**4.2. Main codes**

**4. Short-span bridges**

40 Structural Bridge Engineering

the arrival of truck traffic [76].

**4.1. Dynamic amplification factor**

load effects:

1.0 to 1.8.

total load effect resulting from a loading event, LEt

model, as there is no need to account for vehicle interaction.

Short-span bridges are governed by free-flowing traffic, plus an allowance for dynamic effects. Free-flowing traffic measurements can be used directly or as a basis to generate loading scenarios. The arrival of vehicles in free traffic is often idealised as a Poisson process, which can be described with a negative exponential distribution. If cars are neglected, as usually assumed in short-span bridge loading, other distributions may be more suitable to describe

Firstly, the case of an individual lane is considered. Shorter bridge spans (< ≈30 m) are governed by a single heavy vehicle or, if very short, individual axles. Therefore, commonly available information about axle configuration and weight suffices to generate a realistic (static) load

For longer spans, in-lane multiple presence of heavy vehicles is a possible event. The headway between two following trucks is an important parameter to identify the number of trucks that may be simultaneously present on a bridge. Headways may be estimated from the WIM

For the common case of multi-lane bridges, it is necessary to consider the multiple presence of Side-by-side heavy vehicles, whether across same-direction or opposing lanes. In the development of current European and North American codes, data about actual multiple presence of side-by-side vehicles was not collected but artificially reproduced. For instance, Reference [66] considers that one in 15 trucks has another truck side by side. This conservative assumption, used for the calibration of the current AASHTO load model [71], can be nowadays adapted to site-specific traffic conditions due to the availability of more accurate WIM data [77, 78]. Indeed, a 2-truck side-by-side meeting event is likely to strongly influence the bridge design for shorter spans (< ≈30 m) and sometimes it has also been the only considered event for longer spans [66, 79]. However, as spans get longer, the likelihood of events involving more than two trucks increases and such meeting events should be accounted for [75, 76, 80].

Fast-moving vehicles, typical of free-flowing traffic, interact dynamically with a bridge. The

a static analysis, LEs. The *Dynamic Amplification Factor* (DAF) represents the ratio of these two

*t s*

Dynamic amplification varies significantly and depends on a number of factors, such as span length, vehicle class and speed, axle spacing and weight, suspension stiffness, or the road surface profile. As described in the next section, the main codes use DAFs in the range from

*LE DAF*

, is typically larger than would result from

*LE* <sup>=</sup> (16)

database, as discussed in Section 2.2, or from a calibrated headway model [76].

The Load Model 1 (LM1) in Eurocode 1 [68] was calibrated with 1-week WIM data collected on the A6 Motorway near Auxerre (France). The traffic scenarios were based on a dual twolane carriageway layout. In the simulated free-flowing traffic (spans up to 50 m) a maximum of 25% trucks was considered. Nine influence lines were investigated for nine spans ranging from 5 to 200 m [64]. Several extrapolation methods were tested to find the characteristic values corresponding to the target return period of 1000 years; in general, results were not found to be very sensitive to the extrapolation technique [69]. LM1 is given as a tandem axle and a Uniformly Distributed Load (UDL), whose values depend on the lane but not on the span length. LM 1 incorporates dynamic effects: the considered DAFs were in the range 1.0 to 1.7, with the greater value for shorter span [64]. LM1 may be significantly reduced when used for site-specific bridge assessment [83].

The British code for the design of bridges [84] has been now superseded by the Eurocode. However, its main load model – The HA loading – is still prescribed for the assessment of existing highway bridges up to 50 m [85]. The HA loading is based on UK legal limits and data from roadside truck surveys [69] and consists of a UDL, given as a loading curve depending on the span length, and a Knife Edge Load (KEL). Multi-lane factors are given to consider further lanes. A DAF of 1.8 is included for single-vehicle cases [69]. A *Reduction Factor* between 0.2 and 0.91 is applied to the HA design loading depending on the required assessment level, heavy traffic proportion and road surface condition [69, 85].

In North America, the HL-93 model in AASHTO [71] is based on truck surveys taken in Ontario and weigh-in-motion data. Calibration has been carried out for one- and two-lane girder bridges with single and two spans from 9 to 60 m [70, 86]. The model consists of a design truck, or a tandem, coincident with a design lane load. Multi-lane factors are also specified. It is specified to apply a DAF of 1.33, independent of length or load effect.
