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.

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

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.

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(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

E_d =< C_d

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

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 :

E_d ≤ R_d

E_d = The design value of the effect of actions such as internal force , moment or vectorial representation of several internal forces or moments.
R_d = 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

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(γ_G) 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 Q_k . 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 Q_k) 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 Q_k) 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 Q_k) 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:

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).

..F_k = G_k    and       γ _f = γ _g for a permanent action.
..F_k = Q_k     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 (γ_PP ) 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 (γ_PP ) term only applies to prestressed concrete applications.
ξ = Reduction factor for unfavourable permanent actions G.

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.

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

X _d = η.X _k / γ_m

where
η = a scale factor covering uncertaintly, scaling , conditions etc.
X _k = the characteristic value of a material (ground) property
γ_m = 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 / γ_M

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

The general equation for the resistance of the structure

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

This can be simplified to

where
γ_M,i = γ_Rd .γ_m,i
.

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

Provided to enable estimates of dead loads

Provided to enable estimates of imposed loads

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

Other Values

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 g_n = 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 = G_k = (unit-weight . 0,25 ) + finishes ) Area = (6 + 1) Area = 7 .Area kN,

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

Slab design load vertical load V_{d_s} = 1,35.G_k + 1,5.Q_k

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

Beam design vertical load V_{d_b} = 1,35 . G_k

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

Column design vertical load V_{d_c} = 1,35. G_k

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 = V_{d_s} +V_{d_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 = V_{d_s} +V_{d_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 A1�B1, B1�C1 and B1�B3 and its self-weight.
From the above, the reaction at B1 due to beam B1�C1 is 58,86 kN and from beam B1�B3 is 116,3kN.
Beam A1�B1 supports only its self-weight = 1,35 . 0,7 . 3 = 2.835 kN.    Hence reaction at B1 due to A1�B1 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 B1�C1 and C1�C3 and its self-weight.
From the above, the reaction at C1 due to beam B1�C1 = 58,86 kN.
Beam C1�C3 supports the reactions from B2�C2 (= 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