If $$\phi \, = \,$$ nominal diameter of reinforcing bar, $${f_s}\, = $$ compressive stress in the bar and $${f_{bd}}\, = $$ design bond stress of concrete, the anchorage length, $${L_a}$$ of straight bar in compression is equal to

The loss of prestress due to elastic shortening of concrete is least in

A uniformly distributed load intensity, $$w$$ acting on a simply supported prestressed concrete beam of span $$L,$$ producing a bending moment $$M,$$ at mid-span is to be balanced by a parabolic tendon with zero eccentricity at ends and eccentricity $$e,$$ at mid-span. The prestressing force required depends on

The kern area (core) of a solid circular section column of diameter, $$D$$ is a concentric circle of diameter, $$'d'$$ is equal to