#### 5.1. Test Results

The results of the uniaxial compressive tests are provided in

Table 3 and

Figure 4, where

E^{−} = initial compressive elastic modulus;

E_{2}^{−} = compressive post-yield modulus;

r_{sf} ^{−} = compressive post-yield modulus ratio;

F_{sfy}^{−} = compressive yield load of the SFCB;

σ_{sfy}^{−} = compressive yield stress of the SFCB;

F_{sfu}^{−} = ultimate compressive load of the SFCB;

σ_{sfu}^{−} = ultimate compressive stress of the SFCB;

F_{su}^{−} = ultimate compressive load of the ISB;

σ_{su}^{−} = ultimate compressive stress of the ISB; SFCB-C-4-1 indicates the first SFCB specimen (

λ_{eq} = 4) under uniaxial compressive loading; ISB-C-8-2 indicates the second ISB specimen (length is equal to that of SFCB-C-8-2) under uniaxial compressive loading; ISB-C-4-mean indicates the mean value curve of four ISB specimens (length is equal to that of SFCB-C-4) under uniaxial compressive loading, as shown in

Figure 4a. The average strain in

Figure 4 refers to the macroscopic compressive mean strain, which equaled the displacement obtained by the LVDT sensor, as shown in

Figure 2b, divided by the length of each specimen.

Due to the different compressive characteristics (

Figure 4a–f), the compressive process can be classified into three categories in accordance with the different slenderness ratios, i.e.,

λ_{eq} ≤ 12, 12 <

λ_{eq} ≤ 20, and

λ_{eq} > 20, corresponding to the three failure modes, which are post-yield buckling (PYB), yield buckling (YB), and axial compressive buckling (ACB), respectively (

Figure 5).

When

λ_{eq} ≤ 12, the compressive process of the SFCB can be divided into four stages (

Figure 5). Since most deformations occur in the middle cross-section of the specimen, this section can be defined as the control section (

Figure 2a).

I: Axial compression stage. At the beginning of compression, all specimen cross-sections were under axial compression, and the load-strain curve rose rapidly. With an increase in the strain, a lateral deformation occurred at the control section. Then, the stress condition of the control section gradually transformed from axial compression to eccentric compression, which resulted in a slight decrease in the compressive stiffness (the slope of the load-strain curve) (‘OA’ in

Figure 5).

II: Plastic softening stage. Due to the developing lateral deformation, the inner steel section began to yield. The expansion of the yield area resulted in a further decrease in the compressive stiffness and, consequently, resulted in a significant softening stage on the load-strain curve (‘AB’ in

Figure 5).

III: Post-yield stiffness stage. With a further expansion of the yield area, nearly the entire inner steel section yielded, and the compressive stiffness of the SFCB was primarily provided by the FRP. Consequently, the compressive stiffness tended to be stable, and the load increased linearly with the strain (‘BC’ in

Figure 5). The designable post-yield stiffness stage distinguishes the SFCB from the traditional steel bars by considerably reducing the residual displacement of concrete structures in earthquakes and improving their repairability.

IV: Post-buckling stage. For specimens with a low slenderness ratio (such as

λ_{eq} = 4), a local buckling was observed due to the splitting or buckling of fibers at random locations, as shown in

Figure 6a. A steep decline of the load-strain curve was then observed, as in

Figure 4a. For specimens with a high slenderness ratio (such as

λ_{eq} = 12), an overall buckling of specimen was observed at first, then the load-strain curve began to decline, as in

Figure 4c. With the increase of the specimen’s lateral deformation, the fiber will finally split or fracture (

Figure 6b).

Although four stages were observed in all of the SFCB specimens when

λ_{eq} ≤ 12, the compressive characteristics varied slightly for the specimens with different slenderness ratios. In the axial compression stage, the slope of the load-strain curve increased with an increase in the slenderness ratios (

Figure 4), which was a result of using the test method based on anchoring. As the loading was transferred through the shear stress of the epoxy, the non-uniform stress distribution occurred in the region close to the anchoring tube, which potentially increased the strain of the outer layer of the specimen in this region and was thus reflected by a decrease in the compressive stiffness. In the post-yield stiffness stage, the linear load-strain curve gradually shortened with an increase in the slenderness ratios as a result of the decreasing ultimate compressive stress. In the post-buckling stage, the FRP became completely invalid after buckling for the specimens with a relatively low slenderness ratio (such as

λ_{eq} = 4). However, for specimens with a higher slenderness ratio (such as

λ_{eq} = 12), the FRP was not completely damaged by buckling. Instead, a part of the FRP could continually bear the load until a further split or fracture. The load-strain curve of the specimens with a higher slenderness ratio exhibited a slower approaching speed toward the load-strain curve of the ISB after buckling (

Figure 4a–c).

When 12 <

λ_{eq} ≤ 20, only three stages (

Figure 5) including the axial compression stage (I), plastic softening stage (II), and post-buckling stage (IV), were observed during the compressive process. The characteristics of each stage were essentially similar to the specimens with

λ_{eq} ≤ 12. The primary difference was that the post-yield stiffness stage no longer existed as a result of the advanced buckling in the plastic softening stage and a further decrease in the ultimate compressive stress, which was reduced by an increase in the slenderness ratio. As the slenderness ratio increased, there were only two stages (

Figure 5), i.e., the axial compression stage (I) and the post-buckling stage (IV) when

λ_{eq} > 20. Similar characteristics of each stage were observed during the compressive process when 12 <

λ_{eq} ≤ 20. The compressive failure mode of SFCB was characterized by the fracture or splitting failure of the outside fibers, which is different from the inelastic buckling failure of a steel bar.

#### 5.5. Compressive Yield Load and Stress

The compressive yield load of the SFCB is essentially irrelevant to the slenderness ratio. The mean values of the SFCB compressive yield load remained at 43 kN with the variation in the slenderness ratio, which were generally 19% higher than the mean values of the corresponding squash load, and remained at 36 kN, as shown in

Table 3. This indicates that the squash load of the SFCB tends to be conservative when predicting the compressive yield load of the SFCB. In addition, the equivalent critical global buckling load of the SFCB was generally much higher than the corresponding compressive yield load, as shown in

Table 3. The mean value of the equivalent critical global buckling load of the SFCB was 151% higher than the corresponding compressive yield load even when the equivalent slenderness ratio of the SFCB reached 20, indicating that an inelastic buckling mechanism was initiated in the SFCB within the range of the slenderness ratio studied in this paper, and that the classic Euler buckling load could not be used to predict the compressive yield load of the SFCB.

The mean values of the compressive yield stress of the SFCB (

σ_{sfy}^{−}) remained at 416 MPa with the variation in the slenderness ratio, which was primarily equal to the tensile yield stress of the SFCB (

σ_{sfy}^{+}), i.e., 419 MPa. Therefore, the compressive yield stress of the SFCB can be assumed to be in accordance with its tensile yield stress, which is presented in Equation (10) as follows:

#### 5.6. Ultimate Compressive Load and Stress

The ultimate compressive load of the ISB basically agreed well with the corresponding squash load, especially when the slenderness ratio was relatively low (such as

λ_{eq} = 9.2). The critical global buckling load of the ISB was still 100% higher than the corresponding ultimate compressive load of the ISB even when its slenderness ratio reached 27.6, as in

Table 3, which indicated that the inelastic buckling mechanism also took place on the ISB, within the range of the slenderness ratio studied in this paper.

The mean values of the SFCB ultimate compressive load were higher than the corresponding squash load by 8.3%~77.8% with the variation in the equivalent slenderness ratio, which could be attributed to the elastic fiber of the SFCB restricting the plastic deformation of the ISB after its yielding.

An improvement of approximately 30% was observed when comparing the ultimate compressive stress of the SFCB to the corresponding ultimate compressive stress of the ISB when the slenderness ratio of the SFCB exceeded 8 (

Table 3). Additionally, the ultimate compressive stress of the SFCB was inversely proportional to the slenderness ratio, which was similar to the characteristics of the steel bar when under compression [

4], and a linear relationship between the ultimate compressive stress of the SFCB, and the slenderness ratio was captured using statistical analysis (

Figure 8). The equation of the ultimate compressive stress of the SFCB can be presented in Equation (11) as follows: