditions

EN 10149-2: 1995 Hot-rolled flat products made of high yield strength steels for cold-forming:

Delivery conditions for thermomechanically rolled steels

EN 10149-3: 1995 Hot-rolled flat products made of high yield strength steels for cold-forming:

Delivery conditions for normalised or normalised rolled steels

Assumptions

(1) In addition to the general assumptions of EN 1990 the following assumptions apply:

– those given in clauses 1.3 of EN1992-1-1 and EN1993-1-1.

Distinction between principles and application rules

(1) The rules in EN 1990, 1.4 apply.

Definitions

(1) The terms and definitions given in EN 1990, 1.5, EN 1992-1-1, 1.5 and EN 1993-1-1, 1.5 apply

1.5.2 Additional terms and definitions used in this Standard

1.5.2.1 Composite member a structural member with components of concrete and of structural or cold-formed steel, interconnected by shear connection so as to limit the longitudinal slip between concrete and steel and the separation of one component from the other

1.5.2.2 Shear connection an interconnection between the concrete and steel components of a composite member that has sufficient strength and stiffness to enable the two components to be designed as parts of a single structural member

1.5.2.3 Composite behaviour behaviour which occurs after the shear connection has become effective due to hardening of concrete

1.5.2.4 Composite beam a composite member subjected mainly to bending

1.5.2.5 Composite column a composite member subjected mainly to compression or to compression and bending

1.5.2.6 Composite slab a slab in which profiled steel sheets are used initially as permanent shuttering and subsequently combine structurally with the hardened concrete and act as tensile reinforcement in the finished floor

1.5.2.7 Composite frame a framed structure in which some or all of the elements are composite members and most of the remainder are structural steel members

1.5.2.8 Composite joint a joint between a composite member and another composite, steel or reinforced concrete member, in which reinforcement is taken into account in design for the resistance and the stiffness of the joint

1.5.2.9 Propped structure or member a structure or member where the weight of concrete elements is applied to the steel elements which are supported in the span, or is carried independently until the concrete elements are able to resist stresses

1.5.2.10 Un-propped structure or member a structure or member in which the weight of concrete elements is applied to steel elements which are unsupported in the span

1.5.2.11 Un-cracked flexural stiffness the stiffness E a I 1 of a cross-section of a composite member where I 1 is the second moment of area of the effective equivalent steel section calculated assuming that concrete in tension is un-cracked

1.5.2.12 Cracked flexural stiffness the stiffness E a I 2 of a cross-section of a composite member where I 2 is the second moment of area of the effective equivalent steel section calculated neglecting concrete in tension but including reinforcement

1.5.2.13 Prestress the process of applying compressive stresses to the concrete part of a composite member, achieved by tendons or by controlled imposed deformations

Symbols

For the purpose of this Standard the following symbols apply

A Cross-sectional area of the effective composite section neglecting concrete in tension

A a Cross-sectional area of the structural steel section

A b Cross-sectional area of bottom transverse reinforcement

A bh Cross-sectional area of bottom transverse reinforcement in a haunch

A c Cross-sectional area of concrete

A ct Cross-sectional area of the tensile zone of the concrete

A fc Cross-sectional area of the compression flange

A Cross-sectional area of profiled steel sheeting

A pe Effective cross-sectional area of profiled steel sheeting

A s Cross-sectional area of reinforcement

A sf Cross-sectional area of transverse reinforcement

A s,r Cross-sectional area of reinforcement in row r

A t Cross-sectional area of top transverse reinforcement

A v Shear area of a structural steel section

A 1 Loaded area under the gusset plate

E a Modulus of elasticity of structural steel

E c,eff Effective modulus of elasticity for concrete

E cm Secant modulus of elasticity of concrete

E s Design value of modulus of elasticity of reinforcing steel

(EI) eff Effective flexural stiffness for calculation of relative slenderness

(EI) eff,II Effective flexural stiffness for use in second-order analysis

(EI) 2 Cracked flexural stiffness per unit width of the concrete or composite slab

F c,wc,c,Rd Design value of the resistance to transverse compression of the concrete encasement to a column web

F l Design longitudinal force per stud

F t Design transverse force per stud

F ten Design tensile force per stud

G a Shear modulus of structural steel

I Second moment of area of the effective composite section neglecting concrete in tension

I a Second moment of area of the structural steel section

I at St Venant torsion constant of the structural steel section

I c Second moment of area of the un-cracked concrete section

I ct St Venant torsion constant of the un-cracked concrete encasement

I s Second moment of area of the steel reinforcement

I 1 Second moment of area of the effective equivalent steel section assuming that the concrete in tension is un-cracked

I 2 Second moment of area of the effective equivalent steel section neglecting concrete in tension but including reinforcement

K e , K e,II Correction factors to be used in the design of composite columns

K sc Stiffness related to the shear connection

K 0 Calibration factor to be used in the design of composite columns

L p Distance from centre of a concentrated load to the nearest support

L x Distance from a cross-section to the nearest support

M a Contribution of the structural steel section to the design plastic resistance moment of the composite section

M a,Ed Design bending moment applied to the structural steel section

M b,Rd Design value of the buckling resistance moment of a composite beam

M c,Ed The part of the design bending moment applied to the composite section

M cr Elastic critical moment for lateral-torsional buckling of a composite beam

M Ed,i Design bending moment applied to a composite joint i

M Ed,max,f Maximum bending moment or internal force due to fatigue loading

M Ed,min,f Minimum bending moment due to fatigue loading

M el,Rd Design value of the elastic resistance moment of the composite section

M max,Rd Maximum design value of the resistance moment in the presence of a compressive normal force

M pa Design value of the plastic resistance moment of the effective cross-section of the profiled steel sheeting

M perm Most adverse bending moment for the characteristic combination

M pl,a,Rd Design value of the plastic resistance moment of the structural steel section

M pl,N,Rd Design value of the plastic resistance moment of the composite section taking into account the compressive normal force

M pl,Rd Design value of the plastic resistance moment of the composite section with full shear connection

M pl,y,Rd Design value of the plastic resistance moment about the y-y axis of the composite section with full shear connection

M pl,z,Rd Design value of the plastic resistance moment about the z-z axis of the composite section with full shear connection

M pr Reduced plastic resistance moment of the profiled steel sheeting

M Rd Design value of the resistance moment of a composite section or joint

M Rk Characteristic value of the resistance moment of a composite section or joint

M y,Ed Design bending moment applied to the composite section about the y-y axis

M z,Ed Design bending moment applied to the composite section about the z-z axis

N Compressive normal force; number of stress range cycles; number of shear connectors

N a Design value of the normal force in the structural steel section of a composite beam

N c Design value of the compressive normal force in the concrete flange

N c,f Design value of the compressive normal force in the concrete flange with full shear connection

N c,el Compressive normal force in the concrete flange corresponding to M el,Rd

N cr,eff Elastic critical load of a composite column corresponding to an effective flexural stiffness

N cr Elastic critical normal force

N c1 Design value of normal force calculated for load introduction

N Ed Design value of the compressive normal force

N G,Ed Design value of the part of the compressive normal force that is permanent

N p Design value of the plastic resistance of the profiled steel sheeting to normal force

N pl,a Design value of the plastic resistance of the structural steel section to normal force

N pl,Rd Design value of the plastic resistance of the composite section to compressive normal force

N pl,Rk Characteristic value of the plastic resistance of the composite section to compressive normal force

N pm,Rd Design value of the resistance of the concrete to compressive normal force

N R Number of stress-range cycles

N s Design value of the plastic resistance of the steel reinforcement to normal force

N sd Design value of the plastic resistance of the reinforcing steel to tensile normal force

P l ,Rd Design value of the shear resistance of a single stud connector corresponding to F l

P pb,Rd Design value of the bearing resistance of a stud

P Design value of the shear resistance of a single connector

P Rk Characteristic value of the shear resistance of a single connector

P t,Rd Design value of the shear resistance of a single stud connector corresponding to F t

R Ed Design value of a support reaction

S j,ini Initial rotational stiffness of a joint

V a,Ed Design value of the shear force acting on the structural steel section

V b,Rd Design value of the shear buckling resistance of a steel web

V c,Ed Design value of the shear force acting on the reinforced concrete web encasement

V Ed Design value of the shear force acting on the composite section

V ld Design value of the resistance of the end anchorage

V l,Rd Design value of the resistance to shear

V pl,Rd Design value of the plastic resistance of the composite section to vertical shear

V pl,a,Rd Design value of the plastic resistance of the structural steel section to vertical shear

V p,Rd Design value of the resistance of a composite slab to punching shear

V Rd Design value of the resistance of the composite section to vertical shear

V v,Rd Design value of the resistance of a composite slab to vertical shear

V wp,c,Rd Design value of the shear resistance of the concrete encasement to a column web panel

In structural engineering, various dimensions and widths are critical for design and analysis The spacing between parallel beams, denoted as $b$, is essential for determining load distribution The width of the flange of a steel section and the width of a slab are also represented by $b$ Effective widths, such as $b_{\text{eff,1}}$ for mid-span and $b_{\text{eff,2}}$ at internal supports, play a significant role in assessing structural integrity Additionally, the effective width of the concrete flange on each side of the web, $b_{ei}$, and the effective width of a composite slab, $b_{em}$, are crucial for composite structures The geometric width of the concrete flange, $b_i$, and the width of the rib of profiled steel sheeting, $b_r$, are important for ensuring proper load transfer Other dimensions, such as the clear depth of the web, $d$, and the diameter of the weld collar, $d_{do}$, are vital for detailing connections and ensuring structural performance Understanding these parameters is essential for effective design and construction in steel and concrete structures.

The article discusses various parameters related to the structural analysis and design of composite slabs and profiled steel sheeting Key terms include eccentricity of loading, edge distance, and distances from various axes to extreme fibres in tension It defines critical strength values such as the design and characteristic compressive strengths of concrete, as well as the yield strengths of reinforcing and structural steel Additionally, it addresses factors affecting bending moments, overall depths, and thicknesses of materials involved The document also highlights coefficients and reduction factors that influence design shear resistance and stiffness in structural components.

The article discusses various parameters and factors related to the structural analysis of columns and slabs, particularly focusing on the effects of longitudinal compressive stress on transverse resistance Key parameters include the flexural stiffness of cracked concrete or composite slabs (k₁) and the web (k₂), as well as the lengths associated with bending and load introduction It also highlights the importance of modular ratios (n) for different loading types and the number of shear connectors, which are crucial for ensuring full shear connection Additionally, the article addresses design considerations such as longitudinal and transverse spacing of stud shear connectors, effective lengths, and thicknesses of various structural components, including flanges and webs Understanding these factors is essential for accurate design and analysis in structural engineering.

∆σc Reference value of the fatigue strength at 2 million cycles

∆σE Equivalent constant amplitude stress range

∆σE,glob Equivalent constant amplitude stress range due to global effects

∆σE,loc Equivalent constant amplitude stress rangedue to local effects

∆σE,2 Equivalent constant amplitude stress range related to 2 million cycles

∆σs Increase of stress in steel reinforcement due to tension stiffening of concrete

∆σs,equ Damage equivalent stress range

∆τ Range of shear stress for fatigue loading

∆τc Reference value of the fatigue strength at 2 million cycles

∆τE Equivalent constant amplitude stress range

∆τE,2 Equivalent constant amplitude range of shear stress related to 2 million cycles

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In structural engineering, various Greek lowercase letters represent critical factors and parameters The factor $ \alpha $ signifies a general parameter, while $ \alpha_{cr} $ indicates the factor by which design loads must be increased to induce elastic instability The coefficient $ \alpha_M $ is associated with the bending of composite columns, with $ \alpha_{M,y} $ and $ \alpha_{M,z} $ specifically relating to bending about the y-y and z-z axes, respectively The ratio $ \alpha_{st} $ and the transformation parameter $ \beta $ are also essential, with $ \beta_c $ and $ \beta_i $ serving as specific parameters Additionally, the partial factor for concrete is denoted by $ \gamma_C $, while $ \gamma_F $ accounts for actions, including model uncertainties and dimensional variations The partial factor for equivalent constant amplitude stress range is represented by $ \gamma_{Ff} $, and $ \gamma_M $ pertains to material properties, also considering model uncertainties and dimensional variations Lastly, $ \gamma_{M0} $ is the partial factor for structural steel applied to the resistance of cross-sections, as outlined in EN 1993-1-1.

The article discusses various partial factors and coefficients relevant to structural steel design, including the γM1 factor for member instability resistance, γMf for fatigue strength, and γP for pre-stressing action It also addresses factors such as δ for steel contribution ratio, δmax for sagging vertical deflection, and δs for deflection under weight Additionally, it highlights slip capacity factors (δuk), shear connection degrees (η), and confinement factors (ηa, ηc) The document further elaborates on damage equivalent factors (λ, λglob, λloc) and relative slenderness (λ, λLT), along with coefficients of friction and design factors related to compression and bending.

The article discusses various parameters related to the structural integrity and design of composite slabs, including the reduction factor ($ν$) for longitudinal compression effects on shear resistance, Poisson’s ratio ($ν_a$) for structural steel, and parameters ($ξ$, $ρ$, $ρ_s$) that account for shear connection deformation and reduced design bending resistance It also highlights key stress values such as longitudinal compressive stress ($σ_{com,c,Ed}$), local design strength of concrete ($σ_{c,Rd}$), and extreme fiber tensile stress ($σ_{ct}$) Additionally, it addresses maximum and minimum stress due to fatigue loading ($σ_{max,f}$, $σ_{min,f}$), as well as stresses in reinforcement due to bending moments ($σ_s$, $σ_{s,max}$, $σ_{s,min}$) The design shear strength ($τ_{Rd}$) and various values of longitudinal shear strength for composite slabs ($τ_u$, $τ_{u,Rd}$, $τ_{u,Rk}$) are also examined, along with the diameter of steel reinforcing bars ($φ$) and the creep coefficient ($ϕ$).

28 days χ Reduction factor for flexural buckling χLT Reduction factor for lateral-torsional buckling ψL Creep multiplier

Basis of design

Requirements

(1)P The design of composite structures shall be in accordance with the general rules given in EN

(2)P The supplementary provisions for composite structures given in this Section shall also be applied

(3) The basic requirements of EN 1990, Section 2 are deemed be satisfied for composite structures when the following are applied together:

– limit state design in conjunction with the partial factor method in accordance with EN 1990, – actions in accordance with EN 1991,

– combination of actions in accordance with EN 1990 and

– resistances, durability and serviceability in accordance with this Standard

Principles of limit state design

(1)P For composite structures, relevant stages in the sequence of construction shall be considered.

Basic variables

(1) Actions to be used in design may be obtained from the relevant parts of EN 1991

(2)P In verification for steel sheeting as shuttering, account shall be taken of the ponding effect (increased depth of concrete due to the deflection of the sheeting)

(1) Unless otherwise given by Eurocode 4, actions caused by time-dependent behaviour of concrete should be obtained from EN 1992-1-1

The shrinkage and creep of concrete, along with non-uniform temperature changes, generate internal forces in cross sections, leading to curvatures and longitudinal strains in structural members These effects are classified as primary effects in both statically determinate and indeterminate structures, particularly when the compatibility of deformations is not taken into account.

In statically indeterminate structures, the primary effects of shrinkage, creep, and temperature lead to additional action effects These total effects must be compatible and are classified as secondary effects, which are regarded as indirect actions.

Verification by the partial factor method

(1) For pre-stress by controlled imposed deformations, e.g by jacking at supports, the partial safety factor γP should be specified for ultimate limit states, taking into account favourable and unfavourable effects

Note: Values for γ P may be given in the National Annex The recommended value for both favourable and unfavourable effects is 1,0

2.4.1.2 Design values of material or product properties

(1)P Unless an upper estimate of strength is required, partial factors shall be applied to lower characteristic or nominal strengths

For concrete design, a partial factor $ \gamma_C $ must be applied to determine the design compressive strength, expressed as $ f_{cd} = \frac{f_{ck}}{\gamma_C} $ The characteristic value $ f_{ck} $ should be referenced from EN 1992-1-1, section 3.1 for normal concrete and section 11.3 for lightweight concrete.

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(3)P For steel reinforcement, a partial factor γS shall be applied

Note: The value for γ S is that used in EN 1992-1-1

(4)P For structural steel, steel sheeting and steel connecting devices, partial factors γM shall be applied Unless otherwise stated, the partial factor for structural steel shall be taken as γM0

Note: Values for γ M are those given in EN 1993

(5)P For shear connection, a partial factor γ V shall be applied

Note: The value for γ V may be given in the National Annex The recommended value for γ V is 1,25

(6)P For longitudinal shear in composite slabs for buildings, a partial factor γVS shall be applied

Note: The value for γ VS may be given in the National Annex The recommended value for γ VS is 1,25

(7)P For fatigue verification of headed studs in buildings, partial factors γMf and γMf,s shall be applied

Note: The value for γMf is that used the relevant Parts of EN 1993 The value for γMf,s may be given in the

National Annex The recommended value for γMf,s is 1,0

2.4.1.3 Design values of geometrical data

(1) Geometrical data for cross-sections and systems may be taken from product standards hEN or drawings for the execution and treated as nominal values

(1)P For composite structures, design resistances shall be determined in accordance with EN 1990, expression (6.6a) or expression (6.6c)

(1) The general formats for combinations of actions are given in EN 1990, Section 6

Note: For buildings, the combination rules may be given in the National Annex to Annex A of EN 1990

2.4.3 Verification of static equilibrium (EQU)

(1) The reliability format for the verification of static equilibrium for buildings, as described in

EN 1990, Table A1.2(A), also applies to design situations equivalent to (EQU), e.g for the design of hold down anchors or the verification of uplift of bearings of continuous beams.

Materials

Concrete

(1) Unless otherwise given by Eurocode 4, properties should be obtained by reference to

EN 1992-1-1, 3.1 for normal concrete and to EN 1992-1-1, 11.3 for lightweight concrete

(2) This Part of EN 1994 does not cover the design of composite structures with concrete strength classes lower than C20/25 and LC20/22 and higher than C60/75 and LC60/66

(3) Shrinkage of concrete should be determined taking account of the ambient humidity, the dimensions of the element and the composition of the concrete

(4) Where composite action is taken into account in buildings, the effects of autogenous shrinkage may be neglected in the determination of stresses and deflections

Experience indicates that the shrinkage strain values provided in EN 1992-1-1 may overestimate the effects of shrinkage in composite structures Additionally, the National Annex may offer specific values for concrete shrinkage.

Recommended values for composite structures for buildings are given in Annex C.

Reinforcing steel

(1) Properties should be obtained by reference to EN 1992-1-1, 3.2

(2) For composite structures, the design value of the modulus of elasticity E s may be taken as equal to the value for structural steel given in EN 1993-1-1, 3.2.6.

Structural steel

(1) Properties should be obtained by reference to EN 1993-1-1, 3.1 and 3.2

(2) The rules in this Part of EN 1994 apply to structural steel of nominal yield strength not more than 460 N/mm 2

Connecting devices

(1) Reference should be made to EN 1993-1-8 for requirements for fasteners and welding consumables

(1) Reference should be made to EN 13918.

Profiled steel sheeting for composite slabs in buildings

(1) Properties should be obtained by reference to EN 1993-1-3, 3.1 and 3.2

The guidelines outlined in this section of EN 1994 are applicable to the design of composite slabs that utilize profiled steel sheets These sheets must be produced from steel conforming to EN 10025, cold-formed steel sheets according to EN 10149-2 or EN 10149-3, or galvanized steel sheets as specified in the relevant standards.

Note: The minimum value for the nominal thickness t of steel sheets may be given in the National Annex The recommended value is 0,70 mm.

Durability

General

(1) The relevant provisions given in EN 1990, EN 1992 and EN 1993 should be followed

Profiled steel sheeting for composite slabs in buildings

(1)P The exposed surfaces of the steel sheeting shall be adequately protected to resist the particular atmospheric conditions

(2) A zinc coating, if specified, should conform to the requirements of EN 10147 or with relevant standards in force

(3) A zinc coating of total mass 275 g/m 2 (including both sides) is sufficient for internal floors in a non-aggressive environment, but the specification may be varied depending on service conditions.

Structural analysis

Structural modelling for analysis

5.1.1 Structural modelling and basic assumptions

(1)P The structural model and basic assumptions shall be chosen in accordance with EN 1990, 5.1.1 and shall reflect the anticipated behaviour of the cross-sections, members, joints and bearings

Section 5 applies to composite structures primarily composed of composite materials or structural steel In cases where the structural behavior resembles that of reinforced or pre-stressed concrete, with only a limited number of composite members, global analysis should typically follow the guidelines set forth in EN 1992-1-1.

(3) Analysis of composite slabs with profiled steel sheeting in buildings should be in accordance with Section 9

The behavior of joints can influence the distribution of internal forces and moments within a structure, as well as its overall deformations While these effects are often negligible, they become significant in cases like semi-continuous joints, and should be considered according to Section 8 and EN 1993-1-8.

(2) To identify whether the effects of joint behaviour on the analysis need be taken into account, a distinction may be made between three joint models as follows, see 8.2 and EN 1993-1-8, 5.1.1:

– simple, in which the joint may be assumed not to transmit bending moments;

– continuous, in which the stiffness and/or resistance of the joint allow full continuity of the members to be assumed in the analysis;

– semi-continuous, in which the behaviour of the joint needs to be taken into account in the analysis

(3) For buildings, the requirements of the various types of joint are given in Section 8 and in

(1)P Account shall be taken of the deformation characteristics of the supports where significant

Note: EN 1997 gives guidance for calculation of soil-structure interaction

Structural stability

5.2.1 Effects of deformed geometry of the structure

(1) The action effects may generally be determined using either:

- first-order analysis, using the initial geometry of the structure

- second-order analysis, taking into account the influence of the deformation of the structure

(2)P The effects of the deformed geometry (second-order effects) shall be considered if they increase the action effects significantly or modify significantly the structural behaviour

First-order analysis is applicable when the increase in internal forces or moments due to deformations is under 10% This condition is met if the criterion $ \alpha_{cr} \geq 10 $ is satisfied, where $ \alpha_{cr} $ represents the factor needed to increase design loading to induce elastic instability.

(4)P In determining the stiffness of the structure, appropriate allowances shall be made for cracking and creep of concrete and for the behaviour of the joints

5.2.2 Methods of analysis for buildings

Beam-and-column type plane frames can be evaluated for sway mode failure using first-order analysis if the specified criterion is met for each storey The critical buckling load, αcr, can be determined according to the guidelines in EN 1993-1-1, 5.2.1(4), assuming that axial compression in the beams is minimal It is essential to consider factors such as concrete cracking (refer to 5.4.2.3), concrete creep (see 5.4.2.2), and joint behavior (as outlined in 8.2 and EN 1993-1-8, 5.1).

(2) Second-order effects may be included indirectly by using a first-order analysis with appropriate amplification

When second-order effects and imperfections of individual members are thoroughly considered in the global analysis of the structure, conducting individual stability checks for those members becomes unnecessary.

It is essential to verify the stability of individual members if second-order effects or specific imperfections, such as flexural and lateral-torsional buckling, are not adequately considered in the global analysis.

(5) If the global analysis neglects lateral-torsional effects, the resistance of a composite beam to lateral-torsional buckling may be checked using 6.4

(6) For composite columns and composite compression members, flexural stability may be checked using one of the following methods:

(a) by global analysis in accordance with 5.2.2(3), with the resistance of cross-sections being verified in accordance with 6.7.3.6 or 6.7.3.7, or

The analysis of individual members must consider end moments and forces derived from the global structural analysis, including relevant global second-order effects and imperfections It is essential to account for second-order effects and member imperfections, as outlined in section 5.3.2.3, while verifying the resistance of cross-sections in accordance with sections 6.7.3.6 or 6.7.3.7.

For members subjected to axial compression, it is essential to utilize buckling curves to address second-order effects and imperfections, as outlined in section 6.7.3.5 The verification process must consider end forces derived from the global analysis of the structure, incorporating relevant global second-order effects and imperfections Additionally, the buckling length used in this assessment should correspond to the system length.

(7) For structures in which the columns are structural steel, stability may also be verified by member checks based on buckling lengths, in accordance with EN 1993-1-1, 5.2.2(8) and 6.3.

Imperfections

In structural analysis, it is essential to include appropriate allowances for imperfections, which encompass residual stresses and geometric irregularities such as lack of verticality, straightness, flatness, fit, and minor eccentricities in the joints of the unloaded structure.

The shape of imperfections must reflect the elastic buckling mode of the structure or member, considering the most unfavorable direction and form in the plane of buckling.

Equivalent geometric imperfections, as outlined in sections 5.3.2.2 and 5.3.2.3, must be utilized with values that account for the potential impacts of both global and local imperfections This is necessary unless the resistance formulas for member design already incorporate the effects of local imperfections, as referenced in section 5.3.2.3.

In a global analysis, imperfections in composite compression members can be disregarded when first-order analysis is applicable, as stated in section 5.2.1(2) However, if second-order analysis is required, these member imperfections may still be neglected in the global analysis under specific conditions.

0 N N λ ≤ (5.2) where: λ is defined in 6.7.3.3 and calculated for the member considered as hinged at its ends;

N pl,Rk is defined in 6.7.3.3;

N Ed is the design value of the normal force

(3) Member imperfections should always be considered when verifying stability within a member’s length in accordance with 6.7.3.6 or 6.7.3.7

(4) Imperfections within steel compression members should be considered in accordance with

(1) The effects of imperfections should be allowed for in accordance with EN 1993-1-1, 5.3.2

(1) Design values of equivalent initial bow imperfection for composite columns and composite compression members should be taken from Table 6.5

(2) For laterally unrestrained composite beams the effects of imperfections are incorporated within the formulae given for buckling resistance moment, see 6.4

(3) For steel members the effects of imperfections are incorporated within the formulae given for buckling resistance, see EN 1993-1-1, 6.3.

Calculation of action effects

(1) Action effects may be calculated by elastic global analysis, even where the resistance of a cross- section is based on its plastic or non-linear resistance

(2) Elastic global analysis should be used for serviceability limit states, with appropriate corrections for non-linear effects such as cracking of concrete

(3) Elastic global analysis should be used for verifications of the limit state of fatigue

(4)P The effects of shear lag and of local buckling shall be taken into account if these significantly influence the global analysis

(5) The effects of local buckling of steel elements on the choice of method of analysis may be taken into account by classifying cross-sections, see 5.5

(6) The effects of local buckling of steel elements on stiffness may be ignored in normal composite sections For cross-sections of Class 4, see EN 1993-1-5, 2.2

(7) The effects on the global analysis of slip in bolt holes and similar deformations of connecting devices should be considered

Non-linear analysis is essential for accurately assessing the impact of slip and separation on internal forces and moments at the interfaces between steel and concrete This is particularly relevant when shear connections are implemented as specified in section 6.6.

5.4.1.2 Effective width of flanges for shear lag

Allowance must be made for the shear lag effect on steel or concrete flanges, which can be addressed through rigorous analysis or by applying an effective width of the flange.

(2) The effects of shear lag in steel plate elements should be considered in accordance with

(3) The effective width of concrete flanges should be determined in accordance with the following provisions

In elastic global analysis, a uniform effective width can be assumed throughout each span This effective width is represented as \$b_{eff,1}\$ at the mid-span for spans supported at both ends, or as \$b_{eff,2}\$ at the support for cantilever spans.

At mid-span or an internal support, the total effective width $ b_{\text{eff}} $ can be calculated using the formula $ b_{\text{eff}} = b_0 + \sum b_{ei} $, where $ b_0 $ represents the distance between the centers of the outstand shear connectors The effective width $ b_{ei} $ of the concrete flange on each side of the web is taken as $ L_e/8 $, but it should not exceed the geometric width $ b_i $ The value $ b_i $ is defined as the distance from the outstand shear connector to a point midway between adjacent webs, measured at the mid-depth of the concrete flange; however, at a free edge, $ b_i $ is the distance to the free edge The length $ L_e $ is approximately the distance between points of zero bending moment For typical continuous composite beams, where the design is governed by a moment envelope from various load arrangements, and for cantilevers, $ L_e $ can be assumed as illustrated in the relevant figure.

The effective width at an end support can be calculated using the formula: \$b_{eff} = b_0 + \sum \beta_i b_{ei}\$, where \$\beta_i = (0.55 + 0.025 \frac{L_e}{b_{ei}}) \leq 1.0\$ In this context, \$b_{ei}\$ represents the effective width of the end span at mid-span, and \$L_e\$ denotes the equivalent span of the end span, as illustrated in Figure 5.1.

(7) The distribution of the effective width between supports and midspan regions may be assumed to be as shown in Figure 5.1

(8) Where in buildings the bending moment distribution is influenced by the resistance or the rotational stiffness of a joint, this should be considered in the determination of the length L e

( 9) For analysis of building structures, b 0 may be taken as zero and b i measured from the centre of the web

(1) Allowance should be made for the effects of cracking of concrete, creep and shrinkage of concrete, sequence of construction and pre-stressing

L /4 1 L /4 2 L /2 2 L /4 2 b eff,1 b eff,2 b eff,0 b eff,1 b eff,2

Figure 5.1 : Equivalent spans, for effective width of concrete flange

(1)P Appropriate allowance shall be made for the effects of creep and shrinkage of concrete

Creep effects can be considered for concrete members, except for those with both flanges composite, by utilizing modular ratios $ n_L $ These modular ratios vary based on the type of loading applied.

= n n L (5.6) where: n 0 is the modular ratio E a / E cm for short-term loading;

E cm is the secant modulus of elasticity of the concrete for short-term loading according to

According to EN 1992-1-1, the creep coefficient $ \phi(t,t_0) $ is defined in Table 3.1 or Table 11.3.1, and it varies based on the age of the concrete at the time of consideration (t) and the age at loading (t₀) The creep multiplier $ \psi_L $ is determined by the type of loading, with values set at 1.1 for permanent loads, 0.55 for primary and secondary effects of shrinkage, and 1.5 for prestressing due to imposed deformations.

For composite structures cast in multiple stages, a single mean value $ t_0 $ can be utilized to determine the creep coefficient for permanent loads This approach is also applicable for pre-stressing through imposed deformations, provided that the age of all concrete in the relevant spans exceeds 14 days at the time of pre-stressing.

(4) For shrinkage, the age at loading should generally be assumed to be one day

When utilizing prefabricated slabs or implementing pre-stressing of concrete slabs prior to the activation of shear connections, it is essential to apply the creep coefficient and shrinkage values from the moment the composite action becomes effective.

In continuous beams with mixed structures comprising both composite and non-composite spans, significant changes in the bending moment distribution at time $ t_0 $ due to creep must be taken into account This is particularly important for time-dependent secondary effects, except in global analyses for ultimate limit states where all cross-sections are classified as Class 1 or 2 For assessing these time-dependent effects, a creep multiplier $ \psi_L $ of 0.55 can be utilized to determine the modular ratio.

When analyzing the ultimate limit states of composite members with Class 1 or 2 cross-sections, the primary and secondary effects of concrete shrinkage and creep can often be disregarded, except in cases of fatigue However, for serviceability limit states, it is essential to refer to Section 7 for guidance.

(8) In regions where the concrete slab is assumed to be cracked, the primary effects due to shrinkage may be neglected in the calculation of secondary effects

(9) In composite columns and compression members, account should be taken of the effects of creep in accordance with 6.7.3.4(2)

(10) For double composite action with both flanges un-cracked (e.g in case of pre-stressing) the effects of creep and shrinkage should be determined by more accurate methods

For structures that meet the criteria of expressions (5.1) or 5.2.2(1), which are not primarily designed for storage and lack controlled pre-stressing, the impact of creep in composite beams can be addressed by substituting the concrete areas $ A_c $ with effective equivalent steel areas $ A_c/n $ This adjustment applies to both short-term and long-term loading scenarios, where $ n $ represents the nominal modular ratio linked to an effective modulus of elasticity for concrete, defined as $ E_{c,eff} = E_{cm}/2 $.

5.4.2.3 Effects of cracking of concrete

(1)P Appropriate allowance shall be made for the effects of cracking of concrete

To determine the effects of cracking in composite beams with concrete flanges, the internal forces and moments for characteristic combinations must be calculated, as outlined in EN 1990, 6.5.3 This calculation should include long-term effects and utilize the flexural stiffness $E_a I_1$ of the un-cracked sections, a process referred to as "un-cracked analysis."

In areas where the extreme fiber tensile stress in concrete surpasses twice the strength values $ f_{ctm} $ or $ f_{lctm} $ as outlined in EN1992-1-1, Table 3.1 or Table 11.3.1, it is necessary to reduce the stiffness to $ E_a I^2 $ according to section 1.5.2.12 This adjusted stiffness distribution can be applied for ultimate limit state considerations.

A cracked analysis involves re-evaluating the distribution of internal forces, moments, and deformations to assess limit states, including serviceability limit states This process is crucial for ensuring structural integrity and performance.

Classification of cross-sections

(1)P The classification system defined in EN 1993-1-1, 5.5.2 applies to cross-sections of composite beams

A composite section should be categorized based on the least favorable class of its steel elements under compression Typically, the classification of a composite section is influenced by the direction of the bending moment at that specific section.

(3) A steel compression element restrained by attaching it to a reinforced concrete element may be placed in a more favourable class, provided that the resulting improvement in performance has been established

For classification purposes, the plastic stress distribution is applicable, except at the boundary between Classes 3 and 4, where the elastic stress distribution must be considered, factoring in the construction sequence along with creep and shrinkage effects Design values of material strengths should be utilized, while tension in concrete should be disregarded Stress distribution should be assessed for the gross cross-section of the steel web and the effective flanges.

(5) For cross-sections in Class 1 and 2 with bars in tension, reinforcement used within the effective width should have a ductility Class B or C, see EN 1992-1-1, Table C.1 Additionally for a section

According to the guidelines set by BSI, a minimum area of reinforcement, denoted as A s, must be provided within the effective width of the concrete flange to meet the resistance moment requirements specified in sections 6.2.1.2, 6.2.1.3, or 6.2.1.4.

The effective area of the concrete flange is denoted as \$A_c\$, while \$f_y\$ represents the nominal yield strength of the structural steel measured in N/mm² Additionally, \$f_{sk}\$ indicates the characteristic yield strength of the reinforcement, and \$f_{ctm}\$ refers to the mean tensile strength of the concrete, as outlined in EN1992-1-1, Table 3.1.

11.3.1; k c is a coefficient given in 7.4.2; δ is equal to 1,0 for Class 2 cross-sections, and equal to 1,1 for Class 1 cross-sections at which plastic hinge rotation is required

Welded mesh must demonstrate adequate ductility when incorporated into a concrete slab to be considered part of the effective section; otherwise, it should be excluded to prevent potential fracturing.

(7) In global analysis for stages in construction, account should be taken of the class of the steel section at the stage considered

5.5.2 Classification of composite sections without concrete encasement

A steel compression flange can be classified as Class 1 when it is effectively attached to a concrete flange with shear connectors, provided that the spacing of these connectors complies with the requirements outlined in section 6.6.5.5.

The classification of steel flanges and webs in compression for composite beams without concrete encasement must adhere to EN 1993-1-1, Table 5.2 If an element does not meet the criteria for Class 3, it should be classified as Class 4.

(3) Cross-sections with webs in Class 3 and flanges in Classes 1 or 2 may be treated as an effective cross-section in Class 2 with an effective web in accordance with EN1993-1-1, 6.2.2.4

5.5.3 Classification of composite sections for buildings with concrete encasement

(1) A steel outstand flange of a composite section with concrete encasement in accordance with (2) below may be classified in accordance with Table 5.2

For a concrete encased section, the encasing concrete must be reinforced, mechanically connected to the steel section, and able to prevent buckling of both the web and any part of the compression flange towards the web These requirements can be considered satisfied if certain conditions are met.

The concrete encasing a web is reinforced with longitudinal bars, stirrups, or welded mesh, ensuring compliance with the ratio requirements specified in Table 5.2 The concrete between the flanges is securely attached to the web by welding stirrups or using bars of at least 6 mm diameter through holes or studs larger than 10 mm The longitudinal spacing of the studs or bars on each side of the web must not exceed 400 mm, and the distance from the inner face of each flange to the nearest row of fixings should be no more than 200 mm For steel sections with a depth of at least 400 mm and multiple rows of fixings, a staggered arrangement of studs or bars may be implemented.

(3) A steel web in Class 3 encased in concrete in accordance with (2) above may be represented by an effective web of the same cross-section in Class 2

Table 5.2 : Classification of steel flanges in compression for partially-encased sections

Ultimate limit states

Beams

Composite beams, as defined in section 1.5.2, typically feature cross-sections that include either a solid slab or a composite slab, as illustrated in Figure 6.1 Partially-encased beams consist of a steel section whose web is encased in reinforced concrete, with shear connections established between the concrete and steel components.

Figure 6.1 : Typical cross-sections of composite beams

The design resistances for composite cross-sections subjected to bending and vertical shear must be calculated according to section 6.2 for composite beams featuring steel sections, and section 6.3 for partially-encased composite beams.

(3)P Composite beams shall be checked for:

– resistance of critical cross-sections (6.2 and 6.3);

– resistance to lateral-torsional buckling (6.4);

– resistance to shear buckling (6.2.2.3) and transverse forces on webs (6.5);

– sections of maximum bending moment;

– sections subjected to concentrated loads or reactions;

– places where a sudden change of cross-section occurs, other than a change due to cracking of concrete.

(5) A cross-section with a sudden change should be considered as a critical cross-section when the ratio of the greater to the lesser resistance moment is greater than 1,2

To assess resistance to longitudinal shear, it is essential to identify a critical length that represents the interface between two critical cross-sections These critical cross-sections notably include the free ends of cantilevers.

In tapering members, it is essential to select sections such that the ratio of the greater to the lesser plastic resistance moments, when subjected to flexural bending in the same direction, for any pair of adjacent cross-sections does not exceed 1.5.

(7)P The concepts "full shear connection" and "partial shear connection" are applicable only to beams in which plastic theory is used for calculating bending resistances of critical cross-sections

A beam or cantilever exhibits full shear connection when adding more shear connectors does not enhance its design bending resistance; conversely, if additional connectors do improve resistance, the shear connection is considered partial.

Note: Limits to the use of partial shear connection are given in 6.6.1.2

6.1.2 Effective width for verification of cross-sections

The effective width of the concrete flange for cross-section verification must be determined as per section 5.4.1.2, considering the distribution of effective width between the supports and mid-span areas.

In the analysis of buildings, a constant effective width can be assumed for sagging bending across each span, using the mid-span value $ b_{\text{eff},1} $ Similarly, for hogging bending at intermediate supports, the effective width is represented by the value $ b_{\text{eff},2} $ at the respective support.

Resistances of cross-sections of beams

The design bending resistance should be assessed using rigid-plastic theory exclusively when the effective composite cross-section falls within Class 1 or Class 2, and in cases where pre-stressing with tendons is not applied.

(2) Elastic analysis and non-linear theory for bending resistance may be applied to cross-sections of any class

In elastic analysis and non-linear theory, it is assumed that the composite cross-section remains plane when the shear connection and transverse reinforcement are designed according to section 6.6, taking into account suitable distributions of the design longitudinal shear force.

(4)P The tensile strength of concrete shall be neglected

(5) Where the steel section of a composite member is curved in plan, the effects of curvature should be taken into account

6.2.1.2 Plastic resistance moment M pl,Rd of a composite cross-section

In calculating $ M_{pl,Rd} $, it is essential to assume full interaction among structural steel, reinforcement, and concrete The effective area of the structural steel member should be stressed to its design yield strength $ f_{yd} $ in both tension and compression Additionally, the effective areas of longitudinal reinforcement must be stressed to their design yield strength $ f_{sd} $ in tension or compression, with the option to neglect compression reinforcement in a concrete slab Furthermore, the effective area of concrete in compression is assumed to resist a constant stress of $ 0.85f_{cd} $ throughout the depth from the plastic neutral axis to the most compressed fiber of the concrete, where $ f_{cd} $ represents the design cylinder compressive strength of concrete.

Typical plastic stress distributions are shown in Figure 6.2 b eff

Figure 6.2 : Examples of plastic stress distributions for a composite beam with a solid slab and full shear connection in sagging and hogging bending

For composite cross-sections made of structural steel grades S420 or S460, if the distance $ x_{pl} $ between the plastic neutral axis and the extreme fibre of the concrete slab in compression exceeds 15% of the overall depth $ h $, the design resistance moment $ M_{Rd} $ should be calculated as $ \beta M_{pl,Rd} $, where $ \beta $ is the reduction factor illustrated in Figure 6.3 Additionally, for $ x_{pl}/h $ values greater than 0.4, the bending resistance must be determined according to sections 6.2.1.4 or 6.2.1.5.

(3) Where plastic theory is used and reinforcement is in tension, that reinforcement should be in accordance with 5.5.1(5)

(4)P For buildings, profiled steel sheeting in compression shall be neglected

(5) For buildings, any profiled steel sheeting in tension included within the effective section should be assumed to be stressed to its design yield strength f yp,d

Figure 6.3 : Reduction factor β for M pl,Rd

6.2.1.3 Plastic resistance moment of sections with partial shear connection in buildings

(1) In regions of sagging bending, partial shear connection in accordance with 6.6.1 and 6.6.2.2 may be used in composite beams for buildings

The plastic resistance moment for hogging bending must be determined as per section 6.2.1.2, unless verified otherwise, and adequate shear connections should be implemented to guarantee the yielding of tension reinforcement.

Figure 6.4 : Plastic stress distribution under sagging bending for partial shear connection

In the presence of ductile shear connectors, the resistance moment of the beam's critical cross-section, denoted as $ M_{Rd} $, can be calculated using rigid plastic theory as outlined in section 6.2.1.2 However, it is essential to apply a reduced compressive force in the concrete flange, $ N_c $, instead of the force $ N_{cf} $ specified in 6.2.1.2(1)(d) The shear connection degree is represented by the ratio $ \eta = \frac{N_c}{N_{c,f}} $ Additionally, the position of the plastic neutral axis in the slab must be determined using the new force $ N_c $, as illustrated in Figure 6.4 Furthermore, a second plastic neutral axis exists within the steel section, which is crucial for classifying the web.

Figure 6.5 : Relation between M Rd and N c (for ductile shear connectors)

(4) The relation between M Rd and N c in (3) is qualitatively given by the convex curve ABC in

Figure 6.5 illustrates the design plastic resistances for sagging bending, denoted as \$M_{pl,a,Rd}\$ for the structural steel section alone and \$M_{pl,Rd}\$ for the composite section with full shear connection.

(5) For the method given in (3), a conservative value of M Rd may be determined by the straight line

Rd c a, pl, Rd pl, Rd a, pl,

6.2.1.4 Non-linear resistance to bending

(1)P Where the bending resistance of a composite cross-section is determined by non-linear theory, the stress-strain relationships of the materials shall be taken into account

The composite cross-section is assumed to remain plane, with the strain in bonded reinforcement, whether under tension or compression, matching the mean strain of the surrounding concrete.

(3) The stresses in the concrete in compression should be derived from the stress-strain curves given in EN 1992-1-1, 3.1.7

(4) The stresses in the reinforcement should be derived from the bi-linear diagrams given in EN

The stresses in structural steel, whether in compression or tension, must be determined using the bi-linear diagram outlined in EN 1993-1-1, section 5.4.3(4) It is essential to consider the construction method, such as whether the structure is propped or un-propped, when calculating these stresses.

For Class 1 and Class 2 composite cross-sections with the concrete flange under compression, the non-linear bending resistance, denoted as M$_{Rd}$, can be calculated based on the compressive force in the concrete, N$_c$ This can be achieved using the simplified expressions provided in equations (6.2) and (6.3), as illustrated in Figure 6.6.

M = + − for N c ≤ N c, el (6.2) el c, f c, el c, c Rd el, Rd pl, Rd el,

M el,Rd = M a,Ed + k M c,Ed (6.4) where:

M a,Ed is the design bending moment applied to the structural steel section before composite behaviour;

The design bending moment applied to the composite section is represented by $ M_c $, while $ k $ denotes the minimum factor required to meet the stress limit specified in section 6.2.1.5(2) Additionally, when utilizing un-propped construction, it is essential to consider the construction sequence.

Licensed Copy: Puan Ms Norhayati, Petroliam Nasional Berhad, Tue Oct 04 01:42:46 BST 2005, Uncontrolled Copy, (c) BSI el ,

N c is the compressive force in the concrete flange corresponding to moment M el,Rd

For cross sections where 6.2.1.2 (2) applies, in expression (6.3) and in Figure 6.6 instead of M pl,Rd the reduced value β M pl,Rd should be used

(7) For buildings, the determination of M el.Rd may be simplified using 5.4.2.2(11)

Figure 6.6 : Simplified relationship between M Rd and N c for sections with the concrete slab in compression 6.2.1.5 Elastic resistance to bending

Stresses must be determined using elastic theory, applying the effective width of the concrete flange as specified in section 6.1.2 For Class 4 cross-sections, the effective structural steel section should be calculated according to EN 1993-1-5, section 4.3.

(2) In the calculation of the elastic resistance to bending based on the effective cross-section, the limiting stresses should be taken as:

– f cd in concrete in compression;

– f yd in structural steel in tension or compression;

– f sd in reinforcement in tension or compression Alternatively, reinforcement in compression in a concrete slab may be neglected

(3)P Stresses due to actions on the structural steelwork alone shall be added to stresses due to actions on the composite member.

(4) Unless a more precise method is used, the effect of creep should be taken into account by use of a modular ratio according to 5.4.2.2

(5) In cross-sections with concrete in tension and assumed to be cracked, the stresses due to primary

(isostatic) effects of shrinkage may be neglected

(1) Clause 6.2.2 applies to composite beams with a rolled or welded structural steel section with a solid web, which may be stiffened

6.2.2.2 Plastic resistance to vertical shear

The resistance to vertical shear, denoted as \$V_{pl, Rd}\$, should be considered as the resistance of the structural steel section \$V_{pl, a, Rd}\$, unless a contribution from the reinforced concrete portion of the beam has been determined.

(2) The design plastic shear resistance V pl,a,Rd of the structural steel section should be determined in accordance with EN 1993-1-1, 6.2.6

(1) The shear buckling resistance V b,Rd of an uncased steel web should be determined in accordance with EN 1993-1-5, 5

Contributions from the concrete slab should not be considered unless a more accurate method than EN 1993-1-5 is employed, and the shear connection is specifically designed to accommodate the relevant vertical force.

When the vertical shear force \$V_{Ed}\$ surpasses half of the shear resistance, represented by either \$V_{pl,Rd}\$ in section 6.2.2.2 or \$V_{b,Rd}\$ in section 6.2.2.3, it is essential to consider its impact on the resistance moment.

Resistance of cross-sections of beams for buildings with partial encasement

Partially-encased beams, as defined in section 6.1.1(1), can include a concrete or composite slab as part of their effective section, given that it is connected to the steel section through a shear connection in accordance with section 6.6 Typical cross-sections of these beams are illustrated in Figure 6.8.

(2) Clause 6.3 is applicable to partially encased sections in Class 1 or Class 2, provided that d/t w is not greater than 124ε b c c w b d t b b

Figure 6.8 : Typical cross-sections of partially-encased beams

(3) The provisions elsewhere in EN 1994-1-1 are applicable, unless different rules are given in 6.3

(1) Full shear connection should be provided between the structural steel section and the web encasement in accordance with 6.6.

The design resistance moment can be calculated using plastic theory, where the reinforcement in compression within the concrete encasement can be disregarded Typical plastic stress distributions are illustrated in Figure 6.9.

(3) Partial shear connection may be used for the compressive force in any concrete or composite slab forming part of the effective section.

When utilizing partial shear connections with ductile connectors, the plastic resistance moment of the beam must be determined following sections 6.3.2(2) and 6.2.1.2(1) However, it is important to apply a reduced value for the compressive force in the concrete or composite slab, as specified in section 6.2.1.3(3).

(4) and (5) pl pl pl sd f yd f sd f f yd f sd

Figure 6.9 : Examples of plastic stress distributions for effective sections

(1) The design shear resistance of the structural steel section V pl,a,Rd should be determined by plastic theory in accordance with 6.2.2.2(2)

The design shear resistance of a cross-section can incorporate the contribution of the web encasement when stirrups are utilized, as illustrated in Figure 6.10 It is essential to ensure proper shear connection between the encasement and the structural steel section If the stirrups are open, they must be securely attached to the web using full strength welds; otherwise, the shear reinforcement's contribution should be disregarded.

The total vertical shear \$V_{Ed}\$ can be distributed into two parts, \$V_{a,Ed}\$ and \$V_{c,Ed}\$, which correspond to the steel section and the reinforced concrete web encasement, respectively This distribution can be assumed to follow the same ratio as the contributions of the steel section and the reinforced web encasement to the bending resistance \$M_{pl,Rd}\$, unless a more precise analysis is conducted.

The vertical shear resistance of the web encasement must consider potential concrete cracking and should be validated according to EN 1992-1-1, section 6.2, along with other applicable design criteria from that standard.

2 open stirrups welded to the web

Figure 6.10 : Arrangement of stirrups 6.3.4 Bending and vertical shear

When the design vertical shear force \$V_{a,Ed}\$ surpasses half of the design plastic resistance \$V_{pl,a,Rd}\$ of the structural steel section, it is essential to consider its impact on the resistance moment.

The impact of vertical shear on bending resistance can be modified as outlined in section 6.2.2.4(2) Specifically, in expression (6.5), the ratio \$V_{Ed}/V_{pl,Rd}\$ is substituted with \$V_{a,Ed}/V_{pl,a,Rd\$ to determine the reduced design steel strength in the shear region of the structural steel section Subsequently, the design reduced plastic resistance moment \$M_{Rd}\$ should be calculated following the guidelines in section 6.3.2.

Lateral-torsional buckling of composite beams

A steel flange connected to a concrete or composite slab through shear connection, as outlined in section 6.6, can be considered laterally stable if measures are taken to prevent lateral instability of the concrete slab.

(2) All other steel flanges in compression should be checked for lateral stability

The methods outlined in EN 1993-1-1, specifically sections 6.3.2.1 to 6.3.2.3 and more broadly 6.3.4, are applicable to the steel section based on the cross-sectional forces of the composite section These methods consider the effects of construction sequence as per section 5.4.2.4, and they also account for lateral and elastic torsional restraint at the shear connection level to the concrete slab.

(4) For composite beams in buildings with cross-sections in Class 1, 2 or 3 and of uniform structural steel section, the method given in 6.4.2 may be used

6.4.2 Verification of lateral-torsional buckling of continuous composite beams with cross- sections in Class 1, 2 and 3 for buildings

(1) The design buckling resistance moment of a laterally unrestrained continuous composite beam

(or a beam within a frame that is composite throughout its length) with Class 1, 2 or 3 cross- sections and with a uniform structural steel section should be taken as:

M = χ (6.6) where: χ LT is the reduction factor for lateral-torsional buckling depending on the relative slenderness λLT;

M Rd is the design resistance moment under hogging bending at the relevant internal support

(or beam-to-column joint)

Values of the reduction factor χ LT may be obtained from EN 1993-1-1, 6.3.2.2 or 6.3.2.3

For Class 1 or 2 cross-sections, the design moment resistance (M Rd) should be calculated based on the applicable theory: use section 6.2.1.2 for plastic theory, section 6.2.1.4 for non-linear theory, or section 6.3.2 for partially-encased beams The yield strength (f yd) must be determined using the partial factor γM1 as specified in EN 1993-1-1, section 6.1(1).

For Class 3 cross-sections, the design moment resistance, M Rd, is calculated using expression (6.4) This calculation considers the smaller value between the tensile stress, f sd, in the reinforcement and the compression stress, f yd, in the extreme bottom fiber of the steel section The value of f yd is determined using the partial factor γM1 as specified in EN 1993-1-1, section 6.1(1).

(4) The relative slenderness λLT may be calculated by: λLT cr

M Rk is the resistance moment of the composite section using the characteristic material properties;

M cr is the elastic critical moment for lateral-torsional buckling determined at the internal support of the relevant span where the hogging bending moment is greatest

When a slab is connected to one or more supporting steel members that are approximately parallel to the composite beam, and the conditions outlined in 6.4.3(c), (e), and (f) are met, the elastic critical moment $ M_{cr} $ can be calculated using the "continuous inverted U-frame" model This model, illustrated in Figure 6.11, considers the lateral displacement of the bottom flange, which leads to bending of the steel web, as well as the rotation of the top flange that is countered by the bending of the slab.

Figure 6.11 : Inverted-U frame ABCD resisting lateral-torsional buckling

(6) At the level of the top steel flange, a rotational stiffness k s per unit length of steel beam may be adopted to represent the U-frame model by a beam alone:

The flexural stiffness of the cracked concrete or composite slab, denoted as $ k_1 $, is calculated using the formula $ k_1 = \alpha \frac{(EI)^2}{a} $ Here, $ \alpha $ takes the value of 2 for edge beams, regardless of whether they have a cantilever, and 3 for inner beams In cases where there are four or more similar inner beams in a floor, $ \alpha $ can be set to 4 The variable $ a $ represents the spacing between the parallel beams.

The flexural stiffness per unit width of the concrete or composite slab, denoted as $EI$ 2, is determined by the lower value between the mid-span for sagging bending and the supporting steel section for hogging bending Additionally, $k$ 2 represents the flexural stiffness of the steel web.

= − (6.10) for an uncased steel beam, where : νa is Poisson’s ratio for structural steel and h s and t w are defined in Figure 6.11

(7) For a steel beam with partial encasement in accordance with 5.5.3(2), the flexural stiffness k 2 may take account of the encasement and be calculated by:

= + (6.11) where: n is the modular ratio for long-term effects according to 5.4.2.2, and b c is the width of the concrete encasement, see Figure 6.8

(8) In the U-frame model, the favourable effect of the St Venant torsional stiffness G a I at of the steel section may be taken into account for the calculation of M cr

For a partially-encased steel beam, the torsional stiffness of the encasement, whether reinforced with open or closed stirrups, can be incorporated into the steel section's value of \$G_a I_a\$ This additional stiffness is calculated as \$\frac{G_c I_{ct}}{10}\$, where \$G_c\$ represents the shear modulus of concrete, approximated as \$0.3E_a/n\$ (with \$n\$ being the modular ratio for long-term effects), and \$I_{ct}\$ is the St Venant torsion constant of the encasement, assumed to be un-cracked and matching the overall width of the encasement.

6.4.3 Simplified verification for buildings without direct calculation

A continuous beam with Class 1, 2, or 3 cross-sections can be designed without additional lateral bracing if specific conditions are met: adjacent spans must not differ in length by more than 20% of the shorter span, and cantilever lengths should not exceed 15% of the adjacent span The loading on each span must be uniformly distributed, with the design permanent load exceeding 40% of the total design load The top flange of the steel member should be connected to a reinforced concrete or composite slab using shear connectors, and this slab must also be attached to another supporting member to form an inverted-U frame If the slab is composite, it should span between the two supporting members of the inverted-U frame Each support of the steel member must provide lateral restraint for the bottom flange and stiffening for the web, which may remain un-stiffened elsewhere For IPE or non-partially encased HE sections, the depth must not exceed the limits specified in Table 6.1, while partially encased sections must not exceed these limits by more than 200 mm for steel grades up to S355, and by 150 mm for grades S420 and S460.

Note: Provisions for other types of steel section may be given in the National Annex

Table 6.1 : Maximum depth h (mm) of uncased steel member for which clause 6.4.3 is applicable

Nominal steel grade Steel member

Transverse forces on webs

The guidelines outlined in EN 1993-1-5, sections 5 and 6, for calculating the design resistance of both unstiffened and stiffened webs under transverse forces applied via a flange, are relevant to the non-composite steel flange of a composite beam and its adjacent web area.

(2) If the transverse force acts in combination with bending and axial force, the resistance should be verified according to EN 1993-1-5, 7.2

For buildings, transverse stiffening is required for beams with an effective web in Class 2, as per section 5.5.2(3), unless it is confirmed that the un-stiffened web can adequately resist crippling and buckling.

6.5.2 Flange-induced buckling of webs

According to EN 1993-1-5, section 8, the area $ A_{fc} $ should be defined as either the area of the non-composite steel flange or the transformed area of the composite steel flange, considering the modular ratio for short-term loading, with the smaller value being used.

Shear connection

(1) Clause 6.6 is applicable to composite beams and, as appropriate, to other types of composite member

Shear connections and transverse reinforcement are essential for effectively transferring longitudinal shear forces between concrete and structural steel elements, disregarding the influence of natural bonding between the two materials.

(3)P Shear connectors shall have sufficient deformation capacity to justify any inelastic redistribution of shear assumed in design

(4)P Ductile connectors are those with sufficient deformation capacity to justify the assumption of ideal plastic behaviour of the shear connection in the structure considered

(5) A connector may be taken as ductile if the characteristic slip capacity δuk is at least 6mm

Note: An evaluation of δ uk is given in Annex B

When multiple types of shear connections are utilized within the same span of a beam, it is essential to consider the notable differences in their load-slip characteristics.

(7)P Shear connectors shall be capable of preventing separation of the concrete element from the steel element, except where separation is prevented by other means

To prevent slab separation, shear connectors must be designed to withstand a nominal ultimate tensile force, perpendicular to the steel flange, of at least 0.1 times the design ultimate shear resistance of the connectors If needed, anchoring devices should be added for additional support.

(9) Headed stud shear connectors in accordance with 6.6.5.7 may be assumed to provide sufficient resistance to uplift, unless the shear connection is subjected to direct tension

(10)P Longitudinal shear failure and splitting of the concrete slab due to concentrated forces applied by the connectors shall be prevented

(11) If the detailing of the shear connection is in accordance with the appropriate provisions of 6.6.5 and the transverse reinforcement is in accordance with 6.6.6, compliance with 6.6.1.1(10) may be assumed

When using a method of interconnection other than the shear connectors specified in section 6.6 to transfer shear between steel and concrete elements, the design behavior should be informed by testing and a conceptual model Additionally, the design of the composite member should align with that of a similar member utilizing the shear connectors outlined in section 6.6, to the extent that it is feasible.

For buildings, the minimum number of connectors must equal the total design shear force for the ultimate limit state, as specified in section 6.6.2, divided by the design resistance of a single connector, denoted as PRd The design resistance for stud connectors should be calculated in accordance with sections 6.6.3 or 6.6.4, as applicable.

In buildings where all cross-sections are classified as Class 1 or Class 2, partial shear connection can be utilized for beams The required number of connectors should be established based on partial connection theory, which considers the deformation capacity of the shear connectors.

6.6.1.2 Limitation on the use of partial shear connection in beams for buildings

Headed studs, with a post-welding length at least four times their diameter and a nominal shank diameter between 16 mm and 25 mm, can be classified as ductile This classification is applicable within specific limits for the degree of shear connection, represented by the ratio $ \eta = \frac{n}{n_f} $.

For steel sections with equal flanges:

For steel sections having a bottom flange with an area equal to three times the area of the top flange:

L e is the distance in sagging bending between points of zero bending moment in metres; for typical continuous beams, L e may be assumed to be as shown in Figure 5.1;

In accordance with sections 6.6.1.1(13) and 6.6.2.2(2), the variable \$nf\$ represents the number of connectors required for a full shear connection over a specified beam length, while \$n\$ denotes the actual number of shear connectors installed within that same length.

For steel sections where the bottom flange area is greater than the top flange area but less than three times that area, the limit for η can be calculated using linear interpolation based on expressions (6.12) to (6.15).

(3) Headed stud connectors may be considered as ductile over a wider range of spans than given in

The studs must have a minimum overall length of 76 mm after welding, with a nominal shank diameter of 19 mm Additionally, the steel section should be a rolled or welded I or H shape featuring equal flanges.

(c) the concrete slab is composite with profiled steel sheeting that spans perpendicular to the beam and the concrete ribs are continuous across it,

Each rib of sheeting is supported by a single stud, positioned either centrally or alternately on the left and right sides along the span For sheeting where the ratio $ b_0 / h_p \geq 2 $ and $ h_p \leq 60 $ mm, the force $ N_c $ is determined using the simplified method outlined in Figure 6.5 Under these conditions, the ratio $ \eta $ must also be satisfied.

Note: The requirements in 6.6.1.2 are derived for uniform spacing of shear connectors

6.6.1.3 Spacing of shear connectors in beams for buildings

Shear connectors must be strategically spaced along the beam to effectively transmit longitudinal shear and prevent separation between the concrete and the steel beam, while also considering a suitable distribution of the design longitudinal shear force.

(2) In cantilevers and hogging moment regions of continuous beams, tension reinforcement should be curtailed to suit the spacing of the shear connectors and should be adequately anchored

(3) Ductile connectors may be spaced uniformly over a length between adjacent critical cross- sections as defined in 6.1.1 provided that:

– all critical sections in the span considered are in Class 1 or Class 2,

– η satisfies the limit given by 6.6.1.2 and

– the plastic resistance moment of the composite section does not exceed 2,5 times the plastic resistance moment of the steel member alone

When the plastic resistance moment is more than 2.5 times that of the steel member alone, it is essential to conduct further evaluations of the shear connection's adequacy at intermediate points, roughly halfway between adjacent critical cross-sections.

The distribution of shear connectors should be placed between the maximum sagging bending moment and the nearest support or maximum hogging moment, based on the longitudinal shear determined by elastic theory for the specific loading conditions.

Where this is done, no additional checks on the adequacy of the shear connection are required

6.6.2 Longitudinal shear force in beams for buildings

6.6.2.1 Beams in which non-linear or elastic theory is used for resistances of one or more cross- sections

(1) If non-linear or elastic theory is applied to cross-sections, the longitudinal shear force should be determined in a manner consistent with 6.2.1.4 or 6.2.1.5 respectively

6.6.2.2 Beams in which plastic theory is used for resistance of cross sections

The total design longitudinal shear must be calculated in alignment with the design bending resistance, considering the variations in normal force within concrete or structural steel across a critical length.

(2) For full shear connection, reference should be made to 6.2.1.2, or 6.3.2, as appropriate

(3) For partial shear connection, reference should be made to 6.2.1.3 or 6.3.2, as appropriate

6.6.3 Headed stud connectors in solid slabs and concrete encasement

(1) The design shear resistance of a headed stud automatically welded in accordance with EN 14555 should be determined from:

Composite columns and composite compression members

Clause 6.7 is relevant for the design of composite columns and compression members, including concrete-encased sections, partially encased sections, and concrete-filled rectangular and circular tubes, as illustrated in Figure 6.17.

Licensed Copy: Puan Ms Norhayati, Petroliam Nasional Berhad, Tue Oct 04 01:42:46 BST 2005, Uncontrolled Copy, (c) BSI y z c z t f h c z h c c y c y b c b t w y z t f h = h c b = b c t w y z t f h = h c b c b t w

Figure 6.17 : Typical cross-sections of composite columns and notation

(2)P This clause applies to columns and compression members with steel grades S235 to S460 and normal weight concrete of strength classes C20/25 to C50/60

(3) This clause applies to isolated columns and columns and composite compression members in framed structures where the other structural members are either composite or steel members

(4) The steel contribution ratio δ should fulfil the following condition:

(5) Composite columns or compression members of any cross-section should be checked for:

– resistance of the member in accordance with 6.7.2 or 6.7.3,

– resistance to local buckling in accordance with (8) and (9) below,

– introduction of loads in accordance with 6.7.4.2 and

– resistance to shear between steel and concrete elements in accordance with 6.7.4.3

(6) Two methods of design are given:

– a general method in 6.7.2 whose scope includes members with non-symmetrical or non- uniform cross-sections over the column length and

– a simplified method in 6.7.3 for members of doubly symmetrical and uniform cross section over the member length

For composite compression members experiencing bending moments and normal forces from independent actions, it is recommended to reduce the partial factor γF for internal forces that enhance resistance by 20%.

(8)P The influence of local buckling of the steel section on the resistance shall be considered in design

Local buckling effects can be disregarded for a fully encased steel section as per 6.7.5.1(2), and for other cross-section types, provided that the maximum values specified in Table 6.3 are not surpassed.

Table 6.3 : Maximum values ( d/t ), ( h/t ) and ( b/t f ) with f y in N/mm 2

Cross-section Max (d/t), max (h/t) and max (b/t)

44 ) ( max f 6.7.2 General method of design

Structural stability design must consider second-order effects such as residual stresses, geometric imperfections, local instability, concrete cracking, creep and shrinkage of concrete, and yielding of both structural steel and reinforcement It is essential to ensure that instability is avoided under the most unfavorable combination of actions at the ultimate limit state.

Ms Norhayati from Petroliam Nasional Berhad emphasizes that the resistance of individual cross-sections must not be exceeded when subjected to bending, longitudinal force, and shear, as stated in the licensed copy from BSI dated October 4, 2005.

(2)P Second-order effects shall be considered in any direction in which failure might occur, if they affect the structural stability significantly

(3)P Internal forces shall be determined by elasto-plastic analysis

(4) Plane sections may be assumed to remain plane Full composite action up to failure may be assumed between the steel and concrete components of the member

(5)P The tensile strength of concrete shall be neglected The influence of tension stiffening of concrete between cracks on the flexural stiffness may be taken into account

(6)P Shrinkage and creep effects shall be considered if they are likely to reduce the structural stability significantly

Creep and shrinkage effects can be disregarded if the increase in first-order bending moments caused by creep deformations and longitudinal forces from permanent loads does not exceed 10%.

(8) The following stress-strain relationships should be used in the non-linear analysis :

– for concrete in compression as given in EN 1992-1-1, 3.1.5;

– for reinforcing steel as given in EN 1992-1-1, 3.2.7;

– for structural steel as given in EN 1993-1-1, 5.4.3(4)

(9) For simplification, instead of the effect of residual stresses and geometrical imperfections, equivalent initial bow imperfections (member imperfections) may be used in accordance with Table

This simplified method is applicable only to members with a doubly symmetrical and uniform cross-section throughout their length, specifically for rolled, cold-formed, or welded steel sections It cannot be used for structural steel components that consist of two or more unconnected sections Additionally, the relative slenderness λ, as defined in section 6.7.3.3, must meet specific conditions.

(2) For a fully encased steel section, see Figure 6.17a, limits to the maximum thickness of concrete cover that may be used in calculation are: max c z = 0,3h max c y = 0,4 b (6.29)

(3) The longitudinal reinforcement that may be used in calculation should not exceed 6% of the concrete area

(4) The ratio of the depth to the width of the composite cross-section should be within the limits 0,2 and 5,0

(1) The plastic resistance to compression N pl,Rd of a composite cross-section should be calculated by adding the plastic resistances of its components: sd s cd c yd

Expression (6.30) applies for concrete encased and partially concrete encased steel sections For concrete filled sections the coefficient 0,85 may be replaced by 1,0

The resistance of a cross-section to combined compression and bending can be determined using rectangular stress blocks, as illustrated in Figure 6.18 This calculation incorporates the design shear force $ V_{Ed} $ as per equation (3), while the tensile strength of the concrete is disregarded.

N Ed pl, N, Rd f sd M f sd f yd

Figure 6.18 : Interaction curve for combined compression and uniaxial bending

When assessing the interaction curve, it is crucial to consider the impact of transverse shear forces on bending resistance and normal force This is particularly important if the shear force \$V_{a,Ed}\$ on the steel section surpasses 50% of the design shear resistance \$V_{pl,a,Rd}\$ of the section, as outlined in section 6.2.2.

Where V a,Ed > 0,5V pl,a,Rd , the influence of the transverse shear on the resistance in combined bending and compression should be taken into account by a reduced design steel strength (1 - ρ) f yd in the shear area A v in accordance with 6.2.2.4(2) and Figure 6.18

The shear force \$V_{a,Ed}\$ must not surpass the shear resistance of the steel section as specified in section 6.2.2 Additionally, the shear resistance \$V_{c,Ed}\$ of the reinforced concrete component should be validated in accordance with EN 1992-1-1, section 6.

(4) Unless a more accurate analysis is used, V Ed may be distributed into V a,Ed acting on the structural steel and V c,Ed acting on the reinforced concrete section by :

M pl,a,Rd is the plastic resistance moment of the steel section and

M pl,Rd is the plastic resistance moment of the composite section

For simplification V Ed may be assumed to act on the structural steel section alone

The interaction curve can be simplified using a polygonal diagram, as illustrated by the dashed line in Figure 6.19 This figure exemplifies the plastic stress distribution across a fully encased cross section from points A to D For concrete encased and partially concrete encased sections, the value of \$N_{pm,Rd}\$ should be considered as \$0.85 f_{cd} A_{c}\$, while for concrete filled sections, it should be taken as \$f_{cd} A_{c}\$, as shown in Figures 6.17(a) to (c) and Figures 6.17(d) to (f), respectively.

B sd pl,Rd pl,Rd n 2h f f

D 0,85 f cd f yd f sd pm,Rd

Figure 6.19 : Simplified interaction curve and corresponding stress distributions

For circular concrete-filled tubes, the strength increase due to confinement can be considered if the relative slenderness ratio, λ, is less than or equal to 0.5 and the eccentricity of loading, e, is less than 0.1 times the external diameter, d The plastic resistance to compression can be determined using the specified formula.

= η η (6.33) where: t is the wall thickness of the steel tube

For members with e = 0 the values ηa = ηao and ηc = ηco are given by the following expressions: ηao = 0,25 (3 + 2λ) (but ≤ 1,0) (6.34) ηco = 4,9 – 18,5λ + 17λ 2 (but ≥ 0) (6.35)

For members in combined compression and bending with 0 < e/d ≤ 0,1, the values ηa and ηc should be determined from (6.36) and (6.37), where ηao and ηco are given by (6.34) and (6.35): ηa = ηao + (1 – ηao) (10 e/d) (6.36) ηc = ηco (1 – 10 e/d) (6.37)

6.7.3.3 Effective flexural stiffness, steel contribution ratio and relative slenderness

(1) The steel contribution ratio δ is defined as:

N pl,Rd is the plastic resistance to compression defined in 6.7.3.2(1)

(2) The relative slenderness λfor the plane of bending being considered is given by: cr

N pl,Rk is the characteristic value of the plastic resistance to compression given by (6.30) if, instead of the design strengths, the characteristic values are used;

N cr is the elastic critical normal force for the relevant buckling mode, calculated with the effective flexural stiffness (EI)eff determined in accordance with (3) and (4)

To determine the relative slenderness \$\lambda\$ and the elastic critical force \$N_{cr}\$, it is essential to calculate the characteristic value of the effective flexural stiffness \$(EI)_{eff}\$ for the cross section of a composite column.

K e is a correction factor that should be taken as 0,6

I a, I c, and I s are the second moments of area of the structural steel section, the un-cracked concrete section and the reinforcement for the bending plane being considered

Consideration must be given to the long-term effects on the effective elastic flexural stiffness The modulus of elasticity of concrete, denoted as \$E_{cm}\$, should be adjusted to the effective value \$E_{c,eff}\$ using the following formula: \$E_{c,eff} = E_{cm} \cdot (1 - G) / (1 + G)\$.

E = + (6.41) where: ϕ is the creep coefficient according to 5.4.2.2(2);

N Ed is the total design normal force;

N G,Ed is the part of this normal force that is permanent

6.7.3.4 Methods of analysis and member imperfections

(1) For member verification, analysis should be based on second-order linear elastic analysis

(2) For the determination of the internal forces the design value of effective flexural stiffness

(EI)eff,II should be determined from the following expression:

(EI eff, II = K o E a I a + E s I s + K e, II E cm I c (6.42) where:

K e,II is a correction factor which should be taken as 0,5;

K o is a calibration factor which should be taken as 0,9

Long-term effects should be taken into account in accordance with 6.7.3.3 (4)

(3) Second-order effects need not to be considered where 5.2.1(3) applies and the elastic critical load is determined with the flexural stiffness (EI)eff,II in accordance with (2)

Serviceability limit states

Composite joints in frames for buildings

Composite slabs with profiled steel sheeting for buildings

Tiêu đề	Eurocode 4: Design of composite steel and concrete structures — Part 1-1: General rules and rules for buildings
Người hướng dẫn	Puan Ms. Norhayati
Trường học	British Standards Institution
Chuyên ngành	Engineering
Thể loại	British standard
Năm xuất bản	2005
Thành phố	London

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