W 1 single-storey steel-frames_structures

Poznan University of
Technology
Institute of Structural
Engineering

Section 3
Single-storey steel frames structures

Bibliography
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, 2008
4. 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

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

Bibliography
1.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

Technology
Engineering

Structural forms of
steel frames

7

Introduction
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

Introduction
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 economical buildings 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

Introduction
Designers designing steel
structures have to cover specific
activity area, therefore seems
important to select the optimal
spacing column which 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

Elements of the single-storey structure
The typical elements of single-storey steel frames are:
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.

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
11

Elements of the single-storey structure / Cladding systems
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
12

Elements of the single-storey structure / Cladding systems / Sandwich panels
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 summer
temperatures and snow loading with winter temperatures)
13

Elements of the single-storey structure / Cladding systems / Sandwich panels
1 & 2 – examples/ 3 – shear failure/ 4 & 5 – wrikling failure

14

Elements of the single-storey structure / Cladding systems / Standing seam system
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

15

Elements of the single-storey structure / Cladding systems / Standing seam system

16

Elements of the single-storey structure / Secondary elements

The secondary elements, purlins and rails, supports cladding and transmit
the external loads to main steel structure

The span of 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.

17

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

18

Typical side rails sections:

a) & d) hot rolled sections
b), c) & f) cold rolled sections
e) double hot rolled sections

19

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.

20

Elements 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 vary in the range of 1 in 10
to 1 in 3
Generally, the centre-to-centre distance between frames is of the order 6 to
7.5 m, with eaves height ranging from 6 – 15 m
Moment-resisting connections are to be provided at the eaves and crown to
resist lateral and gravity loadings
The column bases may behave as either pinned 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

Technology
Engineering

Structural actions
and transmission
of loading

26

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 dynamic
27

Introduction

Parts of Eurocode 1:
Subject
Actions on structures
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 :
EN 1991-1-1
−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

Introduction

Subject
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
EN 1991-1-2 (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

Introduction

Subject
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.
EN 1991-1-3
−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

Introduction

Subject

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.
EN 1991-1-4
−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

Introduction

Subject
General actions – actions during execution
−provides guidance for determination of actions occur
during the execution of buildings, structural alterations,
EN 1991-1-6
reconstruction, partial or full demolition and for the
execution phases (falsework, scaffolding, propping systems,
bracing).
General actions – accidental actions
−provides guidance for reducing hazards, for low sensitive
EN 1991-1-7
structural form, for survival of local damage and for
sufficient warning at collapse.
EN 1991-2 Traffic loads on bridges
EN 1991-3 Actions induced by cranes and machinery
EN 1991-4 Silos and tanks

32

Introduction
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

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

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

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

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

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

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

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

Technology
Engineering

General rules
of static calculation
and design limit
states

44

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 design and verification
gives guidelines for 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

Design situations / Basis of structural design according to Eurocode EN 1990
Summing up the structure and their members should be designed,
executed and 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

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

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

Verification by partial factor method

49

The design situations and their verifications

Design situation Verification
Persistent Normal use ULS, SLS
Execution, temporary conditions applicable
Transient ULS, SLS
to the structure
Normal use ULS
Accidental
During execution ULS
Normal use ULS, SLS
Seismic
During execution ULS,SLS

50

Representative values of actions

valueaction permanent variable accidental seismic
characteristic Gk Qk AEk
nominal Ad AEd = γI AEk
combination Ψ0Qk
frequent Ψ1Qk
quasi-permanent Ψ2Qk

51

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

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

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

Verification of the limit states / Combinations of actions
combinations of
action for
ULS and SLS
according to
EN 1990
section 6
and
Annexes
A1 and A2

55

Verification of the limit states / Scheme of structural design according to EN
1990 section 5

56

1990 section 5
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)

57

1990 section 5
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

58

1990 section 5
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

59

1990 section 5
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

60

Technology
Engineering

Global analysis

61

Global analysis
Effects of deformed geometry on the structure (EN 1993-1-1, 5.2)
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:
Fcr Fed – is the design loading on the structure
α cr = ≥ 15 for plastic analysis
FEd
Fcr – is the elastic critical buckling load for global
F
α cr = cr ≥ 10 for elastic analysis instability mode based on initial elastic stiffnesses
FEd

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

62

Global analysis
Effects of deformed geometry on the structure (EN 1993-1-1, 5.2)
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 structures αcr may be calculated
using the following approximative formula, provided that the axial compression in
the beams or rafters is not significant

 H Ed   h  HEd – is the design value of the horizontal reaction at the
α cr = 
V ⋅
 δ

 bottom of the storey to the horizontal loads and fictitious
 Ed   H , Ed  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 loads
which are applied at each floor level

h – is the storey height

63

Global analysis
Structural stability of frames (EN 1993-1-1, 5.2)
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 appropriate
buckling 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

64

Global analysis
Structural stability of frames (EN 1993-1-1, 5.2)
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 horizontal
loads HEd (e.g. wind) and equivalent loads VEd φ due to imperfections and other
possible sway effects according to first order theory by the factor 1
1
1−
α cr

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
65

Global analysis
Imperfections (EN 1993-1-1, 5.3) / Basis
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

66

Global analysis
Imperfections (EN 1993-1-1, 5.3) / Imperfections for global analysis of frames
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 φ = φ0 ⋅α h ⋅α m
φ0 = 1200 (is the basic value)
αh – is the reduction factor for height h
αm – is the reduction factor for the number of
columns in a row
m – 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

67

Global analysis
Imperfections (EN 1993-1-1, 5.3) / Imperfections for global analysis of frames
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 H Ed ≥ 0.15 ⋅ V Ed
... see more in EN 1993-1-1, 5.3.2

68

Global analysis
Imperfections (EN 1993-1-1, 5.3) / Imperfections for analysis of bracing systems
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
L
e0 = α m ⋅
500
where
L − is the of the bracing system
 1
α m = 0.5 ⋅ 1 + 
 m
m − is the number of members to be restrained

69

Global analysis
Imperfections (EN 1993-1-1, 5.3) / Imperfections for analysis of bracing systems
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
e0 + δ q
q= ∑ N Ed ⋅ 8 ⋅
L2
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
M Ed
N Ed =
h
where:
MEd – is the maximum moment in the beam, h – is the overall depth of the beam

70

Technology
Engineering

Examples of the portal
frame building

71

What 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 occupancy
and 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

What steel structures in single storey buidings can offer? / EXAMPLES


Modern architecture is rich with solutions that defy simple categorization, even in single storey
structures. 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. Some
illustrations 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 in
Figure 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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