A Novel Hybrid Self-Centering Piston-Based Bracing Fitted with SMA Bars and Friction Springs: Analytical Study and Seismic Simulation

Functional recovery evaluation of hybrid self‐centering piston‐based braced frames

“…The yield, post-yield, and ultimate strengths (F yi , F yp , F u ) of SC-PBB at their corresponding displacements (d yi , d yp , d u ) are determined using the austenite and ultimate strengths of the SMA bars (F dS , F uS ), and the pre-compressed and ultimate strengths of the FS (F dF , F uF ). In case the austenite displacement of the bars (d dS ) is higher than pre-compressed displacement (d dF ), that is, d dS > d dF , the F yi , F yp , and F u strengths of the SC-PBB can be defined as follows 41 :…”

“…Subsequent phases involve the determination of the design strength (F d ) of elements and the first-mode period of the building through equivalent linear analysis and modal analysis. To design components, the design strength of FS (F dF ) and SMA bars (F ds ) can be allocated using the strength factor (η) as follows 41 :…”

“…The required number of rings (n r ) and the length (l F ) of FS can be designed using taper angle (Ɛ), friction coefficient (μ), friction angle (ρ = tan −1 (μ)), effective diameters (D kF ), and cross-sectional areas (A kF ) of the rings in terms of their geometric parameters (C, a k , and b k ), as follows 41 :…”

“…The yield, post‐yield, and ultimate strengths ( F yi , F yp , F u ) of SC‐PBB at their corresponding displacements ( d yi , d yp , d u ) are determined using the austenite and ultimate strengths of the SMA bars ( F dS , F uS ), and the pre‐compressed and ultimate strengths of the FS ( F dF , F uF ). In case the austenite displacement of the bars ( d dS ) is higher than pre‐compressed displacement (d dF ), that is, d dS > d dF , the F yi , F yp , and F u strengths of the SC‐PBB can be defined as follows 41 : $$$$\begin{equation}{F}_{yi} = {F}_{dF} + {k}_{iS}{d}_{dF};\,\,{F}_{yp} = {F}_{yi} + ({k}_{iF} + {k}_{hS})\left| {{d}_{dS} - {d}_{dF}} \right|;\,\,{F}_u = {F}_{yp} + ({k}_{hS} + {k}_{iF})\left( {{d}_u - {d}_{dS}} \right)\end{equation}$$$$…”

“…Subsequent phases involve the determination of the design strength ( F d ) of elements and the first‐mode period of the building through equivalent linear analysis and modal analysis. To design components, the design strength of FS ( F dF ) and SMA bars ( F ds ) can be allocated using the strength factor ( η ) as follows 41 : $$$$\begin{equation}{F}_{dF} = (1 - \eta ){F}_d;\,\,\,\,\,{F}_{dS} = \eta {F}_d\,\,\,\,\,\,(0 < \eta < 1)\end{equation}$$$$…”