Steel Plate Shear Wall Systems Research Articles

Ultimate drift ratio prediction of steel plate shear wall systems: a machine learning approach

Ultimate drift ratio prediction of steel plate shear wall systems: a machine learning approach

Determination of response modification coefficient of SPSW in RC frame using plastic design method

ABSTRACT In the last few decades, the idea of using thin steel plate shear walls (SPSW) as a resistant system against lateral loads in designing and reinforcing buildings has been of concern to researchers and designers. In this research, we studied the response modification coefficient (R), the overstrength factor (Ω0), and the deflection amplification factor (C d ) in a reinforced concrete special moment frame (RC-SMF) with thin SPSW. We used the performance-based plastic design (PBPD) method. For this purpose, we consider frames with SPSW systems with different story numbers. Static pushover analysis is performed on these frames using the strip model in OpenSees software. OpenSees software is the Open System for Earthquake Engineering Simulation located at http://opensees.berkeley.edu. Simulation results were compared with experimental results, and acceptable matching was observed between the two. Finally, the values of response modification coefficient (R), overstrength factor (Ω0), and deflection amplification factor (C d ) for RC-SMF with thin SPSW were calculated based on the Uang method. The ultimate limit design method proposed them as 9.37, 2.21, and 11.06.

COMPARISON BETWEEN SMF AND SPSW STEEL BUILDING FOR MIXED-USE RESIDENCE USING THE AHP METHOD

The objective of this work is to compare the Special Moment Frame (SMF) system and the Steel Plate Shear Wall (SPSW) system using the AHP multi-criteria comparison method with the two Seismic Load Resisting Systems (SFRS). From the linear static analysis, dynamic analysis, and nonlinear static analysis (Pushover), representative characteristics of each Seismic Force-Resisting System (SFRS) are determined. These characteristics include the structure's self-weight, target displacement, floor drifts, and seismic response modification factor (R). As a result, two buildings are obtained with different SFRS that comply with the design of their elements and checks according to the regulatory requirements. After determining the capacity curve of each Seismic Force-Resisting System (SFRS) and assessing the performance level of the buildings, the conclusion is drawn that the Special Plate Shear Wall (SPSW) system is more suitable and advantageous compared to the Special Moment Frame (SMF) system. This preference is due to the SPSW system's ability to provide ductility, which translates into higher energy dissipation capacity, and stiffness, which leads to reduced floor drifts in the building.

Wall-frame interactive behavior in GFRP-reinforced steel plate shear walls with circular cutout openings

The present study investigates the effect of glass fiber reinforced polymers (GFRPs) on the nonlinear and energy dissipation behavior characteristics of steel plate shear walls (SPSWs) with a single circular cutout opening using the finite element method. In the study, the effect of the opening features (diameter and location), geometrical properties of the SPSW systems (aspect ratio and height) and properties of fiber laminates (number of layers and orientation angle) on the FRP-wall-frame interactive behavior is investigated. The results show that the introduction of opening does affect the distribution of stresses across the wall. The use of an adequate amount of FRPs can successfully compensate the impact of the opening on the system strength and energy dissipation capacity. The use of fibers does not change the system initial stiffness significantly, while it reduces the ductility to some extent. There is an interaction effect between FRPs, infill wall and frame, and the use of FRPs results in a better distribution of stresses across the perforated wall area at the ultimate state, although it causes a delay in the onset of wall yielding. The presence of opening in the infill wall of different SPSWs, especially in taller multi-story cases, improves the system ductility. Finally, a procedure is presented for design of FRP-reinforced perforated SPSWs and the accuracy of the proposed equations is compared with the finite element results.

Methodical Investigations on Seismic Retrofitting of Steel Plate Shear Wall Systems

An efficient retrofitting technique is expected to improve the seismic performance of a lateral force-resisting system without increasing the seismic demand on the structure, which can unfavorably lead to irreparable damages during a seismic event. On this basis, the present study aims to introduce an optimal strategy for seismic retrofitting of steel plate shear wall (SPSW) systems using low yield point (LYP) steel material and to demonstrate its effectiveness through systematic investigations. To this end, detailed nonlinear static, cyclic, and dynamic analyses, as well as fragility analyses, have been performed on single- and multi-story, code-designed as well as retrofitted SPSWs. The aim is to identify the most efficient retrofitting approach and to demonstrate its effectiveness in enhancing the seismic performance and lowering the seismic vulnerability of the system. It is shown that replacing the original, conventional steel infill plate in an SPSW system with an LYP steel plate having twice the original thickness can improve not only the buckling capacity and serviceability, but also the structural performance and seismic response of the system, without increasing the demand on the structure and creating overstrength concerns. Fragility analysis also shows that the vulnerability, as well as probability, of damage to system can be considerably lowered as a result of the implementation of such a retrofitting strategy.

Seismic behavior of a novel slotted steel plate shear wall under monotonic, cyclic, and time history analysis

Steel plate shear walls (SPSWs) are lateral load-resistant systems used as energy dissipation members in new or existing structures due to their stable hysteretic behavior. However, structures equipped with conventional SPSWs may have a higher initial stiffness, which causes them to be subjected to too much force during moderate earthquakes. In the present study, a novel slotted SPSW is developed to minimize the lateral forces of traditional SPSWs. The slotted SPSW consists of horizontal boundary elements (HBEs), vertical boundary elements (VBEs), and two layers of incline-slotted infill plates (ISIPs) connected by high-strength steel bolts. The proposed system's seismic behavior and damaged mode were compared with those of conventional SPSW using monotonic and cyclic analysis. The research results show that the slotted SPSW exhibits stable hysteretic behavior with a significant energy dissipation capacity. Furthermore, the slotted SPSW was applied to a three-story frame structure. Nonlinear time history analysis was conducted under far-field and near-field ground motion records to determine how a slotted SPSW system affects structure response. According to numerical results, the base force of the structure equipped with a slotted SPSW system was minimized to 37.0% and 49.6% under near-field and far-field earthquakes, respectively.

Analysis and design of a novel segmented energy absorbing steel plate shear wall system

A steel plate shear wall (SPSW) system capable of providing strength and stiffness under normal load conditions and dissipating energy under extreme load conditions is proposed. The infill plate of this proposed Segmented Energy Absorbing SPSW (SEA-SPSW) system consists of two trapezoidal plate segments. For each plate segment, one edge is connected to the beam while the opposite edge is joined together by steel strips. The steel strips are held together using high strength bolts with long-slotted holes. Under normal load conditions, the SEA-SPSW behaves like a conventional SPSW. However, under extreme load conditions, the plate segments will slide between the steel strips and dissipate energy through friction. Because the proposed system does not rely on yielding or buckling to dissipate energy, it can be reset and reused after a severe load event. The behavior of this SEA-SPSW is studied using finite element and compared to an all steel conventional SPSW system. It is found that the proposed system not only helps reduce inter-story displacement, it also offers a desirable equivalent viscous damping ratio as well as a rather favorable energy dissipation to mass ratio.

Seismic behaviors of CFT-column frame-four-corner bolted connected buckling-restrained steel plate shear walls using ALC/RAC panels

A Frame-Buckling Restrained Steel Plate Shear Walls (BRSPSWs) system has been designed, featuring a steel plate connected to frame elements, to withstand lateral loads like seismic or wind forces. This system incorporates recycled aggregate concrete (RAC) to create concrete-filled and concrete panels, promoting eco-friendly and sustainable construction materials. Two single-span, two-floor specimens were tested under cyclic quasi-static load. A four-corner bolted connection was used to connect the steel plate to the square concrete-filled steel tubes (CFTs) column and H-section beam, minimizing the potential deformation of the frame elements produced by the tension field of the steel plate after high-order bucking. The steel plate was sandwiched using either autoclaved lightweight concrete (ALC) or RAC panels. The study analyzed failure modes, load-displacement responses, and characteristic capacities. Test results inferred that BRSPSWs exhibited favorable cyclic behavior, with similar failure modes observed using both ALC and RAC panels. The buckling of steel plates was reduced, and the type of restrained panels had a negligible impact on buckling. Consequently, ALC panels can effectively replace RAC panels. Furthermore, bearing capacities and yield stiffness were primarily determined by the bolted connection forms. A finite element (FE) modeling was developed using ABAQUS software and validated against test results. This FE modeling method successfully simulated failure modes and load-displacement curves. Parametric analyses were conducted and revealed that bearing capacity and yield stiffness positively correlated with steel plate thickness, bolt diameter, and the number of bolts but negatively correlated with the axial compression ratio. In contrast, the panel thickness and span length had a minor impact due to shear deformation in the bolted connection. Based on the test results and parametric studies, an equation for the yield-bearing capacity of BRSPSWs was proposed and verified.

Combined SCD-SPSW system subjected to ground excitation

PurposeIn this study, the application of a novel combined steel curved damper (SCD) and steel plate shear wall (SPSW) system in the 5-, 10- and 15-storey steel moment-resisting frames (SMR) subjected to earthquake excitation has been investigated. The proposed system is called here as the SMR-WD (steel moment resisting–wall damper).Design/methodology/approachAt the beginning of this research, an SMR-W and an SMR-D are separately modeled in ABAQUS software and verified against the available experimental data. After that, three different heights SMR-WD systems (5-, 10- and 15-storey) are designed and simulated. Then, their performances are examined and compared to the corresponding SMR-W under the effects of six actual earthquake records.FindingsThe obtained results show that the proposed system increases the mean values of the base shear for 5-, 10- and 15-storey SMR-WD equal to 27, 20.15 and 16.51%, respectively compared to the corresponding SMR-W. Moreover, this system reduces the drift of the floors so that the reduction in the average values of maximum drift for 5-, 10- and 15-storey SMR-WD is equal to 10, 7 and 29%, respectively with respect to the corresponding SMR-W. The results also reveal that the considered system dissipates more energy than SMR-W so that the increase in the mean values of the energy absorption for 5-, 10- and 15-storey SMR-WD is 30.8, 25.6 and 41.3%, respectively when compared to the SMR-W. Furthermore, it is observed that SMR-WD has a positive effect on the seismic performance of the link beams and panel zones of the frames. By increasing the height of the structure in the SMR-WD, the energy dissipation and base shear force increases and the drift of floors decreases. Hereupon, the proposed SMR-WD system is more useful for tall buildings than SMR-W frames.Originality/valueFor the first time, the application of a novel combined steel curved damper (SCD) and steel plate shear wall (SPSW) system in the 5-, 10- and 15-storey steel moment-resisting frames (SMR) subjected to earthquake excitation has been investigated.

Seismic performance assessment of steel plate shear walls equipped with passive dampers

The main objective of the current study is to improve the structural resilience and damage control of steel plate shear walls (SPSWs) equipped with a unique passive visco-plastic damper. The proposed damper is made of a high-damping rubber layer with self-centering characteristics and ductile steel bolts. The seismic response of the novel SPSW system equipped with the aforementioned visco-plastic damper is evaluated using a three-dimensional nonlinear finite element analysis validated with experimental data. Furthermore, a parametric study is conducted to see the effect of different parameters such as the bolt diameter-to-height ratio, rubber thickness, number of bolts, number of dampers, location of the damper connection, and bolt material on the behavior of SPSW equipped with visco-plastic dampers under cyclic loading. Results showed that the suggested damper could concentrate most of the damages merely in itself and preserve the primary structural components in the undamaged elastic range, which acted as a structural fuse. The results indicated that to obtain the research objective, the bolt diameter-to-height ratio needs to be 0.2 or less, which in this case, more than 85% of the total input energy is absorbed by merely the damper and steel boundary columns and beam remained elastic and undamaged, while the infill plate had a relatively low energy absorption rate of roughly 10%. On the contrary, the infill plate of the conventional SPSW absorbed the highest energy, accounting for more than 75% of the total input energy. The beam also had a relatively high energy absorption rate of around 24%. In addition, the self-centering behavior of the proposed system could reduce nearly 36% of the residual lateral displacement compared with the conventional SPSW.

Seismic behavior of concrete-filled steel tubes column frame-buckling restrained steel plate shear walls connected with bolt/weld

In this study, a buckling restrained steel plate shear wall (BRSPSW) system, consisting of a steel plate linked to frame elements using a double-sides connection bolt/weld and sandwiched by autoclaved lightweight concrete (ALC) panels, was designed to resist the lateral load. Concrete-filled steel tubes (CFTs) and H-section beams were adopted to build the vertical and horizontal frame elements. Three single-bay, two-floor specimens were tested under lateral cyclic load. Besides, this study offered an eco-friendly and sustainable application for recycled aggregate concrete (RAC) as concrete infills. The hysteretic load–displacement response associated with failure patterns was deeply reported and analyzed. The three tested specimens were evaluated based on characteristic capacities. The experimental outcomes demonstrated that all specimens have excellent cyclic performance, and buckling of the steel plates was significantly reduced using bolts connection. Although yield-bearing capacity and stiffness with weld connection were relatively higher than with bolt connection, the peak-bearing capacity was almost the same with bolt or weld. In addition, the ductility, energy consumption, and displacement characteristics were improved using bolts compared with weld. Finite element (FE) models were generated and verified to analyze out-of-displacement and equivalent plastic strain. Based on validated FE models, parametric analyses were performed to examine the impact of five crucial parameters on characteristic capacities. The parametric studies presented considerable indications for the seismic behavior of BRSPSWs. The findings of this study serve as a valuable point of reference for the implementation of engineering applications.

Experimental and numerical investigation of a new type of steel plate shear wall with diagonal tension field guiding stiffeners

A novel type of steel plate shear wall for withstanding lateral forces was proposed. Inclined stiffeners (acting as tension field guiding stiffeners) were added at the corners of the shear wall and a middle link beam was created, similar to the eccentrically braced frames (EBF). Therefore, upon adding diagonal members to the shear wall, the system resembled a combination of a steel plate shear wall system with an EBF system.To study the cyclic performance of the system equipped with the guiding stiffeners, a scaled specimen of the shear wall was made and subjected to cyclic loading. Finite element model of the wall was simulated and validated using the corresponding laboratory data. Then, a comparison between the proposed shear wall and the corresponding unstiffened steel plate shear wall was made. In the proposed system, the guiding stiffeners can alter the pattern of the tension field, pushing away the plastic strains from the column face toward the link beam. This helps the columns and connections remain intact. As a result, the system failure mechanism includes two-stage ductile fuses, including the steel plate yielding in tension, and flexural stresses or shear plastic hinges at the link beam ends. Compared to the unstiffened steel shear wall, the fuses help dissipate more energy in the proposed shear wall. In general, diagonal tension field guiding stiffeners can enhance the lateral force capacity, ductility, energy absorption, and stiffness of the system simultaneously.

Numerical Analysis of Infill Plate Performance on Steel Plate Shear Wall (SPSW)

Steel Plate Shear Wall (SPSW) is one of the systems that can be used to minimize the effect of earthquakes on buildings. The main energy-absorbing element of the steel plate shear wall system is on the thin steel plate that are located on the center of the steel frame. This thin steel plate is called infill plates. This infill plate will later experience buckling and form a series of tension field action. This paper will prove that the infill plates in the steel plate shear wall system provides significant strength contribution in resisting lateral loads.The analysis was carried out by comparing the strength provided by steel plate shear wall system and simple beam-column steel frame system (without infill plate) with some aspect ratio variation (width per height). The material used for the infill plates was low yield strength (LYS) steel plate of 1.30 mm thick, while the column (vertical boundary element) used WF 400.200.8.12, and the beam (horizontal boundary element) used WF 350.175.7.11. The loading used a monotonic pushover loading of 2% drift (68.8 mm) for each specimen.The analysis result proved that the steel plate shear wall system (frame with infill plates) had significant strength advantage compared to the plateless frame system. The aspect ratio (L/h) on infill plates were also affects the strength of the entire system, where the greater the aspect ratio, the greater the strength. The strength value of the SPSW specimen at 2% drift loading on aspect ratio L/h = 1.00, 1.50, 2.00, 2.50 respectively was 614.95 kN, 634.88 kN, 646.69 kN, and 688.03 kN. Meanwhile, the strength increment percentage between steel plate shear wall systems compared to plateless frame systems in each aspect ratio was 21.67%, 32.39%, 42.48%, and 54.20%.

Seismic performance investigation of an innovative steel shear wall with semi-rigid beam-to-column connections

Steel plate shear walls (SPSWs) are a robust lateral load resistance structure because of their high ductility and efficient energy dissipation when subjected to seismic loads. This research investigates the seismic performance of an innovative infill web strip (IWS-SPSW) and a typical unstiffened steel plate shear wall (USPSW). As a result, two 1:3 scale specimens of an IWS-SPSW and USPSW with a single story and a single bay were built and subjected to a cyclic lateral loading methodology. In the prototype, semi-rigid end-plate connectors for the beam-to-column connections were utilized. The test result of IWS-SPSW showed outstanding ductility and shear load-bearing capacity without cracks or damage. Additionally, the IWS-SPSW exhibited strong energy dissipation without substantial beam-column connection distortion. USPSW showed excellent shear load-bearing capacity, low ductility, extensive infill plate corner tearing, and large infill web plate cracks. The FE models were developed and verified against experimental data. It has been shown that the infill web strips can affect the high performance and overall energy dissipation of an SPSW system. In addition, a parametric study was conducted to investigate the infill web strip material properties, such as steel strength and thickness, that can significantly enhance the system’s seismic performances.

Investigation of the fire effect on the behavior of corrugated steel plate shear walls considering environmental aspects

Fire can be an adverse event with tangible costs for property and human life. In addition to its physical costs, fire has a range of obvious adverse consequences on the environment. One of the fire’s adverse outcomes is its effect on the structures. Corrugated Steel Plate Shear Walls (SPSWs) are environmentally friendly since they can be manufactured in the factory, reducing the environmental disturbance around the construction site, and also, they can be easily dismounted and recycled. In this paper, the effect of fire on the behavior of corrugated SPSWs was investigated numerically and parametrically. In so doing, the hysteresis of the system before (at the ambient temperature) and after applying the fire was investigated. For the parametrical study, the effect of the thickness (t) and the length-to-height ratio (ω=L/H) of the infill plate were investigated on the ultimate strength, stiffness, and yielding of the corrugated SPSW system. The finite element (FE) results showed that by increasing the thickness as well as the length-to-height ratio, the behavior of the corrugated SPSWs was improved. Also, the results indicated that fire affects the ultimate strength, yielding over the wall and hysteresis curve; additionally, the stiffness is affected by the fire. It was proposed to account for the fire by applying the reduction factor of 0.4 to the ultimate strength.

Experimental and Numerical Study of an Innovative Infill Web-Strips Steel Plate Shear Wall with Rigid Beam-to-Column Connections

Steel plate shear walls (SPSWs) offer good energy dissipation capability when subjected to seismic forces as a robust lateral load resisting structure. This research investigated the cyclic behaviors of innovative infill web-strips (IWS-SPSW) and conventional unstiffened steel plate shear (USPSW) experimentally and numerically. As a result, two specimens of a 1:3 scale three-story single-bay IWS-SPSW and USPSW were fabricated and tested under cyclic lateral loading. Rigid moment-resistant connections were used for the steel plate shear wall beam-column connection. The steel shear walls with infill web strips showed high ductility and less shear load-bearing than the USPSW. The hysteresis results showed that the IWS-SPSW had high energy dissipation with no severe beam-columns damages. On the other hand, the USPSW displayed severe post-buckling, infill panel cracks, and first-floor column damages. Moreover, the IWS-SPSW shear strength did not fall in the test specimen beyond 2.5% average story drift, where the structure exhibited great seismic behavior. FE models were created and validated with experimental data. It has been proven that the infill web-strips can affect an SPSW system’s high performance and overall energy dissipation. From a parametric study, the material features of the infill web-strips, such as steel strength and thickness, can enhance the system’s impact even more.

A Numerical Investigation on the Limitations of Design Equations for Steel Plate Shear Walls

In previous studies various design issues on steel plate shear wall (SPSW) systems under lateral loading were investigated using analytical and experimental methods. However, these studies tried to examine the interactive effect of only a few of design parameters, such as panel aspect ratio, column flexibility parameter, axial load ratio on the boundary frame columns, web plate thickness, stiffness of horizontal and vertical boundary elements and top anchor beam, etc., on the drift capacity and shear force distribution among frame and panel components of SPSWs at a time. This study investigates the effect of all of these parameters in the same framework. A parametric study is conducted on finite element models of 292 3-story SPSWs with rigid beam-to-column connections and designed for specified parameters. By evaluating failure forms from finite element analyses, the limiting (undesired) cases resulting from different combinations of specified geometric properties are identified. A column flexibility factor of 2.2 is proposed instead of the current limit value of 2.5 for satisfactory column performance, improved drift capacity and balanced strength distribution among frame and panel of SPSW. The value of 0.75 for the ratio of plate shear force to total shear force has emerged as a critical threshold value for the strength distribution among plate and frame components in order to conform capacity design principles. This study provides a comprehensive look on the behavior of SPWS for determining the most suitable combination of various parameters in the design of SPSW structures.

Seismic performance quantification of buckling-restrained steel plate shear wall-RC frame structures

The beam-connected buckling-restrained steel plate shear wall (SPSW) has the advantages of high bearing capacity, strong energy dissipation and good ductility, and flexible arrangement in the structure, which can reduce the force acting on the frame columns and avoid premature failure of the frame columns. To determine the SPSW configuration in structures to fully exploit the seismic performance, a plastic design method of the steel plate shear wall-RC frame structure (SPSW-RCF) was proposed based on energy balance in this paper. The expected global failure mechanism was constructed and the double lateral resistance SPSW-RCF system was decomposed into SPSW system and RC frame system by using shear force ratio. The design base shear was calculated based on the energy balance principle to determine the design lateral story shear forces of the SPSW and RC frame systems, and then the design of SPSWs could be completed. Considering the post-yield behavior of SPSWs and the plastic internal force distribution mechanism, internal forces of beams and columns were calculated, and then the design of the RCF could be completed. 56 SPSW-RCF structures with different story numbers and story shear ratios were designed, SPSW thickness and reinforcements of the SPSW-RCF were compared. By performing the nonlinear dynamic analysis under 22 ground motions, the maximum interstory drift ratios, SPSW maximum displacement ductility, yield mechanism, residual drift ratio and story shear ratio of structures with different story numbers and story shear ratios were comparatively investigated. Furthermore, the actual SPSW-resisted story shear ratio was quantified and the recommended design SPSW-resisted story shear ratio was suggested.

Assessment of cyclic behavior and performance of hybrid linked-column steel plate shear wall system

An innovative hybrid linked columns steel plate shear wall (HLCS) system provided, and its cyclic behavior and energy absorption are investigated by finite element method in this study. The objective of the designed HLCS system was to reduce or possibly prevent damage to the SPSW at low and medium seismic levels by focusing the seismic damage to interchangeable link beams (the energy dissipation components of the presented HLCS system). In this study, the cyclic behavior and energy dissipation of HLCS systems were investigated using numerical methods. To evaluate the hysteresis behavior and energy absorption of the proposed HLCS system, parametric studies were performed. Also, the accuracy of finite element models was evaluated by comparing test results that showed the good accuracy of finite element models in predicting the specimens' hysteresis behavior and failure modes. Due to the failure mechanisms, the coupling ratio amounts meaningfully affect the onset of the first surrender mechanism between the infill steel plate and link beams. In general, by increasing the number of link beams in the floor, the ultimate shear force to the weight ratio of the structure was increased. Also, the type of beam in terms of flexural and shear behavior did not significantly affect the ratio of base shear force to the structure weight. The proposed HLCS system has increased the ratio of base shear force to the weight by an average of 4%–27%, indicating that this system is economically comparable to the SPSW systems. Moreover, the energy dissipation in the HLCS system exhibited a 14%–91% enhancement compared to the SPSW system.

Experimental and numerical study of concrete frames with steel plate shear walls

Steel plate shear wall systems have appropriate behavior in high seismic zones. They could be combined with concrete or precast concrete structures to compensate susceptibility of these structures to strong earthquakes. This article presents an experimental and numerical study on seismic behavior of various types of steel plate shear walls installed in simple and rigid concrete frames. These frames were subjected to quasi-static cycling loading in accordance with ACI T1.1–01. Compared to the bare moment frame, erection of the steel plate in simple concrete frame by bearing bolted connection led to an increase in lateral load capacity, initial stiffness, energy dissipation and equivalent hysteretic damping up to 1.7, 2.2, 3.5 and 3 times, respectively. These ratios for the steel plate shear wall with moment frame, and connected by friction bolted connections were 3, 7.2, 7.7 and 3.2 times. The horizontal and vertical stiffeners in the steel plate shear wall with the openings over the main diameters contributed to 13% and 27% increase in energy dissipation and equivalent damping, respectively, while the load bearing capacity and initial stiffness did not decrease significantly. At the bearing bolted connections, crippling and tearing of the steel plate was observed, but no any damage occurred at the friction bolted connections. Whereas, all the steel connecting components embedded in concrete were in the elastic range and also, equations governing the angle of inclination of the tensile field, were valid. Finally, the samples were simulated in Abaqus finite element software, and the pushover curves of experimental load-displacements diagrams were predicted.