Concrete Design Guide

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1 Number 7 38 TheStructuralEngineer Technical July 2015 Post-tensioned slabs Concrete Design Guide No. 7: Design of post-tensioned slabs This series is produced by The Concrete Centre to enable designers to realise the potential of concrete. The Concrete Centre, part of the Mineral Products Association (MPA), is a team of qualified professionals with expertise in concrete construction, engineering and architecture. Table 1: Comparison of PT systems Bonded Localises effect of accidental damage Develops higher ultimate strength Does not depend on anchorages after grouting Can be demolished in same way as reinforced concrete structures Unbonded Figure 1 Unbonded and bonded tendons and components Reduced covers to strand Reduced prestressing force Tendons can be prefabricated leading to faster construction Tendons can be deflected around obstructions more easily Greater eccentricity of strand Grouting not required Useful when only one strand is required, e.g. in rib in ribbed slab Introduction Post-tensioned (PT) concrete floors are now widely used in the UK, particularly for high-rise buildings. PT flat slabs provide the thinnest readily available structural option for spans of 7m or more, and can economically be used for spans up to 13m 13m. For longer spans, a one-way spanning slab onto band beams is frequently used. Most PT floors are designed in the UK by specialist designers as part of a performance specification procurement route. However, the design is not necessarily complicated and the main designer should have knowledge of the benefits and limitations of PT design so that a reasonable scheme design might be considered as a structural option and produced for the tender documentation, and also so that the designer can factor the design and its benefits into the overall stability and robustness of the structure. This article provides information on how to scheme a PT slab and how the use of posttensioning affects the rest of the structure. A more detailed guide to the design of PT floors can be found in the Concrete Society Technical Report 43 (TR43), Post-tensioned concrete floors: Design handbook 1. This guide can be used for the design of PT floors to Eurocode 2 2 as it is quoted as noncontradictory complementary information (NCCI) in the UK National Annex 3. Bonded and unbonded systems There are two types of post-tensioning system available to the engineer: bonded and unbonded (Figure 1). Most of the posttensioning work in the UK is bonded, being

2 39 W Figure 2 Typical floor layouts about 90% of the market. Bonded systems have prestressing tendons running through a duct which is then grouted after prestress has been applied. The ducts can be circular or flat and hold a number of tendons. The benefit of using a bonded system is that the anchorages are no longer live after the grouting has set, which means that any damage to a tendon (e.g. if a tendon is cut through by a post-drilled fixing) is limited to the bond length of the tendon on either side of the cut. The tendon is also protected from corrosion by the grout, in the same way as normal reinforcement is protected in reinforced concrete. Finally, bonded systems are as easy to demolish as normal reinforced concrete or possibly slightly easier, due to less reinforcement within the structure. Unbonded systems are more prevalent in North America and in other parts of Europe. Here the tendons run through a greased sheath and are always independent of the concrete. This has no effect on the serviceability design or performance of a structure under normal working conditions. It does, however, change both the design theory and structural performance at the ultimate limit state (ULS). The anchorages for an unbonded system are live throughout the lifetime of the structure and if the tendon suffers damage, the prestress provided by that tendon is lost along the whole of its length. Both systems can be used in the same slab if the design dictates it. Table 1 gives a comparison between the two systems. Restraint At the early stages of a project using PT floors, care must be taken to avoid the problems of restraint. This is where the free movement in the length of the slab under the prestress forces is restrained, e.g. by the unfavourable positioning of shear walls or lift cores (Figure 2). All concrete elements shrink due to drying and early thermal effects but, in addition, prestressing causes elastic shortening and ongoing shrinkage due to creep. Stiff vertical members, such as stability walls, restrain the floor slab from shrinking, which prevents the prestress from developing and thus reduces the strength of the floor. E Figure 3 Typical infill strip Where the restraining walls are in a favourable arrangement and the floor is in an internal environment, the length of the floor without movement joints can be up to 50m. However, full consideration should be given to the effects of shrinkage due to drying, early thermal effects, elastic shortening and creep in the design. A strain of 650με should be considered normal. Where the walls are unfavourably arranged, a calculation of the effects of movement should be carried out and suitable measures taken to overcome them. This could involve: using infill strips, also known as pour strips, which are usually cast around 28 days after the remainder of the floor, to allow initial shrinkage to occur (Figure 3) increasing the quantity of conventional reinforcement, to control the cracking using temporary release details using a proprietary temporary release detail reducing the stiffness of the restraining elements The effect of the floor shortening on the columns should also be considered in their design, as this may increase the design moments. Design to prevent disproportionate collapse PT floor systems are usually designed to resist disproportionate collapse through detailing of the tendons and reinforcement.

3 Number 7 40 TheStructuralEngineer Technical July 2015 Post-tensioned slabs E Figure 4 Design flow chart for PT slabs In bonded systems, the tendons can be considered to act as horizontal ties. In unbonded systems, the tendons cannot be relied on and the conventional reinforcement acts as the horizontal ties. Materials and specification PT slabs do not require particularly highstrength concrete and often class C32/40 is used in a typical flat slab design. For speed of construction the concrete should have high early strength. This allows initial prestressing to be carried out as early as possible, usually after 24 hours, to prevent cracking. Final stressing can take place after three days, once the concrete has reached a predetermined strength, allowing striking of formwork. Higher levels of cement replacements, e.g. ground-granulated blastfurnace slag (GGBS) or fly ash, can be used, but will increase the programme length and may change the parameters used in design, such as the strains due to creep and early age shrinkage. Common strand types used in the UK are given in Table 2. It is recommended that only one of these strand types is used on any project. A specification for the execution of PT floors is given in the National Structural Concrete Specification 4, section 7. Cover As with other forms of reinforced concrete, the cover is determined by consideration of: corrosion protection bond fire protection The cover required for bond considerations for bonded systems is the diameter of the duct for circular ducts; for flat ducts it is the larger of half the larger dimension or the smaller dimension. For unbonded systems, the cover required for bond is the diameter of the sheath. Design process Figure 4 presents a flow chart for the design of PT slabs. Recommendations for the design of prestressed concrete are given in Eurocode 2. Design methods for PT flat slabs are relatively straightforward, and detailed guidance, based on Eurocode 2, is available in TR43. At the serviceability condition, the concrete section is checked at all positions to ensure that both the compressive and tensile stresses lie within the acceptable limits given in Eurocode 2. Stresses are checked in the concrete section at the initial condition when the prestress is applied, and at serviceability conditions when calculations are made to determine the deflections and crack widths for various load combinations. At the ULS the pre-compression in the section is ignored and checks are made to ensure that the section has sufficient moment capacity. Shear stresses are also checked at the ULS in a similar manner to that for reinforced concrete design, although the benefit of the prestress across the shear plane may be taken into account. At the serviceability limit state (SLS), a prestressed slab is generally always in compression and therefore flexural cracking is uncommon. This allows the accurate prediction of deflections as the properties of the uncracked concrete section are easily determined. Deflections can therefore be estimated, and limited to specific values rather than purely controlling the span-to-depth ratio of the slab, as in reinforced concrete design. In carrying out the above checks, extensive use can be made of computer software either to provide accurate models of the

4 41 Figure 5 Principles of prestress design structure, taking into account the effect of other elements, or to enable different load combinations to be applied, or to carry out both the structural analysis and prestress design. The basic principles of prestressed concrete design can be simply understood by considering the stress distribution in a concrete section under the action of externally applied forces or loads. Figure 5 illustrates the simplicity of the basic theory. In essence, the design process for serviceability entails checking the stress distribution under the combined action of both the prestress and applied loads, at all positions along the beam, in order to ensure that both the compressive and tensile stress are kept within the limits stated in design standards. PT beams and slabs are usually designed to maximise the benefit of the continuity provided by adjacent spans. In this situation secondary effects should be considered in the design. The secondary effects are not necessarily adverse and an experienced designer can use them to refine a design. Figure 6 Load-balancing technique

5 Number 7 42 TheStructuralEngineer Technical July 2015 Post-tensioned slabs Figure 7 Idealised tendon profile for two spans with single cantilever In the majority of prestressed slabs it will be necessary to add reinforcement, either to control cracking or to supplement the capacity of the tendons at the ultimate load condition. The technique known as load balancing offers the designer a powerful tool. In this, forces exerted by the prestressing tendons in catenary are modelled as equivalent upward forces on the slab. These forces are then proportioned to balance the applied downwards forces (Figure 6). By balancing a chosen percentage of the applied loading, it is possible to control deflections and also make the most efficient use of the slab depth. In order to use the load-balancing technique, the prestressing tendons must be set to follow profiles that reflect the bending moment envelope from the applied loadings. Generally parabolic profiles are used. In PT concrete floors, the load-balancing technique can enable the optimum depth to be achieved for any given span. The final thickness of the slab, as with reinforced concrete flat slabs, may also be controlled by the punching shear around the column. For a parabolic profile the upward uniformly distributed load w is: This can be extended to several spans and provides a more economical design as the drape is larger (Figure 7). The anchorages are normally placed at the centroid of the section in order to prevent a moment being placed at the end of the beam or slab. Initial sizing of PT slabs PT slabs can initially be sized using spanto-depth ratios. TR43 gives span-to-depth ratios for various different slab types, as does the Concrete Centre book, Economic Concrete Frame Elements to Eurocode 2 5. Figure 8 gives typical span-to-depth ratios for flat slabs, band beams and ribbed slabs for different imposed loads. Table 3 gives the range of spans that are normally used for PT floors. Prestress losses From the time that a post-tensioning tendon is stressed, to its final state many years after stressing, various losses take place which reduce the tension in the tendon. These losses are grouped into two categories: short-term and long-term losses. Short-term losses Short-term losses include: friction losses in the tendon wedge set or draw-in elastic shortening of the structure These losses take place during stressing and anchoring of the tendon. Long-term losses Long-term losses include: shrinkage of the concrete creep of the concrete, including the effect of the prestress relaxation of the steel tendon Although these losses occur over a period of 10 or more years, the bulk occurs in the first two years following stressing. The loss in prestress force following stressing can be significant (between 10% and 50% of the initial jacking force at transfer and between 20% and 60% after all losses) and therefore the losses should, in all instances, be calculated. TR43 gives advice on prestress losses in Appendix B. where s is the span, a is the drape and P is the prestress force. This upward load normally balances the self-weight and the superimposed dead load. Depending on the design, it is also sometimes used to balance some of the live loads. Table 3: Span ranges for PT floors Floor type Span range PT flat slab 6 13m PT band beam 8 18m PT ribbed slab 7 18m PT waffle slab 8 18m

6 43 Table 2: Specification of commonly used strand in the UK Strand type Nominal tensile strength (MPa) Nominal diameter (mm) Crosssectional area (mm 2 ) Nominal mass (kg/m) Characteristic value of maximum force (kn) Maximum value of maximum force (kn) Characteristic value of 0.1% proof force (kn) 12.9 Super Super Euro Drawn Figure 8 Span-to-depth ratios for PT floors Conclusion This article does not provide a full explanation of the design of PT floors. It is recommended that the designer makes themselves familiar with TR43 when starting the design process. The design of PT floors allows the designer to play with the different aspects prestress force, tendon profile etc. to arrive at the most economic design. There are many software packages that can help, both 2D design and finite-element analysis. The Post-Tensioning Association (PTA) in the UK can also help. It produces technical design guidance and is in the process of producing a model performance specification for PT floors to help main designers understand what is required by specialist designers and what can be expected from the specialist designers and contractors. The PTA website can be accessed at References and further reading 1) The Concrete Society (2005) Technical Report No. 43: Posttensioned concrete floors: Design handbook (2nd ed.), Camberley, UK: The Concrete Centre 2) British Standards Institution (2014) BS EN :2004 Eurocode 2: Design of concrete structures. General rules and rules for buildings, London, UK: BSI 3) British Standards Institution (2009) NA to BS EN :2004 UK National Annex to Eurocode 2. Design of concrete structures. General rules and rules for buildings, London, UK: BSI 4) CONSTRUCT (2010) National Structural Concrete Specification (4th ed.), Camberley, UK: The Concrete Centre 5) Goodchild C. H., Webster R. M. and Elliott K. S. (2009) Economic Concrete Frame Elements to Eurocode 2, Camberley, UK: The Concrete Centre