A comprehensive breakdown of CIRIA Guide 1: Understanding structural behavior, primary prisms, equilibrium, detailing, and bearing stresses in prestressed members.
In a post-tensioned prestressed concrete member, the prestressing force is applied through relatively small anchorages, creating high localized stresses. As the force spreads out over the cross-section, the stress pattern within this region—the anchor block—is vastly different from the main body of the member.
This guide, based on the authoritative CIRIA Guide 1 (1976), outlines the structural behavior of anchor blocks, provides design instructions for rectangular and non-rectangular members, and offers a step-by-step design methodology to ensure safety and serviceability.
Understanding the Force System
Compressive stress trajectories spread out from the anchorage, forming an “S” shape. Where these trajectories are curved, they exert lateral forces on the concrete. These lateral forces cause bursting stresses (tension) that require reinforcement. Additionally, spalling stresses occur immediately behind the loaded face.
1. The 3-Step Design Process for Rectangular Members
For situations where there is no change of section between the anchor block and the main member, the design process consists of three main steps:
- Primary Reinforcement: Determine the size of the “Primary Prism” around each anchorage and provide reinforcement over a length equal to the side of the prism.
- Secondary (Equilibrium) Reinforcement: Check the overall equilibrium of the end block to resist out-of-balance moments and shear forces.
- Spalling Reinforcement: Provide steel close to the loaded end face to resist surface cracking.
2. Primary Prisms and Bursting Forces
The first distribution of stress is assumed to affect a zone defined by the largest right prism symmetrical about the line of action of the force. This is the Primary Prism. Its dimension, \(2y_o\), is twice the smaller of:
- The distance from the force to the nearest concrete surface.
- Half the distance between the force and its nearest neighbor.
The design bursting force (\(F_{bst}\)) depends on the ratio of the loaded area (\(2y_{po}\)) to the prism side (\(2y_o\)):
💡 Group Anchorage Reduction Factor (K)
For groups of anchorages, cracking is inhibited in the middle. The design bursting force may be divided by a factor K:
- K = 1.0 (Anchorages on the perimeter)
- K = 1.5 (Anchorages distributed in one direction)
- K = 2.0 (Anchorages distributed in two directions)
Primary reinforcement should be distributed between \(0.2y_o\) to \(2y_o\) from the loaded face. Steel stress must not exceed \(0.87f_y\), and strain must be limited to 0.001. Helical reinforcement and closed box cages are more efficient than straight mat reinforcement.
3. Equilibrium and Spalling Reinforcement
Beyond the primary prisms, the overall equilibrium of the end block must be verified. Out-of-balance moments (\(M\)) and shear forces (\(V_h\)) must be resisted. Secondary reinforcement should be provided to carry the maximum moment, assuming a lever arm of \(0.5h\) (half the length of the end block).
The 0.04 \(P_k\) Rule for Spalling
Spalling stresses occur near the loaded face. To prevent surface concrete from breaking away, effectively-bonded reinforcement must be placed close to the end face. This steel must resist a force equal to \(0.04 P_k\) in either direction, with a steel strain not exceeding 0.001.
Unsymmetrical Prisms: If the force acts on an unsymmetrical prism (where \(d_1 > 2d_2\)), additional spalling reinforcement is required to resist a force of:
\(0.2\left[\frac{d_1 – d_2}{d_1 + d_2}\right]^3 P_k\)
4. Non-Rectangular Members & Flanges
When a rectangular anchor block is placed on a flanged member (like an I-beam or T-beam), a second lateral tensile zone occurs near the change of section. The block acts as a deep beam spanning between the flanges.
For the second zone, assume all load is carried by the flanges. The required steel area can be determined using CEB deep beam methods or truss theory. If this is greater than the equilibrium requirement, additional closed links must be uniformly distributed over a distance of \(0.2h\) from the flange interface.
Anchorages in the Body of a Member
For anchorages in a pocket or on an external rib, additional longitudinal reinforcement is required at the pocket edges. Leonhardt suggests this steel should carry at least \(0.5P_k\) and be fully anchored. Lateral bursting reinforcement should be provided, ideally as a spiral.
5. Additional Design Considerations
Curved Cables
Curved tendons exert lateral components of force on the anchor block. Reinforcement must be provided along the taper to prevent cracking and transfer out-of-balance forces to the main structure.
Influence of Support Reaction
A support reaction near the end of a beam reduces the bursting force of the lowest anchorage. The bursting force may be factored by \((1 – R/P_k)\). The reduction should not exceed 20% and should only apply to the lowest anchorage.
Anchorages Near Corners
There is a risk of local failure. Particular care must be taken to tie the anchorage to the bulk of the member, and shear must be checked on possible planes of rupture.
Bearing Stresses
While the manufacturer typically determines anchorage size, early stressing or non-standard concrete strengths require the designer to check bearing stresses. The bearing capacity of concrete can be much higher than standard cube tests suggest. CP 110 limits contact stress to \(0.4f_{cu}\) (or \(0.8f_{cu}\) with binding reinforcement).
6. Detailing of Reinforcement
Congestion is a major issue in anchor blocks. Detailing must allow space for vibrators and concrete compaction. The guide recommends specific bar shapes:
7. Design Example: T-Beam Anchor Block
The guide provides a detailed example of a T-beam with three tendons, each prestressed to 1170 kN, with 160 mm square anchorages.
- Primary Reinforcement: Required 1170 mm² vertically for tendon 1, 1340 mm² for tendons 2 and 3, and 700 mm² laterally. Used 10 mm bars in a 5-turn spiral (785 mm²).
- Equilibrium: Maximum clockwise moment was 370 kNm (requiring 1850 mm²) and max anticlockwise was 210 kNm (requiring 1050 mm²). Nine closed 12 mm links were used.
- Shear Check: Max shear was 940 kN, giving a stress of 1.96 N/mm², which is below the allowable 2.25 N/mm².
- Spalling: Required 46 kN laterally and vertically. An additional 33 kN vertical was required due to an unsymmetrical prism. A pair of 12 mm closed links (452 mm²) and three 10 mm U-bars (236 mm²) were provided.
8. A Brief History of Research
The document reviews decades of research. Key takeaways from the literature:
- Zielinski and Rowe provided the first comprehensive practical investigation, noting a second tensile zone in flanged beams (70% of the force near the anchorages).
- Guyon developed the “successive prism” method, which remains a standard approach.
- Leonhardt proposed a bursting force equation of \(0.3P_k(1 – y_{po}/y_o)\).
- Codes like CP 110 (British) and the French Code offer varying levels of detail. The French Code is noted as the most comprehensive for anchor blocks.
Key Takeaways for Engineers
Anchor block design requires a holistic understanding of force flow. By correctly identifying primary prisms, checking overall equilibrium, and detailing spalling reinforcement, engineers can ensure the safety and serviceability of post-tensioned structures.
Always refer to your local codes of practice (like CP 110 or ACI 318) and ensure that detailing allows for proper concrete compaction, as congestion is the most common practical issue in anchorage zones.
Frequently Asked Questions About Anchor Block Design
Expert insights from CIRIA Guide 1 for post-tensioned concrete members
1. What exactly is an “anchor block”?
In post-tensioned concrete, the anchor block is the region in the immediate vicinity of the prestressing tendons. Because the prestressing force is applied through relatively small anchorages, it creates high local stresses. The anchor block is the zone where this force spreads out over the cross-section of the member, requiring special design consideration.
2. What are the three main steps for designing a rectangular anchor block?
According to CIRIA Guide 1, the process involves:
- Primary Reinforcement: Determine the size of the primary prism around each anchorage and provide primary reinforcement.
- Secondary (Equilibrium) Reinforcement: Check the overall equilibrium of the end block to resist out-of-balance moments and shear forces.
- Spalling Reinforcement: Provide reinforcement near the loaded end face to resist surface cracking.
3. How is the size of the “Primary Prism” determined?
The primary prism is the largest right prism symmetrical about the line of action of the force. Its dimension (\(2y_o\)) is twice the smaller of two measurements: the distance from the force to the nearest concrete surface, or half the distance to the nearest neighboring anchorage.
4. Can the design bursting force be reduced for groups of anchorages?
Yes. Cracking is inhibited in the middle of a group by the outer concrete. The bursting force can be divided by a reduction factor \(K\): 1.0 for perimeter anchorages, 1.5 for anchorages distributed in one direction (like a slab), and 2.0 for anchorages distributed in two directions.
5. What causes spalling stresses, and how much reinforcement is required?
Spalling is caused by strain compatibility (Poisson’s ratio effects) and the shape of the stress trajectories near the loaded face, which can cause concrete to break away. Reinforcement must be placed close to the end face to resist a force equal to \(0.04P_k\) in both directions.
6. Why is designing an anchor block on a flanged member (like a T-beam) more complex?
A rectangular anchor block on a flanged member creates a second lateral tensile zone near the change of section. The block effectively acts as a deep beam spanning between the flanges. Additional reinforcement (closed links) must be distributed over a distance of \(0.2h\) from the flange interface to handle this.
7. How does a support reaction influence the bursting force?
A support reaction near the end of a beam reduces the bursting force induced by the lowest anchorage. The bursting force can be factored by \((1 – R/P_k)\), provided the reduction does not exceed 20%. No reduction applies to other anchorages.
8. How should an anchorage in a “pocket” or on an external rib be reinforced?
For a pocket anchorage, provide longitudinal reinforcement at the pocket edges capable of carrying at least \(0.5P_k\). For an external rib, because the tendon is curved, additional reinforcement must be anchored back into the main body to resist the lateral component of the prestressing force.
9. What shape codes are recommended for primary and secondary reinforcement?
For primary reinforcement, use spirals (Shape Code 86) or closed links (Shape Code 60) with specific bend radii. For secondary/equilibrium steel, use closed links (Shape Code 60) that extend the full height of the block. For end face steel, use vertically placed links (Code 60) and horizontally placed U-bars (Code 38).
10. What are the allowable bearing stresses behind the anchor plate?
According to CP 110, the maximum compressive stress in the contact area should generally not exceed \(0.4f_{cu}\). This can be raised to \(0.8f_{cu}\) if well-defined bearing areas and binding reinforcement are provided. Any stress exceeding \(0.8f_{cu}\) must be justified by testing.