Understanding Prestress Losses
Prestressed concrete allows slender members to span great distances by introducing a deliberate compressive force that counteracts tensile stresses from external loads. Engineers achieve this by tensioning high-strength steel tendons either before casting the concrete (pretensioning) or after the concrete has gained sufficient strength (post-tensioning). While the initial jacking force may be substantial, various mechanisms reduce the prestress over time, diminishing the efficiency of the system. Accurately estimating these losses is essential to ensure that the effective prestress remains high enough to control cracking and deflection throughout the structure's service life.
The losses in prestressed members fall into two broad categories. Immediate losses occur during or shortly after tensioning and include elastic shortening of the concrete, anchorage slip and friction along curved ducts. Time-dependent losses evolve over months or years as the concrete creeps and shrinks and the steel relaxes under sustained stress. The simplified calculator presented here focuses on the major contributors: elastic shortening, creep, shrinkage and relaxation. By summing these components, designers can approximate the final prestressing force and the corresponding steel stress after all losses have taken effect.
Elastic shortening occurs because the concrete member shortens when prestress is applied, causing the tendons to lose some elongation. For a prismatic member, the loss is proportional to the ratio of tendon area to concrete area and the relative moduli of the two materials. Using MathML, the elastic loss is expressed as , where Pi is the initial prestressing force, Aps the area of prestressing steel, Ac the concrete area, and Ec and Es are the moduli of concrete and steel respectively. This formula assumes uniform distribution of stress and straight tendons; complex geometries or partial prestressing may require more refined analysis.
Creep is the gradual increase in concrete strain under sustained stress. In a prestressed member, the compression induced by the tendons causes the concrete to creep, leading to further shortening and additional loss in tendon force. The creep loss is often estimated by multiplying the elastic shortening loss by a creep coefficient φ, giving . The coefficient depends on factors such as concrete age at loading, humidity, member size and mixture proportions. Values between 1.0 and 2.0 are common for typical bridge girders, but more aggressive environments or early loading can produce higher coefficients.
Shrinkage represents the reduction in concrete volume as moisture evaporates and hydration products develop. Because the prestressing steel does not shrink, the differential strain between steel and concrete reduces tendon stress. The shrinkage loss can be approximated by , where εsh is the shrinkage strain expressed in decimal form. Typical total shrinkage strains for normal weight concrete range from 400 to 800 microstrain, though they vary with cement content, curing conditions and member dimensions.
Relaxation is a property of high-strength steel whereby stress decreases under constant strain. Even if the tendon length remains fixed, internal metallurgical processes reduce the force over time. Manufacturers provide relaxation data for different tendon types. Low-relaxation strands may lose only 2 to 3 percent of their initial force over 1000 hours, while conventional strands may lose 5 percent or more. The simplified expression uses a relaxation percentage r to estimate the loss.
The total effective prestress after accounting for the major losses is calculated as . Dividing by the steel area yields the effective stress in the tendons, an important quantity for checking serviceability and ultimate strength criteria. Understanding each component helps engineers refine their designs. For instance, delaying load application reduces creep losses, while improved curing practices lower shrinkage.
Other potential losses, such as friction in post-tensioning ducts or seating of wedge anchors, are not explicitly modeled here but can be significant in practice. Friction losses arise when tendons curve or run over surfaces that create resistance during stressing. Anchorage slip occurs when wedges or grips seat into the anchorage hardware, releasing a small amount of tendon length. Designers often compensate by over-stressing the tendon initially or by performing staged stressing operations. Although these factors fall outside the scope of this calculator, understanding their qualitative effects is essential for comprehensive prestress design.
The table below summarizes representative values for creep coefficients, shrinkage strains and relaxation percentages used in preliminary design. These ranges provide context for the input parameters but should be replaced with project-specific data whenever possible. Material testing, climate considerations and construction methods all influence the actual losses experienced in the field.
| Parameter | Typical Range |
|---|---|
| Creep Coefficient φ | 1.0 – 2.5 |
| Shrinkage Strain εsh | 400 – 800 με |
| Relaxation Percentage r | 2% – 5% |
To illustrate how the calculator works, imagine a bridge girder pretensioned to an initial force of 1000 kN using 1500 mm² of strand. The elastic shortening loss might reduce the force by roughly 20 kN, creep doubles that loss, shrinkage removes another 18 kN, and relaxation subtracts 20 kN. The resulting effective force of approximately 922 kN still provides substantial compression but demonstrates the importance of accounting for time-dependent phenomena. Adjusting the tendon area, using low-relaxation steel or improving curing could recover several percent of prestress if needed.
Prestress loss calculations highlight the interplay between material properties and structural behavior. Higher modulus concrete reduces elastic and creep losses but may be more brittle, while low-relaxation tendons cost more but yield long-term benefits. Engineers must weigh these tradeoffs alongside construction logistics and budget constraints. The simplified model here enables quick exploration of different scenarios, fostering intuition about how each parameter affects the effective prestress. For final design, codes such as AASHTO LRFD or Eurocode 2 provide detailed procedures and recommended values based on extensive research and field observations.
Ultimately, prestressed concrete remains a powerful tool for achieving long spans and slender structural profiles. By carefully estimating prestress losses, designers ensure that members maintain adequate compression to resist service loads, limit cracking and deliver durability over decades of service. This calculator offers an educational glimpse into the calculations behind the scenes and encourages further study into the nuanced field of prestressed concrete engineering.