Time-Dependent Prestress Losses According to Eurocode 2

Description

In prestressed concrete design, it is essential to account for the fact that the applied prestressing force decreases over time. Eurocode 2, Part 1-1, clause 5.10.6, defines the models for calculating these time-dependent prestress losses. They are mainly caused by:

• Concrete creep – long-term deformation under sustained stress.

• Concrete shrinkage – volume reduction due to hydration and drying.

• Steel relaxation – stress reduction in the prestressing tendons at constant strain.

These mechanisms combine to reduce the effective prestress in the structure. Correctly accounting for them is crucial to ensure that the structure maintains adequate safety, serviceability, and durability during its entire service life.

Why it matters

If time-dependent prestress losses are underestimated, the residual force in the tendons may be lower than assumed in design. This can lead to:

• Larger crack widths and deflections.

• Reduced shear and flexural capacity.

• Long-term serviceability problems.

By applying Eurocode’s methodology, engineers can estimate the realistic level of prestress at different stages of the bridge or building’s life cycle, from early age to long-term service conditions.

Guide - How the Excel Tool Works

The provided Excel sheet “Calculating Time-Dependent Losses for Prestress” is designed to automate Eurocode’s procedure for prestress losses. It consists of two main sheets:

1. User Input

Here the engineer defines:

• Material properties (elastic modulus of concrete, creep/shrinkage data, relaxation class of tendons).

• Environmental parameters (relative humidity, notional size, etc.).

• Time definitions (age at stressing - often t₀ = 28 days, age at loading, service life stages).

• Initial tendon stress levels.

This forms the basis for all subsequent calculations.

2. Tendon Definition

This sheet contains geometric and section-related information, such as:

• Tendon layout relative to the concrete centroid.

• Cross-sectional area of tendons and concrete section.

• Stress distribution across the section at different times.

It also handles unit conversions and can export tendon data for use in BRIGADE/Standard.

Step-by-Step guide

The Excel sheet follows Eurocode 2 step-by-step:

• Immediate losses
  Elastic shortening of the concrete at the time of stressing.

• Time-dependent losses

  • Shrinkage of concrete (calculated from relative humidity and notional size).

  • Creep of concrete (stress-dependent, develops with time).

  • Relaxation of steel (dependent on tendon class and stress level).

• Effective prestress
  The sheet then combines these effects to estimate the remaining prestress force at specified times, such as:

  • End of construction phase.

  • Long-term (e.g., 50 years service life).

Purpose and Benefit

By using this Excel tool, engineers can:

• Apply Eurocode’s loss models consistently and efficiently.

• Avoid manual and error-prone calculations.

• Capture the complexity of time-dependent prestress losses in a simplified and unified way.
  The spreadsheet factors the full system of equations into four parameters (A, b, c, d).
  These parameters together describe the combined effect of elastic shortening, creep, shrinkage, and relaxation at any chosen time point.

The formulation enables engineers to easily evaluate prestress losses at different stages of the structure’s life cycle, while still fully complying with the Eurocode models. It ensures that prestress effects in bridges and buildings are modelled both realistically and practically, improving safety and serviceability assessments.

Limitations

-

Attachments

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Keywords

BRIGADE/Plus, BRIGADE/Standard, Prestress Cables Eurocode losses