3.3.2. Embedded Length

The relative bond strength is defined as the ratio of the average bond strength to the tensile strength (τ/ *ft*), and the relative embedded length is defined as the ratio of the embedded length to the height of the section steel (*Le*/*d*). The relationship between the embedded length and the average initial bond strength, the average ultimate bond strength, and the average residual bond strength are shown in the following equations:

$$
\overline{\tau\_s} = (-0.011L\_\text{x}/d + 0.440)f\_t \tag{6}
$$

$$
\overline{\tau\_{\mathcal{U}}} = (-0.070L\_{\mathfrak{t}}/d + 1.247)f\_{\mathfrak{t}} \tag{7}
$$

$$
\overline{\pi\_r} = \left(-0.0411L\_\text{c}/d + 0.736\right)f\_l \tag{8}
$$

As can be seen from Figure 8b, the bond stress decreases as the embedded length increases. The reduction effect of the average initial bond strength is not obvious, and the average ultimate bond strength decreases significantly.

#### 3.3.3. Cover Thickness

The relative cover thickness is calculated from the ratio of the cover thickness to the height of the section steel (*Css*/*d*). The cover thickness refers to the distance between the section steel and the outer surface of RAC. The relationship is shown in the following equations:

$$
\overline{\tau\_{\sf s}} = (1.566 \mathcal{C}\_{\sf s\sf s}/d - 0.318) f\_{\sf t} \tag{9}
$$

$$
\overline{\tau\_u} = (0.983 \mathcal{C}\_{\infty}/d + 0.317) f\_t \tag{10}
$$

$$
\overline{\tau\_r} = (0.469 \text{C}\_{\text{ss}}/d + 0.243) f\_t \tag{11}
$$

It can be seen from Figure 8c that the average characteristic bond strength obviously increases with the increase of the cover thickness.

#### 3.3.4. Lateral Stirrup Ratio

The effect of the lateral stirrup ratio is similar to that of the cover thickness, which can effectively prevent the lateral deformation of the RAC and delay the cracking time. The equations are as follows.

$$
\overline{\tau\_s} = (2.934 \rho\_{ss} - 0.206) f\_t \tag{12}
$$

$$
\overline{\tau\_u} = (0.269\rho\_{\rm ss} - 0.770)f\_t \tag{13}
$$

$$
\overline{\pi\_r} = (1.556 \rho\_{\text{sys}} - 0.172) f\_l \tag{14}
$$

It can be seen from Figure 8d that the average characteristic bond strength increases with the increase of the lateral stirrup ratio, and the average initial bond strength increases obviously. The effect of increasing the ultimate bond strength is poor, indicating that the increase of the lateral stirrup ratio can effectively delay the appearance of the initial crack and increase the cracking load, but the effect on improving the average ultimate bond strength is not significant.
