A $$10m$$ long prestressing bed is used to cast $$4$$ (pretensioned) prestressed concrete beams of $$2.3$$ $$m$$ each. A schematic representation of the bed is given in the following figure. The continuous prestressing reinforced is pulled at the end $$'Y'$$ of the bed through a distance of $$20$$ $$mm$$ to introduce the required prestress, before the concrete is cast. After the concrete has hardened, the prestressing reinforcement is cut at points $$A,B,C,D$$ and $$E.$$ Assume that the prestress is introduced without eccentricity, what is the loss in prestress on account of elastic deformation of concrete. Assume $${E_s} = 200000\,\,N/m{m^2},$$ reinforcement is $$500\,\,m{m^2},$$ size of beams $$ = 200\,\,mm\,\left( b \right) \times 400\,\,mm\,\left( h \right).$$

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 $$6.$$