A simply supported rectangular concrete beam of span $$8$$ $$m$$ has to be prestressed with a force of $$1600$$ $$kN.$$ The tendon is of parabolic profile having zero eccentricity at the supports. The beam has to carry an external uniformly distributed load of intensity $$30$$ $$kN/m.$$ Neglecting the self - weight of the beam, the maximum dip (in meters, up to two decimal places) of the tendon at the mid-span to balance the external load should be _______________

A pre-tensioned rectangular concrete beam $$150$$ $$mm$$ wide and $$300$$ $$mm$$ depth is prestressed with three straight tendones, each having a cross-sectional area of $$50$$ $$m{m^2},$$ to an initial stress of $$1200$$ $$N/m{m^2}.$$ The tendons are located at $$100$$ $$mm$$ from the soffit of the beam. If the modular ratio is $$6,$$ the loss of prestressing force (in $$kN,$$ up to one decimal place) due to the elastic deformation of concrete only is ________

In a pre-stressed concrete beam section shown in the figure, the net loss is $$10\% $$ and the final prestressing force applied at $$X$$ is $$750$$ $$kN.$$ The initial fiber stresses (in $$N/m{m^2}$$ ) at the top and bottom of the beam were:

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.