# Multi-Step Prestressing with Hybrid SMA Wires
## 1 Introduction  
Concrete is strong in compression and weak in tension. In prestressed concrete girders, compressive force is applied in the tension area to compensate for the disadvantages of concrete. This prestressing force is induced in a girder during its construction, which helps reduce the tensile stress generated during service. Prestressing is divided into two types: post-tension and pre-tension. In the pre-tensioning method tendons are tensioned before concrete is poured and the tension is retained until completing hardening of the concrete. Thereafter, the tendons are gradually released to introduce prestress into the concrete. In the post-tension method, prestress is introduced by tensioning tendons and fixing one of their ends to a concrete girder after the concrete hardens. In this method, the tendons and the concrete should not be attached at the time of tensioning the tendons, which means that the duct for arranging the tendon should be installed in advance. After the introduction of tension, grouting should be performed with cementitious grout to prevent corrosion of the tendons and to ensure that the tendons adhere to the concrete. After the tendons are grouted this way, re-tensioning is impossible. To overcome these disadvantages of conventional prestressing, many researchers are exploring prestressing techniques that employ shape memory alloys (SMAs). SMAs have several unique properties. The two most important properties are the shape memory effect (SME) and superelasticity. SME refers to the phenomenon that if an SMA is deformed, it regains its former shape upon heating [1; 2; 3]. Superelasticity refers to the phenomenon of an SMA undergoing a large amount of inelastic deformation and recovering its shape after unloading automatically without heating [4; 5]. The SME of an SMA strip/bar can be used to prestress concrete. For example, in principle,if a straight SMA bar is deformed by pulling and then heated above a certain temperature, it will shrink to its original length. However, if the deformation recovery is restrained by embedding the SMA in concrete structures, a mechanical stress is induced in the SMA when it is heated and cooled subsequently. This stress is called \"recovery stress,\" and it can be used to introduce prestressing forces in concrete structures to improve their serviceability. One of the advantages of such a prestressing technique compared to conventional prestressing is the lack of frictional losses due to the development of uniform bond stress along the length of the embedded SMA tendon. In comparison to the conventional prestressing techniques, SMA tendons can be used for prestressing thin concrete members without having to use anchor heads, oil hydraulic cylinders, ducts, or grout injection [6]. [PERSON] and [PERSON] [7] studied a smart prestressing method using SMA wires. The method uses the SME of prestrained SMA wires. Therefore, it does not require tensioning of the wires by using a hydraulic jack. Prestressing techniques that employ SMA wires or strands are relatively simple compared to mechanical prestressing, and they can be used to introduce prestressing force whenever necessary. [PERSON] and [PERSON] [8] used SMA wires in cement composites to demonstrate their self-stressing capacity and compared SMA prestressing with mechanical and chemical prestressing. [PERSON] et al. [9] showed that externally installed SMA bars closed cracks in concrete structures because of the post-tensioning force generated by the SME. However, this method is associated with the problem of drilling holes and anchorage on concrete members. [PERSON] et al. [10] and [PERSON] et al. [11; 12] showed the crack-closing capacity of SMA wires in concrete beams by using the closing force generated because of the recovery stress of SMA wires. There are many more studies related to crack closure by using SMA wires [13; 14; 15; 16; 17; 18]. Moreover, there are several types of SMA wires. Most researchers have used NiTi SMA, which is considerably more expensive than steel. [PERSON] et al.