A concrete beam prestressed with a parabolic tendon is shown in the sketch. The eccentricity of the tendon is measured from the centroid of the cross-section. The applied prestressing force at service is $$1620$$ $$kN.$$ The uniformly distributed load of $$45$$ $$kN/m$$ includes the self-weight. The stress (in $$N/m{m^2}$$) in the bottom fibre at mid-span is

The cross-section at mid-span of a beam at the edge of a slab is shown in the sketch. $$A$$ portion of the slab is considered as the effective flange width for the beam. The grades of concrete and reinforcing steel are $$M25$$ and $$Fe415,$$ respectively. The total area of reinforcing bars $$\left( {{A_{st}}} \right),$$ is $$\,4000\,\,m{m^2}.$$ At the ultimate limit state, $${x_u}$$ denotes the depth of the neutral axis from the top fibre. Treat the section as under-reinforced and flanged $$\left( {{x_u} > 100\,\,mm} \right).$$

The ultimate moment capacity (in $$kNm$$) of the section, as per the Limit State Method of $$IS$$ $$456$$ - $$2000$$ is

As per $$IS$$ $$456:2000,$$ in the Limit State Design of a flexural member, the strain in reinforcing bars under tension at ultimate state should not be less than

The cross-section at mid-span of a beam at the edge of a slab is shown in the sketch. $$A$$ portion of the slab is considered as the effective flange width for the beam. The grades of concrete and reinforcing steel are $$M25$$ and $$Fe415,$$ respectively. The total area of reinforcing bars $$\left( {{A_{st}}} \right),$$ is $$\,4000\,\,m{m^2}.$$ At the ultimate limit state, $${x_u}$$ denotes the depth of the neutral axis from the top fibre. Treat the section as under-reinforced and flanged $$\left( {{x_u} > 100\,\,mm} \right).$$

The value of $${{x_u}}$$ (in $$mm$$) computed per the Limit State Method of $$IS$$ $$456:2000$$ is