A launched (varying depth) reinforced concrete beam is simply supported at both ends, as shown in the figure. The beam is subjected to a uniformly distributed factored load of intensity $$10$$ $$kN/m.$$ The design shear force (expressed in $$kN$$) at the section $$X$$-$$X$$ of the beam is ____________

As per $$IS$$ $$456$$ - $$2000$$ for the design of reinforced concrete beam, the maximum allowable shear stress $$\left( {{\tau _{c\,\,\max }}} \right)$$ depends on the

Two bolted plates under tension with alternative arrangement of bolt holes are shown in figures $$1$$ and $$2.$$ The hole diameter, pitch, and gauge length are $$d, p$$ and $$g$$ respectively.

Which one of the following conditions must be ensured to have higher net tensile capacity of configuration shown in figure $$2$$ than that shown in figure $$1$$?

A $$450$$ $$mm$$ long plain concrete prism is subjected to the concentrated vertical loads as shown in the figure. Cross section of the prism is given as $$150\,\,mm\,\, \times \,\,150\,\,mm.$$ Considering linear stress distribution across the cross-section, the modulus of rupture (expressed in $$MPa$$) is ______________