This article presents guidance on the application of combination of actions for buildings according to EN 1990 and UK National Annex to EN 1990. In this article, the UK National Annex to EN 1990 is often shorten as UK NA when referenced, and alternative information from the UK NA to the one recommended in the standard is often provided in bracket.
Readers are enjoined to read “Basis of Actions and Load Combinations” if they do not have adequate background on actions as modelled in EN 1990.
Annex A1 of EN 1990 gives rules and methods for establishing combinations of actions for buildings. It also gives the recommended design values of permanent, variable and accidental actions and Ѱ factors to be used in the design of buildings.
Rules guiding Application of Load Combination
Section A12.1 of the standard gives specific rules guiding combination of actions such as:
- Effects of actions that cannot exist simultaneously due to physical or functional reasons should not be considered together in combinations of actions.
- The combinations of actions given in expressions 6.9a to 6.l2b should be used when verifying ultimate limit states.
- The combinations of actions given in expressions 6.l4a to 6.l6b should be used when verifying serviceability limit states.
- Combinations of actions that include prestressing forces should be dealt with as detailed in EN 1992 to EN 1999.
- To aid simplicity for the design, EN 1990 allows the combinations of actions to be based on not more than two variable actions (clause A1.2.1(1), note 1)
- Every combination of actions should include a leading or main variable, or an accidental action
Values of Ѱ factors for building
EN 1990 provides recommended values for Ѱ factors for building in table A1.1 which is reproduced below. These values are consistent with values given in other parts of EN 1991. It is also permitted that National Annexes gives alternatives values for Ѱ. The UK National Annex provides alternative values in Table NA. A1.1.
Design values for actions
The design values of actions are obtained by multiplying the representative value of the actions by required partial safety factor. The values of partial safety factor to be applied for limit states in different design situations is discussed below for both ultimate limit state and serviceability limit state.
Ultimate Limit State
Design value of Actions in persistent and transient design situations
The partial safety factors of actions for ultimate limit states in the persistent and transient design situations (considering expressions 6.9a to 6.10b of EN 1990) should be in accordance with Tables AI.2(A) to (C) (Alternatively, Table NA. A1.2 (A) to (C) in the UK NA).
Static Equilibrium (EQU)
The static equilibrium of a structure or of any part of it is verified using design values of actions in Table A1.2(A) of the standard (Table NA. A1.2 (A) in the UK NA).
Strength (STR)
The design of structural members (Limit state of STR) not involving geotechnical actions should be verified using design values of actions from Table A1.2(B) (Table NA. A1.2 (B) in the UK NA).
Design of structural members (footings, piles, basement walls, etc.) (STR) involving geotechnical actions and the resistance of the ground (GEO) should be verified using one of the following three approaches supplemented, for geotechnical actions and resistances, by EN 1997:
Approach I: Applying in separate calculations design values from Table A l.2(C) and Table AI.2(B) to the geotechnical actions as well as the other actions on/from the structure. In common cases, the sizing of foundations is governed by Table A 1.2(C) and the structural resistance is governed by Table AI.2(B);
Approach 2: Applying design values from Table A l.2(B) to the geotechnical actions as well as the other actions on/from the structure
Approach 3: Applying design values from Table A 1.2(C) to the geotechnical actions and, simultaneously, applying partial factors from Table A1.2(B) to the other actions on/from the structure,
The standard allows that the use of approaches 1,2 or 3 is chosen in the National annex. The UK National Annex favours approach 1.
Note: Overall stability for building structures (e.g., the stability of a slope supporting a building) should be verified in accordance with EN 1997.
Hydraulic (HYD) and buoyancy (UPL) failure (e.g., in the bottom of an excavation for a building structure) should be verified in accordance with EN 1997.
Design Values of Actions in accidental and Seismic design situations
The partial factors for actions for the ultimate limit states in the accidental and seismic design situations (considering expressions 6.11a to 6.12b of EN 1990) should be 1,0. This is consistent with the values given in the UK NA.
Serviceability Limit state
The partial factors for actions for serviceability limit states (considering expressions 6.14b, 6.15b, and 6.16b of EN 1990) should be 1,0. This is also consistent with the values given in the UK NA.
Worked Example on Load Combination
This worked example demonstrates application of load combination on a 10-storey building shear wall.
Loads on shear wall
Permanent Load supported by base of shear wall = 10 x 108 = 1080KN
Imposed floor Load supported by base of shear wall = 10 x 72 = 720KN
In-plane Moment due to wind at the base of the shear wall = 4050KNm
Design Situation: Persistent and transient design situation
Limit State to be verified: Ultimate limit state
Load Combination
Since the design situation and limit state are as specified above, load combination shall be according to equation 6.10 and. A1.1, and A1.2(B) of EN 1990:2002 + A1:2005.
(NB: Ideally, the most critical of load combination of 6.10, 6.10a, and 6.10b should be used. However, to reduce computational effort load combination according to equ 6.10 shall only be used)
$$
\sum_{j\,\,\geqslant \,\,1}{\gamma _{G.j}\,\,G_{k.j}\,\,”+”\,\,\gamma _pP\,\,”+”\,\,\gamma _{Q,1}Q_{k,1}\,\,”+”\,\,\sum_{i\,\,\geqslant \,\,1}{\gamma _{Q,i}\,\,\varPsi _{o,i}Q_{k,i}}}\,\,\left( Equation\,\,\text{6:10,} EN 1990 \right)
$$
There shall be two cases of load combinations. 1) When the variable floor load is the leading variable and the wind action (or action effect due to wind) is the accompanying variable 2) When the wind action (or action effect due to wind) is the leading and the variable floor load is the accompanying variable.
These two cases are demonstrated below:
Load Combination Case 1
Dead + Imposed floor load as leading variable (Qk, 1) + Wind as accompanying variable (Qk, i)
γGj,sup = 1.35, γQ, 1 = 1.5, γQ, i = 1.5, ψo, i = 0.6
Ultumate Axial Load = 1.35 x 1080 + 1.5 x 720 = 2538KN
Ultimate Moment due to wind Load = 1.5 x 0.6 x 4050 = 3645KNm
Load combination Case 2)
Dead + Wind as leading variable () + Imposed as accompanying variable ()
γGj,sup = 1.35, γQ, 1 = 1.5, γQ, i = 1.5, ψo, i = 0.7
Ultimate Axial Load = 1.35 x 1080 + 1.5 x 0.7 x 720 = 2214KN
For detailed analysis and design of the 10-storey shear wall, read “Design of Planar Shear Wall – Worked Example”.
References
EN 1990: Basics of Structural design
