## Abbreviations  
\begin{tabular}{l l} \(X\) & = & design variable vector; \\ \(i\) & = & refer to the \(i\)th layer of the SRHPC frame structure; \\ \(j\) & = & refer to the \(j\)th row column or beam of the given floor; \\ \(W(X)\) & = & life-cycle total cost; \\ \(C_{0}(X)\) & = & initial cost of structure; \\ \(C_{fi}\) & = & loss value of structure corresponding to each performance level; \\ \(\widetilde{P}_{fi}(X)\) & = & fuzzy failure probability of structure corresponding to each performance level; \\ \(P_{fi}(\widetilde{X})C_{fi}\) & = & loss expectation of structure corresponding to each performance level; \\ \(\left[P_{fi}\right]\) & = & reliability target value corresponding to each performance level; \\ \(p\), \(q\) & = & the number of constraints in equality and inequality; \\ \(\alpha_{1}\), \(\alpha_{2}\) & = & weighted coefficient, used to reflect the importance of different structures; \\ \(b_{ij,c}\), \(h_{ij,c}\) & = & the width and height of the SRHPC frame column; \\ \(h_{ij,b}\) & = & the height of the SRHPC frame beam; \\ \(A^{a}_{ij,c}\), \(A^{a}_{ij,b}\) & = & the area of section steel in SRHPC frame column and beam; \\ \(A^{w}_{ij,b}\), \(A^{w}_{ij,c}\) & = & the web's area of section steel in SRHPC frame beam and column; \\ \(\rho^{ss}_{ij,b}\), \(\rho^{ss}_{ij,c}\) & = & stirrup's reinforcement ratio of beam and column; \\ \(C_{fs}\), \(C_{fm}\), \(C_{fl}\) & = & the loss value of structure corresponding to \"no damage\", \"moderate damage\", \\  & & and \"severe damage\" performance levels; \\ \(\widetilde{P}_{fs}\), \(\widetilde{P}_{fm}\), \(\widetilde{P}_{fl}\) & = & the fuzzy failure probability corresponding to \"no damage\", \"moderate damage\", \\  & & and \"severe damage\" performance levels; \\ \(\lambda_{ij,c}\), \(\lambda_{ij,b}\) & = & the shear span ratio of column and beam; \\ \(f_{c}\) & = & the strength grade of concrete; \\ \(h_{0 ij,c}\), \(h_{0 ij,b}\) & = & the calculated height of frame column; \\ \(f_{yov}\), \(f_{a}\) & = & the yield strength of the stirrup and section steel; \\ \(N_{ij,c}\) & = & the design value of axial pressure of frame column considering seismic \\  & & action combination; \\ \(\gamma_{RE}\) & = & the seismic adjustment coefficient of bearing capacity; \\ \(V_{ij,c}\), \(V_{ij,b}\) & = & shearing force design value of column and beam; \\ \(d^{sp}_{ij,c}\), \(d^{sp}_{ij,c}\), \(d^{sp}_{ij,c}\), \(s^{sp}_{ij,c}\) & \(s^{sp}_{ij,b}\) & = \\ \(\Delta si\), \(\Delta mi\), \(\Delta li\) & = & \(\begin{array}{l}\text{diameter and spacing of stirrup in column and beam};\\ \text{story drift of structures corresponding to ``no damage\", ``moderate damage\",}\\ \text{and ``severe damage\" performance levels;}\\ \end{array}\) \\ \([\Delta s]\), \([\Delta m]\), \([\Delta l]\) & = & threshold for story drift corresponding to \"no damage\", \"moderate damage\", \\ \(E^{\text{c}}I^{c}_{ij,c}\), \(E^{\text{b}}I^{b}_{ij,b}\) & = & the flexural stiffness of the column and beam; \\ \(E^{\text{a}}I^{a}_{ij,c}\), \(E^{\text{a}}I^{a}_{ij,b}\) & = & the shear stiffness of the section steel of column and beam; \\ \(b^{a}_{ij,c}\), \(d^{sp}_{ij,c}\), \(d^{sp}_{ij,c}\), \(d^{sp}_{ij,c}\), \(d^{sp}_{ij,c}\), \(d^{sp}_{ij,c}\), \(d^{sp}_{ij,c}\) & = & the section steel flange's width and thickness of column and beam; \\ \(h^{sp}_{ij,c}\), \(t^{sp}_{ij,c}\), \(h^{sp}_{ij,b}\), \(t^{sp}_{ij,b}\) & = & the section steel web's height and thickness of column and beam; \\ \(\rho^{ss}_{ij,c}\) & = & the volume radio of reinforcement; \\ \(\mu_{0}\) & = & the random variable used to express the structural resistance term, which represents \\  & & inter-story drift, whose standard value can be seen in Table 3; \\ \(\mu(X,P)\) & = & the load effect term, which represents in-story drift. \\ \end{tabular}