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.

Ignoring the presence of tension reinforcement, the value of load $$P$$ in $$kN$$ when the first flexure crack will develop in the beam is

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

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