*4.3. Ductility*

The ductility coe fficient and shift angle are important parameters to assess the seismic performance of the structure, and they also are the essential characteristics to evaluate the deformation ability of the specimen.

Nowadays, the calculation methods for ductility are di fferent, and each method has its characteristics. In this paper, the displacement ductility coe fficient (μ = Δ*u* <sup>Δ</sup>*y* ) is used for representing the ductility, where <sup>Δ</sup>*y* is the yield displacement, which is obtained by using the equivalent energy method [33], Δ*u* is the displacement corresponding to the lateral load of 85% of the ultimate load. The Shift angle is calculated as θ = Δ*u H* , where H is the distance from the top surface of the bottom beam to the lateral loading point. The ductility coe fficient and shift angle of each wall are shown in Table 5.


**Table 5.** Ductility coe fficients and shifts angle of specimens.

As can be seen from Table 5, the mean values of ductility coe fficient μ of bare walls are between 1.191 and 3.123, and the mean values of ductility coe fficient of W2 are smallest. Compared to W2, the increase in ductility was 42.6% and 162.2% for the specimens W1 and W3, indicating that increasing the compression stress could decrease the ductility of specimens, but increasing the aspect ratio could increase the ductility of specimens.

The ductility coe fficients of reinforced walls were higher than 3, meeting the specification requirements of GB 50003-2011 [34] (μ ≥ 3), which indicated that the structural columns enhanced the deformation ability of both walls, and decreased the brittleness of specimens. According to the results of Table 5, the ductility coe fficient and the lateral shift angle of W4 were higher than that of W5, which reflected that the ductility of the ordinary concrete structural columns was better than that of the RAC structural columns.

### *4.4. Sti*ff*ness Degradation*

The sti ffness degradation factor ( *Ki*) is expressed as follows:

$$\mathcal{K}\_{\bar{i}} = \frac{|P\_{\bar{i}}| + |-P\_{\bar{i}}|}{|\Delta\_{\bar{i}}| + |-\Delta\_{\bar{i}}|},$$

In which *Pi* is the maximum load and Δ*i* is the corresponding displacement. The sti ffness degradation of all specimens is shown in Figure 11.

**Figure 11.** Sti ffness deterioration curves of specimens: (**a**) W1, W2, and W3; (**b**) W4 and W5.

The sti ffness degradation tendency of all the specimens is plotted in Figure 11. This figure shows that the sti ffness of bare walls gradually decreases with the increase of the displacement. After the displacement reached the ultimate displacement, the sti ffness of bare walls degraded quickly due to the accumulation of cracks. It can be easily observed that the sti ffness degradation rate of W2 was lower than that of W1 and W3 after cracking. In comparison with W1, the sti ffness of W2 generally degraded, which indicated that the increase of vertical compression could reduce the degradation rate of the sti ffness of specimens. In addition, when other factors were equal, a comparison of the sti ffness degradation rate of W2 and W3 showed that the aspect ratio had a negative influence on the degradation rate of the sti ffness of specimens.

It can be seen from Figure 11b that the stiffness degradation tendency of W4 nearly coincides with that of W5. In the initial stage, the stiffness of the specimens decreases quickly with the increase of the displacement. After the displacement reached the ultimate displacement, the stiffness degradation of reinforced specimens tended to be more smooth. The analysis stated that the effective constraint applied by structural columns could significantly alleviate stiffness degradation. In comparison with W5, the stiffness of W4 deteriorated rapidly at an early stage and deteriorated slowly at a late stage, but in general, the stiffness curves of W4 and W5 were nearly overlapping, indicating that the stiffness degradation of the specimen with RAC structural columns was close to that of ordinary concrete structural columns.

Table 6 lists the secant stiffness of characteristic points. It can be found that the stiffness degradation rate of W4 was higher than that of W5 before cracking, and after cracking, the stiffness degradation rate of W4 was slightly lower than that of W5.


**Table 6.** Secant stiffness of all the specimens at characteristic points.

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#### *4.5. Energy Dissipation Capacity*

Energy dissipation performance refers to the energy dissipation capacity of the wall under the action of the earthquake load, which is obtained by calculating the area enclosed by the overall hysteresis loop of the first loading cycle. It is an important indicator to measure the seismic performance of the structure. The curves of energy dissipation per cycle are presented in Figure 12.

**Figure 12.** Energy dissipation per cycle for all test specimens: (**a**) W1, W2, and W3; (**b**) W4 and W5.

As shown in Figure 12a, the energy dissipation increases with the increasing lateral displacement, and the energy dissipation of W2 was the best, then the next was W1, and the worst was W3. Comparing of W1 and W2, the energy dissipation capacity of W2 was higher, indicating that, within a certain range, the vertical compression had a positive influence on the energy dissipation capacity of the specimens. The energy dissipation of W3 was lower compared with W2, indicating that increasing the aspect ratio could decrease the energy dissipation capacity of specimens.

The energy dissipation curves of the specimens W4 and W5 are shown in Figure 12b. The specimens W4 and W5 were found to have a higher energy dissipation in comparison with the bare walls, indicating that the structural columns could significantly increase the energy dissipation capacity of walls.

To further quantify the hysteretic energy dissipation performance of the specimens, the equivalent viscous damping coefficient is used to measure the energy dissipation capacity of the structure under earthquake resistance. *he*,*<sup>u</sup>* and *he*, *f* are the equivalent viscous damping coefficients corresponding to the maximum load and the ultimate load, respectively. The equivalent viscous damping can be calculated as follows:

$$h\_{\mathfrak{e}} = \frac{1}{2\pi} \cdot \frac{S\_{ABC}}{S\_{\Delta OBD}}$$

where *S*Δ*BOD* and *SABC* are the areas enclosed by the shaded hysteresis loop in Figure 13, respectively.

**Figure 13.** Calculated graphics of the equivalent viscous damping coefficient.

The value of the equivalent viscous damping coefficient and energy dissipation per cycle can be observed from Table 7 and Figure 13, respectively. In comparison with W1, the value of *he*,*<sup>u</sup>* of W2 was 18.6% higher than that of W1, which indicated that the vertical compression could increase the energy dissipation performance of specimens. In terms of W2 and W3, the value of *he*,*<sup>u</sup>* of W3 was 54.8% lower than that of W2, which illustrated that increasing the aspect ratio had a negative influence on the energy dissipation performance of specimens. It should be noted that W1 and W3 were almost destroyed after reaching the ultimate load, and the hysteresis curve of W2 was not closed when the specimens were destroyed. Therefore, the value of *he*, *f* of W1, W2, and W3 was ignored.

**Table 7.** Equivalent viscous damping coefficients of all specimens.


It can be easily found that the value of equivalent viscous damping ratio of W4 and W5 were more significant than that of bare walls, which illustrated that, whether each of the specimens were constrained by ordinary concrete structural columns or RAC structural columns, the equivalent viscous damping ratio and the energy dissipation of the walls were improved. Compared to W4, the energy dissipation viscous damping ratio of W5 exhibited a 12.5% and 8.9% increase at maximum load and ultimate load, which illustrated that the energy dissipation capacity of ordinary concrete structural columns was close to that of RAC structural columns.
