A rectangular concrete beam $$250$$ $$mm$$ wide and $$600$$ $$mm$$ deep is pre-stressed by means of $$16$$ high tensile wires, each of $$7$$ $$mm$$ diameter, located at $$200$$ $$mm$$ from the bottom face of the beam at a given section. If the effective pre-stress in the wires is $$700$$ $$MPa,$$ what is the maximum sagging bending moment (in $$kN$$-$$m$$) (correct to $$1$$-decimal place) due to live load that this section of the beam can with stand without causing tensile stress at the bottom face of the beam? Neglect the effect of dead load of beam.

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