PSI - Issue 64

Yunus Harmanci et al. / Procedia Structural Integrity 64 (2024) 2067–2074 Author name / Structural Integrity Procedia 00 (2019) 000–000

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3. Formulation of Long-Term Effects and Numerical Investigations The formulation of long-term effects is mainly based on the fib Model Code 2020 (Béton (fib) 2020). For further details, interested readers are encouraged to refer to the original document. The development of concrete compressive strength and Young’s modulus with time is estimated according to the equations provided in (1), with initial values of compressive strength and Young’s modulus being measured at 28 days and β factors defined in fib Model Code 2020. ( ) ( ) ( ) ( ) cm cc cm ci E ci f t t f and E t t E      (1) Total strain of concrete at time t consists of the sum of the initial strain at loading, creep strain at time ≥ 0 , shrinkage strain at time t and thermal strain at time t. The stress dependent strains due to loading and creep are defined as formulized in Equation (2). , where J(t,t 0 ) is the creep compliance function and φ(t,t 0 ) is the creep coefficient, calculated according to fib Model Code 2020. Similarly, the stress independent strains are also calculated based on this code. The above defined effects were implemented in a vectorized CSA, previously introduced in (Harmanci et al. 2016) and further adapted for prestressed bonded and unbonded CFRP strips (Michels et al. 2016; Sena-Cruz et al. 2015), as well as FRCM (Michels et al. 2014). It relies on representing cross-sectional strains as matrices based on the combination of concrete top-fiber strain ( ) and neutral axis depth ( ), as exemplified in (3) for the FeSMA NSM reinforcement. 1 ( ) T FeSMA c c c h x x                  (3) Subsequently, internal force matrices are calculated and checked which value satisfies cross-sectional force equilibrium for each . Internal moments are computed, and moment vs. curvature relationship is derived. Subsequently, external moment distribution can be provided at discrete locations to extract curvature- and strain distributions, enabling determination of midspan deflection through double integration of curvature. 4. Results and Discussion Since the sustained load application on May 7th, 2015, both beams show an initial deformation followed by a gradual increase with time. As expected, the beam with activated SMA strips exhibits lower initial and long-term deflections. Primary deformations occur within the first three months, with initial mid-span deflections measuring 4.3 mm for B7 and 7.3 mm for B8. By March 16th, 2023, just before unloading, these values increased to 10.3 mm and 13.6 mm, respectively. A similar behavior is observed in mid-span strains. The influence of SMA activation-induced prestressing is evident from reduced strains measured on the bottom side of the beams, while the difference is less pronounced on the top side, influenced more by concrete creeping. 0 0 0 0 0 ( ) t 0 ( ) ( , ) t t 1 ( , ) t t ( ) ( , ) t J t t  c  c  c  ci E t ci E             (2)