Seismic Performance Evaluation of Reinforced Concrete Frame–Shear Wall Structural Systems in Thermal Power Plants

Abstract

The seismic performance of an electric power system is crucial for maintaining the functionality of urban communities following an earthquake. In thermal power plants, the RC frame–shear wall structure plays a key role in providing seismic resistance to the main building’s longitudinal structural system. This study presents the results of a series of pseudo-dynamic tests on a two-span, four-story frame–shear wall model with a scale of 1/8. The prototype structure was a seven-story, seven-bay longitudinal RC frame–shear wall from the main workshop of a large thermal power plant. The cracking process, yielding sequence, hysteresis curves, and skeleton curve were obtained. Based on the test results, the energy dissipation, equivalent viscous damping coefficient, ductility and deformation, stiffness degradation, dynamic response, and displacement response were analyzed. The results showed that the RC frame–shear wall structure exhibits a high energy dissipation capacity and excellent seismic performance, and the shear wall significantly influences the structural bearing capacity and deformation performance. These findings offer valuable guidance for the seismic design of RC frame–shear wall structures in high-rise and large factory buildings. As the shear wall absorbs the majority of seismic forces and minimizes the concentration of plastic deformation, strengthening critical weak areas—such as increasing the horizontal distribution of rebars or improving the concrete strength at the shear wall base—can enhance overall structural performance and seismic resilience in industrial buildings subject to seismic loading.

1. Introduction

Electricity plays a crucial role in modern society, with thermal power plants (TPPs) being among the primary contributors to global electricity generation [1]. Ensuring the continuous functioning of the electricity system is essential for community recovery after natural hazards, particularly earthquakes [2]. The seismic resistance of the reinforced concrete (RC) main workshops in TPPs is a critical issue due to their unique characteristics, including significant height (typically above 50 m) and substantial concentrated loads from heavy equipment, such as coal bunkers, positioned between floors. Consequently, it is vital to conduct research to analyze the mechanical performance of such industrial structures under seismic forces, identify the structural failure mechanisms, and locate their weak parts.

Currently, extensive research has been conducted on the seismic performance of lateral frame structures in TPPs and other lifeline industrial buildings [3,4,5,6,7,8]. However, there is a notable lack of research on the seismic performance of longitudinal structural systems in these buildings, which are crucial for maintaining overall stability during seismic events. In TPPs, the longitudinal structural system typically consists of RC shear walls that extend the full height of the plant between columns, forming a frame–shear wall structure [9]. These longitudinal systems are essential for providing resistance against seismic forces, and yet their behavior under seismic loading remains insufficiently explored in the existing literature.

In civil engineering, RC shear walls are widely used to bear horizontal loads, and the displacement caused by earthquakes must be controlled through the stiffness of these shear walls [9]. Previous studies have explored various failure modes of shear walls based on parameters such as cross-sectional type, reinforcement detailing and quantities, mechanical properties (concrete and reinforcement), concrete compressive strength, and loading conditions [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. Shear walls are fundamental for ensuring structural safety against earthquakes and other lateral loads. The frame–shear wall structure effectively combines both frame and shear wall systems, providing not only larger usable spaces but also superior lateral resistance [17]. Panagiotou et al. [18] conducted shaking table tests on a full-scale, seven-story shear wall building at UC-San Diego to investigate the dynamic response of the entire structure, including the interaction between walls, slabs, and the gravity system. Seo et al. [19] evaluated the seismic performance of a 12-story RC moment-resisting frame structure using response spectrum analysis and nonlinear time-history analysis based on FEMA guidelines. The results indicated a decrease in floor-level fragility for all FEMA performance levels with an increase in building height. Ozkul et al. [20] studied two RC buildings with shear walls damaged in the 2011 Van earthquake and compared the damage distribution between the original and upgraded structures. Their findings showed that appropriate shear wall designs can prevent severe damage, even when the seismic response of beams and columns is poor. Simon et al. [21] analyzed the story shear, drift, displacement, stiffness, torsional irregularity, and time period of a 10-story RC building with shear walls at different locations. Their study concluded that shear walls placed at the periphery of the structure are optimal for controlling deflections and drift. In summary, extensive experimental research has been conducted on the seismic performance of regular RC frame–shear wall structures. However, industrial structures like TPPs, which feature large spans and heights, cannot rely solely on the findings from studies on regular RC frame–shear wall systems for their seismic performance. Moreover, seismic performance research on TPPs has primarily focused on transverse framing systems, making experimental studies on longitudinal frame–shear wall systems particularly necessary.

To address that gap, this study investigated the seismic behavior of the longitudinal RC frame–shear wall structural system in TPPs. A specimen of an RC frame–shear wall structure was constructed and subjected to both pseudo-dynamic and pseudo-static tests. Cracking patterns and plastic hinge development were observed, and the seismic performance of the specimen was studied, including hysteresis curves, skeleton curves, the energy dissipation capacity, equivalent viscous damping coefficient, ductility, deformability, stiffness degradation, dynamic response, and displacement response.

2. Experimental Programs

2.1. Specimen Design

The prototype structure is a seven-story, seven-bay longitudinal RC frame–shear wall forming the main workshop of a large TPP. The concrete strength is C40 for the frame columns and shear walls up to the fourth floor (27.5 m) and C35 for the upper floors.

A scaled model experiment can reflect the seismic behavior of a structure. This involves designing the scaled model based on similitude coefficients and the characteristics of the full-scale structure [22]. Following construction site class II and eight-degree seismic fortification intensity, a two-span, four-story structure at a 1/8 scale was developed. To ensure structural similarity, the stiffness characteristic value of the specimen was designed to closely match that of the prototype (λ = 1.23). The similitude ratios for length, elastic modulus, and acceleration were predetermined, while those for area, mass, and time were calculated using the equations in Table 1.

The reinforcement in the specimen followed the reinforcement ratio of the prototype structure and the code for the design of concrete structures (GB 50010–2010) [23]. Figure 1 shows the geometric dimensions and rebar details of the specimen, and Table 2 lists the measured mechanical properties of the rebars. The distribution bars of the shear wall were HPB235 with a diameter of 6.5 mm, while the stirrup rebars were made of galvanized iron wires with a diameter of 4 mm. Due to the small cross-sectional dimensions of the model’s beams and columns, double-row stirrup rebars were utilized at both ends.

Considering the evolving trend towards high-strength concrete in engineering structures, C30-grade concrete was used for beams and shear wall, with C60 for columns. The compressive strength values of standard concrete cubes were 33 MPa and 62 MPa. Additionally, to minimize the influence of vertical loads on the rotation of the top-floor joints and simplify their design, 100 mm high cantilever columns were incorporated at the top of each column.

2.2. Test Setup

Figure 2 illustrates the loading device and its components. Horizontal loads were applied to the specimen using three actuators, with displacement control at the top floor. The horizontal loads on other floors were calculated proportionally based on their relative positions to the top-floor load.

Vertical loads were applied at the top of the frame column and shear wall using three jacks and a horizontally distributed steel beam. To reflect the prototype structure’s load conditions above the fourth floor, the axial load ratios in the bottom-floor columns were maintained consistent with the prototype. Consequently, the vertical loads on the edge columns, middle columns, and the side columns of the shear wall were 185 kN, 181 kN, 162 kN, and 98 kN, respectively.

2.3. Loading Scheme

The loading scheme consisted of two phases. The first phase involved a pseudo-dynamic test (PDT 1-6), where the initial segment (0–8 s) of El-Centro (NS) seismic waves with varying peak ground accelerations (PGAs) was applied. The test duration of 2.8 s was determined using similarity coefficients (Figure 3). The second phase was a pseudo-static test (PST) that applied an inverted triangular distribution of horizontal forces with displacement-controlled loading, continuing until complete structural failure. Figure 4 shows the framework for conducting the entire test.

In addition, a mass conversion was conducted, considering the gravity loads at the ultimate limit state. When S_m = 1/64, the masses for floors one to four were as follows: 10.5 kN·s²/m, 16.7 kN·s²/m, 7.3 kN·s²/m, and 63.2 kN·s²/m. The damping ratio was 0.05.

2.4. Measurement

Displacement meters were arranged at the center of each floor’s joints to measure horizontal displacement. Electronic dial gauges were installed at the foundation beam to monitor the specimen’s slip. To measure the strain distribution, strain gauges were applied to the longitudinal rebars at both ends of each beam and column and at the base of the shear wall, as well as to the surfaces of beams, columns, and the shear wall.

3. Cracking Pattern and Failure Mode

Figure 5 shows the development of cracks in the specimen. Figure 6 shows the crack pattern of the specimen at the end of first phase. When the tensile reinforcement in the specimen’s end section reaches the yielding strain, it can be considered that the corresponding section has yielded, and a plastic hinge is formed. The cracking and plastic hinge appearance sequence of the specimen are shown in Figure 7.

The failure modes of the specimen are as follows:

1. When the PGA was 0.05 g and 0.1 g, the specimen remained in the elastic stage without visible cracks.

2. When the PGA was 0.2 g, the initial set of flexural cracks emerged at both ends of beam B4. On one side of the shear wall base, multiple inclined cracks extended at a 45° angle, accompanied by a horizontal flexural crack at the lower part of side column WC1. On the other side, reverse inclined cracks and flexural cracks were observed, passing through side column WC2. Additionally, cracks appeared on the wall side of beam B3.

3. When the PGA was 0.4 g, as shear force at the base increased, existing cracks continued to extend and widen. New cracks appeared at beam and column ends, as well as at the B6-C2 joint. The shear wall base was subjected to large forces, resulting in numerous evenly distributed cracks. Furthermore, most of the rebars at the shear wall base reached the yielding strain, indicating that this section yielded initially, causing a significant reduction in its stiffness. Additionally, the rebars at the right end of B7 also experienced yielding.

4. When the PGA was 0.8 g, the pre-existing cracks further developed. At the shear wall base, an inclined crack at an approximate 15° angle reached a maximum width of 1 mm, while another horizontal flexural crack significantly widened, reaching a maximum width of 2 mm. The strains in the shear wall rebars also showed significant increases, and a portion of the concrete at the base was crushed and spalled. In addition, wide cracks also appeared at the intersections of WC2 with B3 and B4, and yielding strains were observed in the rebars located at the right ends of both B4 and B7.

5. When the PGA was 1.2 g, inclined cracks appeared at B5-C1 joint and B7-C3 joint. Cracks at the B6-C2 joint increased and extended. The width of the cracks at the shear wall base reached around 3 mm, with severe crushing of the concrete in this area. Additionally, the rebars at the ends of B3 and B2 underwent yielding strain. Following that, the rebars at C1, C5, and both ends of B5 yielded. As a result, it can be considered that the structure attained its maximum load-carrying capacity during this phase.

6. During the second phase, as the positive displacement at the top floor reached 123 mm, there was a sharp increase in structural deformation, notably evident in shear sliding. Then, the concrete at the base of column C5 was severely crushed, and the bottom web of the shear wall exhibited concrete spalling. This event indicated the complete failure of the specimen.

The test demonstrated that the shear wall significantly influenced the load-bearing capacity of the structure and deformation performance. After yielding in the base section of the shear wall, the beam ends and column bases yielded successively, even with a small increase in load, eventually bringing the entire structure to its ultimate bearing capacity. Moreover, the collaborative action of the frame and shear wall caused the initial formation of plastic hinges in beams and columns at various upper levels rather than at the bottom. It was evident that the seismic performance of the frame–shear wall structure is significantly superior to the frame structure.

4. Results and Discussion

4.1. Hysteretic Loops and Skeleton Curve

The hysteretic loops reflect the load–displacement curve of the seismic behavior of the specimen. The hysteretic curves under different PGAs are shown in Figure 8.

When the PGA was 0.05 g and 0.1 g, the hysteretic curves of each specimen were narrow and slender, with the horizontal load increasing linearly with lateral deformation. As the PGA increased, the hysteresis loop area gradually expanded, indicating an elastic–plastic behavior in the structure. When the input PGA reached or exceeded 0.4 g, the displacement showed a gradual increase, and the plastic behavior became more pronounced as a result of the sequential yielding of the shear wall’s base section and the end sections of some frame beams and columns. At this stage, it can be considered that the entire structure had yielded.

When the PGA exceeded 0.8 g, the hysteresis loops exhibited asymmetry and irregular loop shapes, which differed from the full hysteresis loops observed in similar RC frame–shear wall structures under loading conditions [16,24]. This behavior occurs because, under loading in one direction, cracks form in the concrete on one side of the structure. When the load is applied in the opposite direction, the previously formed cracks can close, resulting in nearly symmetric load–displacement hysteresis curves at lower PGA values. However, when the PGA exceeds 0.8 g, the previous cracks in the concrete fail to close, particularly at the base of the shear wall where the concrete is crushed. This leads to an increasing divergence in the structural responses in both directions, causing the hysteresis loops to become asymmetric.

In a frame structure, the hysteresis loops typically exhibit a noticeable “pinching phenomenon” due to the sliding of rebars in the core area of the joints. This pinching effect leads to a reduction in the structure’s energy dissipation capacity [25,26]. In contrast, in this frame–shear wall structure of a TPP, where the shear wall played a dominant role, the pinching phenomenon was not prominent. However, with increased load and displacement, the stiffness of the shear wall decreased significantly, leading to a redistribution of internal forces between the frame and shear wall. As the frame acted as the second line of defense against seismic forces, its hysteresis curve also exhibited a pinching phenomenon (Figure 9).

The skeleton curve for the tested specimen is shown in Figure 10. The various characteristic points on the skeleton curve reflect its main features, including the crack point C, the yield point Y, the peak point P, and the ultimate point U. The crack point C represents the displacement and load observed when the first batch of cracks appeared.

Throughout the stages of cracking, yielding, and eventual failure, the variation in the skeleton curve remains relatively flat, and the decrease in stiffness occurs slowly. Although plastic hinges form at the beam ends, column bases, and shear wall base, the decline in the negative slope after applying a positive load is minimal, and there is not a substantial decrease in the structure’s load-bearing capacity. Upon reaching the ultimate load, the structure’s load-bearing capacity experiences a significant drop due to the compression failure of the concrete in the side column and the web near the shear wall base. Consequently, the structure quickly loses its load-bearing capacity, resulting in an abrupt failure. Therefore, as long as the shear wall exhibits a good performance, especially with adequate deformability at the base, this can ensure that the overall structural deformability meets the design requirements.

4.2. Energy Dissipation Capacity and Equivalent Viscous Damping Coefficient

The total input energy of an earthquake is dissipated in three forms: kinetic, damping, and hysteretic energy. During a pseudo-dynamic test, the effect of speed is minimal, meaning damping energy dissipation is negligible [27]. Therefore, the input energy of an earthquake is primarily dissipated through hysteretic energy. Hysteretic energy dissipation consists of both recoverable elastic strain energy and non-recoverable plastic strain energy. Equation (1) gives an energy expression of hysteretic energy dissipation.

E_h = E_e + E_p(1)

where E_h is the kinetic energy, E_e is the elastic strain energy, and E_p is the plastic strain energy.

The hysteretic energy dissipation curves at different peak accelerations are shown in Figure 11. This energy dissipation accumulates over time. When the PGA is small or the duration is short, the structure primarily remains in an elastic phase, with hysteretic energy mainly in the form of recoverable elastic strain energy. However, as the structure starts to deteriorate (e.g., cracking, yielding), a significant transition in hysteretic energy occurs within a short period, resulting in a step-like trend in the hysteretic energy curve. The proportion of elastic strain energy in the hysteretic energy varies depending on the input PGA. Additionally, the increase in hysteretic energy dissipation is not substantial once the structure has yielded, indicating that the structure’s energy dissipation capacity is limited.

The equivalent viscous damping coefficient can effectively reflect the energy dissipation capacity of the structure. This coefficient is defined as follows:

(2)${\zeta }_{eq}={\displaystyle \frac{1}{2\pi }}E$

where E is the energy dissipation coefficient.

Table 3 shows the equivalent viscous damping coefficients of the specimen at different PGAs. It is clear that as the PGA increases, the structure’s energy dissipation capacity is enhanced. Specifically, at the PGA of 0.4 g, corresponding to the yielding stage of the structure, both energy dissipation and the damping coefficient increase noticeably. However, from 0.8 g to the PST phase, the increasing prominence of shear in the flexural–shear deformation of the structure leads to a slowing trend in the incremental energy dissipation. Therefore, it is recommended that action should be taken to increase the horizontal distribution of rebars and to raise the concrete strength grade at the base of the shear wall. This will effectively enhance the shear-carrying capacity after yielding, improving the energy dissipation performance of the structure.

4.3. Ductility and Deformability

Ductility exhibits a structure’s ability to deform, and a high ductility value indicates that the structure possesses an effective energy dissipation capacity. The ductility of a specimen is characterized by the displacement ductility coefficient given by Equation (3).

µ = Δ_u/Δ_y(3)

where ∆_u is the ultimate displacement, and ∆_y is the yield displacement.

Table 4 lists loads, displacement, drift, and ductility coefficients for the characteristic points of the specimen. The value in parentheses gives the ductility coefficients at the maximum load. During this test, the structure experienced sudden failure when the positive load was decreased to 89% of the ultimate load and then reversed to 69% of the negative ultimate load. Hence, the displacement ductility coefficients for the ultimate point during negative loading are not given in the table.

The failure sequence of the specimen is as follows: yielding occurred at the base of the shear wall, followed by the appearance of plastic hinges at the beam ends, and finally, yielding occurred at the base of columns. When the specimen was loaded to the peak point, its drifts exceeded the inter-story drift limit of 1/100 for RC frame–shear wall structures in rare earthquakes [28,29]. Additionally, the displacement ductility coefficient reached as high as 6.32, indicating the excellent seismic performance of the structure. This high displacement ductility coefficient suggests that the structure could undergo significant deformation without experiencing catastrophic failure, as it allows the frame–shear wall system to absorb large amounts of seismic energy during an earthquake, thereby reducing the likelihood of structural damage and maintaining its stability [30]. To further enhance its performance, measures such as adding diagonal cross-rebars to effectively restrain diagonal cracks at the base of the shear wall, increasing the cross-sectional area, and reinforcing the shear wall side columns, among others, can to some extent enhance the deformation capacity of the shear wall, ensuring that the entire structure maintains an excellent seismic performance.

4.4. Stiffness Degradation

The stiffness expression of the specimen is given by Equation (4).

(4)$Ki={\displaystyle \frac{\left|+Fi\right|+\left|-Fi\right|}{\left|+\mathrm{\Delta }i\right|+\left|-\mathrm{\Delta }i\right|}}$

where F_i and Δ_i are the maximum load and displacement during the i-th loading cycle, respectively.

The stiffness degradation curve shown in Figure 12 is derived from the experimental data, with K₀ representing the initial stiffness of the structure. As can be observed, the structural stiffness gradually decreases as the displacement increases. In other words, as various members within the structure crack, yield, or form plastic hinges, the entire structure transitions from the cracking stage to the yielding stage. Subsequently, it reaches the ultimate load-carrying capacity and undergoes failure, resulting in a gradual reduction in structural stiffness.

4.5. Dynamic Response

Figure 13 and Figure 14 display the time history responses of the structure at various PGAs (0.1–1.2 g). These curves include time histories of top-story acceleration and base shear force.

It can be observed that as the PGA increases, both the acceleration and restoring force at the top floor of the structure increase. Both the excitation wave and the response wave reach their peak acceleration simultaneously. However, the peak acceleration of the excitation wave does not occur at the same time as the peak values of the restoring force response. This is determined by the spectral composition of the input wave and the natural period of the specimen (see Table 5). As the structural damage accumulates, the specimen’s natural period extends, and the time at which the restoring force response reaches its maximum values increasingly aligns with the time of the input seismic wave’s peak acceleration.

4.6. Displacement Response

Figure 15 shows the story displacement and inter-story drift curves for different characteristic points.

It can be observed that, compared to the deformation pattern resembling a wine barrel shape in the lateral frame structure of TPPs [8], the longitudinal frame–shear wall structure exhibits flexural–shear deformation. This is particularly evident once it enters the yielding phase, where the shear deformation becomes more pronounced in the drift curves. The first and third stories exhibit relatively larger inter-story drift, and after entering the plastic phase, plastic deformations in these stories are noticeably concentrated. Furthermore, after the structure yields, there is a sharp increase in the drift angles (see Table 6). This indicates that after successive yielding of various members, the stiffness of each floor significantly decreases. The flexural–shear deformation of this structure shifts from being dominated by flexure to being dominated by shear, demonstrating effective coordination and deformation adjustments within the frame–shear wall structure.

5. Conclusions

To investigate the seismic performance of the longitudinal frame–shear wall structure in TPPs, a two-span, four-story specimen was constructed, and pseudo-dynamic tests were conducted. Based on the results obtained from this study, the following conclusions can be drawn:

1. We found via testing that the entire structure undergoes a failure mode, where the shear wall yielded at the base, followed by the appearance of plastic hinges at the beam ends, and finally yielding at the column base. This failure sequence allows the structure to have higher lateral load-carrying capacity compared to structures that fail in different orders, while ensuring sufficient ductility.

2. Compared to frame structures, the hysteresis curves of the specimen exhibit a full shape, and the pinching phenomenon in the loops caused by degradation of strength and stiffness, as well as rebar sliding, is not very severe. This suggests a good energy dissipation capacity.

3. In this frame–shear wall structure, the majority of the seismic forces are borne by the shear wall, and the concentration of plastic deformation at each level is less obvious compared to frame structures. The cumulative damage and the crushing of concrete on one side of the shear wall base in the test reduced the seismic performance of the entire structure. It is recommended that action be taken to increase the horizontal distribution of rebars and raise the concrete strength grade at the base of the shear wall, to enhance the energy dissipation capacity of the structure.

4. Unlike the deformation pattern resembling a wine barrel shape in the lateral frame structure of TPPs, as the specimen shifts from elastic to plastic behavior, the flexural–shear deformation of this longitudinal frame–shear wall structure gradually transitions from being dominated by flexure to being dominated by shear.

5. The acceleration of the excitation wave and response wave reaches peak values at the same time, but the peak acceleration of the excitation wave does not occur at the same time as the peak values of the restoring force response. As structural damage accumulates, the natural period of the specimen extends, and the time taken for the restoring force response to reach maximum values increasingly coincides with the time of the input seismic wave’s peak acceleration.

6. The longitudinal RC frame–shear wall of a large TPP main workshop exhibits a favorable seismic performance due to the shear wall. The experimental results provide valuable guidance for the seismic design of RC frame–shear wall structures in high-rise and large factory buildings.

Author Contributions

Conceptualization, Z.X. and J.L.; methodology, J.L.; validation, Z.X.; writing—original draft preparation, J.L.; writing—review and editing, J.L. and X.C.; visualization, J.L.; supervision, X.C.; project administration, Z.X.; funding acquisition, Z.X. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Data are available from the corresponding author upon reasonable request.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

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Figures and Tables

Figure 1. Dimensions and rebar details of the specimen (mm).

Figure 2. Test setup.

Figure 3. Load program.

Figure 4. The framework for conducting the entire test.

Figure 5. The development of cracks in the specimen. (a) Beam. (b) Column. (c) Shear wall.

Figure 6. Failure modes of the specimen.

Figure 7. Cracking and plastic hinge appearance sequence of the specimen. (a) Cracking. (b) Plastic hinge.

Figure 8. The story shear–displacement curves of the specimen. (a) 4th story (PGA = 0.2 g). (b) 1st story (PGA = 0.2 g). (c) 4th story (PGA = 0.4 g). (d) 1st story (PGA = 0.4 g). (e) 4th story (PGA = 0.8 g). (f) 1st story (PGA = 0.8 g). (g) 4th story (PGA = 1.2 g). (h) 1st story (PGA = 1.2 g).

Figure 8. The story shear–displacement curves of the specimen. (a) 4th story (PGA = 0.2 g). (b) 1st story (PGA = 0.2 g). (c) 4th story (PGA = 0.4 g). (d) 1st story (PGA = 0.4 g). (e) 4th story (PGA = 0.8 g). (f) 1st story (PGA = 0.8 g). (g) 4th story (PGA = 1.2 g). (h) 1st story (PGA = 1.2 g).

Figure 9. Hysteresis curves of base shear and roof lateral displacement (PST).

Figure 10. Skeleton curve of the specimen.

Figure 11. Hysteretic energy dissipation capacity curves under different PGAs.

Figure 12. Stiffness degradation curves.

Figure 13. Acceleration curve of the specimen.

Figure 14. Shear force curve of the specimen.

Figure 15. Story displacement and inter-story drift curves for characteristic points. (a) Story displacement. (b) Inter-story drift.

Table 1

Similitude coefficients of the specimen.

Physical Quantity	Length	Elastic Modulus	Acceleration	Area	Mass	Time
Symbol	SL	SE	Sa	SS	SM	St
Similitude ratio	1/8	1	1	1/64	1/64	1/√8

Table 2

Mechanical properties of rebars.

Diameter(mm)	Grade	Yield Stressfy (MPa)	Ultimate Stressfu (MPa)	Elastic ModulusE (×105 MPa)	Yield Strainεy (×10−6)
12	HRB335	392.5	610.1	1.623	2425
10	HRB335	455.5	624.2	1.764	2500
10	HPB235	433.1	475.3	1.863	2325
8	HPB235	350.9	501.0	1.813	1935
6.5	HPB235	304.7	442.5	1.810	1683
4	Galvanized iron wire	349.2	381.0	1.888	1800

Table 3

Equivalent viscous damping coefficients.

PGA	Hysteresis Loop Area	Area of Triangle	Equivalent ViscousDamping Coefficient
0.05 g	15	112	0.021
0.1 g	75	248	0.048
0.2 g	413	849	0.077
0.4 g	3031	3810	0.127
0.8 g	8086	8150	0.157
1.2 g	11,395	9960	0.182
PST	13,550	11,330	0.190

Table 4

Characteristic points of load–displacement results.

Characteristic Point	Positive				Negative
	P (kN)	Δ (mm)	θ	μ	P (kN)	Δ (mm)	θ	μ
Crack point	54.93	6.50	1/587	6.32 (4.85)	60.09	5.20	1/734	(2.93)
Yield point	99.17	19.00	1/206		117.80	20.58	1/193
Peak point	135.08	92.08	1/41		159.97	60.28	1/63
Ultimate point	122.02	120.00	1/33		-	-	-

Table 5

Change of the specimen natural period.

PGA (g)	0.05	0.1	0.2	0.4	0.8	1.2
Period (s)	0.550	0.641	0.746	0.969	1.141	1.798

Table 6

Inter-story drift and ductility coefficients.

Story	Direction	Δc(mm)	θc	Δy(mm)	θy	Δp(mm)	θp	Δu(mm)	θu	μ
1st	Positive	4.17	1/323	8.26	1/163	39.17	1/34	49.83	1/27	6.03
	Negative	1.33	1/1014	6.08	1/222	24.82	1/54	-	-	-
2nd	Positive	1.58	1/549	2.45	1/353	12.40	1/70	26.48	1/33	10.81
	Negative	1.75	1/493	3.52	1/246	8.80	1/98	-	-	-
3rd	Positive	3.17	1/279	5.71	1/155	27.61	1/32	37.37	1/24	6.54
	Negative	1.73	1/510	6.03	1/147	20.19	1/44	-	-	-
4th	Positive	1.21	1/684	4.59	1/181	12.91	1/64	9.40	1/88	2.05
	Negative	0.38	1/2184	4.75	1/175	6.47	1/128	-	-	-

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