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Structures Index

Introduction to Eurocodes

Introduction..... Eurocodes..... Terminology..... Ulitimate limit States..... Serviceability limit States..... Design to ULS..... Symbols..... subscripts..... Actions..... Factor values ..... Action combinations.....
Material design values..... Resistance design value..... Design working life..... Unit masses of materials..... Imposed Loads (occupancy)..... Example Loading calc. .....

The building structures pages have been added over the six months to Dec. 2012.     They are very much work-in-progress and I will be updating them on a regular basis over the next six months.

Introduction

The development work on the Eurocodes was initiated in 1975 and although progress has been very slow the full set of eurocodes and the associated various National Annexes, required for local code variations, have now been issued for use.    These codes relate to the construction industry and are produced by the European Committee for Standardization (CEN), and replace existing national standards in 28 countries.     The codes include the principles, rules and recommended values for ultimate limit design. However safety , durability and economy have be derogated to member states and are included in National Annexes. The Eurocodes are proving to be the most comprehensive coding of structural and civils design in the world.


This page of the website includes outline notes introducing the Eurocodes.    The notes are simply sufficient to provided background information for engineers /students to start off on a course of study or a project.    References and standards are listed which should be used for detail design work.    Links are provided which include, in some detail, information relevant to the Eurocodes.    The notes on this page specifically address actions and the related partial margins .    The construction materials and their related partial safety margins are addressed on the relevant linked pages.






Eurocodes

An outline list of the available eurocodes, but not their subsections or associated standards, are listed below.

BS EN 1990 Eurocode 0: Basis of structural design
BS EN 1991 Eurocode 1: Actions on structures
BS EN 1992 Eurocode 2: Design of concrete structures
BS EN 1993 Eurocode 3: Design of steel structures
BS EN 1994 Eurocode 4: Design of composite steel and concrete structures
BS EN 1995 Eurocode 5: Design of timber structures
BS EN 1996 Eurocode 6: Design of masonry structures
BS EN 1997 Eurocode 7: Geotechnical design (foundations)
BS EN 1998 Eurocode 8: Design of structures for earthquake resistance.(seismic design)
BS EN 1999 Eurocode 9: Design of aluminium structures





Terminology introduced with the Eurocodes

Action = Imposed load
Effect of Action = Resulting stress, strain, deflection,rotation
Permanent Action = Dead Load
Variable Action = Live Load
Execution = Construction process
Limit state = state at which the structure no longer fulfill the relevant design criteria.
Ultimate limit state (ULS) = states associated with collapse or similar structural failure.
Serviceability Limit state(SLS) = state such that the structure remains functional for its intended use subject to routine loading.






Ultimate Limit States

The Eurocodes are based on ultimate limit state design. The Ultimate limit states are divided into the following categories:

EQU Loss of equilibrium of the structure.
STR Internal failure or excessive deformation of the structure or structural member.
GEO Failure due to excessive deformation of the ground.
FAT Fatigue failure of the structure or structural members.

These ultimate states are considered in different combinations in structural detail design.
In geotechical design ultimate limit states for resistance to uplift(UPL) and seepage ((HYD) have also to be considered.

The notes on this website only relate to the STR ultimate limit state.








Serviceability Limit State

Serviceability Limit state(SLS) is the design state such that the structure remains functional for its intended use subject to routine loading.    This affects such situations as doors / windows failing to open due to structural deformation.    It relates to factors others than the building strength that renders the buildings unusable.    Serviceability limit state design of structures includes consideration of durability, overall stability, fire resistance, deflection, cracking and excessive vibration.  This website only considers this limit state in outline.

Verification for serviceability limit states in the ground or structional section or interface shall be such that

Ed =< Cd



Ed = The design value of the effect of actions such as internal force , moment or vectorial representation of several internal forces or moments.
Cd = Nominal value or function of certain design properties of materials- (related to serviceability limit state






Ultimate limit state design

There are a number of criteria for limit state design and various categories generally need to be considered.    As a basic example of the principle involved when considering a limit state of rupture or excessive deformation of a section or connection (STR ) it shall be verified that :

Ed Rd

Ed = The design value of the effect of actions such as internal force , moment or vectorial representation of several internal forces or moments.
Rd = The design value of the corresponding resistance.

In simple English : the value of the product or the maximum expected forces or moments on a section and the associated partial margins should be less than the characteristic value of the strength of the sections divided by the relevant material partial safety margins.   

Notes on the actions and their associated partial margins are found on this page and notes on the Resistance values the associated partial margins are found on the web pages related to the construction materials






Selection of Eurocode symbols related to actions
SymbolDefinition
Cd Nominal value or function of certain design properties of materials
Ed The design value of the effect of actions
Fk Characteristic value of action
Fd Design value of action
Gk Characteristic value of permanent action
Gd Design value of permanent action
Qk Characteristic value of variable/imposed action (single value)
Rd The design value of a component/system restistance.
γGPartial factor for permanent action
γQ Partial factor for variable action
ψ0 Factor for combination value of variable action
ψ1 Factor for frequent value of variable action
ψ2 Factor for quasi-permanent value of variable action
ε Combination factor for permanent actions
ξ Reduction factor for unfavourable permanent actions





Selection of Subscripts
SubscriptDefinition
A Accidental
c Concrete
m Mortar
dDesign
E Effect of action
fi Fire
k Characteristic
R Resistance
wShear reinforcement
yYield strength





Actions

The actions on a structure or a structural element comprise of permanent actions which are in principle unchanging through the life of the structure and variable actions which are not fixed.  The prime example of a permanent action is the weight of the construction materials. Examples of variable actions include wind loading, occupancy loading, storage loading.

The design value of a permanent action or dead load is simply the product of the relevant partial margin(γG) and the resultant load from the combination of all of the static loads e.g. structure weight, weight of installed equipment(static) and services (empty).    Where the results of the verification are very sensitive to variations of the magnitude of a permanent action from place to place in a structure, the unfavourable and favourable parts of this action shall be considered as individual actions

For each variable action there are four representative values.    The principal representative value is the characteristic imposed load e.g Qk . This can be determined statistically or,where there is insufficient data, a nominal value may be used.    The other representative values are obtained by applying to the characteristic value the factors ψ0, ψ1 and ψ2 respectively . These depend on the type of imposed load.    The "combination" value (ψ0 Qk) of an action is intended to take account of the reduced probability of the simultaneous occurrence of two or more variable actions.    The "frequent" value (ψ1 Qk) is such that it should be exceeded only for a short period of time and is used primarily for the serviceability limit states (SLS) and also the accidental ultimate limit state (ULS).    The "quasi-permanent" value (ψ2 Qk) may be exceeded for a considerable period of time; alternatively it may be considered as an average loading over time.    It is used for the long-term affects at the SLS and also accidental and seismic ULS.


The following steps can be followed to determine the value of the variable actions:

  • Identify the design situation (e.g. persistent, transient, accidental)
  • Identify all realistic actions.
  • Determine the partial factors (see below) for each applicable combination of actions.
  • Arrange the actions to produce the most critical conditions


Actions may be forces ( loads applied to the structure or to the ground) and displacements (or accelerations) that are imposed by the ground on the structure, or by the structure on the ground. Actions may be permanent (e.g. self-weight of structures or ground), variable (e.g. imposed loads on building floors) or accidental (e.g. impact loads).

Design values of actions (F d ) are calculated using the general equation:

F d = γ F .f rep

where
F rep is the representative value of an action. This is generally equal to the characteristic F k value of an permanent action or the leading variable action value , or it is equal to the ψ. F k of an imposed (variable action).
γ f is the partial factor for an action (or γ e , for the effect of an action).

..Fk = Gk    and       γ f = γ g for a permanent action.
..Fk = Qk     and     γ f = γ q for an imposed action.

The equation for the effect of an action should be

The general equation for the Effect of actions should be

The part of the equation inside the brackets represents the combination of permanent and variable actions

In BS EN 1990 one of a number of equations for load combinations is equation 6,10

Note: The prestress term (γPP ) only applies to prestressed concrete applications

This is a quick, but conservative, method when compared to the alternative equations (6.10a and 6.10b)which are a little more complicated. 6.10b is generally the governing equation in the UK

Note: Again the prestress (γPP ) term only applies to prestressed concrete applications.
ξ = Reduction factor for unfavourable permanent actions G.






Recommended ψ values
Actionψ0ψ1 ψ2
Imposed loads
Cat A Domestic residential areas 0,7 0,5 0,3
Cat B Office areas 0,7 0,5 0,3
Cat C congregation areas 0,7 0,7 0,6
Cat D shopping areas 0,7 0,7 0,6
Cat E storage areas 1,0 0,9 0,8
Cat F traffic areas vehicle weight < 30kN 0,7 0,7 0,6
Cat G traffic areas vehicle weight < 1600kN 0,7 0,5 0,3
Cat H roofs 0,7 0 0
Snow / windloads
Sites > 1000m above sea level 0,7 0,5 0,2
Sites < 1000m above sea level 0,5 0,2 0
Wind Loads 0,6 0,5 0





Typical Action Scenarios.

It can also be seen that the partial safety factors for actions depend on a number of other aspects including the category of limit state as well as the effect of the action on the design situation under consideration.

Persistent and transient design situations permanent actions Leading variable actions Accompanying variable actions
Unfavourable Favourable Unfavourable Favourable Main (if any Others         
BS EN 1990(eq 6.10)    γG.j,supGk,j,sup γGj,infGk,j,inf γQ,1Qk,1 - γQ,i ψ0,1 Qk,i
Combination of permanent and variable action ( Strength limit States STR )
BS EN 1990(eq 6.10) 1,35Gk 1,0Gk 1,5Qk.1 0 - -
Combination of permanent and variable action and accompanying variable action ( Strength limit States STR )
BS EN 1990(eq 6.10) 1,35Gk 1,0Gk 1,5Qk.1 0 - 1,5 ψ0.1 Qk.1
Combination of permanent and variable action and accompanying variable action ( Equilibrium limit States EQU )
BS EN 1990(eq 6.10) 1,1 Gk 0,9 Gk 1,5Qk.1 0 - 1,5 ψ0.1 Qk.1





Design value of a Material

The design value of the resistance of a material or ground property is given by the equation

X d = η.X k / γm

where
η = a scale factor covering uncertaintly, scaling , conditions etc.
X k = the characteristic value of a material (ground) property
γm = the partial factor for the material property.

Alternatively the scaling factor can be included within the characteristic value or in the partial factor . In this case the equation reduces to

X d = X k / γM

where
γM = the partial factor for the material property including the scaling factor.






Design Resistance

The general equation for the resistance of the structure

where
γRd = the partial factor for the resistance model uncertainty + geometric deviations.
Xd,i = design value of material property
ad = the design value of a geometric property e.g depth.

This can be simplified to

where
γM,i = γRd .γm,i
.






Design Life

The intended design life of the construction should be identified at the initial stage of the design process

table of design lives of buildings in accordance with BS EN 1990 clause 2,3

Design working life
category
Indicative design
working life
(years>
Examples
1 10Temporary structures
2 10 to 25Replacable structures e.g. Gantry girders, bearings
3 15 to 30Agricultural Builidng and similar structures
4 50Buildings and other common structures
5 100Monumental structures , bridges, civil engineering structures





Unit Masses of Building Materials

Provided to enable estimates of dead loads

Material Specific mass
Asphalt Roofing 2 layers, 19 mm thick 42 kg / m2
Bitumen roofing felts Mineral surfaced bitumen 3.5 kg / m2
Blockwork Solid per 25 mm thick stone aggregate , 55 kg / m2
Blockwork aerated per 25 mm thick 15 kg / m2
Blockboard per 25 mm thick 12.5 kg / m.2 12,5 kg / m2
Brickwork Clay, solid per 25 mm thick 55 kg / m2
Brickwork medium density Concrete, solid per 25 mm thick 59 kg / m2
Cast stone 2250 kg / m3
Concrete Natural aggregates 2400 kg / m3
Concrete Lightweight aggregates (structural) 2000- 1600 kg / m3
Flagstones Concrete, 50 mm thick 120 kg / m2
Glass fibre Slab, per 25 mm thick 2.05.0 kg / m2
Gypsum panels and partitions Building panels 75 mm thick 44 kg / m2
Lead Sheet, 2.5 mm thick 30 kg / m2
Linoleum 3 mm thick 6 kg / m2
Plaster Two coats gypsum, 13 mm thick 22 kg / m2
Plastics sheeting (corrugated) 4.5 kg / m2
Plywood per mm thick 0.7 kg / m2
Reinforced concrete 2400 kg / m2
Rendering Cement: sand (1:3), 13 mm thick 30 kg / m2
Screeding Cement: sand (1:3), 13 mm thick 30 kg / m2
Slate tiles (depending upon thickness and source) 24 78 kg / m3
Steel Solid (mild) 7850 kg / m3
Corrugated roofing sheets, permm thick 10 kg / m2
Tarmacadam 25 mm thick 60 kg / m2
Terrazzo 25 mm thick 54 kg / m2
Tiling, roof Clay 70 kg / m2
Timber Softwood 590 kg / m2
Hardwood 1250 kg / m2
Water 1000 kg / m3
Woodwool Slabs, 25 mm thick 15 kg / m2





Characteristic Values of Imposed load (occupancy )

Provided to enable estimates of imposed loads

1, Values based on BS EN 1991-1 table 6,2

Categories of Loaded Areas qk ( kN /m2 ) Qk ( kN )
Category A Domestic Areas 1,5 to 2,0 2,0 to 3,0
Category C1 Areas with Tables 2,0 to to 3,0 3,0 to 4,0
Category C2 Areas with fixed seats 3,0 to to 4,0 2,5 to 7,0
Category C3 Areas with freedom of movement 3,0 to to 5,0 4,0 to 7,0
Category C4 Areas for physical activities 4,0 to to 5,0 3,5 to 7,0
Category C5 Areas for large crowds (Arenas) 4,5 to to 7,5 3,5 to 4,5
Category D1 Shopping Areas (retails shops) 4,5 to to 5,0 3,5 to 7,0
Category D2 Shopping Areas (department stores) 4,0 to to 5,0 3,5 to 7,0

Other Values

Categories of Loaded Areas qk ( kN/m2 ) Qk ( kN )
Boiler rooms , motor rooms , fan rooms inc. machinery weight 7,5 4,5
Kitchens , laundries. 3,0 4,5
Bedrooms 2,0 1,8
Toilets 2,0 -
Bars 5,0 -





Example Loading Calculation

The floor as shown below has and overall depth of 250mm and is designed to carry and imposed load of 2 kN / m 2 plus floor and ceiling finishes of 1 kN /m 2.
Calculate the design loads acting on beams B1-C1, B2-C2 and B1-C3 and columns B1 and C1.
Assuming column heights are 3m and the beam weights are 70 kg/m-run and the column weights are 60 kg/m-run.

Unit weights of materials

Reinforced concrete :
The mass of reinforced concrete is 2400 kg/m3 (see above table ) for simplicity assume gravitational constant gn = 10 m/ s2.
The unit weight of the reinforced concrete is

2400 .10 = 24 kN/m3..

Steel beams :
The unit mass of beam 70 kg /m -run.
The unit weight of steel beam =

70 . 10 = 0,7 kN/m..

Columns :
The unit mass of column = 60 kg /m -run.
The unit weight of column =

60 . 10 = 0,6 kN/m..

Loading of separate items.

Slab permanent (dead ) load = Gk = (unit-weight . 0,25 ) + finishes ) Area = (6 + 1) Area = 7 .Area kN,

Slab variable (imposed) = Qk = 2. Area kN

Slab design load vertical load Vd_s = 1,35.Gk + 1,5.Qk

Beam permanent load (Gk ) = 0,7. Length kN

Beam design vertical load Vd_b = 1,35 . Gk

Column permanent load (Gk ) = 0,6 . Length kN

Column design vertical load Vd_c = 1,35. Gk



Design Vertical loads on beams....Assume slabs are simply supported

Beam B1-C1
This beam supports a uniformly distributed load resulting from 6m long x 1,5m width of slab + self weight of beam

Design load on beam B1-C1 = Vd_s +Vd_b
= 1,35. (7 . 6 . 1,5 ) + 1,5 .( 2 . 6 . 1,5 ) + 1,35.( 0,7 . 6 ) = 85,05 + 27 + 5,67 = 117,72kN



The reactions at B1 and C1 are equal = 117,72 /2 = 58,86kN

Beam B2-C2
This beam supports a uniformly distributed load on 6m long x 3 m width of slab + self weight of beam

Design load on beam B2-C2 = Vd_s +Vd_b
= 1,35. (7 . 6 . 3 ) + 1,5 .( 2 . 6 . 3 ) + 1,35.(0,7 . 6) = 170.1 + 54 + 5,67 =229,77



The reactions at B2 and C2 are equal = 229,77 /2 = 114,885kN

Beam B1-B3
This beam supports a uniformly distributed load from 6m long x 1,5 m width of slab + self weight of beam .
The beam also supporta a concentrated load at the centre resulting from beam B2-C3

Design loads on beam B1-B3
= 1,35. (7 . 6 . 1,5 ) + 1,5 .( 2 . 6 . 1,5 ) + 1,35.( 0,7 . 6 ) = 85,05 + 27 + 5,67 = 117,72kN
+ concentrated load of 114,9kN support force from B2-C2



The reactions at B1 and B3 are equal = (114,9 + 117,72) /2 = 116,3kN

Design Vertical loads on Columns....Assume beams are simply supported

Column B1
Column B1 supports the reactions from beams A1B1, B1C1 and B1B3 and its self-weight.
From the above, the reaction at B1 due to beam B1C1 is 58,86 kN and from beam B1B3 is 116,3kN.
Beam A1B1 supports only its self-weight = 1,35 . 0,7 . 3 = 2.835 kN.    Hence reaction at B1 due to A1B1 is 2.835/2 = 1.42 kN.
Since the column height is 3 m, self-weight of column = 1,35 .0,6 . 3 = 2,43 . kN.

Design load on column B1 = 58,86 + 116,3 + 2,84 + 2,43 = 180,43 kN

Column C1
Column C1 supports the reactions from beams B1C1 and C1C3 and its self-weight.
From the above, the reaction at C1 due to beam B1C1 = 58,86 kN.
Beam C1C3 supports the reactions from B2C2 (= 114,9 kN) and its selfweight (= 1,35 . 0,7 . 6) = 5.67 kN. Hence the reaction at C1 is (114,9 + 5.67)/2 = 60,28 kN.
Since the column height is 3 m, self-weight = 1,35 .0,6 . 3 = 2,43 . kN.

Design load on column C1 = 58,86 +60,28+ 2,43 = 121,57 kN

Useful relevant Links
  1. Eurocode 2 design of concrete structures ... Detailed notes 173 page document
  2. Eurocode 2 How to design concrete structures ... Detailed notes including introduction to eurocodes: 104 page document
  3. Eurocode 2 Worked examples ... Includes examples on application of actions: a 120 page document
  4. Steel Building Design: Concise Eurocodes... document incuding introduction to actions :118 page document


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Last Updated 07/10/2012