The prestressed concrete beam has a rectangular cross section of $1600mm($deep$)500mm($wide$).$ The live load is $25k\frac{N}{m}.$ The only dead load is the self$-$weight. Concrete density is $25k\frac{N}{m^3}.$ Total prestress losses after transfer are $22\%.$

Using load balancing of the total dead load and live load:

a$.$ Calculate the prestress force $($after all losses have occurred$)$ that is necessary to balance the dead and live load.

b$.$ Using the prestress force that you calculated in $($a$)$ above, calculate the midspan concrete stresses $($top and bottom$)$ under the full load after all losses have occurred, and also under self$-$weight load immediately after transfer.

Using partially prestressed design with the requirement that under dead load and live load the maximum tensile stress is $3\mathrm{.}0$ MPa $($i$.$e$.$ numerical value $-3\mathrm{.}0)$ after all losses have occurred:

c$.$ Calculate the required prestress force after all losses have occurred.

d$.$ Using the prestress force that you calculated in $($c$)$ above, calculate the midspan concrete stresses $($top and bottom$)$ after all losses have occurred, and also immediately after transfer.