## 4 Results
### Dependence of Maximum Span of the Bridge to the Ratio of Traffic and Dead Load  
The actual bridges in whose design the first author was involved (Table 2) was investigated, and the ratio of dead load to the sum of the traffic and dead load was calculated for each bridge (Figure 3). These bridges included the following prestressed concrete bridge types (shown in Figure 4), with the range of maximum span between 7 m and 60 m:  
* slab girder bridge,
* ribbed section,
* box girder, and
* precast girders.  
In addition, besides the prestressed concrete bridges, one reinforced concrete culvert is included. The ratio is obtained by comparing the bending moment at support, bending moments at midspan, and shear, and taking the average of these values (weighing equally the bending moment and shear). The national load multiplier, \(\alpha\), for the Eurocode LM 1, used in the design of the bridges shown in Table 2, are provided in the last column of the table. As required by the National Annex used in the design of these bridges, a different set of national load multipliers, \(\alpha\), has been used for bridges on different routes (motorway vs more local roads). However, larger traffic loads in general ask for a larger dead load of structural components to resist the increased load, keeping the G/(G + Q) ratio relatively constant.  
Figure 2: Three-dimensional diagram of interdependence of \(\alpha_{\text{R}}\), \(\
u\), and \(\text{COV}_{\text{R}}\).  
Figure 3: Ratio of dead load to total load vs maximum span.  
\begin{table}
\begin{tabular}{l l l l l l} \hline
**Max Span** & **All Spans** & **Type** & **Bridge Width** & **Ratio v** & **\(\alpha\)** \\
**(m)** & **(m)** & & **(m)** & **Ratio v** & **(LM1 Multiplier)** \\ \hline
60 & 45, 60, 45 & Box girder & 14.8 & 0.775 & 0.8 \\
42 & 32, 4 x 42, 32 & Box girder & 11.3 & 0.675 & 1 \\
54 & 40, 3 x 54, 40 & Box girder & 11.3 & 0.703 & 1 \\ \hline
38 & 30, 38, 38, 38, 38, 30 & Ribbed section & 10.5 & 0.674 & 0.8 \\
23 & 18, 23, 23, 23, 23, 23, 18 & Ribbed section & 9.4 & 0.578 & 0.8 \\
25 & 20, 25, 25, 25, 25, 20 & Ribbed section & 9.4 & 0.597 & 0.8 \\
31 & 22, 31, 31, 31, 22 & Ribbed section & 9.4 & 0.622 & 0.8 \\ \hline
25 & 20, 5 x 25, 20 & Slab girder & 14.8 & 0.736 & 0.8 \\
26 & 18, 26, 26, 26, 26 & Slab girder & 7.8 & 0.604 & 1 \\
28 & 28, 28 & Slab girder & 10.5 & 0.719 & 0.8 \\
16 & 16 & Slab girder & 11.3 & 0.648 & 0.8 \\
25 & 25, 25 & Slab girder & 10.5 & 0.699 & 0.8 \\ \hline
22 & 3 \(\times\) 22 & Precast girders & 11.2 & 0.563 & 1 \\
20 & 17, 20, 20, 17 & Precast girders & 8 & 0.406 & 1 \\
35 & 35 & Precast girders & 11.2 & 0.593 & 0.8 \\
24 & 24, 24 & Precast girders & 10.5 & 0.524 & 0.8 \\
7 & 7 & Precast girders & 14.75 & 0.453 & 1 \\
15 & 15 & Precast girders & 14.75 & 0.376 & 1 \\
11 & 11 & Precast girders & 14.75 & 0.413 & 1 \\ \hline
7 & 7 & Culvert & 14.75 & 0.440 & 1 \\ \hline \end{tabular}
\end{table}
Table 2: Bridge considered for dependence of ratio of traffic to dead load and maximum span.  
As can be seen from Figure 3, the ratio of dead to total load, i.e., \(\
u\), depends on the following factors:  
* Span--the longer the span, the larger the ratio, as the influence of the Tandem System (TS) part of the Eurocode Load Model 1 (LM1) decreases when compared with the uniform dead load;
* Width of the bridge--the wider the bridge, the larger the ratio, since the wider bridge means that third lane and remaining area will be added, which are the lighter parts of the Eurocode LM1, while the dead load should increase significantly with the bridge width increase;
* Type of the section--the slab bridge has a larger ratio \(\
u\) due to disadvantageous cross-section optimization compared with the ribbed section, box section, and pre-cast girders.  
It can be concluded that the typical range of ratio \(\
u\) is 0.40-0.75 for the concrete bridge. For steel bridges, \(\
u\) is expected to be lower.