The permissible flexural stress in a dowel bar of diameter 'd' is '$$F_f$$' and the permissible bending stress in concrete used in the pavement is '$$F_b$$'. In order to obtain balanced design for equal capacity in bending and bearing, the length of embedment of the dowel bar ‘$$L_d$$’ to be provided at a joint of with $$\delta$$ can be expressed as _______________

$$L_d = 5d \left[\frac{F_b}{F_f} \times \frac{L_d + 8.8 \delta}{L_d + 1.5 \delta}\right]^{\frac{1}{2}}$$

$$L_d = 5d \left[\frac{F_f}{F_b} \times \frac{L_d + 8.8 \delta}{L_d + 1.5 \delta}\right]^{\frac{1}{2}}$$

$$L_d = 5d \left[\frac{F_b}{F_f} \times \frac{L_d + 1.5 \delta}{L_d + 8.8 \delta}\right]^{\frac{1}{2}}$$

$$L_d = 5d \left[\frac{F_f}{F_b} \times \frac{L_d + 1.5 \delta}{L_d + 8.8 \delta}\right]^{\frac{1}{2}}$$