Compressed reinforcements on reinforced concrete (RC) and steel fibre reinforced concrete (SFRC) columns are generally submitted to cyclic and monotonic loading, which can buckle. This phenomenon can cause the reduction of both ductility and peak loads, which is why design standards propose constructive details to avoid this. Although the bibliography mentions that steel fibres in concrete can delay buckling of reinforcements, design codes do not distinguish between concrete types (with and without fibres) in these constructive details. Analytical models that determine the length and critical buckling stress of reinforcements may consider this effect. Nowadays, analytical models can be classified as discrete and distributed depending on whether they consider transverse reinforcement stiffness and the stiffness of the concrete cover that concentrates on transverse reinforcements, or if they are distributed along the element, respectively. Both discrete and distributed models are valid for small transverse reinforcement separations, while distributed models that only consider the concrete cover effect are valid for large transverse reinforcement separations. This paper proposes a mixed model to determine critical buckling loads of compressed reinforcements subjected to monotonic loading to use the stress-strain relationships of reinforcing bars, including buckling, that are found in the scientific-technical literature. This model considers transverse reinforcements discretely and concrete cover distributedly. The model can be applied to any transverse reinforcement configuration, and to any concrete type (with or without fibres). An analytical equation is also proposed to determine critical compressed reinforcement loads, whose result is presented as abaci. Finally, to calibrate the model in normal-strength concrete columns under eccentric loading, with or without fibres, a programme is presented in which the critical load of longitudinal reinforcements is experimentally determined. The proposed analytical model is calibrated and a procedure to determine critical buckling loads of compressed reinforcements under monotonic loading is proposed.

SMA (Shape Memory Alloys) is a type of material suitable for using in civil engineering as concrete rein-47 forcement because of their shape memory effect or superelasticity and their high ductility and damping 48 capacity. However, Ni-Ti alloys Young modulus could be 3 or 4 times lower than steel (200 GPa) depend-49 ing on the composition and thermal treatment, which can cause the instability of compressed bars. The 50 main objective of this work is to provide a modified constitutive model of SMA bars, particularized for Ni-51 Ti bars, that considers instability in compression. The inclusion of this effect in the constitutive equation 52 allows for simulating Ni-Ti bars under compression in a simple way as if they were perfectly straight bars. 53 To achieve this, six 12-mm diameter SMA bars made of Ni-Ti were tested under compression. The 54

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h i g h l i g h t s Three VHPC and Ni-Ti and four HPC and Ni-Ti column were tested. A numerical model made in OpenSees was calibrated based on experimental data. A parametric study was conducted to study more variables beyond experimentation. Ductility and damage were higher in the HPC than in the VHPC specimens.

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h i g h l i g h t s 10 VPHC columns with steel reinforcements were tested to study bar buckling.2 VPHC and 2 HPC columns with Ni-Ti reinforcements were tested to study bar buckling.Columns with both Ni-Ti and steel reinforcements were compared.

Buckling of structural elements is a phenomenon that has great consequences on the bearing capacity of structures. Historically, there have been serious buckling-related structural accidents that have resulted in loss of human lives and high material costs. In this article, an attempt is made to perform a historical analysis of the diverse models that experts have been using in designing and calculating compression buckling of simple metallic elements in the last 275 years. The analysis covers the lapse from the mid-18th century, in which the pioneers in this classic field of structural design are located, up to the present, highlighting the main standards that have been applied to steel structural analysis in the past and at present all over the world. What the study tries to provide is an overall view and a sense of continuity of the methods used for improving structural safety regarding buckling failures in the last three centuries. Each analyzed buckling model is compared with the results of a numerical finite element model of compressed steel columns. Finally, the conclusion reached is that in the last one hundred years, the convergence of solutions proposed in the field is gradually greater and more accurate.