A simply supported rectangular prestressed concrete beam $$200$$ $$mm$$ wide and $$400$$ $$mm$$ deep has an effective span of $$12$$ $$m.$$ The prestressing cable has a triangular profile with zero eccentricity at ends and $$70$$ $$mm$$ at the midspan as shown in the figure below. The effective prestress is $$800$$ $$kN$$ after all losses. Determine the value of point load, the beam can support at the midspan if the pressure line passes through the upper kern of the section. The weight density of the material of the beam can be taken to be $$25$$ $$kN/{m^3}$$

A beam with a rectangular cross section of size $$250$$ $$mm$$ wide and $$350$$ $$mm$$ deep is prestressed by a force of $$400$$ $$kN$$ using $$8$$ numbers $$7$$ $$mm$$ $$\phi $$ steel cables located at an eccentricity of $$75$$ $$mm.$$ Determine the loss of prestress due to creep of concrete. Grade of concrete is $$M40;$$ Coefficient of creep is $$2;$$ stress at transfer is $$80\% $$, Modulus of elasticity of steel $$\left( {{E_s}} \right)$$ is $$2.0 \times {10^5}\,\,MPa.$$

The cross-section of a pretensioned pre-stressed concrete beam is shown in Figure. The reinforcement is placed concentrically. If the stress in steel at transfer is $$1000$$ $$MPa,$$ compute the stress in steel immediately after transfer. The modular ratio is $$6.$$