W 1 single-storey steel-frames_structures

Poznan University of Technology

Institute of Structural Engineering

Section 3Single-storey steel frames structures

1. Crawley S.W., Dillon R.M., Steel Buildings: Analysis and Design, 4th Edition, John Wiley & Sons, 2008.

2. Davison B., Owens G.W., Steel Designers’ Manual, 6th Edition, Blackwell, 2008. 3. Galambos T.V, Surovek A.E., Structural Stability of Steel: Concepts and

Applications for Structural Engineers, John Wiley & Sons, 20084. Geschwindner L.F., Unified Design of Steel Structures, 1st Edition, John Wiley &

Sons, 2008.5. Lawrence M., Structural Design of Steelwork to EN 1993 and 1994, Elsevier, 2007.6. Nageim H.A., MacGinley T.J., Steel Structures: Practical Design Studies,

Balkema, 2005.7. Trahair S., Bradford M.A., Nethercot D.A., L. Gardner, The Behaviour and Design

of Steel Structures to EC3, Balkema, 2007. 8. G.W. Owens; P.R. Knowles, STEEL DESIGNERS MANUAL 5TH EDITION.

Blackwell Science 1994 9. J. Bródka, M. Broniewicz, PROJEKTOWANIE KONSTRUKCJI STALOWYCH

ZGODNIE Z EUROKODAMI 3-1-1 WRAZ Z PRZYKŁADAMI OBLICZEŃ.Wydawnictwo Politechniki Białostockiej, Białystok 2001

10. R.L. Brockenbrough, STRUCTURAL STEEL DESIGNER’S HANDBOOK. McGraw-Hill, Inc, USA 1999

Bibliography

Bibliography

1. Eurocode: Basis of structural design.

2. Eurocode 1: Actions on structures.3. Eurocode 1: Actions on structures – Part 1-1: General actions -Densities, self-weight,

imposed loads for buildings.4. Eurocode 1: Actions on structures – Part 1-2: General actions – Actions on structures

exposed to fire.5. Eurocode 1: Actions on structures – Part 1-3: General actions – Snow Loads.6. Eurocode 1: Actions on structures – Part 1-4: General actions – Wind Loads. 7. Eurocode 1: Actions on structures – Part 1-5: General actions – Thermal action. 8. Eurocode 1: Actions on structures – Part 1-6: General action – Actions during

execution.9. Eurocode 1: Actions on structures – Part 1-7: General action – Accidental action.10. Eurocode 1: Actions on structures – Part 3: Actions induced by cranes and machinery

Bibliography1.Eurocode 3: Design of steel structures. 2.Eurocode 3: Design of steel structures – Part 1.1: General rules and rules for

buildings.Eurocode 3: Design of steel structures – Part 1.2: General rules – Structural fire design.

3.Eurocode 3: Design of steel structures – Part 1.3: General rules – Supplementary rules for cold formed members and sheeting.

4.Eurocode 3: Design of steel structures – Part 1.4: General rules – Supplementary rules for stainless steels.

5.Eurocode 3: Design of steel structures – Part 1.5: Plated structural elements (in-plane loaded).6.Eurocode 3: Design of steel structures – Part 1.6: Strength and stability of shells.7.Eurocode 3: Design of steel structures – Part 1.7: Plated structural elements (transversely

loaded).8.Eurocode 3: Design of steel structures – Part 1.8: Design of joints.9.urocode 3: Design of steel structures – Part 1.9: Fatigue. 10.Eurocode 3: Design of steel structures – Part 1.10: Material toughness and through-thickness

properties.11.Eurocode 3: Design of steel structures – Part 1.11: Design of structures with tension

elements.12.Eurocode 3: Design of steel structures – Part 3.1: Towers and masts.13.Eurocode 3: Design of steel structures – Part 3.6: Crane supporting structures.

Lecture outline� Structural forms of steel frames

� Elements of the single-storey structure � cladding systems, secondary elements, main steel frames

� Structural actions and transmission of loading� Action on single-storey structures

� permanent actions (G), variable actions (Q), accidental actions (A), design values of actions

� General rules of static calculation and design limit states� Design situations

� basis of structural design according to Eurocode EN 1990, limit state design

� Verification of the limit states� ultimate limit state ULS, serviceability limit state SLS, combinations of actions

� Scheme of structural design according to EN 1990 section 5

� Global analysis� Effect of deformed geometry of the structure

� Examples of the portal frame building

5

Lecture outline� Worked example of the portal frame building designed according to

EN 1990 and EN 1993� Determinations of loads on building envelope

� Combinations of actions

� Preliminary design. Envelopes of the internal forces, strains and displacements

� Design of the secondary elements: purlins and side rails

� Frame stability

� Design of steel column

� Design of girder

� Design of certain joints

6

Structural forms of steel frames

7



Structural forms of steel framesIntroduction

� The building environment of Europe contains many examples of single-storey steel structures. These structures include exhibition halls, sports

complexes, factory units or warehouses

� Figure belowe presents the percentage size of the market of steel single-storey industrial buildings in the selected countries from United Europe

� Depicted above phenomenon demonstrates the dominance and importance of steel constructions in this class of buildings

8


� Single-storey structures among others are characterized by:� long span coupled with relative small weight,

� an easiness of transport

� an easiness of erection in all weather conditions.

� Single-storey structures allow to: � design economicalbuildings of an attractive appearance

� have the potential for easy changes during the building’s life

� The total cost of the single-storey building consist of:� the cost of primary frame (35%),

� the secondary structure i.e. purlins and side rails (15%)

� the cladding elements (50%).

9


� Designers designing steel structures have to cover specific activity area, therefore seems important to select the optimalspacing columnwhich fulfil users expectations’ and gives maximum freedom of use of the space respecting the economic constraints. Usually span of those structures is in the range 12 m to 40 m; however larger spans are also possible.

� Figure shows how steel weight varies with structural form and span

10

Structural forms of steel framesElements of the single-storey structure

11

1 – roof cladding, 2 – roof bracing, 3 – ridge purlin, 4 – indirect purlin,5 – eaves purlin, 6 – main beam, 7 – column, 8 – longitudinal bracing, 9 – secondary column for wind load, 10 – wall cladding, 11 – side rails.

The typical elements of single-storey steel frames are:

Moreover, the building requires also foundations which are designed and erected to transmit all actions to the soil. In order to do that properly the geotechnical characteristics of the soil must be known. The Eurocode EN 1997 contains geotechnical information’s

Moreover, the building requires also foundations which are designed and erected to transmit all actions to the soil. In order to do that properly the geotechnical characteristics of the soil must be known. The Eurocode EN 1997 contains geotechnical information’s

Structural forms of steel framesElements of the single-storey structure / Cladding systems

12

� The cladding system is required in order to:� watertight the building interior

� provides thermal insulation

� makes appropriate daylight penetration (windows, skylights)

� gives wide variety of colours and shapes of the building

� The cladding elements capacity has to withstand:� mechanically induced loadings

� and thermally induced loadings

� In the market several systems which fulfil all the environmental and economical requirements are available:� sandwich panels

� single-skin trapezoidal roofing

� standing seam system

� and external firewall

� the walls can be also formed with precast concrete, or brick

Structural forms of steel framesElements of the single-storey structure / Cladding systems / Sandwich panels

13

� Sandwich panels consist of:� external facings: thin, high strength (steel)

� core: thick, soft (polyurethane, mineral wool, styrofoam )

� Sandwich panels are characterized by:� high bending stiffness coupled with small weight,

� very good thermal properties

� easiness of transport

� and easiness of erection.

� Designing sandwich panels requires taking into account several problems:� the cooperation of two different materials (facings and core)

� the requirements of the ultimate and serviceability limit states

� the failure mechanisms

� structural behaviour strongly depends on the influence of the thermally induced deformations (therefore the critical combinations are wind suction with summertemperatures and snow loading with winter temperatures)

Structural forms of steel framesElements of the single-storey structure / Cladding systems / Sandwich panels

14

1 & 2 – examples/ 3 – shear failure/ 4 & 5 – wrikling failure

Structural forms of steel framesElements of the single-storey structure / Cladding systems / Standing seam system

15

� Characteristics of the system:� Suitable for roofs or walls with ≥ 1.5°grade

� The system can be executed on spot as its construction is very easy,

� Wide span ≤ 200m

� Excellent:� drainage

� anti-seepage performance

� unique anti-heat-expansion performance

� anti-wind-pressure performance

� With an advanced secondary molding technique (melon-peel technique and sector curve technique), this system can easily settle problems of single or double curved surface overlay

� High quality, low power-consumption, practical, good looking

Structural forms of steel framesElements of the single-storey structure / Cladding systems / Standing seam system

16

Structural forms of steel framesElements of the single-storey structure / Secondary elements

17

� The secondary elements, purlins and rails, supportscladding and transmitthe external loads to main steel structure

� The spanof those elements are determined by spacing of the frames, which are usually in the range of 5 m to 9 m. This span can be reduce introducing

the secondary column for wind load

� In turn the capacity of the claddings elements impose on secondary elements the spacing in the range of 2 m to 4 m. For this spacing the most suitable

elements seems to be the hot-formed section.

� In case of smaller spacing i.e. 1 m to 1.5 m the most appropriate are cold-formed light-gauge sections. These sections are produce on computer

numerically controlled (CNC) rolling machines.


18

Typical purlin sections:

a) & b) hot rolled sections;

c) double hot rolled section;

d), f) & h) cold rolled sections;

e) & g) double cold rolled sections


19

Typical side rails sections:

a) & d) hot rolled sections

b), c) & f) cold rolled sections

e) double hot rolled sections


20

� It is worth noticing that for the design of structures made of cold formed (secondary) members and claddings a distinction should be made between “structural classes” associated with with failure consequences according to EN 1990 – Annex B defined as follows:� structural Class I – construction where cold-formed members and cladding are

designed to contribute to the overall strength and stability of a structure;

� structural Class II – construction where cold-formed members and cladding are designed to contribute to the strength and stability of individual structural (secondary) elements;

� structural Class III – construction where cold-formed members and cladding are used as an elements that only transfer loads to the structure.

� The current single storey buildings have generally a structural Class II according to EN 1993-1-3, therefore the cladding elements (roof and/or walls) generally contributes to the strength and stability of individual structural (secondary) elements.

Structural forms of steel framesElements of the single-storey structure / Main steel frames

� Loads are transferred from the cladding on the purlins and side rails which are supported by steel frames, hence it is necessary to consider and chose the appropriate structural frame solution

� Portal frames are the most commonly used structural forms for single-storey industrial structures

� They are constructed mainly using hot-rolled sections, supporting the roofing and side cladding via cold-formed purlins and sheeting rails

� They may also be composed of tapered columns and rafters fabricated from plate elements

� Portal frames of lattice members made of angles or tubes are also common, especially in the case of longer spans

21


� Typical structural frame solutions: � a) portal frame – medium span

� b) portal frame from welded plates

� c) portal frame with mezzanine floor

� d) portal frame with integral office

� e), f) portal frame with prestressed element, medium and large span respectively

22


� The slopes of rafters in the gable portal frames varyin the range of 1 in 10 to 1 in 3

� Generally, the centre-to-centre distance between frames is of the order 6 to7.5 m, with eaves height ranging from 6 – 15 m

� Moment-resisting connections are to be provided at the eaves and crown toresist lateral and gravity loadings

� The column bases may behave as eitherpinned or fixed, depending upon rotational restraint provided by the foundation and the connection detail between the column and foundations

� The foundation restraint depends on the type of foundation and modulus of the sub-grade

� Frames with pinned bases are heavier than those having fixity at the bases

� Frames with fixed base may require a more expensive foundation

23


� Due to transportation requirements, field joints are introduced at suitable positions

� Therefore, connections are usually located at positions of high moment, i.e. at the interface of the column and rafter members (at the eaves) and also between the rafter members at the apex (ridge)

� It is very difficult to develop sufficient moment capacity at these connections by providing 'tension' bolts located solely within the small depth of the rafter section. Therefore the lever arm of the bolt group is usually increased by haunching the rafter members at the joints. This addition increases the section strength.

24


� The structural analysis requires defining the resistance and stiffness of any connection in the structure, according to EN 1993-1-8

� The main connections of the portal frame are presented belowe

� The connections will be describe in detailed in next section

25

Structural actions and transmission

of loading

26



Structural actions and transmission of loading Introduction

� The term actions means a load, or an imposed deformation (e.g. temperature effects or settlement) applied to a structure.

� The term action effects means an internal moments and forces, bending moments, shear forces and deformations caused by actions.

� In case of single-storey building actions are transferred from the cladding onto the purlins and side rails, which are supported by a portal frame structure. The basic natural classification of actions divided them into four main groups:

� permanent, variable, accidental and seismic.

� In accordance with EN 1990 the classification of actions is as follows:

� by variation in time: G – permanent, Q – variable and A–accidental;

� by origin: direct or indirect;

� by spatial variation: fixed or free;

� by nature of structural response: static or dynamic27


Parts of Eurocode 1:Actions on structures

Subject

EN 1991-1-1

General actions –densities, self weight, imposed loads for buildings−gives design guidance and actions for the structural design of buildings and civil engineering works, including the following aspects :−densities of construction materials and stored materials (Section 4, Annex A ),−self-weight of construction elements (Section 5), −imposed loads for buildings(Section 6), according to category of use.

28



Subject

EN 1991-1-2

General actions –actions on structures exposed to fire−describes structural fire design procedure (Section 2),−describes thermal actions for temperature analysis (Section 3),−describes mechanical actions for temperature analysis (Section 4),−contains informative Annexes A – G which describe parametric temperature-time curves, simplified calculation method, localised fires, advanced fire models, fire load densities, equivalent time of fire exposure and configuration factor.

29



Subject

EN 1991-1-3

General actions –snow loads−provides guidance for the determination of the snow load for sites at altitudes under 1500m but, in the case of altitudes above 1500m advice may be found in the appropriate National Annex.−does not give answers in the following aspects: impact loads due to snow falling from a higher roof, additional wind loads resulting from changes in shape or size of the roof profile, loads in areas where snow is present all the year, loads due to ice.

30



Subject

EN 1991-1-4

General actions –wind actions−provides guidance for buildings with heights up to 200m, for bridges with span less than 200m and for masts and lattice towers treated in EN 1993-3-1.−does not give answers in case of torsional vibrations, bridge deck vibrations from transverse wind turbulence, wind actions on cable supported bridges, vibrations where more than the fundamental mode needs to be considered.

EN 1991-1-5 General actions – thermal actions

31



Subject

EN 1991-1-6

General actions –actions during execution−provides guidance for determination of actions occur during the execution of buildings, structural alterations, reconstruction, partial or full demolition and for the execution phases (falsework, scaffolding, propping systems, bracing).

EN 1991-1-7

General actions –accidental actions−provides guidance for reducing hazards, for low sensitive structural form, for survival of local damage and for sufficient warning at collapse.

EN 1991-2 Traffic loads on bridgesEN 1991-3 Actions induced by cranes and machineryEN 1991-4 Silos and tanks

32


� Examples of way of classification of actions:

� The self-weight of construction works is usually classified as a permanent fixed action, however, when is represented by upper and lower characteristic values, could be variable in time, and when is free (e.g. moveable partitions) could be treated as an additional imposed load.

� The imposed loads on structure are generally a variable free actions, however loads resulting from impacts on buildings due to vehicles or accidental loads should be determined from EN 1991-1-7 as a accidental actions

33

Structural actions and transmission of loading Action on single-storey structures / Permanent actions (G)

� The permanent actions in single-storey building consist of self weights of:

� portal frame elements (girders, trusses, columns)

� secondary elements (purlins and side rails)

� bracings (roof and longitudinal)

� claddings

� floors with finishes and services (lighting, sprinklers etc.)

� The service loads are very individual and strongly depends from the way of use of the building. For example in literature occurs the term global service roof load which is in the range of 0.1kN/m2 to 0.2kN/m2

� The weights of the materials are presented in Eurocode EN 1991-1-1

34

Structural actions and transmission of loading Action on single-storey structures / Permanent actions (G)

� In case of concrete elements e.g. floors filled in site the shrinkage must be considered as well as the effects produced by changes of temperature cause by length of the steel structure

� Another group of permanent actions are:

� water and soil pressures

� settlements of supports

� prestressing forces

� and mechanically and thermally induced distortions

35

Structural actions and transmission of loading Action on single-storey structures / Variable actions (Q)

� The variable actions (Q) consist of:

� the imposed floor or roof loads

� snow and wind loads

� in case of cranes or/and conveyors occur the gravity loads and the effects of acceleration and deceleration. There is several types of cranes in portal frame buildings for example:

� monorail crane,

� overhead crane,

� swivel crane

� and “goliath” crane

36


� The imposed loads (generally classified as variable free actions) include:

� small allowance for impact

� and other possible dynamic effects

� The character of imposed loads is generally quasi-static and allow for limited dynamic effects in static structures, if there is no risk of resonance

� In case of actions causing significant acceleration of structural members are classified as dynamic and need to be considered via a dynamic analysis

37


� The imposed loads on buildings arises from occupancy and the values given include:

� normal use by persons

� furniture and moveable objects

� vehicles

� and rare events such as concentrations of people and furniture or the moving or stacking of objects during times of re-organisation and refurbishment

� The roof and floor areas are sub-divided into 11 categories of use. � 4 categories (A, B, C and D) for areas are as follows: residential, social,

commercial and administration

� 2 categories (E1 an E2) for storage and industrial activities areas respectively

� 2 categories (F and G) for garages and vehicle traffic (excluding bridges)

� 3 categories (H, I and K ) for roof areas

38


� Action due to snow are classified in accordance to EN 1990 as variable for which the variation in magnitude with time is negligible, as fixed (distribution and position is fixed over the structure) and static (does not cause significant acceleration of the structure or structural members). The magnitude of this load depends on the roof slope

� The wind action are expressed as static pressure or suction and should be determined for each design situation identified in accordance with EN 1990. The magnitude of this load depends on the wind velocity, terrain roughness, shape and height of the building

� The thermal actions induced by temperature changes are considered as variable and indirect actions. The characteristic values have probability 0,02 of being exceeded by annual extremes

39

Structural actions and transmission of loading Action on single-storey structures / Accidental actions (A)

� The accidental actions (A) consist of:

� actions during execution process,

� impact and explosion actions,

� accidental crane actions

� and in some areas earthquake effects.

� The EN 1991-1-6 gives general rules for the determination of actions during execution of buildings and civil engineering works. Additionally gives rules for the determination of actions to be used for the design of auxiliary construction works (falsework, scaffolding, propping systems, bracing), needed for the execution phases. Therefore a designers should have knowledge of the most likely method of erection.

40

Structural actions and transmission of loading Action on single-storey structures / Accidental actions (A)

� The EN 1991-1-7 gives general rules about impact and explosions. A structure should be designed and executed in such a way that it will not be damaged by events like explosion, impact and consequences of human errors to an extent disproportionate to the original cause.

� The EN 1991-1-8 gives the information about the internal forces which have to be calculated

41

Structural actions and transmission of loading Action on single-storey structures / Design values of actions

� Partial safety factors allow for the probability that there will be a variation in the effect of the action

� They taking into consideration the both the inaccurate modelling and uncertainties in the assessment of the actions

� The characteristic value term means main representative value and is assumed as follows:

� mean value if the variability is small (Gk, Pm)

� upper or lower value if the variability is not small:

� Gk,inf (5% fractile), Pk,inf

� Gk,sup (95% fractile, i.e. probability of exceeding 5%), Pk,sup

� Qk (climatic actions, the probability of exceeding 2 %/year)

� AEk (seismic actions)

� nominal value when statistical data are insufficient,

� value specified for an individual project (Ad)

42

Structural actions and transmission of loading Action on single-storey structures / Design values of actions

� The other representative values of actions are as follows:

� combination values Ψ0·Qk , for ultimate limit states of permanent and transient design situation and for irreversible serviceability limit states

� frequent values Ψ1·Qk (e.g. during 1 % of the reference period), for ultimate limit states of involving accidental actions and for reversible serviceability limit states)

� quasi-permanent values Ψ2·Qk (e.g during 50 % of the period), for ultimate limit states involving accidental actions and for reversible serviceability limit states

� The limit states will be describe in detailed in next section

43

General rules of static calculation

and design limit states

44



General rules of static calculation and design limit states Design situations / Basis of structural design according to Eurocode EN 1990

� The Eurocode EN 1990::

� establishes principles and requirements for safety, serviceability,and durability of structures

� describes the basis for structure designand verification

� gives guidelinesfor related aspects of structural reliability

� is related to eurocodes EN 1991 to EN 1999

� The EN 1990 is applicable for:

� the structural appraisal of existing construction

� developing the design of repairs and alterations

� assessing changes of use

45

General rules of static calculation and design limit states Design situations / Basis of structural design according to Eurocode EN 1990

� Summing up the structure and their members should be designed, executedand maintained in such a way that can fulfil the presented below fundamental requirements:

� safety requirement i.e. that the structure during its intended life with appropriate degrees of reliability and in an economic way, will sustain all actions and influences likely to occur during execution and use

� serviceability requirement i.e. that the structure during its intended life with appropriate degrees of reliability and in an economic way, will remain fit for the use for which it is required

� robustness requirement i.e. that the structure will not be damaged by events such as explosion, impact or consequences of human errors, to an extent disproportionate to the original cause

� fire requirement i.e. that the structural resistance shall be adequate for the required period of time

� . 46

General rules of static calculation and design limit states Verification of the limit states / Serviceability limit state SLS

� Serviceability Limit States concern (SLS) concerns the functioning of the structure and their members under normal use. Concerns also the comfort of people and the appearance of the construction work. The verification of SLS considers:

� the deformations that affect the appearance, comfort of users or functioning of the structure (including machines and services)

� the vibrations that cause discomfort to people or limit the functional effectiveness of the structure

� the damage that is likely to affect the appearance, durability, or functioning of the structure

47

General rules of static calculation and design limit states Design situations / Limit state design

� The structural design is based on the limit state concept used in conjunction with the partial safety factor method

� Limit states are the states beyond which the structure no longer fulfils the relevant design criteria

� Two different types of limit states are considered:

� Ultimate Limit State (ULS)

� Serviceability Limit State (SLS)

� Based on the use of structural and load models, it is verified that no limit state is exceeded when relevant design values for actions, material and product properties, and geometrical data are used. This is achieved by the partial factor method

48


49

� Verification by partial factor method


� The design situations and their verifications

50

Design situation VerificationPersistent Normal use ULS, SLS

TransientExecution, temporary conditions applicable to the structure

ULS, SLS

AccidentalNormal use ULSDuring execution ULS

SeismicNormal use ULS, SLSDuring execution ULS,SLS


� Representative values of actions

51

value\action permanent variable accidental seismiccharacteristic Gk Qk AEk

nominal Ad AEd = γI AEk

combination Ψ0Qk

frequent Ψ1Qk

quasi-permanent Ψ2Qk

General rules of static calculation and design limit states Verification of the limit states / Ultimate limit state ULS

� Ultimate Limit States (ULS) concern the safety of people and/or the safety of structures. Nevertheless in special circumstances the ULS concerns also the protection of the contents. These states are associated with both global and local failure mechanisms i.e. with:� EQU which means loss of static equilibrium of the structure or any part of it

considered as a rigid body

� STR which means internal failure or excessive deformation of the structure or structural members, including footings, piles, basement walls

� GEO which means the failure or excessive deformation of the ground where the strengths of soil or rock are significant in providing resistance

� FAT which means the fatigue failure of the structure or structural members

52

General rules of static calculation and design limit states Verification of the limit states / Ultimate limit state ULS

� The EN 1990 considers the following design situations for Ultimate Limit State: � persistent situations (conditions of normal use)

� transient situations (temporary conditions)

� accidental situations (exceptional conditions)

� seismic situations

� The EQU state is verified according to static equilibrium presented below: � Ed,dst≤ Ed,stb(where Ed,dst is destabilising action and Ed,stb is stabilising actions)

� The STR and/or GEO states are verified according to resistant equilibrium presented below:� Ed ≤ Rd (where Ed is effect of action and Rd is corresponding resistance)

� The FAT limit states verification is given in detailed in EN 1991

� Summing up the ULS concerns: rupture, collapse, loss of equilibrium, transformation into a mechanism and failure caused by fatigue

53

General rules of static calculation and design limit states Verification of the limit states / Serviceability limit state SLS

� The EN 1990 considers the following combinations of actions for SLS: � the characteristic combination for function and damage to structural and non-structural

elements;

� the frequent combination, for comfort to user, use of machinery, etc

� the quasi-permanent combination, for long-term effects

� the appearance of the structure

� These are verified according to equilibrium below:� Ed ≤ Cd (where Cd is design effect Ed is design criterion)

� Summing up the SLS concerns: deformations, vibrations, cracks and damages adversely affecting use

54

General rules of static calculation and design limit states Verification of the limit states / Combinations of actions

55

combinations of action for

ULS and SLS according to

EN 1990 section 6

and Annexes

A1 and A2

General rules of static calculation and design limit states Verification of the limit states / Scheme of structural design according to EN 1990 section 5

56


57

� THE CALCULATION OF APPROPRIATE STRUCTURAL MODELS CONSIST OF:� predicting the structural behaviour at limit state (see 5.1.1)

� involving relevant variables (see 5.1.1)

� acceptable accuracy (see 5.1.1)

� established engineering theory and practise, where necessary verified experimentally

� DESIGN ASSISTED BY TESTING:� design may be based on combination of calculations and tests (see Annex D)

� the limited number of tests to be considered in the reliability required (see 5.2)

� partial factors should be as in EN 1991 -1999 (see 5.2)


58

� MODELLING FOR STATIC OR EQUIVALENT STATIC ACTION� modelling based on appropriate choice of force-deformation relationship of:

� members (see 5.1.2)

� connections (see 5.1.2)

� ground (see 5.1.2)

� boundary conditions intended (see 5.12)

� 2nd order theory when increase of actions effects significant (see 5.1.2)

� indirect actions to be introduce in:

� linear elastic analysis directly or by equivalent forces

� non-linear analysis as imposed deformation


59

� MODELLING FOR DYNAMIC ACTION (see 5.1.3)

� modelling based on: masses, stiffness, damping characteristic, boundary conditions as intended, strengths for all structural and non-structural members

� contribution of soil modelled by equivalent springs and dash pots

� Where relevant (for wind and seismic actions) from modal analysis or where the fundamental mode is relevant from equivalent static forces

� Dynamic actions also expressed as time histories or in the frequency domain to be dealt with by appropriate methods

� Where relevant dynamic analysis also for SLS (see Annex A)

� In case of determination of equivalent static action dynamic parts either included implicitly or by magnification factors


60

� FOR FIRE DESIGN (see 5.1.4)

� Structural fire design analysis based on fire scenarios considering models for:

� temperature evolution in the structure

� mechanical non-linear behaviour of structure at elevated temperature

� Fire exposure as:

� nominal fire exposure

� modelled fire exposure

� Verification of the required performance by either:

� global analysis

� analysis of subassemblies or member analysis or by tabulated data or test results

� Specific assessment methods within:

� uniform or non uniform temperature with cross-section and along members

� analysis of individual members and interaction of members

Global analysis

61



Global analysisEffects of deformed geometry on the structure (EN 1993-1-1, 5.2)

62

� The internal forces and moments may generally be determined using either:� first-order analysis, using the initial geometry of the structure or

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

� 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 may be used for the structure, if the increase of the relevant internal forces or moments or any other change of structural behaviour caused by deformations can be neglected. This condition may be assumed to be fulfilled, if the following criterion (5.1) is satisfied:

analysiselasticforF

F

analysisplasticforF

F

Ed

crcr

Ed

crcr

10

15

≥=

≥=

α

α

αcr – is the factor by which the design loading would have to be increased to cause elastic instability in a global mode

Fed – is the design loading on the structure

Fcr – is the elastic critical buckling load for global instability mode based on initial elastic stiffnesses

Global analysisEffects of deformed geometry on the structure (EN 1993-1-1, 5.2)

63

� Portal frames with shallow roof slopes and beam-and-column type plane frames in buildings may be checked for sway mode failure with first order analysis if the criterion (5.1) is satisfied for each storey. In these structuresαcr may be calculated using the following approximative formula, provided that the axial compression in the beams or rafters is not significant

⋅

=

EdHEd

Edcr

h

V

H

,δα

HEd – is the design value of the horizontal reaction at the bottom of the storey to the horizontal loads and fictitious horizontal loads, see 5.3.2

VEd – is the total design vertical load on the structure on the bottom of the storey

δH, Ed – is the horizontal displacement at the top of the storey, relative to the bottom of the storey, when the frame is loaded with horizontal loads (e.g. wind) and fictitious horizontal loadswhich are applied at each floor level

h – is the storey height

Global analysisStructural stability of frames (EN 1993-1-1, 5.2)

64

� The verification of the stability of frames or their parts should be carried out considering imperfections and second order effects

� According to the type of frame and the global analysis, second order effects and imperfections may be accounted for by one of the following methods� both totally by the global analysis

� partially by the global analysis and partially through individual stability checks of members

� for basic cases by individual stability checks of equivalent members using appropriatebuckling lengths according to the global buckling mode of the structure

� Second order effects may be calculated by using an analysis appropriate to the structure (including step-by-step or other iterative procedures). For frames where the first sway buckling mode is predominant first order elastic analysis should be carried out with subsequent amplification of relevant action effects (e.g. bending moments) by appropriate factors

Global analysisStructural stability of frames (EN 1993-1-1, 5.2)

65

� For single storey frames designed on the basis of elastic global analysis second order sway effects due to vertical loads may be calculated by increasing the horizontalloadsHEd (e.g. wind) and equivalent loadsVEd φ due to imperfections and other possible sway effects according to first order theory by the factor

� In accordance with 5.2.2(3) the stability of individual members should be checked according to the following:� if second order effects in individual members and relevant member imperfections (see

5.3.4) are totally accounted for in the global analysis of the structure, no individual stability check for the members according to (6.3) is necessary

� if second order effects in individual members or certain individual member imperfections (e.g. member imperfections for flexural and/or lateral torsional buckling, see 5.3.4) are not totally accounted for in the global analysis, the individual stability of members shall be checked according to the relevant criteria in 6.3 for the effects not included in the global analysis. This verification should take account of end moments and forces from the global analysis of the structure, including global second order effects and global imperfections (see 5.3.2) when relevant and may be based on a buckling length equal to the system length

crα1

1

1

−

Global analysisImperfections (EN 1993-1-1, 5.3) / Basis

66

� Appropriate allowances shall be incorporated in the structural analysis to cover the effects of imperfections, including residual stresses and geometrical imperfections such as:

� lack of verticality

� lack of straightness

� lack of flatness

� lack of fit

� and any minor eccentricities present in joints of the unloaded structure

� Equivalent geometric imperfections, see 5.3.2 and 5.3.3, should be used, with values which reflect the possible effects of all type of imperfections unless these effects are included in the resistance formulae for member design, see section 5.3.4

� The following imperfections should be taken into account:

� global imperfections for frames and bracing systems

� local imperfections for individual members

Global analysisImperfections (EN 1993-1-1, 5.3) / Imperfections for global analysis of frames

67

� The assumed shape of global imperfections and local imperfections may be derived from the elastic buckling mode of a structure in the plane of buckling considered

� Both in and out of plane buckling including torsional buckling with symmetric and asymmetric buckling shapes should be taken into account in the most unfavourable direction and form

� For frames sensitive to buckling in a sway mode the effect of imperfections should be allowed for in frame analysis by means of an equivalent imperfection in the form of an initial sway imperfection and individual bow imperfections of members. The imperfections may be determined from:

� global initial sway imperfections mh ααφφ ⋅⋅= 0

φ0 = 1200 (is the basic value)αh – is the reduction factor for height hαm – is the reduction factor for the number of columns in a rowm – is the number of columns in a row including only those columns which carry a vertical load NEd not less than 50% of the average value of the column in the vertical plane considered

Global analysisImperfections (EN 1993-1-1, 5.3) / Imperfections for global analysis of frames

68

� For frames sensitive to buckling in a sway mode the effect of imperfections should be allowed for in frame analysis by means of an equivalent imperfection in the form of an initial sway imperfection and individual bow imperfections of members. The imperfections may be determined from:

� global initial sway imperfections

� relative initial local bow imperfections of members for flexural buckling

� For building frames sway imperfections may be disregarded where

� ... see more in EN 1993-1-1, 5.3.2EdEd VH ⋅≥ 15.0

Global analysisImperfections (EN 1993-1-1, 5.3) / Imperfections for analysis of bracing systems

69

� In the analysis of bracing systems which are required to provide lateral stability within the length of beams or compression members the effects of imperfections should be included by means of an equivalent geometric imperfection of the members to be restrained, in the form of an initial bow imperfection

restrainedbetomembersofnumbertheism

m

systembracingtheoftheisL

where

Le

m

m

−

+⋅=

−

⋅=

115.0

5000

α

α

Global analysisImperfections (EN 1993-1-1, 5.3) / Imperfections for analysis of bracing systems

70

� For convenience, the effects of the initial bow imperfections of the members to be restrained by a bracing system, may be replaced by the equivalent stabilizing force as shown in figure

� where:

� δq – is the inplane deflection of the bracing system due to q plus any external loads calculated from first order analysis

� where the bracing system is required to stabilise the compression flange of a beam of constant height, the force NEd in figure may be obtained from

� where: � MEd – is the maximum moment in the beam, h – is the overall depth of the beam

∑+

⋅⋅=2

08

L

eNq

qEd

δ

hMN Ed

Ed =

Examples of the portal frame building

71



Examples of the portal frame buildingWhat steel structures in single storey buidings can offer?

� Cost efficiency in construction

� Low maintenance throughout a building’s life

� Long spans that can accommodate changes in building occupancyand activity, thus extending a building’s economic life

� Highly sustainable contributions to Europe’s Built Environment

� Single storey steel buildings are one of the most efficient sectors in the construction industry, with optimized approaches to the primary frames,

secondary structure and cladding from specialist suppliers

� Single storey steel buildings should be provided in a way that ensures that all the specialist suppliers can make maximum contributions to overall client value

� ...

� SEE EXAMPLES*)

72 SOURCES: Eurocodes: Background ans Applications

Examples of the portal frame buildingWhat steel structures in single storey buidings can offer? / EXAMPLES




Modern architecture is rich with solutions that defy simple categorization, even in single storeystructures. They can be formed into gentle arcs or startling expressed structure. Although greatest economy is often achieved with regular grids and standardization, steel structures offer outstanding opportunity for architectural expression and outstanding design opportunities. Someillustrations of the structural forms that are possible in steel construction are shown in Figure 1.1 to Figure 1.4



A steel structure is both flexible and adaptable – design in steel is certainly not limited to rectangular grids and straight members, but can accommodate dramatic architectural intent, as shown in Figure 2.4



Portal frames typically have straight rafters, as shown in Figure 3.3



Portal frame with a curved rafter shown in Figure 3.4



Deep sections with relatively narrow flanges are preferred for roof beams, as shown inFigure 3.12, where they primarily resist bending. Columns, which primarily resist

compression, are usually thicker, shallower sections with wider flanges



Flat trusses are used mainly in rigid frames but they are also employed in pinned frames – an example is shown in Figure 3.17

W 1 single-storey steel-frames_structures

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