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In addition to the extrapolated static effects, the target values evaluation requires also specific knowledge about the dynamic effects, due to vehicle-bridge interactions, to be considered in calibration studies [9].

A.6.1 The inherent impact factors simulated considering the lorries, represented by a sequence of axles with shock-absorbers having suitable dynamic characteristics, running on good roughness pavement resting on rigid foundation.

In this way it was stated that the characteristic values, which are relevant for the ultimate limit states, are affected by an inherent impact factor ϕin=1.10. When serviceability limit states and fatigue are considered, instead, and the range between the 10% and the 90%

fractiles is taken into account, static and dynamic effects practically coincide and ϕin=1.00.

A.6.2 The impact factor

The impact factor depends on several parameters, like type, static scheme, span, natural frequency and damping coefficient of the bridge, dynamic characteristics and speed of the lorries, roughness of the road pavement and so on.

Generally, it results greater when the natural frequency of the bridge is close to the natural frequencies of axles (10÷12 Hz) and lorries (1÷2 Hz).

In the framework of EN 1991-2 pre-normative studies, in order to determine global local impact factors, a number of numerical simulations have been performed considering several bridge schemes with varying traffic scenarios.

Concerning global effects, medium or good road pavement roughness has been considered in turn. Local dynamic effects have been studied taking into account the presence of a stepped irregularity, 30 mm height and 500 mm wide, simulating a road surface discontinuity, like that caused by a damaged expansion joint, a pothole or an ice sheet.

The result of each numerical simulation was a time history of the considered effect, like the one reported in figure A.9, from which the so-called physical impact factor ϕ ^{can be} derived. Physical impact factor is the ratio between the maximum dynamic response and the maximum static response of the bridge

st dyn

max

= max

ϕ ^{. (A.13)}

The physical impact factor refers to a well precise load configuration and it depends on such a quantity of parameters that cannot to be directly employed for load model calibration. Besides, heaviest vehicles, which mainly influence the extreme values of the dynamic distribution of traffic effects, are generally slow and are characterised by small value of ϕ ^factors.

For calibration purposes, two alternative approaches can be adopted:

- the first approach takes into account dynamic effects referring directly to the dynamic effects distribution;

- an alternative method takes into account the static effect distribution multiplied by a suitable calibration value of the impact factor, ϕcal. ϕcal can be defined as the ratio between the dynamic value Edyn(p-fractile) and the static value Est(p-fractile)

corresponding to the same assigned p-fractile

)

Static oscillogram Effect

Dynamic increment

N ⁰ Dynamic

oscillogram

t

t

Figure A.9. Definition of the physical impact factor ϕϕϕϕ

Obviously, due to its conventional nature, ϕcal doesn't have a precise physical meaning; in fact the static and dynamic x-fractiles don’t correspond to the same load configuration.

The characteristic values of the calibration impact factors ϕcal, derived from Auxerre traffic and employed in EN1991-2, are synthesized in figure A.10, depending on the span length L.

The target dynamic values Edyn(x-fractile) can be finally evaluated through the expression

) (

)

( st x fractile

in local cal fractile

x

dyn E

E ₋ = ⋅ ⋅ ₋

ϕ ϕ

ϕ . (A.15)

where ϕlocal represents the local impact factor, when relevant.

Local impact factor ϕlocal takes into account concentrated irregularities of the roadway surface.

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

0 100 200

L [m]

φcal

Bending 1 lane Bending 2 lanes Bending 4 lanes Shear

Figure A.10. Calibration value of the impact factors ϕϕϕϕcal (EN 1991-2).

A.7 Concluding remarks

Traffic load models for road bridges of EN 1991-2 have been defined and calibrated step by step balancing demand for accuracy and demands for ease of use.

Preliminary calibrations highlighted that load models best fitting the target values should consist of concentrated loads and distributed loads:

- at least two concentrated loads should be considered in each relevant lane;

- Introduction of more than two concentrated loads doesn’t affect the precision of the results.

- the intensity of the uniformly distributed loads result slowly decreasing functions of the loaded length L.

The preliminary outcome has been successively modified to simplify the structure and the application rules of the load model, mainly to eliminate any reason for ambiguity, finally arriving to a load model characterised by:

- load values independent from the loaded length;

- dynamic effects include in load values;

- coexistence of concentrated and distributed loads on the same loaded area;

- aptitude to evaluate local and global, even simultaneous, effects;

- width of the notional lane equal to 3.0 m.

For the sake of model coherence, it has been established that, when relevant, the entire carriageway width can be loaded, i.e. not only the part occupied by the physical lanes, but also that one remaining.

In order to reproduce the real traffic effects in secondary elements, characterized by influence surfaces with very small base length, it has been also introduced a local load model, constituted by a single axle, which should be considered alone on the bridge.

Once opportunely calibrated, the so defined load model constitutes the load model of EN 1991 - 2, which is illustrated more precisely in §2 of chapter 3.

Besides characteristic loads, having a probability of about 2% to be exceed in 50 years design working life, i.e. about 1000 years return period, other relevant values of real traffic effects exist, like infrequent, frequent and quasi-permanent values, which are particularly relevant for SLS assessments.

Infrequent and frequent can be identified by one year or one week return period, respectively. Quasi-permanent values result generally negligible and can be set zero, except for particular cases, like, for example, bridges in the urban zone.

Frequent and infrequent values of traffic effects can be determined resorting to methods substantially analogous to those used for the evaluation of characteristic values.

Their detailed illustration is omitted here, stressing only some relevant conclusion, on which the relevant parts of EN 1991-2 are based:

- characteristic values of traffic effects increase slowly with the return period, in fact - taking into account a medium roadway roughness, infrequent values of traffic

effects are about 90% of the corresponding characteristic values;

- taking into account a good roadway roughness, infrequent values reduce a little and become about 80% of the corresponding characteristic values;

- frequent values of traffic effects are 70%÷80% of the corresponding characteristic values;

- since the frequent values of traffic effects depend substantially on flowing traffic, as the span increase frequent values tend to precise lower limits, which are approximately 40%÷50% of the corresponding characteristic values.