انتخاب روش های سیستم بهینه برای بهبود لرزه ای و افزودن عمودی ساختمان های موجود On the selection by MCDM methods of the optimal system for seismic retrofitting and vertical addition of existing buildings

First, the TOPSIS method has been applied through the same phases already accomplished in the previous analyses. In particular, the following steps have been followed: (1) definition of the normalised decision matrix R (Table 15), considering that alternatives are judged on the basis of criteria involving different physical quantities; (2) calculation of the weighted normalised decision matrix V (Table 16), obtained by multiplying each column of the matrix R for the corresponding weight; (3) determination of virtual optimal and worst solutions (Table 17); (4) distance calculation among each alternative and virtual ones; (5) relative distance calculation from the optimal solution (Ci ⁄ ) and establishment of a consequent preference order ranking (Table 18). The applied method has shown that the cold-formed steel system is the optimal super-elevation solution. The results have also been validated through a sensitivity analysis, used to verify that the final results are not influenced by the DM judgments. In fact, by assessing the absolute (AT) and the percentage (PT) variation parameters of the criteria weight, it has been shown that the solution is stable. In fact, as shown in Table 19, C2, C3 and C5 are strong criteria, since S = 1/PT = 0 (that is the C2, C3 and C5 criteria weight change does not involve modifications in the preference order classification), while the influence of other criterion weight variation is quite modest, it producing only in few cases different preference order. Second, the ELECTRE method application has provided the matrixes R and V, reported respectively in Tables 20 and 21. From the analysis of the matrix E it is shown that the dominant alternatives for vertical addition are cold-formed steel and glued laminated timber structures, followed by masonry and hot-rolled steel systems (2nd place) and the reinforced concrete one (3rd place) (Table 22). Finally, from the VIKOR method, the scalar parameters Si and Ri have been firstly calculated, as shown in Table 23. Afterwards, the ranking of alternatives is established by means of the parameter Qi (Table 24). Analogously to the previous methods, the optimal solution is always represented by the cold-formed steel system, which has the lowest value of Qi.