# Optimization of Glulam Regular Double-Tapered Beams for Agroforestry Constructions
## 2 Materials and Methods  
Since large open spaces and long spans are often required, regular double-tapered beams are frequently employed in agro-forestry constructions. In addition, their use also entails a lower construction time, as their characteristic shape, without intermediate joints, enables them to be executed as a single construction element. Therefore, a roof timber structure composed of regular double-tapered beams and purlins is proposed as an alternative to be optimized in this research (Figure 1). The material of both the beams and purlins is gulam GL32h, whose characteristic strength and stiffness are established in the EN 14080 standard [33]. Moreover, a 3D approach is followed; thus, the optimization is not limited to the cross-sections of the structural elements but extends to their arrangement in the structure (i.e., the separation between beams as well as the separation between purlins are also subjected to optimization).  
As illustrated in Figure 1, different values of beam length (Span) were considered in the optimization, ranging from 15 to 30 m in 1.25 m increments. Conversely, fixed values of 30 m, 45 m, 60 m and 75 m were studied for the length of the roof. Similarly, a fixed value of 10\({}^{\circ}\) was selected for the beam inclination angle. This angle was selected as it is the most commonly used value for the type of structure evaluated in this paper.  
Figure 1: Design and dimensions for the 3D roof timber structure optimization.  
The height of the beams (Hb) and purlins (Hp) would depend on the number of sheets of timber glued together. As mentioned by [PERSON] et al. [28], a 40 mm laminate thickness was considered; thus, the height ranges from 120 to 1200 mm, every 40 mm. Likewise, the width of the beams (Wb) and purlins (Wp) would range from 90 to 220 mm in 10 mm increments. The values of the beam spacing (Sb), which is related to the number of beams (Nb), and the purlin spacing (Sp) are also variables, which allows for the determination of the optimal values under a cost-optimization goal. Nevertheless, the range of variation was limited to 4-7 m for the separation between the beams and 0.625-1.25 m for the separation between purlins.  
The optimization process for the timber structure also considered the various types of actions to which it would be subjected. For the permanent surface loads, a dead load of 0.45 kN/m\({}^{2}\), as well as an automatically introduced self-weight load based on the cross-sections of the beams and purlins evaluated during the optimization process, are included. For the variable surface loads, a snow load (Snow) ranging from 0.5 to 2 kN/m\({}^{2}\) is allowed to cover a wide range of geographical situations in Europe. In addition, a wind load is also taken into account, considering a gable roof without openings and a building height of 5, 6, and 7 m, which are typical values for agro-industrial constructions. To determine the wind load value, a basic wind speed of 27 m/s and a terrain category III environment with a roughness length of 0.3 m are contemplated in accordance with Eurocode 1-4 [34]. The combination of all loads followed the criteria established in Eurocode 1 [35] to ensure the structural integrity of the timber structure under the worst-case scenario. It is worth noting that a service class 1, a modification factor (\(k_{\text{mod}}\)) of 0.9 and a partial safety factor for the gulam material of 1.25 were assumed in this research.