Section 6 of EN 1990:2002 describes how the partial factor method is applied in limit state verifications. It provides the overall framework for the applications of the partial factor method, including the way in which actions are combined and partial factors are applied. It is best considered, however, in conjunction with EN 1990:2002, Annex A2 which gives supplementary bridge-specific requirements for establishing combinations of actions, provides ψ-factors and material-independent partial factors, and also gives methods and rules for some material-independent serviceability limit states (e.g. vibrations and deformations of rail bridges).
EQU: see Table A2.4(A) - Design values of actions (EQU) (Set A) from EN-1990 - Annex A2
STR/GEO: see Table A2.4(B) - Design values of actions (STR/GEO) (Set B) from EN-1990 - Annex A2
Accidental and seismic: see Table A2.5 - Design values of actions for use in accidental and seismic combinations of actions from EN-1990 - Annex A2
Recommended values of ψ factors for road bridges: see Table A2.1 from EN-1990-2002.
Combination of action: The simultaneity of the loading systems defined in EN-1991-2 4.3.2 (Load Model 1), 4.3.3 (Load Model 2) and the loads defined in section 5 for footways should be taken into account by considering the groups of loads defined in Table 4.4a from EN 1991-2. Each of these groups of loads, which are mutually exclusive, should be considered as defining a characteristic action for combination with non-traffic loads.
Notes
Load Model 2 is not combined with any other variable load that is not traffic related (see chapter A2.2.2 (2) from EN 1990+A1).
According to EN 1990+A1, chapter A2.2.2 (3), snow loads and wind actions don't need to be combined:
- with the horizontal traffic loads (group 2 - braking, acceleration and centrifugal forces);
- nor with the loads on footways and cycle tracks (group 3);
- nor with Load Model 4 (group 4 - crowd).
Snow loads are not combined with Load Model 1 nor Load Model 2 (see chapter A2.2.2 (4) from EN 1990+A1).
Wind loads should be combined with Load Model 1 (in this case, wind actions are taken with specific ψ factors; see chapter A2.2.2 (5) and Table A2.1 from EN 1990+A1).
Wind actions and thermal actions are not considered simultaneously (see chapter A2.2.2 (6) from EN 1990+A1).
For the French National Annex, all combinations are generated according to the Eurocode, with few changes from France National Annex for gr 1a (see Clause 4.5.1)
The UK National Annex introduces an extra group, gr6 (see Table NA.3). For gr1a, the UK National Annex considers 0.6 times characteristic values. This means the load on footways for gr1a is 0.6 x 5kN/m² = 3.0 kN/m².
The German National Annex introduces an extra group, gr6 (see NCI zu 4.5.1(1)).
The Italian National Annex refers to “Schemi di carico 1,2,3,4,6“. The combinations are generated according to Table 5.1.IV.
Schemi di carico 1 = Load Model 1 from EN1991-2
Schemi di carico 2 = Load Model 2 from EN1991-2.
Schemi di carico 5 = LM4 (crowd loading) from EN1991-2
For the Romanian National Annex, combinations are generated according to the Eurocode.
Load combinations to be considered for ULS and SLS verifications of the bridge are summarized in the following case study, where the following load cases are considered:
Permanent actions
unfavorable: G_{sup}
favorable: G_{inf}
Temperature: Tk
Traffic loads
Group 1a (TS + UDL + Footways & Cycle tracks)
Group 1b (Single axle)
Combination of action for the ultimate limit state
EQU combinations: ∑ γ_{G}*G + γ_{Q1}*Q_{k1} + ∑ γ_{Q}*ψ_{0}*Q_{k}
Thermal action is the leading variable action
1.05*G_{sup} + 0.95*G_{inf} +1.5*T_{k} + 1.35* [0.75*TS + 0.4*UDL + 0.4*Footways & Cycle Tracks]
Note
Load groups are mutually exclusive (gr1a and gr1b cannot be involved in the same combination).
gr1a is the leading variable action
1.05*G_{sup} + 0.95*G_{inf} +1.35*gr1a
Note
We use ψ_{0} = 0 for thermal actions.
gr1b is the leading variable action
1.05*G_{sup} + 0.95*G_{inf} +1.35*gr1b
STR/GEO combinations: ∑ γ_{G}*G + γ_{Q1}*Q_{k1} + ∑ γ_{Q}*ψ_{0}*Q_{k}
Thermal action is the leading variable action
1.35*G_{sup} + 1.00*G_{inf} +1.5*T_{k} + 1.35* [0.75*TS + 0.4*UDL + 0.4*Footways & Cycle Tracks]
gr1a is the leading variable action
1.35*G_{sup} + 1.00*G_{inf} +1.35*gr1a
gr1b is the leading variable action
1.35*G_{sup} + 1.00*G_{inf} +1.35*gr1b
Combination of action for the serviceability limit state
Characteristic combinations: ∑ G + Q_{k1} + ∑ ψ_{0}*Q_{k}
Thermal action is the leading variable action
G_{sup} + G_{inf} + T_{k} + 0.75*TS + 0.4*UDL + 0.4*Footways & Cycle Tracks
gr1a is the leading variable action
G_{sup} + G_{inf} + gr1a
gr1b is the leading variable action
G_{sup} + G_{inf} + gr1b
Frequent combinations: ∑ G + ψ_{1}*Q_{k1} + ∑ ψ_{2}*Q_{k}
Thermal action is the leading variable action
G_{sup} + G_{inf} +0.6*T_{k}
gr1a is the leading variable action
G_{sup} + G_{inf} +[0.75*TS + 0.4*UDL] + 0.5*T_{k}
gr1b is the leading variable action
G_{sup} + G_{inf} +0.5*T_{k}
Quasi-permanent combinations: ∑ G + ψ_{2}*Q_{k1} + ∑ ψ_{2}*Q_{k}
G_{sup} + G_{inf} +0.5*T_{k}
gr1a is the leading variable action
G_{sup} + G_{inf} +0.5*T_{k}
gr1b is the leading variable action
G_{sup} + G_{inf} +0.5*T_{k}
For models involving several load families (Wind, Snow, Thermal actions, Traffic actions, etc.), combinations will be generated using the detailed combination generator:
Concomitance between load cases