A concrete beam prestressed with a parabolic tendon is shown in the sketch. The eccentricity of the tendon is measured from the centroid of the cross-section. The applied prestressing force at service is $$1620$$ $$kN.$$ The uniformly distributed load of $$45$$ $$kN/m$$ includes the self-weight. The stress (in $$N/m{m^2}$$) in the bottom fibre at mid-span is

A rectangular concrete beam of width $$120$$ $$mm$$ and depth $$200$$ $$mm$$ is prestressed by pretensioning to a force of $$150$$ $$kN$$ at an eccentricity of $$20$$ $$mm.$$ The cross sectional area of the prestressing steel is $$187.5\,\,m{m^2}.$$ Take modulus of elasticity of steel and concrete as $$2.1 \times {10^5}\,\,MPa$$ and $$3.0 \times {10^4}\,\,MPa$$ respectively. The percentage loss of stress in the prestressing steel due to elastic deformation of concrete is

A pre-tensioned concrete member of section $$200\,\,mm \times 250\,\,mm$$ contains tendons of area $$500\,\,m{m^2}$$ at the centre of gravity of the section. The prestress in tendons is $$1000\,\,N/m{m^2}.$$. Assuming modular ratio as $$10,$$ the stress $$\left( {N/m{m^2}} \right)$$ in concrete is

A concrete beam of rectangular cross-section of size $$120$$ $$mm$$ (width) and $$200$$ $$mm$$ (depth) is prestressed by a straight tendon to an effective force of $$150$$ $$kN$$ at an eccentricity of $$20$$ $$mm$$ (below the centroidal axis in the depth direction). The stresses at the top and bottom fibres of the section are