This article presents a guide to understanding actions and combinations of actions (Load combinations) as modelled in EN 1990 applicable to verifying limit states for relevant design situations.
EN 1990 describes the principles and requirements for safety, serviceability, and durability of structures. It is based on the limit state concept used in conjunction with a partial factor method. From the criteria that facilitate achieving the objective of EN 1990, especially of meeting safety and serviceability requirements is correct assessment of actions acting on structures. This article seeks to help readers to understand load models as espouse by EN 1990.
What are Actions?
Actions are direct loads applied to a structure, or indirect actions (imposed deformations or accelerations) caused by temperature change, uneven settlement, earthquakes, etc.
Although the Eurocode introduces the term “actions”, it is however not intended to obliterate the term “load” which is adopted in superseded British standards in every instance. Action is more encompassing such that it refers to both direct loads and imposed deformations, unlike the term “load” which only refers to direct loads applied on structures.
EN 1990 gives general principles for classification of actions on structures, and their modelling in verification of structural reliability. It also defines the various design values and combination rules to be used in the design calculations. A detailed description of individual actions is given in various part of EN 1991 (Eurocode 1). A list of different parts of EN 1991 and their actions of interest is given below.
EN 1991-1-1: Densities, Self-weight and Imposed loads for buildings
EN 1991-1-2: Actions on structures exposed to fire
EN 1991-1-3: Snow Loads
EN 1991-1-5: Thermal actions
EN 1991-1-6: Actions during execution
EN 1991-1-7: Accidental Actions
EN 1991-2: Traffic Loads on bridges
EN 1991-3: Actions induced by crane and machinery
EN 1991-4: Action in Silos and Tanks
Classification of Actions
Actions are generally categorized as:
- permanent actions (G) (e.g., self-weight, prestressed force, fixed equipment etc.)
- variable actions (Q) (e.g., weight of occupancy, wind load, traffic load etc.)
- Accidental action (A) (e.g., impact, earthquake, explosion etc.)
Representative value of an action (Frep)
A representative value of an action is a value used for the verification of a limit state. A representative value may be the characteristic value () or any of the other three accompanying value (Ѱ) which are enumerated below. Representative values of actions are always gotten by multiplying the characteristic value of an action by a factor Ѱ. As for characteristic value which itself is also a representative value, the factor Ѱ is always 1.
Practical illustration: A representative value of an action is that exact value (e.g.: 5KN/m²) of a permanent (G or g) or variable action (Q or q) that can be used in actual calculation. This 5KN/m² can either be a characteristic value or accompanying value.
Characteristic Value of Actions (Fk)
Characteristic values for variables are known statistical distribution below which not more than a defined percentage of a population will fall. For Eurocodes, the characteristic values of actions refer to values of such magnitude that only a 5% probability exists that these actions will be exceeded throughout the design life of a structure. The characteristic value can either be for a permanent action (Gk or gk) or a leading variable action (Qk or qk).
It should however be noted that in cases when the limit state is very sensitive to variations in the magnitude of permanent actions, the upper characteristic value (Gp,sup) and lower characteristic values (Gp,inf) of actions should be considered as appropriate.
Accompanying Value (ѰFk)
Accompanying value of an action is a representative value which is only applicable to variable actions. This is necessary when there are more than one variable action acting on a structure; one of these variable actions is considered as the leading variable action which is represented with its characteristic value, while the others are taken as the accompanying variable actions which is represented by multiplying the characteristic value by a factor Ѱ.
Accompanying value of actions are often dubbed as “other representative values” in EN 1990 to distinguish them from the characteristic value. These other representative values are enumerated below.
Combination value (Ѱ0Qk)
The combination value, represented as a product Ѱ0Fk, used for the verification of ultimate limit states and irreversible serviceability limit states. The factor has been introduced to take account of the fact that where a structure is subject to, say, two independent variable actions, there is low probability that both actions will reach their maximum value (characteristics value) simultaneously. Under these circumstances, it is assumed that the ‘leading’ variable action is at its maximum value (i.e. Qk,1) and any ‘accompanying’ variable actions will attain a reduced value (Ѱ0Qk,1)
Frequent Value (Ѱ1Qk)
Design value of an action represented as a product, used for the verification of ultimate limit states involving accidental actions and for verifications of reversible serviceability limit states. A frequent value of a load that is likely to be exceeded for only a short period of time.
Quasi-permanent value (Ѱ2Qk)
The quasi-permanent value, represented as a product Ѱ2Qk, used for the verification of ultimate limit states involving accidental actions and seismic actions. It is also used for the verification of reversible serviceability limit states and for the calculation of long-term effects. They are values of load that is likely to be sustained for a long period of time. They are almost like permanent actions.
NB: Values of ψ0, ψ1 and ψ2 are given in EN 1990: TableA1.1 for buildings (a modified version of which is given in Table NA.A 1.1 from the UK National Annex), and Table A2.1 for bridges (a modified version of which is given in Table NA.A 2.1 from the UK National Annex)
Verification of Designs
Verification is the process of checking that in all relevant design situations, no relevant limit state is exceeded when design values for actions or effects of actions and resistances are used in the design models.
From the above definition of verification, it can be said that three parameters are required in the verification process, which are:
- Limit State to be verified
- Design Situation being considered
- Design value of actions acting on a member or structure
Limit State
A limit state is a state beyond which the structure no longer fulfils the relevant design criteria. And these is categorized into ultimate limit state and serviceability limit state.
Ultimate limit states
Ultimate limit state is the limit state associated with collapse or with other similar forms of structural failure. According to clause 6.4.1 of the standard, the ultimate limit state to be verified when relevant are:
EQU: Loss of static equilibrium of the structure or any part of it considered as a rigid body, where:
STR: Internal failure or excessive deformation of the structure or structural members, including footings, piles, basement walls, etc., where the strength of construction materials of the structure governs
GEO: Failure or excessive deformation of the ground where the strengths of soil or rock are significant in providing resistance;
FAT: Fatigue failure of the structure or structural members.
UPL: loss of equilibrium of the structure or the ground due to uplift by water pressure (buoyancy) or other vertical actions.
HYD: hydraulic heave, internal erosion and piping in the ground caused by hydraulic gradients.
Serviceability limit states
Serviceability limit state is the limit state that correspond to conditions beyond which specified service requirements for a structure or structural member are no longer satisfied. This is the limit state that is concerned with the functioning of the structure under normal use, the comfort of people, and the appearance of the structure. Serviceability limit states may be reversible (e.g. deflection) or irreversible (e.g. yield).
Reversible Serviceability State
This is a serviceability limit states where no consequences of actions exceeding the specified service requirements will remain when the actions are removed, e.g., the elastic deflection of a steel beam, vibration
Irreversible Serviceability State
This is a serviceability limit states where some consequences of actions exceeding the specified service requirements will remain when the actions are removed, e.g., deflection due to creep etc.
Design Situations
Design situations are certain circumstances for which the design will demonstrate that relevant limit states are not exceeded. Design situations recognized by the standard are mentioned below:
Transient design situation
Design situation that is relevant during a period much shorter than the design working life of the structure and which has a high probability of occurrence. Summarily, these are temporary conditions applicable to a structure, e.g. situation during construction or repair.
Persistent design situation
This can be defined as the condition of normal use of a structure.
Accidental design situation
design situation involving exceptional conditions of the structure or its exposure, including fire, explosion, impact or local failure
Seismic Design Situation
Design situations which refer to conditions applicable to the structure when subjected to seismic events.
Design Value of Actions
Design values should be obtained by multiplying the representative value by the partial factor of safety (ϒf). This is express as:
Fd = ϒfFrep
ϒf is the relevant partial factor of safety. They account for the possibility of unfavourable deviations of the action in reality from the representative values. They are denoted as ϒG| and ϒg for concentrated and distributed permanent load, and ϒQ| and ϒq for concentrated and distributed variable load respectively.
Frep is the representative value which can be expressed as
Frep = ѰFk
Where:
Ѱ is either 1.0, Ѱ0,Ѱ1, Ѱ2 based on whether the representative value is characteristic, combination, frequent, or quasi-permanent value as explained earlier.
Combination of actions (Load Combination)
Having determined the design values of individual actions acting on the structure by multiplying their representative value by appropriate partial safety factor as discussed above, it is necessary to consider the possible simultaneous effects of two or more combination of these actions on structures. This allowance for simultaneous effect of actions is what leads to combination of actions in the standard.
Combination of actions is a set of design values used for the verification of the structural reliability for a limit state under the simultaneous influence of different actions
For each critical load case, the design values of the effects of actions (Ed) shall be determined by combining the values of actions that are considered to occur simultaneously. The expressions for combination of actions are provided below for verifying limit state for various design situations.
Ultimate Limit State
Persistent and transient design situation
$$
\sum_{j\,\,\geqslant \,\,1}{\gamma _{G.j}\,\,G_{k.j}\,\,”+”\,\,\gamma _pP\,\,”+”\,\,\gamma _{Q,1}Q_{k,1}\,\,”+”\,\,\sum_{i\,\,\geqslant \,\,1}{\gamma _{Q,i}\,\,\varPsi _{o,i}Q_{k,i}}}\,\,\left( Equation\,\,\text{6:10,} EN 1990 \right)
$$
Alternatively, for STR and GEO limit states, the less favourabe of the two expressions below can be used
$$
\sum_{j\,\,\geqslant \,\,1}{\gamma _{G.j}\,\,G_{k.j}\,\,”+”\,\,\gamma _pP\,\,”+”\,\,\gamma _{Q,1}\,\,\varPsi _{o,1}Q_{k,1}\,\,”+”\,\,\sum_{i\,\,\geqslant \,\,1}{\gamma _{Q,i}\,\,\varPsi _{o,i}Q_{k,i}}}\,\,\left( Equation\,\,\text{6:10a,}EN 1990 \right)
$$
$$
\sum_{j\,\,\geqslant \,\,1}{\xi _j\gamma _{G.j}\,\,G_{k.j}\,\,”+”\,\,\gamma _pP\,\,”+”\,\,\gamma _{Q,1}Q_{k,1}\,\,”+”\,\,\sum_{i\,\,\geqslant \,\,1}{\gamma _{Q,i}\,\,\varPsi _{o,i}Q_{k,i}}}\,\,\left( Equation\,\,\text{6:10b,}EN 1990 \right)
$$
Accidental design situation
$$
\sum_{j\,\,\geqslant \,\,1}{\,\,G_{k.j}\,\,”+”\,\,P\,\,”+”\,A_d\,”+”\,\,\left( \psi _{\text{1,}1}\,\,or\,\,\psi _{\text{2,}1} \right) Q_{k,1}\,\,”+”\,\,\sum_{i\,\,\geqslant \,\,1}{\,\,\varPsi _2Q_{k,i}}}\,\,\left( Equation\,\,\text{6:}11b,\,\,EN 1990 \right)
$$
The choice between Ѱ1,1Qk,1 or Ѱ2,1Qk,1 should be related to the relevant accidental design situation (impact, fire or survival after an accidental event or situation).
Seismic Design situation
$$
\sum_{j\,\,\geqslant \,\,1}{\,\,G_{k.j}\,\,”+”\,\,P\,\,”+”\,A_d\,”+”\,\,\sum_{i\,\,\geqslant \,\,1}{\,\,\varPsi _2Q_{k,i}}}\,\,\left( Equation\,\,\text{6:12b},\,\,EN\,\,1990 \right)
$$
Partial factors for actions and combinations of actions (1) The values of the y and ‘V factors for actions should be obtained from EN 1991 and from Annex A.
Serviceability Limit State
Characteristic Combination
$$
\sum_{j\,\,\geqslant \,\,1}{\,\,G_{k.j}\,\,”+”\,\,P\,\,”+”\,\,Q_{k.1}\,\,”+”\sum_{i\,\,\geqslant \,\,1}{\,\,\varPsi _{\text{0,}i}Q_{k,i}}}\,\,\left( Equation\,\,\text{6:}14b,\,\,EN\,\,1990 \right)
$$
Frequent Combination
This combination is used for reversible limit state
$$
\sum_{j\,\,\geqslant \,\,1}{\,\,G_{k.j}\,\,”+”\,\,P\,\,”+”\,\,\varPsi _{\text{1,}1}\,\,Q_{k.1}\,\,”+”\sum_{i\,\,\geqslant \,\,1}{\,\,\varPsi _{\text{2,}i}Q_{k,i}}}\,\,\left( Equation\,\,\text{6:}15b,\,\,EN\,\,1990 \right)
$$
Quasi-permanent Combination
$$
\sum_{j\,\,\geqslant \,\,1}{\,\,G_{k.j}\,\,”+”\,\,P\,\,”+”\,\,\sum_{i\,\,\geqslant \,\,1}{\,\,\varPsi _{2.i}Q_{k,i}}}\,\,\left( Equation\,\,\text{16b},\,\,EN\,\,1990 \right)
$$
Where:
“+” implies “to be combined with”
Ʃ implies “the combined effect of’;
𝜉 is a reduction factor for unfavourable permanent actions G
P is the representative value of a pre-stressing action
Gk,j is the characteristic value of a permanent action
Qk,1 is the characteristic value of the leading variable action,
Qk,i is the characteristic value of the accompanying variable actions,
γGj is the safety factor for permanent actions,
γQ,1 is the partial safety factor for the leading variable action,
γQ,i is the partial safety factor for the accompanying variable actions,
Ѱ0,i is the combination factor which is applied to the characteristic value Qk of an action not being considered as Qk,1,
Ѱ1,i is the factor for the frequent value of a variable action,
Ѱ2,i is the factor for the quasi-permanent value of a variable action.
Ѱ1,1Qk,1
Reference
EN 1990: Basics of Structural design
BS EN 1990:2002+A 1 :2005 EN 1990:2002+A1:2005 (E)
Design of Structural Elements to Eurocode 2 by McKenzie
