# Experimental and Numerical Analyses of Timber-Steel Footbridges
## 5 Numerical Analysis of the Tested Specimens  
Two computational models were used to numerically analyse each of the three tested sample variants. The first model was created using the software SCIA Engineer [24] by combining shell and beam finite elements. Shell elements with the corresponding  
Figure 10: Photos from the experimental measurements: (**a**) view of specimen A3 during the test, (**b**) bearing failure of the bolted connection, (**c**) splitting of wood due to transverse bending of the timber blocks.  
Figure 9: Arrangement of specimen “C” during the test (dimensions are given in mm).  
thicknesses were used to approximate the timber blocks and cross-girders, including all parts of their connections to the timber blocks, i.e., end plates and stiffeners. Beam elements modelled the stiffening angles and bolts connecting the end plates to the timber blocks. To model the joint itself, the approach used during the creation of the superstructure model was utilised (see Section 3.2). Slips between steel end plates and timber blocks due to the bolt shafts being pushed into wood were accounted for by means of linear elastic supports of the beam elements simulating the bolts. The stiffness of the support was derived from the modulus of elasticity perpendicular to the grains.  
Since the model described above was not able to adequately consider the behaviour of the connection between the cross-girder and the wooden blocks, a more sophisticated model was created in the ANSYS software environment ([[http://www.ansys.com/Industries/Academic](http://www.ansys.com/Industries/Academic)]([http://www.ansys.com/Industries/Academic](http://www.ansys.com/Industries/Academic)) (accessed on 28 March 2024)) [30] using 3D finite elements SOLID186 and SOLID187. This software allows for an optimised consideration of the plasticity and orthotropic properties of wood and the contact points between connected members. Using special contact finite elements, CONTA174, combined with elements TARGE170, bolt deformations and stresses at the contact points between the end plates and the timber blocks were calculated to more precisely reflect actual joint behaviour. Both numerical models of specimen variant \"C\" are shown in Figure 11. Firstly, the previously mentioned models were used for preliminary calculations to optimise the course of the laboratory tests. After experimental analyses, both models were modified implementing the actual material characteristics; they were then used for detailed numerical analyses of the tested samples. The following physical and mechanical properties of the timber blocks were obtained by means of tests performed in accordance with EN 384 [31] and used in numerical calculations:  
- Mean value of wood density, \(\rho_{\text{m}}\) = 433.1 kg\(\cdot\)m\({}^{-3}\);  
- Characteristic value of wood density, \(\rho_{\text{k}}\) = 416.0 kg\(\cdot\)m\({}^{-3}\);  
- Characteristic elasticity modulus of timber blocks in tension and compression, E\({}_{0,05}\) = 8764.4 MPa;  
- Mean value of elasticity modulus in tension and compression parallel to wood grains, E\({}_{0,\text{mean}}\) = 13,081.2 MPa;  
- Mean value of elasticity modulus in tension and compression perpendicular to the wood grain, E\({}_{90,\text{mean}}\) = 436.0 MPa and  
- Mean value of shear elasticity modulus, G\({}_{\text{mean}}\) = 817.6 MPa.