Prestressed Concrete
Prestressed concrete is a form of concrete in which internal compressive stresses are deliberately introduced before the application of service loads, so that the resulting stresses under load are within acceptable limits. High-strength steel tendons are tensioned and anchored against the concrete, counteracting the tensile stresses caused by loads. This technique allows longer spans, thinner sections, and reduced cracking compared to ordinary reinforced concrete, and is widely used in bridges, parking structures, and high-rise floor systems.
Key Formula
f = P/A ± (P·e·y)/I ∓ (M·y)/I
LaTeX: f = \frac{P}{A} \pm \frac{P \cdot e \cdot y}{I} \mp \frac{M \cdot y}{I}
| Symbol | Meaning | Unit |
|---|---|---|
| f | Stress at a fibre | Pa |
| P | Prestressing force | N |
| A | Cross-sectional area of member | m² |
| e | Eccentricity of prestressing tendon from centroid | m |
| y | Distance from neutral axis to fibre of interest | m |
| I | Second moment of area of cross-section | m⁴ |
| M | Applied bending moment at section | N·m |
Worked Example
Problem
A prestressed rectangular beam (b = 200 mm, h = 400 mm) carries a prestress force P = 600 kN at an eccentricity e = 80 mm below the centroid. Find the stresses at top and bottom fibres due to prestress alone (no external load).
Solution
Section properties: A = 200 × 400 = 80,000 mm²; I = 200 × 400³ / 12 = 1,066,666,667 mm⁴; y_top = y_bot = 200 mm. Axial stress component: P/A = 600,000 / 80,000 = 7.5 N/mm². Bending component at top: −P·e·y/I = −(600,000 × 80 × 200) / 1,066,666,667 = −9,000,000 N·mm × 200 / 1,066,666,667 ≈ −9.0 N/mm² (tensile at top). Bending component at bottom: +P·e·y/I = +9.0 N/mm² (compressive at bottom). Top fibre: 7.5 − 9.0 = −1.5 N/mm² (tension). Bottom fibre: 7.5 + 9.0 = +16.5 N/mm² (compression).
Answer
Top fibre: 1.5 MPa tension; Bottom fibre: 16.5 MPa compression
Comparison of Pre-tensioning vs Post-tensioning Systems
| Feature | Pre-tensioning | Post-tensioning | Typical Application |
|---|---|---|---|
| Tendon sequence | Tensioned before casting | Tensioned after hardening | — |
| Bond type | Bonded (direct) | Bonded or unbonded | — |
| Typical span | 10–30 m | 20–100+ m | — |
| Common products | Precast beams, slabs | In-situ bridges, floors | — |
| Losses | Elastic shortening, creep | Friction, anchorage slip | — |
Interactive Tools
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Related Terms
Reinforced Concrete
Reinforced concrete is a composite construction material in which steel reinforcement bars (rebars), plates, or fibers are embedded within concrete to improve its tensile strength. Concrete alone is strong in compression but weak in tension; the steel reinforcement carries tensile stresses and prevents cracking under load. This combination is fundamental to modern structural construction, enabling the building of beams, slabs, columns, foundations, and entire structures.
Bridge Design
Bridge design is the engineering discipline concerned with planning, analysing, and sizing all structural and non-structural components of a bridge to carry specified traffic, wind, seismic, and thermal loads safely and economically over its design life. The process involves selection of bridge type (beam, arch, truss, cable-stayed, suspension), site investigation, load calculations to relevant codes (IRC in India, AASHTO in the USA), structural analysis, material design, and consideration of aesthetics, constructability, and durability. Bridge design integrates structural mechanics, geotechnical engineering, hydraulics, and materials science.
Steel Structure
A steel structure is a construction system in which the primary load-carrying framework is made from structural steel sections such as I-beams, channels, angles, and hollow sections connected by bolts, rivets, or welds. Steel structures offer high strength-to-weight ratios, predictable material properties, rapid erection, and the ability to span large distances, making them ideal for high-rise buildings, industrial sheds, bridges, and towers. Design follows limit-state or allowable-stress methods specified by standards such as IS 800 (India) or AISC (USA).
The prefix 'pre-' is Latin for 'before'; 'stressed' from Old French 'estrece' (tightness, pressure). The modern concept of prestressed concrete was systematically developed by French engineer Eugène Freyssinet between 1928 and 1938, who recognised that high-strength steel was essential to overcome long-term prestress losses from creep and shrinkage.