As per $$IS$$ $$456:2000$$ for $$M20$$ grade concrete and plain barsin tension the design bond stress $${\tau _{bd}} = 1.2\,\,MPa.$$ Further, $$IS$$ $$456:2000$$ permits this design bond stress value to be increased by $$60\% $$ for $$HYSD$$ bars. The stress in the $$HYSD$$ reinforcing steel bars in tension $${\sigma _s} = 360\,MPa.$$ Find the required development length, $${L_d},$$ for $$HYSD$$ bars in terms of the bar diameter, $$\phi $$ ______________.

Maximum possible value of compaction factor for fresh (green) concrete is

A symmetric $${\rm I}$$-section (with width of each flange $$=50$$ $$mm$$, thickness of each flange $$=10$$ $$mm,$$ depth of web $$= 100$$ $$mm,$$ and thickness of web $$=10$$ $$mm$$ ݉݉) of steel is subjected to a shear force of $$100$$ $$kN.$$ Find the magnitude of the shear stress (in ܰ$$N/m{m^2}$$) in the web at its junction with the top flange. ___________

Two steel columns $$P$$ (Length $$L$$ and yield strength $${f_y} = 250\,\,MPa$$) and $$Q$$ (length $$2L$$ and yield strength $${f_y} = 500\,\,MPa$$) have the same cross-sections and end-conditions. The ratio of buckling load of column $$P$$ to that of column $$Q$$ is: