Fundamentals of Prestressing

 

CONTENTS

 

1. Introduction 2. Definitions 3. Advantages 4. Limitations 5. Fundamentals of Prestressing

6. Prestressing Methods 7. Fire Resistance of Prestressed Concrete 8. Construction Applications of Prestressing 9. Conclusions

 

 

 

1. Introduction

 

The prestressing and precasting of concrete are inter-related features of the modern building industry. Through the application of imaginative design and quality control, they have, since the 1930’s, had an increasing impact on architectural and construction procedures. Prestressing of concrete is the application of a compressive force to concrete members and may be achieved by either pretensioning high tensile steel strands before the concrete has set, or by post-tensioning the strands after the concrete has set. Although these techniques are commonplace, misunderstanding of the principles, and the way they are applied, still exists. This paper is aimed at providing a clear outline of the basic factors differentiating each technique and has been prepared to encourage understanding amongst those seeking to broaden their knowledge of structural systems.

 

2. Definitions

 

2.1 Prestressed Concrete

Prestressing of concrete is defined as the application of compressive stresses to concrete members. Those zones of the member ultimately required to carry tensile stresses under working load conditions are given an initial compressive stress before the application of working loads so that the tensile stresses developed by these working loads are balanced by induced compressive strength. Prestress can be applied in two ways - Pre-tensioning or Post-tensioning.

 

2.2 Pre-tensioning
Pre-tensioning is the application, before casting, of a tensile force to high tensile steel tendons around which the concrete is to be cast. When the placed concrete has developed sufficient compressive strength a compressive force is imparted to it by releasing the tendons, so that the concrete member is in a permanent state of prestress.

 

2.3 Post-tensioning

Post-tensioning is the application of a compressive force to the concrete at some point in time after casting. When the concrete has gained strength a state of prestress is induced by tensioning steel tendons passed through ducts cast into the concrete, and locking the stressed tendons with mechanical anchors. The tendons are then normally grouted in place.

 

3.Advanages of Prestressing

 

3.1 General Advantages

The use of prestressed concrete offers distinct advantages over ordinary reinforced concrete. These advantages can be briefly listed as follows:

1. Prestressing minimises the effect of cracks in concrete elements by holding the concrete in compression.
2. Prestressing allows reduced beam depths to be achieved for equivalent design strengths.
3. Prestressed concrete is resilient and will recover from the effects of a greater degree of overload than any other structural material.
4. If the member is subject to overload, cracks, which may develop, will close up on removal of the overload.
5. Prestressing enables both entire structural elements and structures to be formed from a number of precast units, e.g. Segmented and Modular Construction.
6. Lighter elements permit the use of longer spanning members with a high strength to weight characteristic.
7. The ability to control deflections in prestressed beams and slabs permits longer spans to be achieved.
8. Prestressing permits a more efficient usage of steel and enables the economic use of high tensile steels and high strength concrete.

 

3.2 Cost advantages of Prestressing

Prestressed sconcrete can provide significant cost advantages over structural steel sections or ordinary reinforced concrete.

 

4. Limitations of Prestressing

The limitations of prestressed concrete are few and really depend only upon the imagination of the designer and the terms of his brief. The only real limitation where prestressing is a possible solution may be the cost of providing moulds for runs of limited quantity of small numbers of non-standard units.

 

5. Fundamentals of Prestressing

 

5.1 The Tensile Strength of Concrete

The tensile strength of unreinforced concrete is equal to about 10% of its compressive strength. Reinforced concrete design has in the past neglected the tensile strength of unreinforced concrete as being too unreliable. Cracks in the unreinforced concrete occur for many reasons and destroy the tensile capability. See Fig.1.With prestressed concrete design however, the tensile strength of concrete is not neglected. In certain applications it is used as part of the design for service loadings. In ordinary reinforced concrete, steel bars are introduced to overcome this low tensile strength. They resist tensile forces and limit the width of cracks that will develop under design loadings. Reinforced concrete is thus designed assuming the concrete to be cracked and unable to carry any tensile force. Prestressing gives crack-free construction by placing the concrete in compression before the application of service loads.

5.2 The Basic Idea

A simple analogy to prestressing will best explain the basic idea. Consider a row of books or blocks set up as a beam. See Fig.2(a). This "beam" is able to resist compression at the top but is unable to resist any tension forces at the bottom as the "beam" is now like a badly cracked concrete member, i.e. the discontinuity between the books ensures that the "beam" has no inherent tension resisting properties. If it is temporarily supported and a tensile force is applied, the "beam’’ will fail by the books dropping out along the discontinuities. See Fig.2(b). For the beam then to function properly a compression force must be applied as in Fig.2(c). The beam is then "prestressed" with forces acting in an opposite direction to those induced by loading. The effect of the longitudinal prestressing force is thus to produce pre-compression in the beam before external downward loads are applied. The application of the external downward load merely reduces the proportion of precompression acting in the tensile zone of the beam.

 

5.3 The Position of the Prestressing Force

Prestressing can be used to best advantage by varying the position of the prestress force. When the prestress is applied on the centroid of the cross-section a uniform compression is obtained. Consider the stress state of the beam in Fig.3(b). We can see that by applying a prestress of the right magnitude we can produce pre-compression equal and opposite to the tensile force in Fig.3(b).Then by adding the stress blocks we get: i.e. zero stress towards the bottom fibres and twice the compressive stress towards the top fibres. Now apply the pre-compression force at 1/3 the beam depth above the bottom face. As well as the overall compression we now have a further compressive stress acting on the bottom fibre due to the moment of the eccentric prestress force about the neutral axis of the section. We then find it is possible to achieve the same compression at the bottom fibre with only half the prestressing force. See Fig.3(d). Adding now the stress blocks of Fig.3(b) and 3(d) we find that the tensile stress in the bottom fibre is again negated whilst the final compressive stress in the top fibre is only half that of Fig.3(c). See Fig.3(e). Thus by varying the position of the compressive force we can reduce the prestress force required, reduce the concrete strength required and sometimes reduce the cross sectional area. Changes in cross sections such as using T or I or channel sections rather than rectangular sections can lead to further economies.

 

5.4 The Effect of Prestress on Beam Deflection

From 5.3 it is obvious that the designer should, unless there are special circumstances, choose the eccentrically applied prestress. Consider again the non-prestressed beam of Fig.1(a). Under external loads the beam deflects to a profile similar to that exaggerated in Fig.4(a). By applying prestress eccentrically a deflection is induced. When the prestress is applied in the lower portion of the beam, the deflection is upwards producing a hogging profile. See Fig.4(b). By applying the loads of Fig.4(a) to our prestressed beam, the final deflection shape produced is a sum of Figs.4(a) and 4(b) as shown in Fig.4(c). Residual hogging, though shown exaggerated in the Fig.4(c), is controlled within limits by design code and bylaw requirements. Such control of deflection is not possible with simple reinforced concrete. Reductions in deflections under working loads can then be achieved by suitable eccentric prestressing. In long span members this is the controlling factor in the choice of the construction concept an technique employed.

 

5.5 Prestress Losses

Most materials to varying degrees are subject to "creep", i.e. under a sustained permanent load the material tends to develop some small amount of plasticity and will not return completely to its original shape. There has been an irreversible deformation or permanent set. This is known as "creep" Shrinkage of concrete and "creep" of concrete and of steel reinforcement are potential sources of prestress loss and are provided for in the design of prestressed concrete. Shrinkage:The magnitude of shrinkage may be in the range of 0.02% depending on the environmental conditions and type of concrete.With pre-tensioning, shrinkage starts as soon as the concrete is poured whereas with post-tensioned concrete there is an opportunity for the member to experience part of its shrinkage prior to tensioning of the tendon, thus pre-compression loss from concrete shrinkage is less.

 

Creep:With prestressing of concrete the effect is to compress and shorten the concrete. This shortening must be added to that of concrete shrinkage. In the tensioned steel tendons the effect of "creep’’ is to lengthen the tendon causing further stress loss. Allowance must be made in the design process for these losses. Various formulae are available.

 

Pull-in: With all prestressing systems employing wedge type gripping devices, some degree of pull-in at either or both ends of a pre-tensioning bed or post-tensioned member can be expected. In normal operation, for most devices in common use, this pull-in is between 3mm and 13mm and allowance is made when tensioning the tendons to accommodate this.

 

5.6 Materials

 

5.6.1 Steel

Early in the development of prestressing it was found that because of its low limit of elasticity ordinary reinforcing steel could not provide sufficient elongation to counter concrete shortening due to creep and shrinkage. it is necessary to use the high tensile steels which were developed to produce a large elongation when tensioned. This ensures that there is sufficient elongation reserve to maintain the desired pre-compression. The relationship between the amount of load, or stress, in a material and the stretch, or strain, which the material undergoes while it is being loaded is depicted by a stress-strain curve. At any given stress there is a corresponding strain. Strain is defined as the elongation of a member divided by the length of the member. The stress-strain properties of some grades of steel commonly encountered in construction are shown in Fig.5. It is apparent from these relationships that considerable variation exists between the properties of these steels. All grades of steel have one feature in common: the relationship between stress and strain is a straight line below a certain stress. The stress at which this relationship departs from the straight line is called the yield stress, and is denoted by the symbol fy in Fig. 5. A conversion factor may be used to convert either stress to strain or strain to stress in this range. This conversion factor is called the modulus of elasticity E.  Structural grade steels which are commonly used for rolled structural sections and reinforcing bars, show a deviation from this linear relationship at a much lower stress than high strength prestressing steel. High strength steels cannot be used for reinforced concrete as the width of cracks under loading would be unacceptably large. These high strength steels achieve their strength largely through the use of special compositions in conjunction with cold working. Smaller diameter wires gain strength by being cold drawn through a number of dies. The high strength of alloy bars is derived by the use of special alloys and some working.

 

5.6.2 Concrete

To accommodate the degree of compression imposed by the tensioning tendons and to minimise prestress losses, a high strength concrete with low shrinkage properties is required. Units employing high strength concrete are most successfully cast under controlled factory conditions.

 

6. Prestressing Methods

 

6.1 General

Methods of prestressing concrete fall into two broad categories differentiated by the stage at which the prestress is applied.That is, whether the steel is pre-tensioned or post-tensioned. From the definitions para 2.2 pre-tensioning is stated as "the application before casting, of a tensile force to high tensile steel tendons around which the concrete is cast. . ." and para 2.3 "Post-tensioning is the application of a compressive force to the concrete at some point in time after casting. When the concrete has hardened a state of prestress is induced by tensioning steel tendons passing through ducts cast into the Concrete".

 

6.2 Types of Tendon

There are three basic types of tendon used in the prestressing of concrete:

Bars of high strength alloy steel.These bar type tendons are used in certain types of post-tensioning systems. Bars up to 40mm diameter are used and the alloy steel from which they are made has a yield stress (fy Fig.5) in the order of 620 MPa. This gives bar tendons a lower strength to weight ratio than either wires or strands, but when employed with threaded anchorages has the advantages of eliminating the possibility of pull-in at the anchorages as discussed in para. 5.5, and of reducing anchorage costs.

Wire, mainly used in post-tensioning systems for prestressing concrete, is cold drawn and stress relieved with a yield stress of about 1300 MPa. Wire diameters most commonly used in New Zealand are 5mm, 7mm, and 8mm. 

 

Strand, which is used in both pre and post-tensioning is made by winding seven cold drawn wires together on a stranding machine. Six wires are wound in a helix around a centre wire which remains straight. Strands of 19 or 37 wires are formed by adding subsequent layers of wire. Most pre-tensioning systems in New Zealand are based on the use of standard seven wire stress relieved strands conforming to BS3617:"Seven Wire steel strand for Prestressed concrete." With wire tendons and strands, it may be desirable to form a cable to cope with the stressing requirements of large post-tensioning applications. Cables are formed by arranging wires or strands in bundles with the wires or strands parallel to each other. In use the cable is placed in a preformed duct in the concrete member to be stressed and tensioned by a suitable posttensioning method. Tendons whether bars, wires, strands, or made up cables may be used either straight or curved.

1. Straight steel tendons are still by far the most commonly used tendons in pre-tensioned concrete units.

2. Continuously curved tendons are used primarily in post-tensioning applications. Cast-in ducts are positioned in the concrete unit to a continuous curve chosen to suit the varying bending moment distribution along the members.

 

6.3 Pre-Tensioning

As discussed, (para 2.2) pre-tensioning requires the tensile force to be maintained in the steel until after the high strength concrete has been cast and hardened around it. The tensile force in the stressing steel is resisted by one of three methods:

1. Abutment method - an anchor block cast in the ground.

2. Strut method - the bed is designed to act as a strut without deformation when tensioning forces are applied.

3. Mould method - tensioning forces are resisted by strong steel moulds.

It is usual in pretensioning factories to locate the abutments of the stressing bed a considerable distance apart so that a number of similar units can be stressed at the same time, end to end using the same tendon. This arrangement is called the "Long Line Process". After pouring, the concrete is cured so that the necessary strength and bond between the steel and concrete has developed in 8 to 20 hours. When the strength has been achieved tendons can be released and the units cut to length and removed from the bed.

 

Post-tensioning systems are based on the direct longitudinal tensioning of a steel tendon from one or both ends of the concrete member. The most usual method of post-tensioning is by cables threaded through ducts in cured concrete. These cables are stressed by hydraulic jacks, designed for the system in use and the ducts thoroughly grouted up with cement grout after stressing has occurred. Cement grouting is almost always employed where post-tensioning through ducts is carried out to:

– Protect the tendon against corrosion by preventing ingress of moisture.

– Eliminate the danger of loss of prestress due to long term failure of end anchorages, especially where moisture or corrosion is present.

– To bond the tendon to the structural concrete thus limiting crack width under overload.

 

7. Resistance of Prestressed Concrete

All concrete is incombustible. In a fire, failure of concrete members usually occurs due to the progressive loss of strength of the reinforcing steel or tendons at high temperatures. Also the physical properties of some aggregates used in concrete can change when heated to high temperatures. Experience and tests have shown however that ordinary reinforced concrete has greater fire resistance than structural steel or timber. Current fire codes recognise this by their reference to these materials. Prestressed concrete has been shown to have at least the same fire resistance as ordinary reinforced concrete. Greater cover to the prestressing tendons is necessary however, as the reduction in strength of high tensile steel at high temperatures is greater than that of ordinary mild steel.

 

8. Applications of Prestressing

 

8.1 General

The construction possibilities of prestressed concrete are as vast as those of ordinary reinforced concrete. Typical applications of prestressing in building and construction are:

1. Structural components for integration with ordinary reinforced concrete construction, e.g. floor slabs, columns, beams.

2. Structural components for bridges.

3. Water tanks and reservoirs where water tightness (i.e. the absence of cracks) is of paramount importance.

4. Construction components e.g. piles, wall panels, frames, window mullions, power poles, fence posts, etc.

5. The construction of relatively slender structural frames.

6. Major bridges and other structures.

 

9. Conclusions

 

Prestressed concrete design and construction is precise. The high stresses imposed by prestressing really do occur. The following points should be carefully considered:

1. To adequately protect against losses of prestress and to use the materials economically requires that the initial stresses at prestressing be at the allowable upper limits of the material. This imposes high stresses, which the member is unlikely to experience again during its working life.

2. Because the construction system is designed to utilise the optimum stress capability of both the concrete and steel, it is necessary to ensure that these materials meet the design requirements. This requires control and responsibility from everyone involved in prestressed concrete work - from the designer right through to the workmen on the site.

 

We have seen that considerable design and strength economies are achieved by the eccentric application of the prestressing force. However, if the design eccentricities are varied only slightly, variation from design stresses could be such as to affect the performance of a shallow unit under full working load. The responsibility associated with prestressing work then is that the design and construction should only be undertaken by engineers or manufacturers who are experienced in this field.