## Eurocode Basis of structural design

This Eurocode underpins all structural design irrespective of the material of construction. It establishes principles and requirements for safety, serviceability and durability of structures. (Note, the correct title is Eurocode not Eurocode 0.) The Eurocode uses a statistical approach to determine realistic values for actions that occur in combination with each other.

There is no equivalent British Standard for Eurocode: Basis of structural design and the corresponding information has traditionally been replicated in each of the material Eurocodes. It also introduces new definitions (see Glossary) and symbols (see Tables 2a and 2b), which will be used throughout this publication to assist familiarity. Partial factors for actions are given in this Eurocode, whilst partial factors for materials are prescribed in their relevant Eurocode.

### Representative values

For each variable action there are four representative values. The principal representative value is the characteristic value and this can be determined statistically or, where there is insufficient data, a nominal value may be used. The other representative values are combination, frequent and quasi-permanent; these are obtained by applying to the characteristic value the factors Co, Ci and c2 respectively (see Figure 3). A semi-probabilistic method is used to derive the C factors, which vary depending on the type of imposed load (see Table 3). Further information on derivation of the C factors can be found in Appendix C of the Eurocode.

The combination value (c0 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 (C1 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 (C2 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.

### Combinations of actions

In the Eurocodes the term 'combination of actions' is specifically used for the definition of the magnitude of actions to be used when a limit state is under the influence of different actions. It should not be confused with 'load cases', which are concerned with the arrangement of the variable actions to give the most unfavourable conditions and are given in the material Eurocodes. The following process can be used to determine the value of actions used for analysis:

1. Identify the design situation (e.g. persistent, transient, accidental).

2. Identify all realistic actions.

3. Determine the partial factors (see below) for each applicable combination of actions.

4. Arrange the actions to produce the most critical conditions.

Where there is only one variable action (e.g. imposed load) in a combination, the magnitude of the actions can be obtained by multiplying them by the appropriate partial factors.

Where there is more than one variable action in a combination, it is necessary to identify the leading action (Qk,i) and other accompanying actions (Q^.The accompanying action is always taken as the combination value.

Ultimate limit state

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. The Eurocode gives different combinations for each of these ultimate limit states. For the purpose of this publication only the STR ultimate limit state will be considered.

For persistent and transient design situations under the STR limit state, the Eurocode defines three possible combinations, which are given in Expressions (6.10), (6.10a) and (6.10b) of the Eurocode (see Tables 4 and 5).The designer (for UK buildings) may use either (6.10) or the less favourable of (6.10a) and (6.10b).

At first sight it appears that there is considerably more calculation required to determine the appropriate load combination; however, with experience the designer will be able to determine this by inspection. Expression (6.10) is always equal to or more conservative than the less favourable of Expressions (6.10a) and (6.10b). Expression (6.10b) will normally apply when the permanent actions are not greater than 4.5 times the variable actions (except for storage loads (category E,Table 3) where Expression (6.10a) always applies).

Therefore, for a typical concrete frame building, Expression (6.10b) will give the most structurally economical combination of actions.

Table 2a

Selected symbols for Eurocode

For members supporting one variable action the combination

1.25 Ck + 1.5 Qk (derived from (Exp 6.10b)) can be used provided the permanent actions are not greater than 4.5 times the variable actions (except for storage loads).

### Serviceability limit state

There are three combinations of actions that can be used to check the serviceability limit states (see Tables 6 and 7). Eurocode 2 indicates which combination should be used for which phenomenon (e.g. deflection is checked using the quasi-permanent combination). Care should be taken not to confuse the SLS combinations of characteristic, frequent and quasi-permanent, with the representative values that have the same titles.

Table 2a

Selected symbols for Eurocode

 Symbol Definition Gk Characteristic value of permanent action Qk Characteristic value of single variable action gG Partial factor for permanent action gQ Partial factor for variable action Co Factor for combination value of a variable action Ci Factor for frequent value of a variable action C2 Factor for quasi-permanent value of a variable action j Combination factor for permanent actions Table 2b Selected subscripts Subscript Definition A Accidental situation c Concrete d Design E Effect of action fi Fire k Characteristic R Resistance w Shear reinforcement y Yield strength

Figure 3

Representative values of variable actions5

Figure 3

Representative values of variable actions5

Characteristic value of QK

Combination value of CoQk

I

i A Frequent value of CiQk

\ / \ Quasi- A / 111 permanent 1 \ 1 1 1 lvalue of CzQk) I 1

rn rv

Recommended values of C factors for buildings (from UK National Annex)

Table 3

Recommended values of C factors for buildings (from UK National Annex)

Action

C0 1 C 1 C2

Imposed loads in buildings (see BS EN 1991-1-1)

Category A: domestic, residential areas

0.7

0.5

0.3

Category B: office areas

0.7

0.5

0.3

Category C: congregation areas

0.7

0.7

0.6

Category D: shopping areas

0.7

0.7

0.6

Category E: storage areas

1.0

0.9

0.8

Category F: traffic area, vehicle weight < 30 kN

0.7

0.7

0.6

Category G: traffic area, 30 kN < vehicle weight < 160 kN

0.7

0.5

0.3

Category H: roofs*

0.7

0

0

Snow loads on buildings (see BS EN 1991-3)

For sites located at altitude H > 1000 m above sea level

0.7

0.5

0.2

For sites located at altitude H < 1000 m above sea level

0.5

0.2

0

Wind loads on buildings (see BS EN 1991-1-4)

0.5

0.2

0

Temperature (non-fire) in buildings (see BS EN 1991-1-5)

0.6

0.5

0

Key

*See also 1991-1-1: Clause 3.3.2

Design values of actions, ultimate limit state - persistent and transient design situations (table A1.2 (B) Eurocode)

Table 4

Design values of actions, ultimate limit state - persistent and transient design situations (table A1.2 (B) Eurocode)

 Combination Expression reference Permanent actions Leading variable action Accompanying variable actions Unfavourable Favourable Main (if any) Others Exp. (6.10) gG,j,sup Gk,j, sup gG,j,inf Gk,j,inf gQ,1 Qk,1 gQ,1 Co,1 Qk,i Exp. (6.10a) gG,j,sup Gk,j ,sup gG,j,inf Gk,j,inf gQ,1 Co,1 Qk,1 gQ,1 Co,1 Qk,i Exp. (6.10b) jgG,j,sup Gk,j ,sup gG,j,inf Gk,j,inf gQ,1 Qk,1 gQ,1 Co,1 Qk,i Note 1 Design for either Expression (6.10) or the less favourable of Expressions (6.10a) and (6.10b).

Table 5

Design values of actions, derived for UK design, ultimate limit state - persistent and transient design situations

Table 5

Design values of actions, derived for UK design, ultimate limit state - persistent and transient design situations

 Combination Expression reference Permanent actions Leading variable action Accompanying variable actions Unfavourable Favourable Main (if any) Others Combination of permanent and variable actions Exp. (6.10) 1.35 Gka 1.0 Gka 1.5c Qk Exp. (6.10a) 1.35 Gka 1.0 Gka 1.5 Co,1b Qk Exp. (6.10b) 0.925dx 1.35 Gka 1.0 Gka 1.5c Qk Combination of permanent, variable and accompanying variable actions Exp. (6.10) 1.35 Gka 1.0 Gka 1.5c Qk,1 1.5c Co,ib Qk,i Exp. (6.10a) 1.35 Gka 1.0 Gka 1.5 Co,1b Qk 1.5c Co,ib Qk,i Exp. (6.10b) 0.925d x 1.35 Gka 1.0 Gka 1.5c Qk,1 1.5c Co,ib Qk,i a Where the variation in permanent action is not considered significant, G^sup and Gkjjnf may be taken as Gk c Where the accompanying load is favourable, gQ,j = 0 b The value of C0 can be obtained from Table NA A1.1 of the UK National Annex (reproduced here as Table 3) d The value of j in the UK National Annex is 0.925

Table 6

Design values of actions, serviceability limit states

Table 6

Design values of actions, serviceability limit states

 Combination Permanent actions Variable actions Example of use in Eurocode 2 Unfavourable Favourable Leading Others Characteristic Gk,j,sup G k,j, i nf Qk,1 Co,i Qk,i Frequent Gk,j,sup G k,j, i nf C1,1 Qk,1 C2,i Qk,i Cracking - prestressed concrete Quasi-permanent Gk,j,sup G k,j, i nf C2,1 Qk,1 C2,i Qk,i 1 Where the variation in permanent action is not considered significant. Gkfj,sup and Gk,j,jnf may be taken as Gk 2 For values of C0, C1 and C2 refer to Table 3

Table 7

Example design combinations for deflection (quasi-permanent) derived for typical UK reinforced concrete design

Table 7

Example design combinations for deflection (quasi-permanent) derived for typical UK reinforced concrete design

 Combination Permanent actions Variable action Unfavourable Leading Office Gka 0.3b Qk,1 Shopping area Gka 0.6b Qk,1 Storage Gka 0.8b Qk,1 a Where the variation in permanent action is not considered significant Gkfj,sup and Gk,j,inf may be taken as Gk b Values of are taken from UK NA (see Table 3)

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