Problem $\frac{?}{?}$# $3_{?}$

$5\mathrm{.}1.$ The short beam shown in Fig. P$5\mathrm{.}1$ cantilevers from a supporting column at the left. It must carry a calculated dead load of $29k\frac{N}{m}$ including its own weight and a service live load of $38k\frac{N}{m}.$ Tensile flexural reinforcement consists of two No$.36($No$.11)$ bars at a $525mm$ effective depth. Transverse No$.10($No$.3)$ U stirrups with $40mm$ cover are provided at the following spacings from the face of the column: $100mm,3$ at $200mm,5$ at $260mm.$

$($a$)$ If the flexural and shear steel use $f_y=420$MPa and if the beam uses lightweight concrete having $f_c^{\text{'}}=28$MPa, check to see if proper development length can be provided for the No$.36($No$.11)$ bars. Use the simplified development length equations.

$($b$)$ Recalculate the required development length for the beam bars using the basic Eq$.(5\mathrm{.}4).$ Comment on your results.

$50$

$($c$)$ If the column material strengths are $f_y=420$MPa and $f_c^{\text{'}}=35$MPa $($normalweight concrete$),$ check to see if adequate embedment can be provided within the column for the No$.36($No$.11)$ bars. If hooks are required, specify detailed dimensions.