Post Tension Concrete Floor Systems CIVIL3811/9811 PDF

Post Tension Concrete Floor Systems CIVL3811/9811 Engineering Construction and Design School of Civil Engineering | Faculty of Engineering THE UNIVERSITY OF SYDNEY The University of Sydney Page 1  Definition of Pre-stressing – It consists of preloading the structure before application of...

Post Tension Concrete Floor Systems CIVL3811/9811 Engineering Construction and Design School of Civil Engineering | Faculty of Engineering THE UNIVERSITY OF SYDNEY The University of Sydney Page 1  Definition of Pre-stressing – It consists of preloading the structure before application of design loads in such a way so as to improve its general performance. The University of Sydney Page 2  “Prestressing means the intentional creation of permanent stresses in a structure or assembly, for the purpose of improving its behaviour and strength under various service (and strength) conditions.” T.Y. Lin, 1955. Prestressed concrete is an elegant engineering system that improves many of the service and strength performance behaviours of reinforced concrete while achieving cost effective and practical solutions to the design of many engineering structures. The University of Sydney Page 3  Objectives of Pre-stressing  Control or eliminate tensile stresses in the concrete (cracking) at least up to service load levels.  Control or eliminate deflection at some specific load level.  Allow the use of high-strength steel and concrete. The University of Sydney Page 4 Prestressing -The Basic Idea Prestressing - The Basic Idea High tensile wire strands fy ≈ 1870 MPa Higher strength concretes f ’c ≈ 30 – 50 MPa The tendons are cast within the concrete – at first freely within ducts, which are grouted at a later stage to bond the tendons. Prior to grouting, the tendons are jacked to very high stresses. The jacking reactions are pressed against the ends of the concrete member and then transferred permanently to cast-in end anchors. This is shown in a simplified form in the diagram below. In practice, the duct ‘profile’ will vary to suit the purpose of the member. End result: the tendons are permanently ‘pre-stressed’ in tension; the concrete is permanently ‘pre-stressed’ in compression. The University of Sydney Page 5 Terminology Terminology Strand: generally refers to an element in which a number of high tensile wires are woven together as a combined unit. (See multi-strand jack) Tendon: generally defined as the wire, strand or bar (or any discrete group of wires, strands or bars) that is intended to be pre-stressed. Cable: generally refers to groups of tendons, collected together in a duct or anchorage. Pre-stressed: the prior stressing of both the concrete and the tendons prior to the service use of the element. Pre-tensioned: the tendons are tensioned (in a casting bed) prior to pouring of the concrete. The tendons are cut and bonded to the concrete after it attains strength. Used in pre-cast construction. Post-tensioned: the tendons are laid in metal ducts in the concrete and tensioned after the concrete attains strength. This is the most commonly used system in building and other structures in Australia. The University of Sydney Page 6 Construction Systems Some Modern Anchorage Systems (From VSL Catalogue) Mono-strand – strands jacked individually Multi-strand – jacked together After stressing and grouting, the strands become bonded (through the duct) to The University of Sydney Page 7 the member concrete.  strands The University of Sydney Page 8 Wedges The University of Sydney Page 9 Construction Systems Construction Sequence (From VSL Catalogue) The University of Sydney Page 10 Terminology (Cont’d) Bonded tendons: where the ducts which contain the tendons are filled with cement grout after the tendons are stressed – this effectively bonds them to the concrete like reinforcing steel. Tendons. can subsequently develop further stresses under bending actions due to strain compatibility, enabling the full strength of the bonded tendons to be realised at ultimate strength Unbonded tendons: where the tendons are not grouted, but are greased for corrosion protection and contained within a plastic sheath. This method is not permitted under AS 3600 except for slabs on ground. Unbonded tendons can be used in specialised applications such as cable stayed bridge cables for example, allowing the monitoring and replacement of individual strands. The University of Sydney Page 11 Load Balancing Concepts While a suspension bridge cable balances the vertical loads in a catenary action, it is not prestressed: In a prestressed structure we are able to prestress the cables against the slab, and effectively ‘pre-balance’ the load of the slab: The University of Sydney Page 12 Prestressing Concepts - Summary Pre-compression and Load balance Cracking reduces stiffness, increases deflection Pre-compression reduces cracking and deflection Tendons apply prestress ‘Draping’ the tendon provides upward load to carry a % of the Result = Improved deflection and strength self-weight The University of Sydney Page 13 Some Basic Concepts Once the tendons are grouted they effectively become a part of the concrete ‘free body’, which behaves as an integrated whole: This is similar to the load balanced free body considered above Now consider the application of an external load onto the beam, which includes the self weight (conveniently ignored up to now) plus other loads: When we apply an external loading, the C and T forces separate to form a moment couple which resists the externally applied moment. This is the basis of the internal couple approach (GMR 1.4.2). The University of Sydney Page 14 Material Properties Material Properties – Concrete (Refer to AS3600 Section 3.1) Concrete strength f’c = uniaxial compression strength of test cylinders. This is a characteristic value which is to be exceeded by 95% of test samples. AS 3600 8.1.3 limits the maximum strain in the extreme compression fibre to 0.003 – while at this value concrete retains most of its strength, it is starting to diminish. Typically f’c = 32 – 50 MPa for prestressed concrete applications. Prestressing contractors will have specific early transfer stress requirements prior to jacking. The University of Sydney Page 15 Material Properties – Concrete (Cont’d) Concrete experiences time dependent strain due to creep and shrinkage. Concrete has a characteristic tensile strength f’ct which is used in some serviceability calculations. This should never be relied upon for strength however. The University of Sydney Page 16 Material Properties – Reinforcing Steel and Prestressing Tendons Material Properties - Reinforcing Steel and Prestressing Tendons (Refer to AS3600 Sections 3.2 & 3.3) The University of Sydney Page 17 Material Properties - Reinforcing Steel and Prestressing Tendons (cont’d) The tensile strengths of commonly used strands are given in Table 3.3.1 of AS 3600. The ‘characteristic breaking ‘strength’ (fpb) is actually the breaking ‘stress’. We will also used the term Tpb for the ‘breaking load’ Note the highlighted elements – these are the most commonly used in the design of prestressed building structures. The University of Sydney Page 18 Introduction to Losses The prestressing force in a tendon begins to diminish from the instant when the steel is first tensioned and continues through the life of the prestressed member. Even during pre-stressing of the tendons and initiation of the prestress transfer to the concrete member, the actual prestress force in the steel differs from the recorded value in the jack gauge. http://www.mibatec.it/ Overall losses are commonly in the The estimation of the losses range 15 to 30 per cent of the initial magnitude is an important part of jacking force the design process The University of Sydney Page 19 Introduction to Losses Loss of prestressing can be considered in two main categories, depending upon whether the loss takes place during or after the transfer of the prestressing force to the concrete. Immediate losses: depend on the method and equipment used for prestressing Deferred losses: gradual losses that occur with time over the life of the structure The University of Sydney Page 20 Introduction to Losses Elastic compression of the concrete, Elastic deformation during stressing Friction along the member, between tendon and Immediate Duct friction duct, during the prestressing of the tendon losses Movement in the grips as the tendons Anchorage slip are anchored Prestress Losses Stress relaxation In the prestressing steel Factors. Deferred losses Shrinkage In the concrete deformation Creep deformation In the concrete The University of Sydney Page 21 The University of Sydney Page 22 The University of Sydney Page 23 The University of Sydney Page 24 The University of Sydney Page 25 The University of Sydney Page 26 Slab Systems Slab Systems (AS 3600 Section 9) Slab systems can be divided into five main types: (a) One way slab supported on walls or narrow beams. (b) Two way slabs supported on four sides. (c) Two way flat plates – without drop panels (d) Two way flat slabs - with drop panels. (e) One way slab and band beam One way slab systems (a) can be analysed in a similar way to continuous beams. Two way edge supported slabs such as (b) are mostly seen as small areas in cores of buildings and are rarely prestressed. Moment coefficients are given in Table 6.10.3.2 of AS 3600 The University of Sydney Page 27 One-way slab supported on walls or narrow beams. The University of Sydney Page 28 Two-way slabs are supported on four sides ( Waffle). The University of Sydney Page 29 Slab Systems (Cont’d) One way slabs that run across band beams as in (e) might be designed as if fixed at the edges of the band, but consideration must also be given to the additional moments at the change of section; The cables are profiled to reach their highest point at the edge of the band (this is also dictated by the band secondary reinforcement) and extra moments will arise across the band beam. In most cases the extra depth will more than cater for these higher moments. The bands are normally 100-200mm deeper than the slabs. The width should be about 6 times the depth to be considered as a band rather than a beam.. The University of Sydney Page 30  Prestressing key Considerations Higher strength concrete –higher load support and high anchor stresses. High tensile strands –up to 1870 MPa An amount of the prestress is lost due to concrete creep and shrinkage. For example a shrinkage strain of 500 x 10-6 leads to 100 MPa loss of the prestress – significant in lower strength bars. The University of Sydney Page 31 Prestressed Concrete –Improved Serviceability Sections uncracked and load balancing helps support dead load. Much reduced deflections Allows sections to be approximately 70% of the depth of an equivalent Reinforced Concrete section. Post tensioning allows longer spans to be achieved. The University of Sydney Page 32  Determinate and Indeterminate Structures in Prestressed Design Statically Determinate and Indeterminate Structures A structure is said to be ‘statically determinate’ when the forces and bending moments can everywhere be determined by means of the equations of static equilibrium, as for the simple beam spanning from A to C below. A structure is ‘statically indeterminate’ or ‘hyperstatic’ when it possesses more members or is supported by more reactive restraints than are strictly necessary for stability. The excessive restraints are described as ‘redundant’, as is the case for the additional support B introduced to make the two span structure below. However when there are insufficient support the structure becomes unstable, as happens if we remove one of the supports from the simply supported beam. The University of Sydney Page 33  Statically Determinate Beams Statically Determinate Beams Statically determinate beams include simply supported beams or single span beams with single or double cantilever ends; or just single span cantilevers themselves. A good rule of thumb is that post-tensioned beams become more economical than simply supported reinforced beams for spans greater than about 7 – 8m Similarly for cantilevers greater than about 3m. Preliminary sizing could start with a simply reinforced beam and increase the span to depth ratio – L/D – by about 1.2 – 1.4. In other words the depth can be reduced to about 70 – 80% of that required for a comparable reinforced beam, while still satisfying the serviceability requirements. The University of Sydney Page 34  Schematic Design Approaches Another important schematic design tool is the use of span to depth (L/D) ratios for the preliminary sizing of members. The following are intended as guidelines only: The University of Sydney Page 35  Practical Tendon Profiles Practical tendon Profiles So far we have been ‘conceptualising’ the cable profiles in continuous beams as if they follow idealised parabolic patterns. However, if built in this way they would come to support from each side with a slope and form a ‘point’. In real life the cables must follow a ‘minimum’ practical radius over the supports so that there can be a smooth transition for both the duct and the tendons, as shown in the following Figure. A small amount of additional depth is carried into the span near the support as a result of this ‘practical’ profiling. This is useful in dealing with some of the unbalanced live load cases. The flat type of ducts used in band beams and slabs are easier to profile in this way than larger round ducts. The University of Sydney Page 36  Ultimate Shear Strength Prestressed Beams Vuc , the component of shear carried by the concrete, is calculated for two conditions in prestressed beams. In region A there is little shear: moment cracking predominates In region B both the moment and shear are relatively large: moment cracks can extend into shear cracks. This gives rise to: (a) ‘flexure – shear cracking’ In region C shear cracking predominates, giving rise to: (b) ‘web – shear cracking’ The University of Sydney Page 37  Torsion in Beams Torsion in beams creates a diagonalised pattern of cracking around the perimeter of a beam, as shown in the following figure. Torsional reinforcement normally consists of closed ties placed at centres along the beam, which are supplementary or additional to the shear reinforcement. Longitudinal forces are also created in the corners of the section, which in concrete sections are resisted by longitudinal bars placed in all corners of the ties. The University of Sydney Page 38