Design is typically a very complex problem if you especially do not know where to start. Wrong assumptions of a number of strands in design can yield to cycles of designs that may at the end become very time-consuming. In this presentation, a short-cut to assessing minimum required number of prestressing steel will be shown.

The quick assessment of the number of strands is based on a computation of tensile stresses induced by gravity loads that need to be balanced by prestressing. Prestressing will not only overcome tensile stresses but can deflect the girder upwards as will happen at some stages of construction.

Maximum tensile stresses develop at service stage. The amount of prestressing steel needs to overcome these maximum tensile stresses.

Combined gravity stresses and prestressing stresses at mid-span needs to be less than concrete stress limits. As mentioned earlier, gravity loads will deflect the girder downward and prestressing effects will deflect it upwards.

Gravity loads will develop compressive stresses at top fiber and tensile stresses at bottom fiber at the mid-span. These tensile stresses need to be balanced by the counteracting prestressing forces.

Deck is made composite to the girder thru extended ties of the girder that usually work as shear connectors. The effective width of the deck needs to be computed that will be part of the composite section.

The specifications allow some tension at the bottom flanges of the section. Therefore, the tensile stresses that need to be balanced can be reduced by specification allowance.

Total prestressing force can be computed from the tensile stresses that need to be balanced. The final stresses at the bottom will not reach the tensile stress limit of the specification.

The number of strands that will develop the needed prestressing force can be computed based on tensile stress limits of the strands.

Reference;
AASHTO LRFD Bridge Construction Specifications, 4th Edition