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Design actions and combinations

The characteristic values of the actions on the structure are taken from EN 1991 (EC1). For the verifications they are combined in the most unfavourable way according to EN 1990 (EC0). Prestressing is not covered by this program and is therefore omitted from the combinations below.

Ultimate limit states (ULS)

For the persistent and transient design situations the fundamental combination applies (EN 1990 eq. 6.10):

\[\sum_j \gamma_{G,j}\,G_{k,j} \;+\; \gamma_{Q,1}\,Q_{k,1} \;+\; \sum_{i>1} \gamma_{Q,i}\,\psi_{0,i}\,Q_{k,i}\]

where:

  • \(G_{k,j}\) — characteristic value of permanent action \(j\);
  • \(Q_{k,1}\) — characteristic value of the leading variable action;
  • \(Q_{k,i}\) — characteristic value of the accompanying variable actions;
  • \(\psi_{0,i}\) — combination factor (see the table below).

The recommended partial factors for actions (EN 1990 Table A1.2(B)) are:

Action Unfavourable Favourable
Permanent \(\gamma_G\) 1.35 1.00
Variable \(\gamma_Q\) 1.50 0

For the seismic design situation the actions are combined as (EN 1990 eq. 6.12b, EN 1998-1 §3.2.4):

\[\sum_j G_{k,j} \;+\; A_{Ed} \;+\; \sum_i \psi_{2,i}\,Q_{k,i}\]

where \(A_{Ed}\) is the design seismic action and \(\psi_{2,i}\) the quasi-permanent combination factors.

Serviceability limit states (SLS)

Three combinations are used (EN 1990 §6.5.3):

  • Characteristic (irreversible limit states):

    \[\sum_j G_{k,j} + Q_{k,1} + \sum_{i>1}\psi_{0,i}\,Q_{k,i}\]

  • Frequent (reversible limit states):

    \[\sum_j G_{k,j} + \psi_{1,1}\,Q_{k,1} + \sum_{i>1}\psi_{2,i}\,Q_{k,i}\]

  • Quasi-permanent (long-term effects and appearance):

    \[\sum_j G_{k,j} + \sum_i \psi_{2,i}\,Q_{k,i}\]

Combination factors ψ

In the absence of more specific data, the recommended values of EN 1990 Table A1.1 may be used (they may be modified by the National Annex):

Action \(\psi_0\) \(\psi_1\) \(\psi_2\)
Category A – domestic, residential 0.7 0.5 0.3
Category B – office 0.7 0.5 0.3
Category C – congregation areas 0.7 0.7 0.6
Category D – shopping 0.7 0.7 0.6
Category F – traffic, vehicle weight ≤ 30 kN 0.7 0.7 0.6
Snow (buildings, altitude ≤ 1000 m a.s.l.) 0.5 0.2 0
Wind 0.6 0.2 0