Prestressed Concrete

Distinguish pre-tensioning (tendons stressed before casting, force transferred by bond at release) from post-tensioning (ducts cast in, tendons stressed and anchored after hardening), and size the force from P = σ_p A_p.

Add up the individual losses — elastic shortening, shrinkage, creep, steel relaxation, and (for post-tensioning) friction and anchorage slip — and subtract from the jacking force to get the effective prestress P_e.

Superpose the axial (P/A) and eccentricity (Pe/Z) stresses at top and bottom fibres, add the service-load bending stress M/Z, and check the resulting fibre stresses stay within the permissible compression and tension limits at both transfer and service stages.

Compute the concrete shear capacity (enhanced by the axial precompression), and if the factored shear exceeds it, provide stirrups to carry the balance V_s; for torsion combine it with shear into an equivalent action.

Superpose the downward load deflection and the upward prestress camber to get the net deflection, apply a creep multiplier for long-term values, and check crack width for partially prestressed members.