100mm bearing
Figure 3 Typical infill strip
FIGURE 9: TYPICAL FLOOR LAYOUTS
FIGURE 11: TEMPORARY RELEASE DETAIL FIGURE 10 : TYPICAL INFILL STRIP
a) Favourable layout of restraining walls (low restraint)
b) Unfavourable layout of restraining walls (high restraint)
1000 mm
RC infill strip Post-tensionedslab
50mm
seating Slab to remainfully propped until infill strip cured
Infill later
Post-tensioned slab
2 layers of slip strip 100mm bearing
Structural Design of Concrete and Masonry
Design to prevent disproportionate collapse
PT floor systems are usually designed to resist disproportionate collapse through detailing of the tendons and reinforcement.
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 high strength concrete and often class C32/40 is used in a typical flat slab design. For speed of construction, however, 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 Specification4, 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.
›
TheStructuralEngineer 40 Technical Number 7 $ " $ " $ " ! " $ "$ "$ ! "$ " "#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 specifi cation
PT slabs do not require particularly high- strength concrete and often class C32/40 is used in a typical fl at 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 blast- furnace slag (GGBS) or fl y 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 specifi cation for the execution of PT fl oors is given in the National Structural Concrete Specifi cation4, section 7.
Cover
As with other forms of reinforced concrete, the cover is determined by consideration of: • corrosion protection
• bond • fi re protection
The cover required for bond
considerations for bonded systems is the diameter of the duct for circular ducts; for fl at 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 fl ow chart for the design of PT slabs. Recommendations for the design of prestressed concrete are given in Eurocode 2. Design methods for PT fl at 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 defl ections 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 suffi cient moment capacity. Shear stresses are also
checked at the ULS in a similar manner to that for reinforced concrete design, although the benefi t 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 fl exural cracking is uncommon. This allows the accurate prediction of defl ections as the properties of the uncracked concrete section are easily determined. Defl ections can therefore be estimated, and limited to specifi c 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
E
Figure 4Design fl ow chart for PT slabs
Post-tensioned slabs July 2015
TSE43_38-43 CDG v1.indd 40 18/06/2015 11:22
Figure 4 Design flow chart for PT slabs
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 structure,
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Structural Design of Concrete and Masonry
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 8: LOAD BALANCING TECHNIQUE
a) Proposed loading b) Unstressed slab c) Prestressed slab d) Final condition
Figure 6 Load-balancing technique
+ =
FIGURE 7: PRINCIPLES OF PRESTRESSED DESIGN
d) Concrete is strong in compression but not in tension. Only small tensile stresses can be applied before cracks that limit the effectiveness of the section will occur. By combining the stress distributions from the applied precompression and the applied loading it can be seen there is no longer any tension, assuming the magnitude of P has been chosen correctly. a) Consider a beam with a force P applied at each end along the beams’ centre line.
This force applies a uniform compressive stress across the section equal to P/A, where A is the cross sectional area. The stress distribution is shown right.
P P
b) Consider next a vertical load w applied along the beam and the corresponding bending moment diagram applied to this alone.
w
M (max)
+ M/Z P/A+ M/Z
c) The stress distribution from the flexure of the beam is calculated from M/Z where M is the bending moment and Z the section modulus. By considering the deflected shape of the beam it can be seen that the bottom surface will be in tension. The corresponding stress diagram can be drawn. Compression Tension + M/Z - M/Z - M/Z P/A - M/Z P/A 0 0 0 + = P/A 0 Applied load
Resultant Moment Diagram
Structural Design of Concrete and Masonry P e4 L3 w3/m w2/m w1/m drap e Span 3: Span 2: Cantilever Span 1: drap e e3 e2 L2 e1 L1 P
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:
= Pa
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.
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 25. 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.
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 8 ws2
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Structural Design of Concrete and Masonry