## 2 Materials and Methods  
### Design Method for Timber-Concrete Composite Structure with Metal Web Timber Joists  
A simplified method for designing timber-concrete composite roof and floor structures with posi-joists was derived based on the transformed section method and the \(\gamma\)-method outlined in Annex B of EN1995-1-1 for mechanically jointed beams [33; 34; 35], which showed promising results in the case of timber-concrete composite structures with cross-laminated timber panel [20]. To validate the developed design method, timber-concrete composite specimens (see Figure 1a) were prepared for laboratory testing. These specimens featured two posi-joisted beams joined by OSBs as top chords. A group of specimens without a concrete layer have been prepared to assess the increase in load-carrying capacity achieved by the addition of a concrete layer (see Figure 1b). The investigation focused on a structure featuring posi-joisted beams manufactured in accordance with SIA \"MiTek Baltic\" technology, OSB sheets attached to the beams with screws, and a layer of concrete bonded to the OSB sheets using epoxy glue and granite chips. This structure served as the object of study for describing the proposed method. The dimensions of the two groups of the investigated specimens are summarized in Figure 2.  
Figure 1: Considered specimens with posi-joisted beams: (**a**) with a concrete layer; (**b**) without a concrete layer. Figure 2: The investigated two groups of laboratory specimens: (**a**) without a concrete layer; (**b**) with an additional concrete layer; metal web is drawn in blue colour, top OSB sheet—in red colour. The thickness of the concrete layer was chosen to ensure its operation primarily under compression, eliminating the need for principal reinforcement in the concrete layer. The analysis considered a segment of the structure consisting of two posi-joisted beams and corresponding layers of OSB and concrete. The simplified method for designing a timber-concrete composite structure with posi-joisted beams comprises the following stages:  
1. Choice of structural solution:  
Selection of major geometric parameters, including the bay of the posi-joisted beams, depth of the beam cross-sections, thickness of the OSB docking, and thickness of the concrete layer. Recommendations from the existing literature [20; 30] can guide this stage. 2. Determination of loads and actions and the formation of the design scheme:  
Utilization of results from the first stage, considering climatic conditions, and applying recommendations [36] to establish a design scheme. 3. Global analysis and determination of internal forces:  
Conducting global analysis to determine internal forces in all sub-members of the structure. For each posi-joisted beam, the uniformly distributed load on the beam can be replaced by an equivalent system of concentrated forces applied to the nodes of the top chord of the beam. Axial forces in the chords and lattice can be determined using structural mechanics methods. 4. Dimensioning of sub-members cross-sections:  
Sizing the cross-sections of sub-members based on the internal forces identified in the global analysis, considering the requirements of Eurocode 2 for concrete layer, Eurocode 3 for steel web, and Eurocode 5 for timber elements. 5. Check of sub-members by ultimate limit state (ULS):  
Verification of sub-members against the ultimate limit state (ULS). 6. Check of a fragment of the structure by serviceability limit state (SLS):  
Examination of a fragment of the investigated structure to ensure compliance with the serviceability limit state (SLS). Each stage builds upon the results of the previous one, providing a systematic approach to the design process for timber-concrete composite structures with posi-joisted beams. The sizing of timber chords should adhere to strength conditions for the axially tensioned bottom chord and stability conditions for the axially compressed top chord [35]. It is crucial to consider existing recommendations [30] during this process.