$(3$ marks$)$

$($d$)$ At a certain location along a reinforced concrete beam, a $20mm$ diameter reinforcement bar has a tensile stress of $200\frac{N}{m}{m}^2.$

$($i$)$ Calculate from basic principles the minimum anchorage bond length in concrete required to resist the stress if the design bond strength $f_{bu}=3\mathrm{.}2\frac{N}{m}{m}^2.$

$(3$ marks$)$

$($ii$)$ If the bar is lapped with a similar grade bar of $16mm$ diameter, calculate the minimum lap length required in order to transfer the same tensile force across the lap.