reinforced concrete class

Problem $3.(25\%)$

An $RC$ beam requires splicing at locations A and $B$ for flexural reinforcement, with details shown in the figure. For each location, splicing for $2$ flexural steel bars is needed. The positive moment at $A$ is $M_u=163kN-m,$ and the required tensile reinforcement at $A$ is $8\mathrm{.}8c{m}^2($calculated based on this positive moment$)$; the negative moment at $B$ is $M_u=461kN-m,$ and the required tensile reinforcement at $B$ is $20\mathrm{.}1c{m}^2($calculated based on this negative moment$).$ Assuming that the amount of the spliced steel is $50\%$ for A and $B,f{c}^{\text{'}}=35$MPa, and fy $=420$MPa. Please use the $l_{db}$ expression to design the required lap lengths at A and $B.$

$l_{db}={|}_{{?}_{?}}\frac{9}{10}\frac{f_y}{\sqrt[\phantom{2}]{f{c}^{\text{'}}}}\frac{{}_t{}_c{}_s}{((\frac{c_b+K_{tr}}{d_b}){)}_{{?}_{?}}}|d_b,(mm)$