Anchorage Zones for Prestressed Concrete


What is an Anchorage Zone for Prestressed Concrete?

Prestressed concrete contains tendons which are typically stressed to about 1000 MPa. These tendons need to be anchored at their ends in order to transfer (compressive) force to the concrete. In pretensioned concrete, the anchorage consists of a bonded length of tendon, in direct contact with the concrete. In post-tensioned concrete, an achorage plate is used, which bears onto the concrete over a relatively small area.

The tendon is connnected to the plate either through wedges, button-heads or other methods. The plate itself then bears on the concrete. The plates employed for this are very much smaller than the area of concrete which is to be compressed. Therefore, a redistribution of stress occurs behind the anchorage plate as the compression trajectories spread out to form uniform stress patterns some distance into the concrete, according to St Venant's Principle.

It is the distance over which this redistribution occurs that is of interest to the Engineer. This disturbed region is known as the Anchorage Zone.

Why is it Important?

The state of stress in the anchorage zone is extremely complex. It consists of severely curved trajectories, perhaps interfering with 'secondary' stresses due to bearing supports. Therefore, it is in the Engineer's interest to ensure two things in this zone.

1. The zone must not crack at the serviceability limit state (this would allow the ingress of water, leading to possible corrosion problems), and

2. The zone must not fail at the ultimate limit state.

The main thrust of my research has been the determination of ultimate strength of anchorage zones, although I have also considered the serviceability limit state.

What is the background to this field?

Long before prestressed concrete had been invented, work was carried out on studying the problem of concentrated loads acting on stone and concrete. Several theories were proposed for determining the 'bursting' resistance of stone blocks, loaded through patches. These theories all considered ultimate failure to be caused by the tensile strength of the material being reached. This was perfectly reasonable, as bursting cracks occurred simultaneously with ultimate failure.

When prestressed concrete was invented, Engineers continued to use such theories (and indeed several design codes still use these theories for the ultimate limit state today) for the bursting strength of anchorage zones. However, anchorage zones are invariably reinforced with steel, which increases the ductility of the material (and allows redistribution of stress to occur before collapse). Therefore, it is now unreasonable to assume that ultimate failure of anchorage zones occurs as a function of the tensile strength of concrete. The combined strength of the concrete and steel must be allowed for in the determination of the strength of the anchorage zone. Further, collapse will no longer be caused by 'bursting', but by 'wedging' of the plate into the relatively ductile reinforced concrete.

What work was carried out in this research?

It was considered imperative to determine the form of failure of anchorage zones at both the serviceability and ultimate limit states. This was carried by testing over a hundred concrete blocks, reinforced with stirrups to prevent bursting/wedging failure. The effect of several variables were studied.

The relative size of the loading plate was found to be the single most important factor in the determination of the strength of the zone, as expected. The quantity, spacing and positioning of the steel stirrups was found to be a major variable. The presence of ducts was also considered.

Analysis of first cracking of the blocks was carried out using elastic finite elements. Where steel crossed the critical crack line, assumed strains in the steel were employed and an increase in cracking load determined. As expected, such first cracking occurred beneath the centreline of the loading plate. This crack usually opened and extended the length of the specimen, while the load increased. The FE model was relatively accurate in determining this first cracking load.

After this crack had formed, the blocks continued to take more load, until wedging occurred under the loading plate. This wedging was usually 'in-plane', although 'out-of-plane' failure was also encountered. Such wedging occurred in a somewhat ductile manner, so that plasticity theory was considered a possibility in the analysis of these blocks. Both upper- and lower-bound methods were employed and encouraging results found. The theory was able to cloesely predict the type of wedging (curved or straight) and the ultimate load.

Three-dimensional analyses were also conducted, using both pure plasticity as well as a combination of FEs and plasticity theory. Again, encouraging results were obtained.

What principle conclusions have been made?

These points led us to make the following principle conclusions in the research.

1. The serviceability limit state may be considered by using simple equilibrium models/stress variation assumptions. Alternatively, elastic finite element models could be used to calculate when cracking in the concrete ought to occur, coupled perhaps with some assumption about what level of stress is present in the steel reinforcement at this limit state, and

2. The ultimate limit state should be considered as a shear-compression failure in the concrete, leading to wedging into the concrete by the bearing plate. Since failure consists of a shear (rigid-block) mechanism and considerable ductility has been observed in such tests, it is considered useful to look at plasticity theories for this problem.

Where can I read more?

Best to look at my publications list.