Chapter 5: Introduction To Prestressed Concrete Design Prepared by: Koh Heng Boon Faculty of Civil & Environmental Engineering 31 October 2012
5.1 Principles of Prestressed Concrete Design Prestressed concrete can easily be defined as pre-compressed concrete. This means that a compressive stress is put into a concrete member before it begins it working life and positioned to be in areas where tensile stresses will under working load.
Figure 5.1 (a) shows a plain concrete beam carrying a concentrated load. As load increases, the beam deflects slightly and then fails abruptly. Under load, the stresses in the beam will compressive in the top fibres, but tensile in the bottom fibres. We can expect the beam to crack at the bottom and break, even with a relatively small load, because of the low tensile strength of concrete. The tensile strength of concrete is about 10% of its compressive strength.
Figure 5.1
There are two ways of countering this low tensile strength:- 1. By using passive reinforcement (reinforced concrete) Reinforcement in the form of steel bars is placed in areas where tensile stresses will develop under load. The reinforcement absorbs all the tension and, by limiting the stress in this reinforcement, the cracking of the concrete is kept within acceptable limits. (Figure 5.1(b))
2. By using active reinforcement (Prestressed concrete) The compressive stresses introduced into areas where tensile stresses develop under load will resist or annul this tensile stresses. So the concrete now, behaves as if it had high tensile strength of its own and, provided the tensile stresses do not exceed the precompression stresses, cracking is not allow to occur in the bottom of the beam. (Figure 5(C) & 5(d)).
5.2 What Is Prestressing Prestressing is best explained by considering a row of books. Each book is a discrete element but, if they are stacked closely together and an axial compressive force is applied at each end of the stack, it is possible to lift the whole row as a single unit (Figure 5.2). Figure 5.2: Row of books lifted as a single unit
This is prestressing in its simplest form. It provides the unit, in this case a row of books, with a strength and stability that it would not otherwise possess. Other forms of prestressed items in everyday use include: - The barrel and the cartwheel (timber segments held in compression by iron bands in tension). - The bicycle wheel (steel rim held in compression by spokes in tension); - The umbrella (membrane held in tension by ribs in compression). In the case of concrete, prestressing is used as in the row of books, to form beams and similar members, and as in the barrel, to form cylindrical tanks and silos.
5.3 Method Of Prestressing Prestressing tendons may be tensioned before the concrete is placed (pretensioned) or after the concrete has hardened (post-tensioned). The resulting prestressed concrete members are also frequently described as being either pre-tensioned or posttensioned.
1. Pre-Tensioning Here the tendons are tensioned and anchored between fixed supports before the concrete is placed around the tendons. The concrete is either cast in moulds or formed by an extrusion or slip-form process to provide the required cross-section. When the concrete has achieved sufficient strength, the tendons are slowly released from the support at one end (Figure 5.3). Figure 5.3: Pre-tensioning
The prestressing force is transferred from the tendons to the concrete by the bond existing between the hardened concrete and the tendons. The transfer of force occurs over a short transmission length at each end of the concrete, as the tendons outside the concrete revert to their original untensioned condition (Figure 5.4). The elastic shortening of the concrete that occurs at this stage causes a corresponding reduction of the tendon force. Figure 5.4: Transmission zone at end of member
Pre-tensioning may be used on site where large numbers of similar precast units are required, but is usually carried out in a factory where permanent stressing beds have been installed. Single units and units cast side-by-side may be produced in rigid steel moulds, against which the tendons are tensioned and anchored until the forces can be transferred to the concrete, but the most effective use of pretensioning is in long-line production.
In long-line production, a number of similar units are produced in line at the same time. Tendons, generally 7-wire strands, are tensioned between anchor plates placed at opposite ends of a long stressing bed. The anchor plates bear against steel joists embedded in concrete abutments. The base to the casting surface may sometimes act as a strut between the abutments but, in most cases, the abutments are sufficiently massive to be independently stable. In very long stressing beds, intermediate abutments with preformed pockets to receive temporary steel joists may be provided, so that a shorter stressing bed can be created should the need arise. A typical arrangement for long-line production is shown in Figure 5.5. Figure 5.5: Long-line production
Compacting and Curing of Concrete Vibrators are used to achieve full compaction of the concrete. Internal vibrators, if badly handled, can result in small pockets of water adjacent to the tendons that will reduce the effective bond. External vibrators are generally more effective provided there are enough of them and the moulds are sufficiently rigid. As with all concrete, proper curing is essential. In order to obtain a high concrete strength at an early age, the hardening process is often accelerated by raising the temperature of the concrete using steam-curing (Figure 5.6) which enables a more rapid turn-round in production.
Figure 5.6: Typical Steam-Curing Cycle
Altering the Prestress (Deflecting and Debonding) In the arrangements considered so far, the tendons have all been straight and bonded to the concrete for their entire length. Although most pre-tensioned units are made in this way, the arrangement does not provide the most efficient use of the prestressing force in members of constant crosssection. The location of the prestressing force is limited by the conditions that can be permitted at the ends of the member. In large units, where self-weight is significant, a smaller force can be used if the eccentricity of the force can be increased within the central portion of the span without exceeding the critical value at the ends. Typically, the tendons are arranged in several layers with multiple tendons in each layer, and the eccentricity and magnitude of the prestressing force are progressively reduced towards the ends of the unit by deflecting and/or debonding some of the tendons.
Deflecting typically involves holding down the tendons at two symmetrically placed positions within each unit, and holding up the tendons within the gaps between units and at the ends of the line, as shown in Figure 5.7. Figure 5.7: Deflecting pre-tensioned tendons
Debonding is a more straightforward procedure, in which specified lengths of plastic tubing are placed around several tendons in different layers, so that no bond can develop between the tendons and the concrete. In this way, the transmission lengths for the encased tendons begin at the end of the tubing and, by varying the lengths of tubing, both the magnitude and the eccentricity of the prestressing force may be adjusted in steps, as shown in Figure 5.8. Figure 5.8: Debonding of pretensioned tendons
2. Post-tensioning The concrete is cast first in the mould and allowed to harden before the prestress is applied. The steel may be placed in position to a predetermined profile and cast into the concrete, bond being prevented by enclosing the steel in a protective metal sheathing. Or ducts may be formed in the concrete and the steel passed through after hardening has taken place. When the required concrete strength has been achieved, the steel is stressed against the ends of the unit and anchored off, thus putting the concrete into compression (Figure 5.9). Figure 5.9: Prestressing using post-tensioned internal tendons
5.4 Reinforced Versus Prestressed Concrete The similarities and differences between prestressed and reinforced concrete are: 1. Because of the high compression transferred by the prestressing tendons to the concrete, the compressive strength of the concrete to be used in prestressed concrete structures has to be much higher than in reinforced concrete construction. 2. Mild steel and high tensile steel, normally used for reinforced concrete, are unsuitable for prestressing because it cannot be stressed to an adequate extent to overcome the anticipated losses in prestress. 3. A fully prestressed structure behaves as a homogeneous, elastic material and its behavior before the onset of cracking is more akin to that of steel then a heterogeneous material such as reinforced concrete.
4. A fully prestressed structure is a crack-free structure under service loads. On the other hand, a reinforced concrete structure is assumed to be cracked below the neutral axis from the very beginning. Even the cracks in a prestressed structure which open up under overloads, tend to close on the removal of load. 5. The principle stresses in a prestressed beam tend to be small because of the pre-compression of the concrete and the reduction in vertical shear caused by the upward reactions produced by the curved tendons on the concrete. Hence, it is possible to design prestressed concrete beam with very thin webs. The leads to considerable reduction in self weight. 6. In both reinforced and prestressed concrete structures, the external bending moment is resisted by an internal couple, the steel being in tension and the concrete in compression. There is, however, an important difference. In a reinforced concrete beam, the lever arm remains more or less constant and as the beam is progressively loaded, the stress in the steel increases to build up the resisting moment. On the other hand, in a prestressed concrete, the stress in the tendon remains more or less constant and it is the change in the lever arm which contributes to the increase in the resisting moment as the load on the beam is raised. 7. When once the prestress is overcome, the behavior of a prestressed concrete beam does not materially differ from that of a reinforced concrete beam.
5.5 Advantages Of Prestressing 1. Being made of higher strength steel and concrete, prestressed concrete is inherently superior to reinforced concrete. 2. Prestressed concrete structures tend to be more economical than reinforced concrete structures for long spans and heavy loads. 3. A prestressed concrete structure is a crackles structure. This is an advantage in an aggressive atmosphere and for waterretaining and other structures which call for high degree of impermeability.
4. Prestressed structures are lighter, partly because thin webs are practicable. The advantage is quite pronounced in long span bridges where selfweight is a dominant factor controlling the design. 5. They deflect less because the prestressing operation causes an upward camber to start with. 6. It is sometimes claimed that a prestressed structure is a pretested structure. What is implied is that the steel and concrete are subjected to very high stresses during prestressing and, if the structure behaves satisfactorily at his stage, there is a reasonable assurance that it will perform equally well at other stages.
5.6 Disadvantages of Prestressed Concrete 1. Increased cost of materials and shuttering. 2. Greater supervision required to ensure correct concrete strength and magnitude of prestress forces. 3. Design calculations are more extensive.
5.7 Materials 1. Concrete In prestreseed concrete construction, higher grade of concrete is normally used compared to reinforced concrete. Cl 5.10.2.2(3) EN1992-1-1, states that The strength of concrete at application of or transfer of prestress should not be less than the minimum value defined in the relevant Technical Approval. At transfer, the concrete strength must not be less than 0.6f ck (t). where f ck (t) is the characteristic compressive strength of the concrete at time t when it is subjected to the prestressing force.
The development of strength in concrete with age is shown in Table 5.1 Table 5.1: Strength of concrete Grade Characteristic strength, f ck (N/mm 2 ) 7 days Cylinder strength at an age of (N/mm 2 ) 2 months 3 months 6 months 1 year C20 20 13.5 22 23 24 25 C25 25 16.5 27.5 29 30 31 C30 30 20 33 35 36 37 C40 40 28 44 45.5 47.5 50 C50 50 36 54 55.5 57.5 60
2. Steel Prestressing tendons are usually formed from high tensile steel wires or alloy steel bars. The wires can be used singly or twisted together to form strand (usually of seven wires). Several tendons may be arranged in a group with a common anchorage to form a cable (Figure 5.10). Figure 5.10: Types of tendon (from the top): wire, standard strand, drawn strand, cable of seven strands, Dividing bar and Macalloy bar
(i) Wire Cold-drawn wire is produced in coil form from hot-rolled rod which is heat treated to make it suitable for cold drawing. The wire surface is initially smooth but may be indented by a subsequent mechanical process. In the as-drawn condition, the wire has a natural curvature approximately equivalent to the capstan of the drawing machine. A final stress-relieving heat treatment to improve some of the mechanical properties of the wire is carried out before it is wound into large diameter coils. The stress-relieving treatment pre-straightens the wire, so that it will pay out straight from the coil, and enhances its elastic and relaxation characteristics. Wire to be used for pre-tensioning is supplied in a de-greased condition and is often indented to ensure that the maximum bond is obtained between steel and concrete. Wire is used in factory-produced items such as lintels and small flooring units.
(ii) Strand Strand is made from cold-drawn wires: a seven-wire strand consisting of a straight core wire (the king wire) around which are spun six helical wires in one layer. The diameters of the outer wires have to be slightly less than that of the king wire to allow for their helical form. Strand can be supplied with the outer wires having either a lefthand or a right-hand twist and the stressing jacks need to be adjusted accordingly. In BS 5896, there are three types of seven wire strand: standard, super and drawn (Figure 5.11). Figure 5.11: Cross Sections Of (a) Standard And Super Strand, And (b) Drawn Strand
(iii) Bar There are two types of bar in common use: 1. Macalloy bars are produced from hot-rolled carbonchrome steel bars that are then cold-worked by stretching to obtain the specified properties. The bars are available in lengths up to 17.8 m for diameters between 25 mm and 50 mm. Stainless steel bars are available in lengths up to 6 m for diameters between 20 mm and 40 mm. Both types of bar are provided with cold-rolled threads at each end, or over the full length if needed, and can be joined together by threaded couplers to obtain longer tendon lengths. 2. Dywidag threadbars are produced to a German Standard specification in diameters between 20 mm and 40 mm, with a coarse thread extending over the full length of the bar. The bars may be cut to finished length at the factory or on site and couplers can be used to connect or extend bars as required.
The matching between types of tendons and their usage is shown in Figure 5.12. Figure 5.12: Types of tendons and their usage
5.8 Strength of Tendons The strength of a prestressing tendon is specified in terms of characteristic load values for the breaking (or failure) load and the 0.1% proof load, which is defined as the load that produces a permanent elongation equal to 0.1% of the gauge length. For wire and strand, the load at lo/o elongation may be used as an alternative to the proof load (Figure 25). The British (BS 5896 and BS 4486) and European (EN 10138) standards include a range of sizes and strengths for each type of tendon, a selection of which is shown in Table 5.2.
Table 5.2: Dimensions and properties of wires, 7-wire stands and bars
5.9 Prestressing System & Anchorage 1. Pre-Tensioning With pre-tensioning, the wires or strands are held by temporary grips during and after tensioning. The method of tensioning may vary but in all cases the grip consists of a barrel and wedge. Stressing is carried out either by extending the tendons one at a time, or by multi-stressing, where all the tendons are extended at the same time. In both cases, the process starts at the nonjacking end, where grips are forced onto the unstressed tendons close to the anchor plate. Spring-loaded anchors are often used to apply a consistent force and retain the anchor in position when the tendons are being handled. For tendons that are stressed individually, a relatively small power-operated jack is used to enable stressing to be carried out quickly and efficiently. A popular jack for this purpose is shown in Figure 5.13. Once the controls have been set to pre-determined values, the stressing and anchoring operations are carried out automatically.
2. Post-Tensioning A large number of systems have been developed and used throughout the world as shown in the following photos and Figure 5.14 shows the anchorage systems and their components. Figure 5.13: CCL Stressomatic jacks and pump
Figure 5.14: Anchorage system and their components
5.10 Loss of Prestress When stress is applied to concrete, it undergoes dimensional changes: an immediate elastic deformation followed by a time-related creep deformation. These changes are in addition to the shrinkage caused by changes in moisture content. Any shortening of the concrete that occurs after the tendons have been tensioned and anchored causes a loss of prestress that must be allowed for in the design of the member. Concrete shrinks over time by an amount that varies with the initial water content of the mix, the thickness of the section and the relative humidity of the environment. The shrinkage develops rapidly at first and continues at a reducing rate for many years. The resulting loss of prestress that occurs in the tendons depends on the age of the concrete at transfer, and is greater with pretensioning than with post-tensioning.
The loss of prestress due to the elastic deformation of the concrete that occurs at transfer is greatest in pretensioning, since the tendons are already anchored by bond, and all the stress is applied to the concrete at the same time. In post-tensioning, there is no loss if all the tendons are stressed at the same time, since the elastic deformation takes place before the tendons are anchored. When the tendons are stressed sequentially, a progressive loss occurs in any tendons that are already anchored. The total loss is then intermediate between nil and half the value that occurs in pretensioning. Concrete under applied stress also undergoes an inelastic creep deformation. Like shrinkage, creep develops rapidly at first and continues at a decreasing rate for many years. The creep value depends upon the thickness of the section, the relative humidity of the environment and the maturity of the concrete at transfer of prestress. As a result, the loss of prestress that occurs in the tendons is greater with pre-tensioning than with post-tensioning.
5.11 Limitation of Prestressed Concrete Stress The stress limits for prestressed concrete structures under transfer and service condition are stated in clause 5.10.2.2, EN 1992-1-1. The stress limits are summarized in Table 5.3. Table 5.3: Stress Limits Stresses Compressive Transfer 0.6f ck (t) Service 0.6f ck Tensile f ctm 0
5.12 Stress Distribution Figure 5.15 shows the stress distribution of a simply supported prestress concrete member. Figure 5.15
If α = coefficient of short term losses β = coefficient of total losses (short term + long term losses) Stress Distribution at transfer stage. f min = Limit of tensile stress at transfer f max = Limit of compressive stress at transfer
Stress Distribution at service stage. f min = Limit of tensile stress at service f max = Limit of compressive stress at service
Example 1 Given the following data Moment due to selfweight, Mi = 100 knm, Moment due to external load, Ms = 200 knm Initial prestressing force, P i = 2000 kn (e = 0) Rectangular section: b = 400mm, h = 800mm Sketch the stress distribution diagram and state the stress value
Solution: A = bh = 400 x 800 = 320 x 10 3 mm 2 3 3 bh 400x800 I = = = 1.7x10 12 12 10 mm 4 Z I y 1.7x10 400 3 t = Z b = = = 42.5x10 6 mm 3
Example 2 The diagram on the left shows a simply supported prestress concrete beam and its cross section. Given the following data: Z b = Z t = 70.73 x 106 mm 3 Ac = 2.9 x 105 mm 2 α = 0.9 β = 0.8 Concrete strength, f ck = 40 MPa Concrete strength at transfer (7 days), f ck (t) = 28 MPa Check the limiting stress at transfer and service stage.
Solution: 3 2.9x10 i = x24 = 10 W 6 M 6.96kN / m 2 2 W i L 696x15 = = 196 knm 8 8 i = 2 2 WL 50x15 M s = M i + = 196 + = 8 8 1602kNm Limiting stress: f' min = f ctm = 0.3xf ck (t) (2/3) = 0.3(28) (2/3) = 2.77 N/mm 2 f' max = 0.6f ck (t) = 0.6 x 28 = 14 N/mm 2 f min = 0 f max = 0.6f ck = 0.6 x 40 = 24 N/mm 2
Stress Distribution At Transfer Stage
Stress Distribution At Service Stage