Experimental-Numerical Assessment of Mechanical Behavior of Laboratory-Made Steel and NiTi Shape Memory Alloy Wire Ropes

Abstract

The mechanical behaviors of laboratory-fabricated steel and superelastic shape memory alloy (SMA) wire ropes are assessed in this study through a comprehensive approach encompassing both experimental investigations and finite element (FE) numerical simulations. The assessment of steel wire ropes involves experimental scrutiny under sinusoidal cyclic loading and natural earthquake loading conditions. In parallel, SMA wire ropes’ behaviors are analyzed utilizing FE simulations employing the widely acknowledged ABAQUS software version 2020. The validation of all numerical simulations is undertaken against the experimentally observed behaviors. Moreover, full-scale steel wire ropes are subjected to shaking table tests to validate the simulations, facilitating a comparative analysis between the mechanical responses of SMA and steel wire ropes. The findings demonstrate that SMA wire ropes exhibit superelastic behavior akin to SMA wires, with marginal variations in overall response observed across distinct configurations, akin to steel wire ropes. Furthermore, augmenting the helix angle of SMA wire ropes results in reduced stress and increased strain when exposed to the El Centro earthquake scenario. Nevertheless, the mechanical response of SMA wire ropes closely mirrors that of a single wire.

1. Introduction

Cables are a type of structural element capable of resisting high tensile loads. They are formed by twisting multiple wire strands together and are referred to as a “cable” if the diameter is less than 3/8 inch or one centimeter, and “wire rope” if the diameter is greater. Reverse lay cables have wires twisted in the opposite direction to the strands in the cable, providing resistance to pressure and deformation but lower flexibility and wear resistance. Lang lay cables have wires twisted in the same direction as the strands, resulting in higher wear resistance. Cables have become increasingly important in civil engineering, particularly in bridge construction [1,2]. Hosseinzadeh et al. [3] investigated the utilization of cable braces to control lateral displacement and enhance bending frame resistance. Shiravand et al. [4] studied the impact of cable rupture during earthquakes and under uniform support excitation on the seismic response of cable-stayed bridges, considering nonlinear behavior.

SMAs are smart materials known for two remarkable phenomena: shape memory effect and superelasticity. They can adapt to environmental changes and possess significant damping properties, dissipating energy during seismic events. The Martensite phase induces the shape memory effect, enabling SMAs to recover their original shape upon stimulation. The Austenite phase induces the superelastic effect, allowing SMAs to undergo substantial deformations and revert to their original form when the stimulus is removed. Both phenomena entail significant energy dissipation. Numerous studies have investigated using SMAs for vibration control of civil structures. For example, Dolce et al. [5] examined the advantageous characteristics of SMA-based isolation devices and systems for seismic protection. They integrated the optimal mechanical traits of quasi-elastic and elastoplastic devices, along with exceptional fatigue resistance and high corrosion resistance inherited from NiTi-SMA. Han et al. [6] presented the energy dissipation principle of SMA wire and developed an SMA damper device for structural control implementation. Corbi [7] explored the advantages of SMA behavior in the dynamic response of structural systems. They analyzed the impact of SMA tendons on the strength of an elastic-plastic structural model subjected to horizontal shaking and vertical loads. McCormick et al. [8] utilized superelastic NiTi shape memory alloy wires and bars to mitigate seismic vibrations in buildings. Parulekar et al. [9] deliberated on the utilization of memory SMA dampers fabricated from Austenite wires, particularly Nickel Titanium wires, for passive energy absorption in earthquake engineering. Hu et al. [10] developed two innovative bracing systems to enhance the seismic resilience of buildings. The Partially Self-Centering Brace (PSB) combines NiTi-based SMA (NiTi-SMA) and iron-based SMA (Fe-SMA) U-shaped dampers, where the NiTi-SMA provides self-centering capability and the Fe-SMA offers energy dissipation, allowing flexible control of the self-centering function. In addition, they [11] proposed the Hybrid Self-Centering Brace (HSB), which integrates NiTi-based SMA U-shaped dampers and frequency-dependent viscoelastic dampers, with the SMA dampers providing self-centering to avoid structural damage and the viscoelastic dampers introducing velocity-proportional damping for nonstructural damage control. Both studies concluded that these bracing systems have promising potential for enhancing the seismic resilience of buildings. Although the cost of SMA components is higher than that of traditional components, the latest investigations confirmed the life-cycle span benefits of SMA-based braces with reduced initial costs [12]. Alternative configurations for SMA-based superelasticity-assisted sliders (SSS) were proposed by Narjabadifam et al. [13].

SMA elements are frequently employed to manage vibrations in structures, but the manufacturing of large-diameter SMA bars can be relatively expensive. As a result, the use of SMA cables made up of smaller-diameter wires has become a more cost-effective alternative. For instance, a 6.35 mm diameter Nitinol bar can cost around $400 per meter, whereas a comparable 49-wire Nitinol cable with a similar outer diameter of 7 × 7 × 0.711 mm is significantly more affordable at only $60 per meter [14]. This substantial cost difference has driven researchers to investigate the performance and applications of superelastic SMA cables, which can provide the desired vibration control and energy dissipation capabilities at a lower manufacturing cost compared to large solid SMA bars.

Beltran et al. [15] examined the mechanical characteristics and behavior of CuAlBe strands and compared both twisted and parallel configurations under cyclic tension. Reedlunn et al. [14] conducted uniaxial tension experiments to investigate the superelastic behavior of two Nitinol cable constructions: 7 × 7 right regular lay and 1 × 27 alternating lay. Their study revealed that the 7 × 7 construction behaves similarly to 49 straight wires loaded in parallel, while the 1 × 27 construction exhibits different behavior due to its larger helix angles. Additionally, the 1 × 27 construction is more compliant and stable, trading decreased force for additional elongation. Carboni et al. [16] investigated a multiconfiguration rheological apparatus that included Nitinol wires, strands, and steel wire ropes. Their study explored various hysteresis phenomena resulting from interwire friction, Nitinol phase transformations, and geometric nonlinearities. Ozbulut et al. [17] performed uniaxial tensile tests and cyclic tests to evaluate the superelastic properties and low-cycle fatigue characteristics of NiTi SMA cables, respectively. Their study demonstrated that the SMA cable exhibited excellent superelastic behavior, with the capability to undergo deformations of up to 6% strain without residual deformations. Sherif and Ozbulut [18] studied the tensile response and functional fatigue of a superelastic NiTi cable. In their subsequent research [19], they analyzed a multi-layered SMA cable under cyclic loading. Their findings demonstrated that the multi-layered cable displayed superelastic behavior with minimal degradation at lower strain amplitudes. Moreover, the stress levels and elastic modulus were reduced due to the multi-layering of the cable. Fang et al. [20] conducted a comprehensive investigation into superelastic SMA cables, encompassing mechanical behavior, annealing schemes, hysteretic modeling, and seismic applications. Testing on 7 × 7 SMA cable specimens revealed satisfactory properties, with potential for enhancement through moderate annealing. Shi et al. [21] explored the development of an SMA-based hybrid self-centering brace that combines NiTi superelastic cables with viscoelastic dampers. The results indicate that the developed SMA-based hybrid self-centering braces provide an average of 9% equivalent viscous damping with complete self-centering characteristics, leveraging both self-centering ability and energy dissipation capacity. Rajoriya and Mishra [22] investigated the use of an SMA wire to reduce large-amplitude oscillations in taut steel cables of cable-stayed bridges caused by wind. They analyzed the dynamic behavior of the cable with and without the wire in free and forced vibrations. The findings indicate that the SMA wire is found to effectively dissipate cable oscillation.

Existing research on SMA ropes has largely focused on basic tensile tests and the cyclic loading of specific rope designs. However, for practical applications, especially in seismic contexts, it is crucial to thoroughly examine their performance under earthquake conditions through computer simulations, experimental studies, or both. SMA materials, especially in wire rope form, offer promising structural applications due to their super-elastic properties. Despite this potential, current studies have predominantly investigated the direct tension or cyclic behavior of SMA cables and wires, leaving a significant gap in understanding their seismic performance. Given the innovative use of SMA wires for enhancing seismic safety in structures, it is essential to conduct comprehensive studies on their behavior under various cyclic and earthquake loading conditions. The present study aims to evaluate the seismic behavior of SMA ropes with different layouts based on both computer simulations and experimental investigations. This study aims to comprehensively investigate and compare the dynamic performance of steel and SMA ropes with different configurations using finite element (FE) analysis and shaking table modeling. To this end, the commercial SMA rope’s behavior is simulated in ABAQUS [23], and the simulation is verified by reference to the experimentally evaluated behavior. Subsequently, different rope layouts are examined under earthquake excitation and quasi-static sinusoidal loading protocols. To validate the simulations, shaking table tests are performed on full-scale steel ropes, enabling a comparative analysis of the behaviors exhibited by SMA and steel ropes.

2. Research Methodology

As discussed in the introduction, SMA materials are attractive for structural applications due to their super-elastic characteristics, with SMA wire ropes being preferable for their ease of production and wide applications. Most studies have focused on the direct tension or cyclic behavior of SMA cables and wires. However, to ensure seismic safety in structures, it is crucial to comprehensively study the behavior of SMA wires under various cyclic and earthquake loading conditions, which is the main objective of the current study. The materials had been ordered from “nimesis” (a leading French company) in mid-2013 referring to the advertised product name of “NTSE01” and no more specific material-related information were unfortunately available from the manufacturer.

To fulfill the objectives of the investigation, the initial step involved the implementation of FE simulation based on ABAQUS software to analyze the behavior of SMA wires. The outcomes of this simulation were subsequently cross-validated against data obtained from laboratory experiments. Following this, FE analysis was conducted to examine various configurations of SMA wire arrangements subjected to sinusoidal and seismic loading conditions. A parallel investigation was undertaken involving different configurations of steel wire ropes, enabling a comparative assessment of the performance between steel and SMA cables. This comparative analysis facilitated the validation of the FE simulations for SMA wire ropes through real-scale shake table experiments, specifically designed to simulate cyclic and seismic loading scenarios. Detailed elucidations are expounded upon in the subsequent sections.

2.1. Experimental Assessment

2.1.1. Specimen and Material

A wire rope is a composite structure composed of twisted steel wires, organized into strands and wound around a core. These wires are drawn to precise dimensions and intertwined in specific configurations to form each strand. Subsequently, the required number of strands is helically wrapped around the core, which may consist of various materials such as synthetic or natural fibers, metallic strands, or an independent wire rope core (refer to Figure 1). In this study, the rope’s wire size, number, arrangement, strand count, lay, and core type were determined based on prior research [14,24,25].

The primary objective of the study was to comprehensively investigate and compare the dynamic performance of steel and SMA ropes across various configurations. The displacement and stress responses of these ropes were examined under quasi-static, cyclic, and seismic loading conditions. To achieve this objective, six types of ropes were purposefully manufactured and subjected to testing. Additionally, numerical modeling and analysis of the considered ropes were conducted as part of this study.

In Figure 1, cross-section schematics depicting the various components of the wire rope are provided. The first rope features wires with a diameter of 1 mm. An identifier ‘A × B’ was designated for the other five types of ropes, where ‘A’ represents the number of strands and ‘B’ signifies the number of wires in each strand. For example, 1 × 3, 1 × 7, 1 × 19, and 1 × 27 ropes were derived from a single strand comprising 3, 7, 19, and 27 wires, respectively. The 1 × 3 rope was a unilayer cable lacking a core, while all other ropes consisted of single or multi-layered constructions with an inner core. The 7 × 7 rope (left regular lay) comprised 7 strands, with each strand containing 7 wires, each with a diameter of 1 mm. Additionally, it was assumed that one of the ropes with a 1 × 7 configuration was a bundle.

Figure 2 presents side-view images of six rope designs, accompanied by the measured helix angles of the individual wires relative to the global axis (z-axis) of the rope. It is crucial to note that the helix angles reported in Figure 2 differ from those documented in earlier research [14,24,25], where each rope layer featured a distinct angle. This difference can be attributed to the fact that the ropes in this study were manually woven, whereas previous studies focused on industrial ropes. It is noteworthy that the angles of the rope layers are all equal in this study.

The tensile test was employed to obtain the mechanical properties of a steel wire, as illustrated in Figure 3 and

Table 1. Mechanical properties of steel wire.

Mechanical Characteristics	Values
Young Modulus E [N/mm2]	200 × 103
Poisson’s ratio	0.3
Density [g/mm3]	7.85 × 10−3

. In this study, the tensile test according to the ASTM A931 standard [26] was used to obtain the mechanical characteristics of the steel wires. This test involved fixing the wire between two jaws in a tension device and applying force to one of the jaws, leading to the elongation of the wire until rupture occurred. Additionally, this study utilized a NiTi superelastic cable with mechanical properties detailed in

Table 2. Mechanical characteristics of SMA [24].

Mechanical Characteristics	Values
Martensite-to-Austenite start stress	420 (MPa)
Martensite-to-Austenite finish stress	500 (MPa)
Austenite-to-Martensite start reverse-stress	300 (MPa)
Austenite-to-Martensite finish reverse-stress	200 (MPa)
Phase transformation strain	6.5%
Martensite-to-Austenite module of elasticity	40 × 103 (MPa)

, sourced from prior research conducted by Hushmand et al. [24].

2.1.2. Testing Procedure and Setup

In this study, an experiment was undertaken in which a steel structural system was positioned on the shake table at the Laboratory of Structural Earthquake Engineering (SEE-Lab) at the University of Bonab, located in the East Azerbaijan province of Iran. The shake table is a product of SANTAM engineering design company [27] and the tests on the ropes within the steel structural system included both cyclic loading and simulated earthquake excitations.

The primary objective is to design a structural configuration capable of withstanding the tensile forces exerted by the embedded ropes during seismic events. The design process focuses on identifying the rope that generates the highest force within the structure, thereby necessitating the consideration of tension forces for that specific rope only. In this context, the 7 × 7 rope emerges as the critical element responsible for producing the maximum force within the system. An overview representation of the experimental setup is depicted in Figure 4. This figure provides a zoomed-in view of the middle section of the device shown in Figure 5, enabling a closer observation of the central part of the setup.

Figure 5 illustrates the components of the steel structure system requiring design, each labeled with specific numbers. Profile number 1, spanning 500 mm, was designed to accommodate the 7 × 7 cable force, with an IPE140 section chosen for additional robustness. Connection between Profile 1 and the shaking table was achieved using G8.8 screws, 12 mm in diameter, while attachment to the base plate utilized a 100 mm gusset and a 4 mm weld for secure fixation.

Profile number 4, characterized by UNP200 with a length of 2850 mm, was obtained, and Profile number 9 was designed to prevent any deflection in Profile number 4. The connection between Profile 4 and Plate 5 (150 × 200 dimensions) was established through full welding, and subsequently, this plate was connected to the side column using two 8 mm diameter G8.8 screws. Profiles 7 and 8, consisting of plates with dimensions of 100 × 200, were also connected to Profile 4 using full welding techniques. More information regarding the design details is presented in Figure 6.

Special rope fasteners were employed to connect the cables, and their types and cable-tying methods are depicted in Figure 7. To secure smaller cables like the 1 × 3 rope and steel wire where suitable small fasteners were unavailable, an alternative cable was used at the fastener location to prevent slippage. Medium-diameter cables required two fasteners, whereas 1 × 7 and bundle ropes, with lower cable forces and a reduced risk of fastener slippage, necessitated only one fastener.

2.1.3. Experimental Results

The stress–strain and force–strain relationships of ropes under sinusoidal loading with a frequency of 0.1 Hz resulting from the shake table tests are shown in Figure 8. Based on a comparison between Figure 3 and Figure 8a, it can be inferred that the maximum stress and force generated in a steel wire subjected to sinusoidal and pure tension loading exhibit similar values. More accurately, the yield stress is about 200 MPa for both loading scenarios.

According to experimental evidence, it can be inferred that the maximum amount of stress experienced by ropes is equivalent to that of a single wire (i.e., about 290 MPa). However, the maximum force experienced by 1 × 3, 1 × 7, 1 × 7 Bundle, 1 × 19, 1 × 27, and 7 × 7 rope configurations is 3, 7, 7, 19, 27, and 49 times greater than the maximum force experienced by a single wire, respectively. This is due to the fact that the force has been distributed among the cross-sectional areas. It should be noted that due to unintentional reasons encountered during the data acquisition process, some of the data were missing, resulting in the inability to plot the complete cycle in Figure 8g.

The instability or fluctuations observed in the cyclic loading curve of the steel wire ropes during the loading phase can be attributed to a combination of different factors. Frictional effects between the individual twisted wires, the nonlinear behavior of the steel material, geometric nonlinearities arising from changes in the rope structure, manufacturing imperfections, and dynamic effects induced by the cyclic loading can all contribute to the observed instability. Those complex factors, acting individually or in tandem, lead to the fluctuations in the loading response.

2.2. Numerical Assessment

In this section, the ABAQUS FE software [23] was utilized to simulate the behavior of ropes under sinusoidal and seismic longitudinal displacements. Initially, the ropes were designed in SolidWorks using specifications from laboratory experiments and then imported into ABAQUS. The material properties of the steel ropes were defined based on real stress–strain values obtained from tensile testing, while plastic stress–strain values from

Table 3. Plastic stress–strain values.

Yield Stress	Plastic Strain
198.00	0.000
203.94	0.018
220.38	0.030
240.76	0.046
261.40	0.073
270.44	0.093
276.43	0.111
281.01	0.130
285.22	0.156
289.42	0.234

were used for the simulations. Superelastic properties were assigned to SMA materials according to Table 3. The FE modeling employed a hexagonal element shape with a constant mesh size of 2 mm, following Biggs [25] as a reference (see Figure 9). Figure 9 illustrates the schematic of the rope and the loading setup.

The ropes were modeled using C3D8R solid elements, which are eight-node hexahedral elements with hourglass control. The “Surface-to-Surface” contact algorithm was used to simulate the actual contact between the wires in the wire rope. The penalty friction algorithm was applied to model the tangential frictional behavior between the lateral surfaces of the individual wires, and the friction coefficient was set to be 0.5. The normal behavior between the wires was defined as a hard contact [25,28]. As shown in Figure 9c, reference points RP1 and RP2 were defined at the center of each end surface of the rope core. The corresponding nodes on each end surface of the wire rope were coupled with RP1 and RP2. All the degrees of freedom of RP2 were constrained, while reference point 1 was allowed to move solely along the rope’s longitudinal axis.

The loading process in the FE model was simulated using the dynamic explicit method, incorporating two types of loads: sinusoidal (0.01 Hz) and seismic excitation (El Centro scaled earthquake) applied to reference point 1. The loading was displacement-controlled, with 8 mm displacements for the SMA and 11 mm for the steel rope. Sinusoidal loading’s cyclic nature enables the simulation of real vibrations and motions induced by earthquakes, machinery, transportation, and wind effects. The details of the considered earthquake are presented in

Table 4. Details of the earthquake records used in this study.

EQ Name	Magnitude (MW)	Distance (km)	PGD (cm)	PGV (cm/s)	PGA (g)
El Centro	6.9	6.09	8.7	30.9	0.281

and Figure 10, sourced from the Pacific Earthquake Engineering Research Center (PEER), as used in previous publications on structural and earthquake engineering dealing with the application of advanced materials for sustainable resilience against earthquakes [29,30,31,32].

2.3. Validation of Numerical Steel Rope Models

The steel wire used in a tensile test was modeled using the ABAQUS software, with dimensions of 210 mm length and 1 mm diameter. A nonlinear general static analysis was employed to apply linear axial tension to the wire. The tension load–displacement relationship of the wire was compared with the FE model in Figure 11. The results indicate that there is a strong correlation between the FE and experimental outcomes. The minor discrepancies between the FE and experimental results are due to unmodeled parameters, such as potential disparities in the boundary conditions of the specimen and the FE model.

Numerical modeling of steel ropes subjected to sinusoidal (0.01 Hz) and seismic excitation, particularly the El Centro scaled earthquake, was performed using the FE software ABAQUS in accordance with the previously outlined methodology. The stress–strain relationships derived from the simulation were juxtaposed with the experimental data, with the results depicted in Figure 12.

The diagrams in Figure 12 demonstrate a strong correlation between the experimental and FE results. The slight discrepancy between the experimental and numerical results can be attributed to inaccuracies in the setup on the shake table and the method of securing the cables with steel fasteners. It is worth noting that during some laboratory tests, the fasteners were not sufficiently tightened, leading to cable slippage within the fasteners. The observed inconsistency was exacerbated by increasing the number of bundles. Consequently, the most significant discrepancy between FE and test data occurred in the case of the 7 × 7 right regular lay (Figure 12g). The stress–strain curve of the simulated steel ropes, depicted in Figure 13, serves as a fundamental basis for comparing different rope arrangements. The curve indicates that the behavior of all the various rope arrangements is almost similar, with any slight differences attributed to the twisting angle of the ropes.

2.4. Validation of Numerical SMA Rope Models

This section is dedicated to validating the modeling process for SMA cables. The validation is accomplished by employing the FE method to analyze cables with different cross-sectional dimensions: 1 × 3, 1 × 27, and 7 × 7. Following this, the results obtained are compared with both numerical data and experimental findings from previous research studies [14,24,25].

As depicted in Figure 14, the mechanical simulation of SMA cable responses using ABAQUS FEA demonstrates a remarkable level of agreement with the observed responses reported in the work by Houshmand et al. [24].

In Biggs’s study [25], SMA cables with varying helix angles of 10°, 17°, and 21° were investigated. This study conducts comprehensive simulations and derives stress–strain relationships from these simulations. Subsequently, the results are compared to experimental data from Biggs’s research [25], with the comparative analysis presented in Figure 15. The findings demonstrate a notable alignment between the experimental and FE simulation outcomes. Any minor disparities between the two can be attributed to factors such as the specification of material properties, including yielding and ultimate stresses, within the ABAQUS software. In the context of the Biggs model [25], as depicted in Figure 15, it becomes apparent that cable behavior diverges with variations in the twisting angle. Specifically, increasing the twisting angle results in higher levels of strain in the cable, while simultaneously reducing cable stress levels.

As per the data provided by Reedlun [14], an analysis of the behavior of 7 × 7 and 1 × 27 cables was conducted using ABAQUS. The results obtained from ABAQUS were then compared to the ones obtained from Reedlun [14], and the comparison is illustrated in Figure 16. Minor discrepancies between the two results can be ascribed to various factors, including insufficient knowledge of the detailed characteristics of SMA behavior, such as initial and ultimate stresses, as well as disparities in experimental and numerical behavior.

3. Discussions

3.1. Behavior of SMA Ropes under Sinusoidal Load

In Figure 17, the response of the SMA under sinusoidal loading with a frequency of 0.01 Hz is shown as a force versus displacement curve. The findings indicate a nearly linear relationship between the tensile force of ropes and the number of wires comprising them, where the force exerted by the rope is equivalent to the summation of the forces exerted by its individual wires. As illustrated in Figure 17a, the force corresponding to maximum displacement (8 mm) is approximately 365 N for one SMA wire; this translates to about 1.09, 2.40, 6.01, 8.1, and 14 kN, respectively for 1 × 3, 1 × 7, 1 × 19, 1 × 27, and 7 × 7 SMA ropes. It can be inferred that the tensile efficiency of the rope decreases with an increase in the number of wires.

In spite of being stretched to a displacement of 8 mm beyond the loading plateau, all the deformation observed in the SMA rope was fully recovered upon unloading. This unique behavior renders the SMA rope an attractive material for applications requiring high strength and flexibility in a compact form.

3.2. Behavior of SMA Ropes under the El Centro Earthquake

The hysteresis loops representing the responses of SMA-wire, 1 × 3 rope, and 1 × 7 rope under the El Centro earthquake scenario scaled to a peak ground acceleration of 0.6 g are illustrated in Figure 18.

Upon comparing the response of the SMA wire, as depicted in Figure 18a, with that of its steel wire counterpart, as illustrated in Figure 3, it can be deduced that the seismic response of the SMA wire is comparable to that of the steel wire in pure tension, both in terms of maximum force and displacement.

Similarly, upon scrutinizing the responses of SMAs 1 × 3 and 1 × 7, as shown in Figure 18b,c, with those in Figure 17b,c, it can be observed that the SMA 1 × 3 and 1 × 7 ropes exhibit a seismic response that is similar to that under sinusoidal loading, in terms of maximum force. This observation underscores the potential of SMA ropes as a promising material for applications that require high strength and resilience under seismic loads. For example, the maximum force is about 1.1 and 1.09 kN under sinusoidal and earthquake loading, respectively.

3.3. Study on SMA Rope Behavior Sensitivity to Cable Arrangement

The stress–strain behavior of SMA ropes under the El Centro earthquake scenario has been investigated using the FE method. In this regard, Figure 19 presents a comparison of the stress–strain responses of various SMA rope configurations, including wire, 1 × 3, 1 × 7, 1 × 7 bundle, 1 × 19, 1 × 27, and 7 × 7 ropes with helix angles of 0, 3, 5, 7, 9, and 13 degrees, respectively. It is noteworthy that all investigated ropes exhibit superelastic behavior; however, their mechanical responses vary slightly. For instance, the 7 × 7 rope demonstrates a smaller loading plateau stress and a larger plateau strain compared to the other ropes. This observation suggests that increasing the helix angle of the ropes leads to a decrease in stress and an increase in strain. Nonetheless, in general, their mechanical behavior is similar to that of a single wire.

4. Conclusions

In this study, the mechanical behaviors of helically symmetric laboratory-fabricated SMA and steel wire ropes when subjected to earthquake excitation and quasi-static sinusoidal loading protocols are explored. Both experimental and numerical methodologies are employed to investigate their responses. The conclusions drawn are listed as follows:

• The findings indicated a good agreement between numerical calculations and laboratory outcomes for SMA ropes, suggesting FE simulation as a reliable tool for preliminary assessments. Consequently, it is anticipated that the seismic response of SMA wires, akin to their steel counterparts, is somewhat influenced by wire configurations but largely retains the superelastic attributes akin to a single wire.
• The maximal stress and force observed in steel wires under both sinusoidal and pure tension loading are similar. Additionally, under quasi-static sinusoidal loading conditions, the maximal force experienced by various rope configurations (1 × 3, 1 × 7, 1 × 7 Bundle, 1 × 19, 1 × 27, and 7 × 7) is 3, 7, 7, 19, 27, and 49 times greater than that of a single wire, respectively. This discrepancy can be attributed to the effective distribution of force over the cross-sectional area of the ropes.
• The numerical simulation method utilized in this study shows promise for predicting the mechanical characteristics of helically symmetric SMA and steel wire ropes. Furthermore, the mechanical responses of different steel rope arrangements under quasi-static sinusoidal loading are similar, with minor variations due to twisting angles.
• There’s a near-linear relationship between SMA rope tensile force and the number of wires, with full deformation recovery even after stretching beyond the loading plateau.
• The SMA 1 × 3 and 1 × 7 ropes exhibit seismic responses akin to those observed under sinusoidal loading conditions, particularly concerning maximum force. This observation underscores the potential of SMA ropes as a promising material for applications demanding high strength and resilience under seismic loading.
• Under the El Centro earthquake scenario, increasing the helix angle in SMA ropes reduces stress and increases strain, while their overall behavior resembles that of a single wire. However, further investigations under diverse seismic excitations are recommended to enhance our understanding of their performance.

This study of the mechanical behavior of helically symmetric SMA and steel wire ropes under earthquake and quasi-static sinusoidal loading has yielded valuable insights, but several opportunities for further research remain to expand the scope and depth of the investigation. Exploring a broader range of rope configurations, conducting dynamic testing with realistic seismic excitations, investigating the influence of design parameters and evaluating durability, and comparing the performance of steel wire and SMA ropes under the same seismic conditions as well as assessing their feasibility and performance in real-world structures could provide a more comprehensive understanding of the ropes’ behavior and their potential applications in seismic-resistant structures.