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

The semi-compact section of a laterally unsupported steel beam has an elastic section modulus, plastic section modulus and design bending compressive stress of $$500\,\,c{m^3},\,\,650\,\,c{m^3}$$ and $$200$$ $$MPa,$$ respectively. The design flexural capacity (expressed in $$kNm$$) of the section is ___________________

Two plates are connected by fillet welds of size $$10$$ $$mm$$ and subjected to tension, as shown in the sketch. The thickness of each plate is $$12$$ $$mm.$$ The yield stress and the ultimate tensile stress of steel are $$250$$ $$MPa$$ and $$410$$ $$MPa,$$ respectively. The welding is done in the workshop $$\left( {{\gamma _{mw}} = 1.25} \right).$$

As per the Limit State Method of $$IS$$ $$800:2007,$$ the minimum length (rounded off to the nearest higher multiple of $$5$$ $$mm$$) of each weld to transmit a force $$P$$ equal to $$270$$ $$kN$$ (factored) is

A $$3$$ $$m$$ long simply supported beam of uniform cross section is subjected to a uniformly distributed load of $$w = 20$$ $$kN/m$$ in the central $$1$$ $$m$$ as shown in the figure.

If the flexural rrigidity $$(EI)$$ of the beam is $$30 \times {10^6}\,\,N$$ - $${m^2},$$ the maximum slope (expressed in radians) of the deformed beam is