If d is the diameter of a bar, ft is allowable tensile stress and fb, is allowable bond stress, the bond length is given by A. $$\frac{{{{\text{f}}_{\text{t}}}{\text{d}}}}{{4{{\text{f}}_{\text{b}}}}}$$ B. $$\frac{\pi }{4} \times \frac{{{{\text{f}}_{\text{t}}}{\text{d}}}}{{{{\text{f}}_{\text{b}}}}}$$ C. $$\frac{{\pi {{\text{f}}_{\text{t}}}{{\text{d}}^2}}}{{{{\text{f}}_{\text{b}}}}}$$ D. $$\frac{\pi }{4} \times \frac{{{{\text{f}}_{\text{t}}}{{\text{d}}^3}}}{{{{\text{f}}_{\text{b}}}}}$$

The correct answer is $\boxed{\frac{\pi}{4} \times \frac{{{{\text{f}}{\text{t}}}{{\text{d}}^2}}}{{{{\text{f}}{\text{b}}}}}$.

The bond length is the length of a reinforcing bar that is embedded in concrete so that the two materials can transfer forces to each other. The bond length is determined by the following equation:

$$l_b = \frac{\pi}{4} \times \frac{{{{\text{f}}{\text{t}}}{{\text{d}}^2}}}{{{{\text{f}}{\text{b}}}}}$$

where:

• $l_b$ is the bond length
• $f_t$ is the allowable tensile stress in the reinforcing bar
• $f_b$ is the allowable bond stress in the concrete
• $d$ is the diameter of the reinforcing bar

The allowable tensile stress in the reinforcing bar is the maximum tensile stress that the bar can withstand without failing. The allowable bond stress in the concrete is the maximum tensile stress that the concrete can withstand without failing. The diameter of the reinforcing bar is the diameter of the bar measured across its cross-section.

The bond length is important because it ensures that the reinforcing bar is adequately bonded to the concrete so that the two materials can transfer forces to each other. If the bond length is too short, the reinforcing bar may not be able to withstand the tensile forces in the concrete and may fail.