Designing prestressed concrete involves a systematic process to ensure the structural element performs safely and efficiently under various loading conditions throughout its life. This process typically includes several key stages, from initial concept to final detailing.
Here's a breakdown of the essential design steps:
1. Preliminary Design and Section Selection
The first step involves choosing an appropriate cross-section shape and initial dimensions for the concrete element (e.g., beam, slab, pile). This is often based on architectural requirements, span length, anticipated loads, and experience with similar projects. The goal is to select a section that is both structurally viable and economically feasible.
2. Load Estimation
Engineers determine all applicable loads the structure will encounter. This includes:
- Dead Loads: Weight of the concrete element itself, permanent fixtures, flooring, etc.
- Live Loads: Occupancy loads, furniture, traffic, etc.
- Environmental Loads: Wind, snow, seismic forces, temperature effects, creep, shrinkage, and relaxation of steel.
Load combinations are then developed according to relevant design codes to represent the most critical scenarios.
3. Structural Analysis
Detailed analysis is performed to calculate the internal forces (bending moments, shear forces, axial forces) that the element will experience under the determined load combinations. This is done for both serviceability limit states (normal usage conditions) and ultimate limit states (extreme, factored load conditions).
4. Tendon Profile and Prestressing Force Determination
Based on the analysis, the engineer determines the required magnitude and profile (layout) of the prestressing tendons.
- Magnitude: The amount of prestressing force needed to counteract the bending moments and control stresses.
- Profile: The shape of the tendon path within the concrete section (e.g., straight, parabolic, harped) to optimize stress distribution and counteract applied loads effectively.
This step often involves iterative calculations to find the optimal prestressing force and profile.
5. Stress Checks at Transfer (Initial Stage)
Immediately after the prestressing force is applied (transfer), the concrete element is subjected to the prestressing force and its own dead weight. Stresses in the concrete must be checked to ensure they do not exceed allowable limits, preventing cracking or crushing at this early stage.
6. Calculation of Prestress Losses
Over time, the initial prestressing force reduces due to various factors, collectively known as "losses." These include:
- Elastic shortening of concrete
- Creep of concrete
- Shrinkage of concrete
- Relaxation of prestressing steel
- Friction between tendon and duct (for post-tensioning)
- Slight movement at anchorages
These losses are calculated to determine the effective prestressing force available under long-term conditions.
7. Stress Checks at Service Loads (Long-Term Stage)
Stresses in the concrete and steel are checked under typical service load conditions, considering the effective prestressing force after losses. These checks ensure:
- Concrete stresses remain within allowable compressive limits.
- Tensile stresses in the concrete are limited to prevent or control cracking, depending on the desired performance criteria (e.g., Class U, T, or C sections).
- Deflections are within acceptable limits for the intended use of the structure.
8. Ultimate Strength Checks
The section's capacity is verified to resist factored ultimate loads with sufficient safety margins. This involves checking:
- Flexural Strength: Ensuring the section can carry the ultimate bending moment. As stated in the reference, the ultimate design of a prestressed concrete beam is based on the ultimate moment and ductility of the section. The section is proportioned in such a way that the ultimate moment is greater than the moment developed under service loads by a prescribed quantity, and that it deforms a certain amount before it fails. This ensures the structure has sufficient reserve strength and provides warning before collapse.
- Shear Strength: Ensuring the section can resist the ultimate shear forces, designing shear reinforcement (stirrups) if necessary.
9. Anchorage Zone Design
The areas where the prestressing tendons are anchored require special attention. These zones experience complex stress distributions, and they must be designed to safely transfer the large prestressing force to the concrete without causing local failure (bursting, spalling, or splitting).
10. Detailing
The final step involves preparing detailed drawings and specifications for construction. This includes:
- Location and profile of prestressing tendons
- Type and size of prestressing steel and anchorages
- Concrete strength requirements
- Location and amount of non-prestressed reinforcement (rebar) for strength, serviceability, or crack control
- Duct sizes and grouting requirements (for post-tensioning)
- Stressing sequence and jacking forces
Here is a simplified summary of the key stages in a table format:
| Step | Description | Key Output |
|---|---|---|
| 1. Preliminary Design | Select initial section dimensions. | Section size and shape |
| 2. Load Estimation | Determine all applicable loads and combinations. | Service & Ultimate Load Combinations |
| 3. Structural Analysis | Calculate moments, shears, and axial forces. | Internal Forces (M, V, N) |
| 4. Tendon Design | Determine prestressing force and tendon profile. | Prestressing Force & Tendon Layout |
| 5. Stress Check @ Transfer | Verify stresses immediately after prestressing. | Initial Concrete Stresses |
| 6. Prestress Losses | Calculate reduction in prestressing force over time. | Effective Prestressing Force |
| 7. Stress/Serviceability @ Service | Verify stresses, deflection, and cracking under service loads. | Long-term Stresses, Deflection, Cracking Check |
| 8. Ultimate Strength Checks | Verify flexural and shear capacity under ultimate loads (incorporating ref). | Ultimate Capacity (M_n > M_u, V_n > V_u) |
| 9. Anchorage Zone Design | Design the areas where tendons are anchored. | Anchorage Reinforcement Details |
| 10. Detailing | Prepare construction drawings. | Full Construction Drawings |
This systematic approach ensures that prestressed concrete structures are designed to be safe, durable, and perform as intended under all expected conditions.
