The idea of prestress
Concrete cracks under tension. Prestressing puts a deliberate compression into the concrete before the service load arrives, so that when the load tries to pull the bottom of a beam, it first has to cancel that stored compression. The member can stay uncracked, or nearly so, under working loads.
The compression comes from high-strength steel tendons stretched to a high stress and anchored against the concrete. In pre-tensioning, the strands are stretched between abutments, concrete is cast around them, and once it has gained strength the strands are released and grip the concrete by bond. In post-tensioning, ducts are cast in, the concrete hardens, and tendons are threaded, stressed with jacks and locked at anchorages.
Placing the tendon below the centroid adds a hogging moment that opposes the sag from the load. This is why prestressed girders can be slimmer and span further than ordinary reinforced ones, and why they dominate highway and metro viaducts.
Part of the initial prestress is lost over time through elastic shortening, creep, shrinkage, steel relaxation, friction and anchorage slip. Design accounts for these losses.
Fibre stress = P/A ± P e / Z ∓ M / ZWith the tendon at eccentricity e below the centroid, P e / Z adds compression at the bottom fibre
Problem. A 300 × 600 mm beam has P = 900 kN at e = 150 mm. Find the bottom-fibre stress from prestress alone.
- A = 180 000 mm², Z = 300 × 600² / 6 = 18 × 10⁶ mm³.
- P/A = 900 000 / 180 000 = 5.0 MPa.
- P e / Z = 900 000 × 150 / 18 × 10⁶ = 7.5 MPa.
- Bottom fibre = 5.0 + 7.5 = 12.5 MPa compression; top fibre = 5.0 − 7.5 = 2.5 MPa tension.
Answer. 12.5 MPa compression at the bottom
Quick quiz
1Difference between pre- and post-tensioning?
Pre-tensioning stresses strands before casting; post-tensioning stresses tendons in ducts after the concrete hardens.
2Why place the tendon below the centroid?
Its eccentricity creates a moment opposing the load moment.
3Name two causes of prestress loss.
Creep and shrinkage (also relaxation, friction, slip, elastic shortening).
- IS 1343 (India): Design and construction of prestressed concrete.
Cited by number and clause only. We do not reproduce clause text, tables or figures (BIS Act 2016, s.10(5) and s.11). Check the current edition and amendments before use.
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References and further reading
Standard texts, listed in no order of merit. We do not copy text, figures, tables or solved problems from any book; our explanations and examples are original.
- N. Krishna Raju, Prestressed Concrete, McGraw Hill Education (India), latest edition.
- T. Y. Lin, N. H. Burns, Design of Prestressed Concrete Structures, Wiley, 3rd edition.
- E. G. Nawy, Prestressed Concrete: A Fundamental Approach, Pearson, latest edition.
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