$1)$ For the rectangular beam shown here, calculate the

development lengths of top No$.7$ bars and bottom No$.9$

bars. No$.4$ bars are used for stirrups. The spacing of

stirrups is $6$ in$.$ The clear side cover depth is $1\mathrm{.}5$ inch.

$($Clear cover depth means the distance from the beam face

to the outer surface of a bar$).$

Normalweight concrete is used.$l_d=(\frac{f_y{}_t{}_e{}_g}{20\sqrt[\phantom{2}]{f_c^{\text{'}}}})d_b$

$f_c^{\text{'}}=4000$ psi $f_y=f_{yt}=60000$ psi.

Equation $(6\mathrm{.}5)$ and $(6\mathrm{.}6)$ will be used respectively. And the

results shall be compared.

$2)$ From the conditions given in problem $1,$ the yield stresses $f_y$ and $f_{yt}$ have been increased to

$80000$ psi $($f$\text{'}$c $=4000$ psi, and $\{$:$f_y=f_{yt}=80000).$ Determine the development lengths with

the increased yield strength.

$3)$ From the conditions given in problem $1,$ only the yield stress $f_c^{\text{'}}$ has been increased to $8000$ psi

$(f_y=f_{yt}=60000$ psi$).$ Determine the development lengths with the increased compressive

strength.