Consider the singly reinforced section of a cantilever concrete beam under bending, as shown in the figure (M25 grade concrete, Fe415 grade steel). The stress block parameters for the section at ultimate limit state, as per IS 456: 2000 notations, are given. The ultimate moment of resistance for the section by the Limit State Method is ________ kN.m (round off to one decimal place).

[Note: Here, As is the total area of tension steel bars, b is the width of the section, d is the effective depth of the bars, f_ck is the characteristic compressive cube strength of concrete, f_y is the yield stress of steel, and x_u is the depth of neutral axis.]

A reinforced concrete $$(RC)$$ beam with width of $$250$$ $$mm$$ and effective depth of $$400$$ $$mm$$ is reinforced with $$Fe415$$ steel. As per the provisions of $$IS$$ $$456$$ - $$2000,$$ the minimum and maximum amount of tensile reinforcement (expressed in $$m{m^2}$$ ) for the section are, respectively

Consider the singly reinforced beam section given below (left figure). The stress block parameters for the cross-section from $$IS:$$ $$456$$ - $$2000$$ are also given below (right figure). The moment of resistance for the given section by the limit state method is ______ $$kN$$-$$m.$$

For a beam of cross-section, width $$= 230$$ $$mm$$ and effective depth $$= 500$$ $$mm,$$ the number of rebars of $$12$$ $$mm$$ diameter required to satisfy minimum tension reinforcement requirement specified by $$IS:$$ $$456-2000$$ (assuming grade of steel reinforcement as $$Fe500$$) is _______________