CELE Reinforced & Prestressed Concrete — Prestressed ConcreteSummary

Strands or wires are tensioned against external abutments in a casting bed before the concrete is poured. After the concrete hardens and attains sufficient strength (typically 70% of 28-day strength), the strands are released and the prestress force is transferred to the concrete through bond between the strand surface and the hardened concrete. Pre-tensioning is widely used in precast plants for producing standardized members such as hollow-core slabs, double-T beams, I-girders, and piling. The transfer of force is instantaneous upon release, making it predictable and suitable for factory-controlled production. Typical applications include residential and commercial precast systems where speed and repeatability are critical.

High-strength tendons (strands or bars) are placed in ducts or conduits cast into the concrete member. After the concrete cures to adequate strength, the tendons are tensioned using hydraulic jacks, then anchored at the ends using mechanical anchorages (wedges, nuts, or plates). The ducts may be grouted after tensioning to provide corrosion protection and to develop additional bond, or left ungrouted (unbonded) for structures requiring future adjustability. Post-tensioning is ideal for cast-in-place members, bridges with complex geometries, retrofitting existing structures, and applications where draped tendons with varied eccentricity are needed. The tendon profile can be optimized for each span and load condition.

The total stress at any fiber is the superposition of three components: (1) axial stress from prestress force P divided by cross-sectional area A, (2) bending stress from the eccentric moment Pe (prestress at distance e from centroid) divided by section modulus, and (3) bending stress from applied external moment M divided by section modulus. Using the convention that compression is positive and taking top and bottom fibers: f_top = P/A − (Pe·c_top)/I + (M·c_top)/I and f_bot = P/A + (Pe·c_bot)/I − (M·c_bot)/I. The eccentric prestress puts extra compression in the bottom fiber (where the tendon lies) and relieves compression in the top fiber; the sagging applied moment does the opposite. Design requires checking stresses at two critical stages: transfer (using initial prestress P_i with minimal load) and service (using effective prestress P_e with full load) to ensure no fiber exceeds allowable tension or compression limits.

The prestress force inevitably decreases from the jacking value P_i to a smaller effective value P_e. Losses are categorized as immediate (occurring during and shortly after jacking) or time-dependent (developing over months and years). Immediate losses include: elastic shortening of concrete when strands are released or tensioned (calculated from the instantaneous strain in the concrete), anchorage seating (slip of the strand at the anchor end, typically 3–6 mm), and friction losses in post-tensioned ducts (proportional to duct deviation and friction coefficient). Time-dependent losses arise from creep and shrinkage of concrete (which reduce the prestress as the concrete deforms) and stress relaxation of the steel strand (inherent property causing the steel to lose strength at constant strain over time). Total losses typically range from 15–20% for post-tensioned members to 18–25% for pre-tensioned members. The effective prestress is P_e = P_i − (total losses), and the effectiveness ratio is often expressed as R = P_e/P_i ≈ 0.80–0.85.

A draped (parabolic) tendon profile creates a distributed upward force on the concrete that can be designed to balance (cancel) a portion of the gravity load. For a simply supported beam with a parabolic tendon having an average sag (eccentricity) of e and prestress force P over span L, the balanced load is w_bal = 8Pe/L². Under the balanced load, the beam experiences only axial precompression (stress P/A uniformly across the section) with negligible bending moment. This results in minimal deflection, no cracking, and highly efficient stress distribution. Any load exceeding w_bal is carried by bending of the precompressed section. The load-balancing approach is powerful for preliminary design: selecting P and e to balance the dead load (or dead plus a portion of live load) dramatically simplifies analysis and optimization. However, the actual stress distribution must still be verified using full superposition.

Design analysis occurs at two distinct stages. At transfer (immediately after release of pre-tensioned strands or after jacking in post-tensioned members), the full initial prestress P_i acts on the section, but external loads are minimal (only the self-weight of the member). The top fiber, which bears no compression from applied moment, may be the most critical—if P_i and its eccentricity produce tension or excessive compression, the section may crack or suffer permanent damage. In service (after all loads are applied and prestress losses have stabilized), the effective prestress P_e is reduced by losses, but the applied moment M is at its maximum. The bottom fiber, now heavily stressed by the combination of P_e and the sagging moment, becomes critical. Thus the controlling fiber often differs between the two stages. Both stages must be checked; NSCP 2015 and ACI 318 provide allowable stress limits for each.

The effective prestress P_e is the force actually available to control stresses and deflections in service. It is calculated as P_e = P_i − (total losses), where losses are obtained from design codes or direct calculation. The loss ratio or effectiveness ratio R = P_e/P_i quantifies the fraction of jacking force retained. For example, if P_i = 1200 kN and losses total 240 kN (20%), then P_e = 960 kN and R = 0.80. Design codes provide loss tables based on member type, steel grade, concrete strength, and environmental exposure. The Philippines' tropical climate with high humidity and potential corrosion demands careful attention to loss estimates; NSCP 2015 references ACI 318 loss formulas adapted for Philippine conditions. Using the correct P_e is fundamental—using P_i throughout overestimates the prestress benefit.

Post-tensioned tendons require mechanical anchorages at their ends to transfer the large jacking forces safely to the concrete. Common systems include wedge anchorages (strands grip into hardened wedges), button-head anchorages (direct bearing), and threaded bar anchorages. These must be embedded in concrete with adequate development length and strength to prevent localized crushing or cone failure. The anchorage zone (first 1.5 times the tendon diameter) experiences high stresses that require careful design and often transverse reinforcement. Corrosion protection is critical in the humid Philippine environment: grouting of ducts after tensioning provides passive protection by filling voids, while unbonded (ungrouted) tendons require factory coating or sheathing and periodic inspection. Corrosion of tendons is difficult and costly to repair, making preventive measures mandatory. RA 544 (Code of Utilities for Buildings) and NSCP 2015 mandate durability provisions for public safety.

A straight tendon runs parallel to the beam axis at constant eccentricity, producing a constant eccentric moment Pe along the span. A draped tendon follows a parabolic or polygonal path, with eccentricity that varies along the span—typically maximum at mid-span and zero (or minimal) at supports. Draped tendons are more efficient because they provide greater upward load-balancing force in the middle where sagging moment is largest, and less unnecessary compression at the supports. Draped tendons result in shallower required sections and longer achievable spans. Straight tendons are simpler to detail and produce but less optimal; they are often used in shorter-span precast members where simplicity outweighs efficiency. For longer spans and cast-in-place construction, draped profiles are standard. The parabolic profile that exactly balances the dead load is particularly elegant and is a recurring theme in exam problems.

Hollow-core slabs are pre-tensioned in casting beds, achieving fast production and quality control. The prestress enables long unsupported spans (typically 6–8 m or more) with shallow depth (~300–400 mm), reducing floor-to-floor height and saving building material and weight. After casting, the slabs are released, transported, and erected with minimal on-site labor. The hollow cores reduce weight and allow utilities to pass through. This application is very common in Philippine residential and commercial projects. Service-stage stress checks ensure no tension develops in the bottom fiber under full load; allowable stress limits are per NSCP 2015 Section 10.2.

Long-span bridges (e.g., 30–50 m or more per span) use post-tensioned cast-in-place or precast-then-post-tensioned girders. Draped tendons are designed to balance the dead load, resulting in nearly zero mid-span deflection and minimal cracking even under heavy traffic. The tendons are typically draped with high eccentricity at mid-span and low eccentricity at supports, following a parabolic profile. Staged construction (e.g., cantilever segments) uses phased tensioning to optimize stress distribution at each stage. Post-tensioning's flexibility allows optimization of tendon geometry and staging. Load balancing simplifies analysis: the structure carries live load by bending of a precompressed beam, minimizing dynamic effects and fatigue concerns. This is a staple of Philippine bridge design.

Double-T beams (or TT beams) are precast with straight or slightly draped prestressing strands, achieving spans of 10–15 m with minimal deflection. The wide top flange acts compositely with a cast-in-place concrete slab poured on top, increasing effective moment capacity. The beams are manufactured in plants, quality-controlled, and shipped to site. They are erected quickly, reducing on-site time and weather exposure. The precompression keeps the beam crack-free under service loads, important for durability in corrosive environments (e.g., coastal areas, parking garages). Service-stage stress checks verify that the bottom fiber stays in compression, and transfer-stage checks prevent splitting or over-compression at the top.

An older reinforced concrete building shows excessive deflection or cracking in its beams due to added loads or material degradation. Post-tensioning strands are installed in drilled ducts and then jacked, introducing beneficial precompression that closes existing cracks and reduces deflection. This is far cheaper and faster than demolishing and rebuilding. The retrofit strengthens the beams without adding to the dead load (unlike adding external bracing). This application is growing in the Philippines as aging buildings are renovated. The design must account for the current state of the concrete (strength, moisture content, creep already incurred) and the timing of load application relative to jacking.

Transfer beams carry loads from columns above to fewer or differently located columns below, typical in the setback stories of high-rise buildings. These beams are heavily loaded and often require large spans. Post-tensioning with draped tendons balances the heavy load, resulting in zero or minimal bending moment and negligible deflection. The flat soffit (no sag) accommodates floor finishes and utilities. The balanced load-path minimizes vibration and cracking. This application showcases the elegance of load balancing: the beam becomes essentially a compression strut carrying its load by axial precompression, with only minimal bending. The design is efficient and economical.

Prestressed concrete piles are cast in plants with circumferential and longitudinal prestressing wires, then driven or vibro-installed into the ground. The precompression resists the tensile stresses induced by driving impact and lateral soil forces. Pre-tensioned piles achieve excellent quality and repeatability. They are lighter and easier to handle than unprestressed piles of equivalent capacity. In subsea applications (e.g., Manila Bay or Laguna de Bay bridges), prestressed piles resist corrosion better than ordinary RC (though marine-grade coatings are still required). The prestress ensures the pile remains in compression even under combined bending and axial loads from environmental forces. Transfer-stage checks are critical to prevent splitting or spalling during driving.

Flat-plate or flat-slab buildings use unbonded (ungrouted) post-tensioning to control deflection and cracking. The tendons run through the slab, draped to follow the moment envelope, and are anchored at the perimeter. Because the tendons are ungrouted, they can slide slightly relative to the concrete, allowing for some stress redistribution. The unbonded system is faster to install (no grouting wait time) and allows future detensioning if needed. Unbonded tendons require factory coating and regular inspection for corrosion; the Philippine tropical climate demands vigilance. This system reduces slab thickness and long-term deflection, improving floor flatness—important for sensitive applications like hospitals or precision manufacturing facilities.