# Experimental and Numerical Analyses of Timber-Steel Footbridges
## 2 Parametric Study of Timber Footbridges
All other footbridge members were  
Figure 1: Shape of the main girder of the investigated footbridges. considered as beam elements. Cross-girders were always modelled as hinged in the plane of the bridge deck and rigidly connected to the main beam for vertical bending. To ensure the stiffness required for main girder stability, reinforcing haunches were included at both ends of the cross-girders. Stringers in bridge deck type I were connected to the cross-girders via hinges. Figure 2: Cross-sections of the investigated timber footbridges (dimensions are given in mm). Similarly, the placement of bridge coverings, if part of the individual model variant, had to allow for rotation on both main axes. All bracing joints were considered perfect hinges. For the sake of illustration, we present a geometric scheme and visualisation of computational models of footbridge superstructures with a theoretical span of 16 m, including all three types of bridge member decks considered in this study (Figures 3 and 4). Load was calculated in accordance with the applicable Eurocodes. In addition to self-weight and all permanent loads, variable traffic load was computed according to EN 1991-2 [25] in the form of a uniformly distributed load with a value of 5.0 kN\(\cdot\)m\({}^{-2}\). Wind load was also considered, in accordance with EN 1991-1-4 [26]. As the first step, the stresses and deformations of individual elements were determined via static analysis. Subsequently, the resistance of the main girder against lateral-torsional buckling was verified via linear buckling analysis (LBA). The wooden members of the bridge superstructure were assessed using EN 1995-1-1 [4] or EN 1995-2 [5], whereas steel structural members were assessed in accordance with EN 1993-1-1 [27] or EN 1993-2 [28]. Finally, dynamic analysis was used to determine the natural vibration modes of the superstructures. The corresponding natural vibration frequencies were verified to ensure that they do not fall into dangerous intervals when resonance phenomena occur. Table 1 summarises several key parameters, providing an overview of the static and dynamic behaviour of the designed footbridges. The different bridge deck types only  
Figure 4: Geometric scheme and visualisation of 16 m span footbridge model, bridge deck type III. Figure 3: Geometric scheme and visualisation of 16 m span footbridge model, bridge deck types I and II. minimally affect the stress on the main girders. The main contribution of cross-girders and bracings is to protect the main girders against lateral-torsional buckling and confer favourable dynamic properties in the horizontal direction. In Table 1, the following designations are used:  
\(\sigma_{\rm d}\)--design value of stress caused by all relevant combinations of actions;  
\(\rm f_{\rm d}\)--design value of wood strength;  
\(\rm\delta_{\rm k}\)--characteristic value of the maximum deflection of main girders;  
\(\rm\delta_{\rm lim}\)--limit value of main girder deflection;  
\(\rm\alpha_{\rm cr}\)--minimum force amplifier to reach elastic critical buckling;  
\(\rm f_{\rm VI}\)--value of the first natural frequency of main girder vibration in vertical direction;  
\(\rm f_{\rm H1}\)--value of the first natural frequency of main girder vibration in horizontal direction. As we can see in Table 1, the footbridges with the larger spans already reach the interval of dangerous frequencies in the vertical direction. For spans larger than 24 m, it would probably be appropriate to increase the height of the girders to 1/12 or to 1/10 of the span. It is also obvious that the serviceability limit state, represented by the deflections of the main girders, do not play a significant role. As for comparing between the three deck variants, bridge deck type I seems to be the least advantageous in terms of material consumption as well as production difficulty.