Derivation of Closed-Form Solution for Prestress Loss Due to Elastic Shortening
| Terms | Definition |
|---|---|
| Ac | Area of concrete section |
| As | Total area of strands |
| e | Eccentricity of centroid of strands |
| Eci | Modulus of elasticity of concrete at release |
| Es | Modulus of elasticity of prestressing steel |
| ES | Loss due to elastic shortening (difference between stress in prestressing steel immediately before and immediately after release) |
| fcir | Net stress immediately after release at the centroid of the strands at the section of maximum moment |
| I | Moment of inertia of beam cross-section |
| Mself | Self-weight moment of beam at midspan |
| P | Prestress force immediately before release (includes effects of relaxation of the steel between tensioning and detensioning, RET) |
| P' | Prestress force immediately after release, that is, after elastic shortening |
For the calculation of elastic shortening when using transformed section properties, refer to the Transformed Section Properties section.