# Optimization of Glulam Regular Double-Tapered Beams for Agroforestry Constructions
## 4 Conclusions  
According to the data obtained from the optimization of the roof and the statistical analysis carried out, the following conclusions were drawn for a 45 m long roof structure comprising double-tapered beams and purlins composed of GL32h glued laminated timber:  
* Both the structural program created and genetic algorithm tool developed were proven to be valid methods for determining the optimal geometries of the structural elements, in accordance with the Eurocode criteria. * Using the proposed statistical model for a known snow load and span, reliable predictions arise for the optimal values of cost, beam height, beam base, purlin height, purlin base, beam spacing and purlin spacing. After analyzing the combinations of variables, it can be seen that wind has no significant effect on the overall cost; therefore, neither does the height of the building, which was evaluated between 5 and 7 m.
* The cost is 99.9% dependent on the span and snow load. Therefore, the amount of glued laminated timber required for the structure rises with increasing snow load (2.6-4.4% per 0.1 kN/m\({}^{2}\)) and span (9.5-11.6% per meter). * Snow load, span, and purlin height have a significant influence on the beam height. For instance, the beam height increases by approximately 40 mm for every surge of 0.2 kN/m\({}^{2}\) of the snow load or the increase of 1.2 m and 1.5 m in span, depending on whether the purlin height is 160 or 200 mm, respectively. * Similarly, the span, snow load and purlin height significantly affect the beam width. It is found that for purlin heights of 160 mm, the optimal value of the beam width is usually 90 mm. However, for spans ranging from 26 to 30 m, it was noted that the optimal beam width increases to a range of 100-110 mm. On the other hand, when the purlin height is 200 mm, the optimal beam width is 90-100 mm, 110-120 mm and for 130-160 mm for each span range (15-20 m, 20-25 m and 25-30 m, respectively). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**Effect**} & \multirow{2}{*}{**Estimate**} & \multirow{2}{*}{**SE**} & \multicolumn{2}{c}{**95\% Confidence Interval**} \\ \cline{5-6}  & & & & **Lower** & **Upper** \\ \hline (Intercept) & (Intercept) & 1.203 & 0.203 & 0.796 & 1.610 \\ Roof length & Roof length & 0.191 & 0.005 & 0.180 & 0.201 \\ Snow range 1 & 2–1 & 0.755 & 0.322 & 0.110 & 1.399 \\ Roof length \(\times\) Snow range 1 \(\times\) Snow range 1 \(\times\) Snow range 1 \(\times\) Snow & 0.027 & 0.004 & 0.020 & 0.034 \\ Roof length \(\times\) Snow range 2 \(\times\) Snow & Roof length \(\times\) Snow range 2 \(\times\) Snow & 0.025 & 0.004 & 0.018 & 0.032 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Estimation of the effects of the considered variables on the response variable Nb. * The optimum value for the height of the purlins is 160 mm for snow loads ranging between 0.5 and 1.4 kN/m\({}^{2}\) and 200 mm when the snow load is in the range of 1.4 and 2.0 kN/m\({}^{2}\), provided that the remaining conditions of length and spacing between purlins are fulfilled. * Regardless of the variation in span and snow load, the optimum value of the purlin width is invariably 90 mm. * The most favorable purlin spacing is typically the maximum allowable. For purlins with a height of 160 mm, a value between 1.0 and 1.25 m is generally observed as optimal. Conversely, for purlins with a height of 200 mm, the optimum spacing is 1.25 m.
* As the required number of beams depends on the actual roof length, to determine the optimum arrangement of beams, two prediction equations are proposed according to the specific snow load. Conceptualization, M.S.-P., J.R.V.-G., D.R.-R. and P.V.-L.; methodology, M.S.-P., J.R.V.-G., D.R.-R. and P.V.-L.; software, M.S.-P., J.R.V.-G., D.R.-R and P.V.-L.; validation, M.S.-P., J.R.V.-G., D.R.-R. and P.V.-L.; formal analysis, M.S.-P., J.R.V.-G., D.R.-R. and P.V.-L.; investigation, M.S.-P., J.R.V.