The state of two dimensional stresses acting on a concrete lamina consists of a direct tensile stress, $${\sigma _x} = 1.5\,\,N/m{m^2},$$ and shear stress, $$\tau = 1.20\,N/m{m^2},$$ which cause cracking of concrete. Then the tensile strength of the concrete in $$N/m{m^2}$$ is

If $$'YY'$$ is the centroidal axis of a $$T$$-beam section, subjected to plastic moment, $${M_P},$$ the neutral axis lies

The ratio of the stiffness of a beam at the near end when the far end is hinged to the stiffness of the beam at the near end when the far end is fixed is

A single bay portal frame of height $$'h'$$ fixed at the base is subjected to a horizontal displacement $$'\delta '$$ at the top. The base moments developed is proportional to _____, where $$'{\rm I}'$$ is the moment of inertia of the cross section.