A reinforced concrete beam, size $$200$$ $$mm$$ wide and $$300$$ $$mm$$ deep overall is simply supported over a span of $$3$$ $$m.$$ It is subjected to two point loads $$P$$ of equal magnitude placed at middle third points. The two loads are gradually increased simultaneously. Beam is reinforced with $$2$$ $$HYSD$$ $$415$$ bars of $$16$$ $$mm$$ diameter placed at an effective cover of $$40$$ $$mm$$ on bottom face and nominal shear reinforcement. The characteristic compressive strength and the bending tensile strength of the concrete are $$20.0\,\,N/m{m^2}$$ and $$2.2\,\,N/m{m^2}$$ respectively.

The theoretical failure load of the beam for attainment of limit state of collapse in flexure is

Maximum strains in an extreme fibre in concrete and in the tension reinforcement (Fe-$$415$$ grade and $${E_s} = 200\,\,kN/m{m^2}$$) in a balanced section at limit state of flexure are respectively

Read the following two statements

$${\rm I}.\,\,\,\,\,\,\,\,\,\,\,\,$$ Maximum strain in concrete at the outermost compression fibre is taken to be $$0.0035$$ in bending
$${\rm II}.\,\,\,\,\,\,\,\,\,\,\,\,$$ The maximum compressive strain in concrete in axial compression is taken as $$0.002$$ Keeping the provisions of $$IS$$ $$456$$-$$2000$$ on limit state design in mind, which of the following is true?

As per provision of $$IS$$ $$456$$-$$2000$$, in the limit state method for design of beams, the limiting value of the depth of neutral axis in a reinforced concrete beam of effective depth $$'d'$$ is given as