AASHTO-LRFD prestressed precast girder design is governed by crushing of concrete under compression or cracking of concrete under tension. At construction stages or at service state, we aim to prevent such negative cases.

Usually, girders cracked at construction stages are rejected to be used at the site and girders cracked at service times will decrease the economic life of the structure.

Immediately after prestressing, the end zones of prestressed precast girder can crack due to excessive prestressing. At service state, a section at mid-span can crack due to some overloading of the section. As known, cracking can reduce the economic life of the structure.
Gravity loads developed over the time of construction and service typically results in downward deflection. Usually, compression develops at top fibers and tension develops at bottom fibers in absence of prestressing. Prestressing reverses the gravity effects.

Components of stresses induced by different load cases can be superimposed on to each other to determine cumulative stresses at top and bottom fibers of the element at any section. At mid-span usually, top fibers are in compression and bottom fibers may or may not be in tension depending on the level of prestressing.

Longitudinal cracks can develop due to excessive compression that can decrease the durability of the concrete. Therefore, it is better to limit the compression stresses to a limit.

The prestressed precast girder design requires a crack-free design to maintain the durability of the element. The selected tensile stress limits are lower than a tensile strength of concrete that will not allow any cracking.

Prestressing steel do not have much elongation capacity due to its high strength. Therefore, to avoid any accidental breaks, the tensile stresses are limited in pulling the steel. Low-relaxation properties of steel will reduce the prestress losses.

Reference;
AASHTO LRFD Bridge Construction Specifications, 4th Edition