COMBINATION OF ACTIONS

2.1 General

The effects of actions that cannot occur simultaneously due to physical or functional reasons should not be considered together in combinations of actions. In case when specific measures are provided preventing some actions to act simultaneously, these combinations need not be considered in analysis (e.g. when it is assured that some construction loads are not simultaneously acting during a specific construction phase).

The expressions 6.9a to 6.12b in EN 1990 [1] are applied for the verification of ultimate limit states and the expressions 6.14a to 6.16b are applied for the verification of the

serviceability limit states in bridge design.

2.2 Fundamental combination of actions

Three alternatives procedures for fundamental combination of actions is provided for bridges, similarly as for buildings. The choice of combination is the National Determined Parameter (NDP) which may be nationally selected.

For example the fundamental combination of actions in bridge design in the Czech Republic is based on the twin expressions (6.10a), (6.10b) given as

i

where the less favourable expression needs to be considered. Where relevant, the favourable or unfavourable design values of permanent actions G_d,sup or G_d,inf should be considered.

The application of the combination of actions according to the twin expressions (6.10a), (6.10b) gives in common cases more uniform reliability level of bridges for various ratios of the characteristic values of variable loads and permanent loads. Furthermore, it was also decided in the Czech Republic to allow application of the unique expression (6.10)

+ ∑ Selected results of application of alternative combination rules for a prestressed concrete road bridge is shown in the example 5.2 at the end of this Chapter.

The rules for simultaneous combinations of individual traffic load models and their arrangements are provided in EN 1991-2 [3]. Five different and mutually exclusive groups of traffic loads as given in [3] are shown in Table 1. Any group of traffic loads should be taken into account as one variable action which is acting in combination with other variable actions.

Table 1. Assessment of groups of traffic loads (characteristic values of the multi-component action)

Carriageway Footways and

cycle tracks

Vertical loads Horizontal loads Vertical loads

only

verification of ultimate and serviceability limit states during execution and for combination of construction loads with other variable loads remain till now in Annex A2 of EN 1991-1-6 [5].

It should be taken into account in appropriate cases that construction loads Qc act simultaneously with other types of actions. Different construction loads (Q_ca to Q_ce) should be considered according to the project conditions as one single action, or also as several individual construction loads that are combined with other variable actions. In some cases it need not be considered in one combination some variable actions. For example, it is rather unlikely the simultaneous occurrence of construction load Qca due toworking personnel with small site equipment together with maximum wind or snow actions. For individual project however, it may need be considered in combination snow and wind simultaneously with other types of construction loads, e.g. with cranes. The characteristic values of climatic actions may be reduced for short-time construction periods on the basis of EN 1991-1-6 [6].

Where relevant, the thermal actions and water loads should be considered simultaneously with construction loads. The various parameters governing water actions and components of thermal actions should be taken into account when identifying appropriate combinations with construction loads. The selection of actions to load combinations need to be considered according to the conditions of individual project.

2.3 Combinations of actions for road bridges

Suplementary rules are introduced for load combinations on road bridges. The snow load and wind actions need not to be combined with

- the braking and acceleration forces or the centrifugal forces or the associated group of loads gr2

- the loads on footways and cycle tracks or with the associated group of loads gr3, - the crowd loading (LM 4) or the associated group of loads gr4.

In common cases it is not necessary to consider the snow loads together with models LM1 and LM2. However, in some mountain areas it may be also necessary to consider the combination of snow with traffic.

LM1 or group of loads gr1a need not to be considered with wind actions greater thanF_W^* or ψ₀F_Wk.

For certain serviceability limit states of concrete bridges the infrequent combination of actions is also recommended in EN 1990/A1 [2] given as

{

}

E _{, 1,infq ,1 1, ,} ≥ >

= G P Q Q j i

E_{d k j} ψ _k ψ _{i ki} (4)

where the combination of actions in braquet may be expressed as

i

2.4 Combination rules for footbridges

Infrequent combination of variable actions is not considered in footbridge design. The concentrated load (wheel load) Qfwk need not to be combined with any other variable actions than those due to traffic.

In general, wind loads and thermal actions need not be taken into account simultaneously in common cases.

Snow loads need not be combined with groups of loads gr1 and gr2 for footbridges unless otherwise specified for particular geographical areas and certain types of footbridges.

In case that fotbridges provide protection of the pedestrians and cyclists against all kinds of unfavourable weather, the specific load combinations may be determined. The combination similar to actions on buildings may be applied in which instead of relevant category of imposed load the specific group of traffic loads is applied.

2.5 Combinations of actions for accidental design situations

One accidental action should be considered only in accidental load combination which need not be combined with snow load or wind actions.

Models of accidental actions on bridges are given in EN 1991-2 [3], models of impact forces due to cars, heavy vehicles and vessels on bridge substructures in EN 1991-1-7 [7].

Additional combinations of actions for other accidental design situations (e.g. combination of road or rail traffic actions with avalanche, flood or scour effects) may be agreed for the individual project.

2.6 Values of ψ factors

ψ factors for traffic loads, wind, thermal actions and construction loads are given for road bridges in the following Table 2. The recommended values of ψ factors are given for the road traffic corresponding to adjusting factors αQi, αqi, αqr and βQ equal to 1. The recommended ψ0 value for thermal actions may in most cases be reduced to 0 for ultimate limit states EQU, STR and GEO.

The characteristic values of wind actions and snow loads during execution are defined in EN 1991-1-6 [6]. Representative values of water loads are not given in EN 1990/A1 [2].

They may be defined as NDP in the National Annex or for the individual project.

Table 2. Recommended values of ψψψ factors for road bridges. ψ

Type of action ψ0 ψ1,infq ψ1 ψ2

Traffic loads

gr1a (LM1 + pedestrian or cycle-track loads)¹⁾

TS (tandem system) 0.75 0.8 0.75 0

UDL (uniform) 0.40 0.8 0.40 0

pedestrian or cycle-track loads ²⁾

0.40 0.8 0.40 0

gr1b (single axle) 0 0.8 0.75 0

gr2 (horizontal forces) 0 0 0 0

gr3 (pedestrian loads) 0 0.8 0.40 0

gr4 (LM4 – crowd loading) 0 0.8 0.75 0

gr5 (LM3 – special vehicles) 0 0 0 0

Wind actions Fw – persistent design situation – transient design situation

0.6 0.8

0.6 -

0.2 -

0 0

Fw* 1.0 1 - -

Thermal actions Tk 0.6 0.8 0.6 0.5

Snow loads QSn,k – transient design situation 0.8 - - -

Construction loads Qc 1.0 - - 1.0

The recommended values of ψ0, ψ1 and ψ2 for gr1a and gr1b are given for road traffic corresponding to adjusting factors αQi, αqi, αqr and β_Q equal to 1. Those relating to UDL correspond to common traffic scenarios, in which a rare accumulation of lorries can occur.

Other values may be expected for other classes of routes, or expected traffic, related to the choice of the corresponding α factors.

Recommended ψ factors for footbridges are given in Table 3. The combination value of the pedestrian and cycle-track load, mentioned in Table 4.4a of EN 1991-2 [3] is a reduced value to which the factorsψ0 and ψ1 may be used.

The recommended ψ0 value for thermal actions may in most cases be reduced to 0 for ultimate limit states EQU, STR and GEO.

Table 3. Recommended values of ψψψ factors for footbridges. ψ

Action ψ0 ψ1 ψ2

gr1 0.40 0.40 0

Traffic loads Qfw 0 0 0

gr2 0 0 0

Wind forces Fw 0.3 0.2 0

Thermal actions T 0.6 0.6 0.5

Snow loads QSn (transient design situation) 0.8 - 0

Construction loads Qc 1.0 - 1.0