PSI - Issue 44

Massimiliano Ferraioli et al. / Procedia Structural Integrity 44 (2023) 974–981 Massimiliano Ferraioli et al./ Structural Integrity Procedia 00 (2022) 000–000

976

3

Table 1. Parameters of NiTi-based Shape Memory Alloy (SMA). Modulus (MPa) Transformation Temperature (°C) Transformation Stresses (MPa)

Transformation strains  Ms =0.078653  Mf =0.005156  As =0.013125

Superelastic plateau strain length

E M =22222

M S =14 M F =-16 A S =-10 A F =18

 Ms =420  Mf =450  As =195  Af =165

 L 

  

E A =32000

 Af =0.09025

Stress

gE A

 Ms  Mf

aE A

b Ms

E M

 As  Af

E A

 Ms

 Mf = m ·  Ms

(a)

(b)

Strain

Fig. 2. (a) Stress-strain-temperature curves of NiTi-based shape memory alloys; (b) Typical stress-strain model of NiTi-based SMA.

The super-elastic hysteretic behavior may be idealized using straight lines (Fig. 2b) as a function of the different parameters (Tab. 1): elastic modules of austenite ( E A ) and martensite ( E M ), transition stresses in the phase transformations from austenite to martensite (i.e., σ Ms and σ Mf ) and from martensite to austenite (i.e., σ As and σ Af ) and corresponding transition strains (i.e.,  Ms ,  Mf ,  As and  Af ), post-yield stiffness ratio ( α ), hysteresis width ( β ), and hardening stiffness ratio ( γ ). The ductility ( μ ) is very high for FeNiCuAlTaB- and CuAlBe-based SMAs and, therefore, the strain hardening behavior is usually not activated. On the contrary, for NiTi-based SMAs the strain hardening behavior occurs for strains of 6–8% but it can be avoided through proper treatment (Dolce et al. 2000, 2001). This paper uses the uniaxial model proposed by Auricchio et al. (1997) as modified by Fugazza (2003). Its parameters are calibrated using the cyclic uniaxial tests carried out by Rizzoni et al. (2015) on commercial super-elastic NiTi wires. 3. Case study building The SC-SMA dampers are applied for the seismic retrofit of a school residential building built at the end of the 1950s in Pisa (Tuscany, Italy) (Fig. 3a). The eight-story structure is composed of reinforced concrete frames in both directions and floors made up of cast-in-place concrete and brick. The retrofit design project provides the addition of RC shear walls in the first two stories and buckling restrained braces in the other stories (Fig. 3b). Extensive in-site and laboratory tests were carried out, and a refined structural model was implemented (SAP2000, 2019) (Fig. 3b). Tab. 2 shows the dynamic properties of the first three mode shapes. The seismic assessment and corresponding safety verifications have been carried out according to the Italian Code (NTC-Guidelines, 2018) All details about these activities can be found in Ferraioli et al. (2021). The original building shows many deficiencies such as inadequate lateral stiffness, insufficient shear capacity of RC elements and joints, and inadequate chord rotation capacity of the columns of the staircase structure due to their poor reinforcement detailing. 4. Design of the RSMAD braces The design of the RSMAD braces is carried out using a procedure originally proposed for elasto-plastically damped systems (Ferraioli et al. 2021) and here applied also to flag-shaped damped systems. This design procedure is based on the formulation of an optimal stiffness ratio between the damped brace and the main structure that was originally proposed by Kasai et. al. (2004) and then implemented in JSSI Manual (2007).