# Load-Carrying Capacity of Bailey Bridge in Civil Applications
## 3 Global Analyses  
### Numerical Models  
Several studies have been executed to verify the static and dynamic behaviour of Bailey bridge structures by in situ loading tests and numerical analyses [8; 9; 10].  
The global analyses of all alternatives of the BB in the present study were carried out using spatial computational FEM models properly derived in the commercial software SCIA Engineer [11]. This software was selected as it is commonly used in design practice for bridge structures. The application of a more complex approach was not considered since it is believed that it would increase the computational effort without significantly improving the quality of the results [12; 13].  
Beam-type elements, with six degrees of freedom at each node were applied for the steel members of the BB superstructure, Figure 7. The one-dimensional elements are confirmed to be suitable for approximation of such type of structure [14; 15]. The geometry and individual dimensions of steel elements fully respect the BB bridge layout [4; 5]. It was assumed that each alternative of the bridge is completely assembled. All relevant geometrical and cross-sectional characteristics were taken into account. Each connection of cross beams to the bottom chords of panels was performed considering a semi-rigid joint connection with a stiffness of 150 MN/m in compression and with stiffness of 60 MN/m in tension, but with zero rotational stiffness in all directions, so that approximates the real behaviour of perfectly tightened 'transom clamp'. The eccentric junctions of continuous stringers and cross beams can be modelled as hinged while allowing for their certain longitudinal displacement over the cross beams. The sway trace elements were modelled as rods capable of bearing tension forces only. Based on non-destructive hardness tests on actual bridges of this type, steel with yield strength \(f_{y}\) = 360 MPa was considered for the needs of the presented study. Modulus of elasticity \(E\) = 210,000 MPa was utilized in the analysis as well.  
The timber deck does not interact with other bearing components due to negligible stiffness of its connection to the stringers. The only function of the timber deck is to provide the carrying surface for passing vehicles. Therefore, the timber deck of the bridge was introduced into the model by shell elements with reduced modulus of elasticity to a very small value [E\({}_{\text{deck}}\) = 10 MPa]. This almost completely prevented the interaction of the deck with the steel elements of the bridge deck, but it made it possible to place a traffic load anywhere on the surface of the bridge deck. The second advantage of this modelling approach is that it allows the redistribution of a modelled traffic load to the corresponding stringers. Figures 8 and 9 present the finished models for the shortest and the longest span analysed in the study.  
Figure 6: Two alternatives of timber roadway deck: (**a**) standard solution of timber deck; and (**b**) more stiff timber deck.  
Figure 8: Geometry of complete spatial FEM model in the case of the shortest analysed span TS-12 (40 ft): (**a**) model from beam and shell elements; and (**b**) front view visualization.  
Figure 9: Geometry of compete spatial FEM model in the case of the longest analysed span TD-36 (120 ft): (**a**) model from beam and shell elements; and (**b**) front view visualization.