The vector field $$\,F = x\widehat i - y\widehat j\,\,$$ (where $$\widehat i$$ and $$\widehat j$$ are unit vectors) is

A concrete column carries an axial load of $$450$$ $$kN$$ and a bending moment of $$60$$ $$kN$$-$$m$$ at its base. An isolated footing of size $$2m \times 3m$$ side along the plane of the bending moment is provided under the column. Centers of gravity of column and footing coincide. The net maximum and the minimum pressures in $$kN/{m^2}$$ on soil under the footing are respectively.

The effective length of a column in a reinforced concrete building frame, as per $$IS:$$ $$456$$-$$2000,$$ is independent of the

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