On completion of smessing, the ducts are pumped full of cement grout which effectively bonds the strand to the structure as well as ensuring corrosion protection. Further information can be obtained from reference Anchorages Anchorage companents should comply with BS 'L Details of these are shown i n Figures 22 and In the case of unbonded anchorages corrosion protection should comply with Class A exposure as defined in reference Bonded tendons: The cover to the tendons should be in accordance with the requiremens for prestressed concrete in BS, P r 1, Clause 4.
It should be noted Lhat the cover to the centre of the tendon will be more than that to the centre of the duct, since the tendon will press againsr the wall of the duct.
Unbonded tendons: There is no durability requirement for unbonded tendons protected in accordance with 4. Fire pmtec6on shall be provided in accordance with BS, P r 1. Clause 4. The tendon is normally specified as a nominal diameter e.
Un-tensioned reinforcement: The cover to the un-tensioned reinforcement should be in accordance with the requirements for reinforced concrete in BS, P r 1, Clause at. Anchorages: The cover to anchorages should be as for bonded tendons given in BS, P r 1, Clause 4. As in most reinforced and prestressed concrete design work, the customary design process is of an iterative nature following the cycle: 1. Preliminary design Check design by analysis Revise design as required Repeat steps 2 and 3 if necessary.
The analysis is normally bzsed on semi-empirical procedures such as the equivalent frame method. More rigomus analyses based on, for example, finite element methods are m d y adopted. They should only be considered for large pmjcts of unusual form where the high design costs and the inapplicability of h e empirical method justify them.
In reinforced concrete the reinforcement is inidally unstressed: the suess in the reinforcementresults fmm h e deformation and cracking of the structure underapplied load. In this way the reinforcemenr may be considered lo acl passively. On the other hand, the tendons in a post-tensioned flwr are actively stressed by h e jacks so that they are loaded before the application of other loads. The force in the tendon is chosen by the designer and does not vary much with the application of Serviceability Limit State dead and live loads.
The analysis of equivalent frames may be undemken by hand, using moment distribution or flexibility methods. There are also available on the market several computer programs specially written for post-tensioned flooring systems. These programs not only undenake the analysis of the frame under applied loading and loading from the tendons, but also calculate the flexural stresses.
For more complex or detailed analysis, grillage or finite element methods may be used. Whichever Whnique is used for the smctural analysis it must cake into account not only the dead and live loads but also the loads which the tendons apply to the structure see Section 6. The choice of layout and m e m k r sizing has been d i s c u s 4 in Section 3, and is probably the most important decision in the design process.
Unless previous experience or ovemding factors dictate the exact form and section, seveml possibilities should be studied, although the designer should be able to limit the possible solutions by considering the various consuaints and by rough design and costing exercises. With regard to slab thickness and concrete suengths, the relationship of structural layout, slab thickness and loading has been referred to in Section 3. A determination of a trial m e m k r depth must b made at an early stage in the calculation process.
The loading for Serviceability Limit State should consider the dead load and post-tensioning effects acting with those combinations of live loads which result in the maximum stresses. Unless there are specific abnormal loads present, it will generally be sufficient to consider the post-tensioning effects in combination wilh the live loads as given in BS, P r 1, Clause 4. Where the applied loads change significantly during conshuction or phased stressing is employed, the various stages should each b checked for transfer mess limits.
Secondary effects of prestressing should be included in the applied loads with a load factor of 1. Eqdvait-nt frame anaijsis It is usual lo divide the smchlre inlo subframe elements in each direction. Each frame usually comprises one line of columns together with beamlslab elements of one bay width. The frames chosen for analysis should cover all the element types of the complete smcture.
The ends of the columns remote from the sub-frame may generally be assumed to be fixed unless the assumption of a pinned end is clearly more reasonable e. The use of the equivalent frame method does not take account of the two-dimensional elastic loaddisnibution. It will give different support reactions from the analyses in the two orthogonal directions unless the width of slab chosen caincides with the paints of zero shear in the o h dimtion.
Normally for internal bays the width of slab will be the full panel width. However for a regular layout, Lhe penultimate frame will pick up more than half the width on the side of the end bay see Figure Provided the reaction on each column is taken as the larger value from the two analyses litrle accuracy will be lost However where the size and arrangement of edge columns is different from the internal columns the width of slab should be estimated more accurately.
This will ensure the correct selection of the number of presuess tendons with the profile appropriate for the frame being analysed. It should be noted that these elastic effects are automatically taken into account when the floor is analysed using grillage or fmite element methods. Irrespective of which analytical technique is used, care should be laken to ensure that the assumptions made are appropriate to the structure under consideration. In particular the prestress applied to two adjacent frames should not be very dissimilar athenvise the prestress fmm the more highly stressed frame will dissipate into the adjacent frames.
Lines of zero shear in! BS, P s 1, Section 3. Other methods may also be used. It is now common to analyse smctures using plane frame computer programs. However, when longhand momencdisnibution calculations are employed, sliffness.
These can be quite complicated for varying sections, column heads and drop-panels and, although often ignored in hand calculations, the effect on stiffness of the complete beam moment of inertia over the column width can be most significant, particularly for wide columns. It should also be noted that BS, Part 1, Section " allows reduction of Tendon p m p a d balanced load Ideally the tendon profile is one which will produce a bending moment diagram of similar shape. This is nor always possible because of varying loading conditions and geomemc limitations see Section 5.
It should te noted that for bonded systems the centroid of the snands will not coincide with the centroid of the duct. This is particularly true in the case of circular ducts. Further information may be available h m the manufacturer's literature. In the simplest case, for a uniformly loaded simply-supported beam, the bending moment is parabolic, as is the ideal tendon profile.
The total 'sag' in the parabola is referred to as the tendon 'drape' see Figure At the suppons the lendon has no eccentricity and hence there is no bending momenc due to the tendon forces. Tendon profiles are not always symmewic. However, the point of maximum drape is still at the centre of the points of inflection, but may not correspond to the point of maximum sag.
The upward forces applied to the concrete by a parabolic profiled tendon, as shown in Figure At the ends of the tendon downward forces are applied to the concrete by the anchorages.
I h e upward and downward forces are in equilibrium sn that no external forces occur. The set of forces applied to the member by the tendon are known as the 'equivalent' or 'balanced' loads, in that the upward forces counter-balance a proportion of the downward forces due to dead and live loads.
For a parabolic profile the upward uniformly distributed load, w, can be calculated as follows:. Note that this may not be position of maximum sag average presEessing force in tendon. Usually, in continuous members, the most effective use of a tendon in producing 'balanced loads' is achieved by having the tendon at its lowest possible point in positive moment locations, and at its highest possible point in negative moment locations.
In this way the drape, and consequently the 'balanced loads', is increased to a maximum. The 'equivalent' or 'balanced' loads may be applied to the smctural frame in order to obtain the total effects of prestressing. The total effects are a combination of the Primary and Secondary effects as described in Section 6. It is beyond the scope of this publication to give an extensive treatise on prestressing theory or load-balancing design. Funher details may be oblained fmm reference In post-tensioned design it is common to roughly 'balance' equal proponions of the dead and applied loads in each span.
Some designers set out with a preconceived idea of what load they wish to balance as a proponion of the dead or total load.
Othen balance the minimum amount which will result in the final stresses due to the out-ofbalance loads k i n g as close as pssible to the maximum allowable stresses.
This latter approach is usually the most economical overall but may not always k the most suitable for deflection or congestion of un-tensioned reinforcement. Figure 27 illusuates an idealised tendon profile for a two-span memkr with a cantilever. The parabolic profiles result in the balanced loads w,, w, and w, as shown, calculated from the tendon profile and hence the 'drapes'.
Figure 2'1: I d e a l i d tendon profile for two spans with single cantilever. Figure 28 illushates a two-span member with an idealised tendon profile to provide a uniform uplift over span 1 and a concenmted uplift in span 2.
The concenmed effect is useful in members transferring column or similar point loads. While te bending moments 'peak' over the supports. Remember that the peak is where the tendon is 'dumping' the load it has picked up by its parabolic shape Figure In practice, tendon profiles are of the form shown in Figure Appendix C provides information from which the parabolic tendon geometry can be calculated. The resultant balancing forces are therefore as shown in Figure P is the prestressing force at ths section under consideration.
Note: that the centre of gravity of the concrete and the centre of gravity of the tendon coincide at the end of the member so that no equivalent load moments are applied at the end of the member. Figure Resultant balancing forces. For the reverse parabala at the support the toul load downwards:. Prestmss forces and losses From the time that a post-tensioning tendon is stressed, to its find state many years alter stressing, various losses take place which reduce the tension irr the tendon.
Short-term Losses, which include: a Friction losses in ihe tendon b Wedge set or 'draw-in' c Elastic shortening of the structure. These losses take place during stressing and anchoring of the tendon. Lang-term Losses, which include: a Shrinkage of lhe concrete b C a p of the concrete under the effect of fhe prestress c Relaxation of the steel tendon.
Although lhese losses occur over a period of up lo ten or more years, the bulk occurs in the Grsr two years following stressing. The calculation of losses is discussed in more d d l in Appendix B. Secondary effects The secondary effecrs of presmssing are sometimes called 'parasitic effects' but that implies that the effects are unwanted and harmful. This is not in fact the case. For most structures the secondary moment will be a sagging moment and will increase the moments due to applied loads at midspan but reduce the momenrs at the support.
In some structures it is possible lo 'tune' the secondary effecrs by adjusting the shape of the tendon profile to obtain the optimum solution. This is more likely to be of use in the design of beams rather than slabs. Primary prestressing forces and moments are fhe direct result of the prestress force acting at an eccentricity from the section centroid The primary moment at a section is simply the sum of the producc; of each lendon force with its eccenuicity; h e primary shear is the sum of transverse componenls of the tendon forces and the primary axial load is the sum of rhe axial components of lhe tendon forces.
When an element of a structure is prestressed its s h a p changes. It will always shorten, and will bend if the cenuoid of the prestress force does not coincide at all positions with the section centroid.
It is possible, however, to select a tendon profile which results in no rotation of the elemenl ends. If the element is part of a statically determinate structure then lhese changes in shape will not affect the distribution of forces and momenls Figure Unstressed element on supports Unstressed isolated element Stressed element still compatible with supports Figure Restressed element as part of a statically determinate structure But when the element forms part of an indeterminate suucture, the changes in shape resulting from prestressing will modify the support reactions.
Additional reactions are required to make h e prestressed member pass through support points and have suitable orientxion where appropriate Figure Figure Reactions on a prestressed element due to secondary effects These secondary reactions result in secondary forses and moments in the members. These are typically consrant axial and shear forces throughout a span and uniformly varying moments. The calculation of these secondary effects can be difficult when staged construction, creep and shrinkage are considered.
Note hat secondary effects cannot develop in cantilevers as they are statically determinate. Methods of calculating secondary effects are given in Appendix D. Equivalent loads will automatically generare'the primary and secondary effects when applied Lo the structure.
Seniceability calculations do not require any separation of the primary and secondary effects, and analysis using the equivalent loads is suaightfonvard. However, at Ultimate Limit State the two effects must be separated because the secondary effects are treated as applied loads. The primary prestressing forces and moments must therefore be subtracted from the equivalent load analysis to give the secondary effects. To calculate the ultimate loading oii an element, rhe secondary forces and moments are combined with the ultimate forces and moments horn dead and live loads.
The Handboak to BS8llO'"', suggests that the partial load factor on secondary effects should b 1. The total ultimate moments can be redishibuted in accordance w t e ih BS Pan 1, Section 4. The bending moments calculated from the critical loading conditions given in Section 6. One-way spanning floors Bonded tendons: The maximum allowable concrete compressive and tensile stresses for floors with bonded tendons are given in BS, Pan 1, Section 4.
Most buildings will be satisfactory as Class 3 suuctures and thenature of the loading must be considered when deciding on a 0. Unbonded tendons: The maximum allowable concrete compressive stresses in floors with unbonded tendons are as for floors with bonded tendons and are given in BS8ll0.
Part 1, Section 4. The maximum concrete tensile stresses should be taken as those given for group b in Table 4.
These values must be adjusted for section depth as given by Table 4. If the suesses are enhanced by increasing the un-tensioned reinforcement as is allowed for bonded rendons in BS"'. All concrete tension shall be canied by untensioned reinforcemenr see Section 6. Flat slabs two-way spanning Flat slabs may be analysed in either of two ways. The more common method is to analyse equivalent frames in each direction. In this case some account must be taken of rhe peaking of the moments at the columns, described in Section 2.
The analysis results in moments and stresses averaged across the width of the panel. The stresses should be limired to those given in Table 2. Grillage or finite element analysis may be used, but this is normally only justified with floors of unusual configuration or where a design is f be constructed many o times, such as in a high-rise building.
If such analytical techniques are used which take into account the distribution of moments and suesses across a panel, then the allowable stresses given for one-way spanning floors may be used.
Particular care must be taken in modelling the columnlfloorintersection and in the interpolation of the results obtained. Allowable average stresses in nat slabs, hvo-way spanning , analysed using ille equivalent frame method. Bonded reinforcement may be either bonded tendons or un-tensioned reinforcement. In Table 2, the support zone shall be considered as any part of the span under consideration within 0 2 x L of the suppon, where L is the effective span.
Outside of this zone is considered to be the span zone. Additional designed un-tensioned reinforcement is required in the suppon zone ofall flat slabs, and in the span zone oE slabs using unbonded tendons where the tensile stress exceeds 0. The design of this reinforcement is presented in Section 6. These are likely to be more onerous for floors with high imposed loads.
Un-tensioned reinforcement shall be calculated in a similar manner u the , reinforcement for the Serviceability Lirnit'State see Section 6. One-way spanning floors BS, Part 1. Flat slabs two-way spanning The allowable sh'esses given in Table 2 for the Serviceability Limit State also apply lo the transfer condition for slabs analysed using the equivalent Erame method, o however, h should be substituted by f,. F r slabs analysed by the grillage or finite element methods, the allowable suesses are those given for one-way spanning floors.
In this condition, the factored dead and applied loads are considered together with the secondary effects of the prestressing see Section 6. The primary prestress effectr are considered as pan of the section strength.
Additional un-tensioned reinforcement may be required in order to generate an adequate moment capacity. BS , P r 1, Section 4. In the above Section, equation 52 for unbonded tendons has been developed from the results of tests in which the stress in the tendons and the lenglh of the zone of inelasticity in the concrete were both determined. The floor is considered to develop both elastic and inelastic zones and the length of the inelastic zone is taken to be 10 x the neutral axis depth.
The extension of the concrete at the level of the tendons is assumed to be negligible in the elastic zones and the extension in the inelastic zone is assumed to be mken up uniformly over the length. This is discussed further in references 29 and Hence, for a simply supported flwr there is only one inelastic zone associated with the failure, but with a continuous floor the numbee of inelastic zones required for failure is more complex see Figure The length of tendon.
I, in equation 52 can be modified, bearing in mind that if the tendon does not continue the full length of the continuous floor it may not include all the inelastic zones necessary for failure. It is therefore prudent to assume no more than one inelastic zone per span, and no more than two inelastic zones for the full length.
In unbonded memters there is also the risk that if tendons are severed accidentally there will be a 'progression' of failure for the full length of the lendons. This is pasticularly relevant for one-way spanning members such as beams. In the case of one-wa , members where horizontal progressive collapse is of concern, it is necessary to reiiiforcewiihun-tensionedsteel.
Pan 1, Clause 2. Reinforcement should be in accordance with normal BS8llO limits and arrangements. Experimental and practical evidence in the USA has established that this problem does not occur in the iniernal bays of flat slabs due to the overall 'plale' or membrane action.
The possibility of horizontal progressive collapse of edge and comer panels of flat slabs must be considered These panels should be supponed for the situation where the tendons parallel to the edge have been severed.
This support can typically be provided by bonded reinforcement in the panel or an edge beam. Ail locations in me-way spanning flwrs where transfer stresses exceed 0.
Support zones in all flat slabs. Span zones in flat slabs using unbonded tendons where the tensile smss exceeds 0. The reinforcementshall be designed for the soesses ar Serviceability Limit State, both afler all prestress 1osses. It shall be placed in the tensile zone, as near as practicable to the outer fibre see Section 7.
Under mnsfer conditions any designed reinforcement is likely t be on the opposite face to thar o required after all losses. At Ultimare Limit State, additional un-tensioned reinforcement may also be required see Section 6. Any reinforcement provided for the Serviceability Limit State may also be used in the calculation of the moment capacity at Ultimate Limit Stare.
The designed reinforcement shall be checked against the minimum requirements given in Section 6. One-way spanningfIoors Bonded tendons: There are no minimum un-tensioned reinforcementrequirement5 for one-way spanning floors with bonded tendons. It is considered that these flwrs have sufficient tendon-to-concrete bond to distribute flexural cracking.
Care should be taken to ensure sufficient reinforcement is provided to guard against cracking before stressing, if early phased suessing is not employed.
Unbonded tendons: One-way spanning floors with unbonded tendons should have minimum reinforcement in accordance with BSgllO, Part I, Table 3. This reinforcement should be spread evenly across the full width of slab in accordance with the spacing rules given in BS, Pan 1.
Section 3. Flat slabs two-way spanning A 1 flat slabs shall have minimum un-tensioned reinforcement at column positions to 1 dismbute cracking. The cross-sectional area of such reinforcement shall be at least 0.
WO75 x AJ, and shall be concentrated between lines that are 1. The reinforcement shall be placed as near as practical to the top of the nwr, with due regard for cover and tendon location, and shall exrend at least 0.
The maximum pitch of the reinforcement should be 3Wmm. In the span zone, there are no minimum requirements. However, when unbonded tendons are used it would normally be necessary to provide designed un-tensioned reinforcement in the hotlam of the slab see Section 6.
This reinforcement should extend at leas1 to within a distance of 0 2 x L, measured from the centre of the support It should be placed at a spacing of 3 x slab thickness or mm, whichever is the lesser. Slab edges Un-tensioned reinforcement should be placed along edges of all slabs. This should include U-bars laced with at least two longitudinal bars top and bottom, as shown in Figure See also Section 6.
Reinforcement should k provided in the triangular unstressed area between anchorages. Section 4'" should be used. Where unbonded tendons are used, the value of v, in equation 55 of BS'41should be reduced by a factor of 0.
The working party considered a number of-different methods while preparing this handbook, with a view IO satisfying the following aims:.
Design capacities to be in line with other international standards. Increased punching shenr capacity for bonded tendons. Increased punching shear capacity when tendons are concenhated in the vicinity of the column. A design method which complements BS '4' as far as possible.
A design method which allows a smooth transition from reinforced concrete to prestressed concrete and allows for situations where the slab is prestressed in one direction only. The following method achieves these aims and is recommended. The shear resistance, V. The shear resislance of each side of the critical perimeter should be calculated in accordance with BS, Clauses 4.
Fiat slabs are generally not heavily prestressed and will therefore be governed by the design for "sections cracked in flexure", using equation 55 BS, clause 4. Equation 55 does not, however, provide a smooth transition from reinforced to prestressed concrete because of the term:. For lighrly presuessed structures the inclusion of this term in equation 55 can lead to a shear capacity less than that which would be calculated for the same slab but without prestress.
This is obviously incorrect The British Cement Association I1 has recently compared various forms of shear calculation with published test results and concluded that equation 55 would be more consistent with the test results if the above term were omitted. It is thaefore recommended that the shear resistance of each side of the critical perimeter be calculated from equation 55 moditied'as follows:. The value of v, should be calculated taking into account both A, and A,, for bonded tendons in accordance with BS Clause 4.
However the presence of unbonded tendons should be neglected in this calculation of v,. No further reduction is considered necessary e. The de-compression moment, M,,, should be calculated for the width of the side of the critical perimeter under consideration. Hence the two contributions to M, have to k calculated separately as follows for a hogging moment region :.
If tendons are terminated at the edges of large openings, such as at stairwells, an analysis should be made to ensure sufficient strength and proper behaviour. Edges amund openings may be reinforced similarly to conventionally reinforced slabs: in the case of large openings, supplementary post-tensioning tendons may be used to strengthen the edges around openings.
Anchorage bursting reinforcement Reinforcement is usually required to resist the tensile suesses caused by the concenlrauon of the forces applied at the anchors. At some distance from the edge of the floor or the anchorages it can be assumed Ihat the distribution of stresses is the classic linear distribution and depends only on the magnitude and position of the resultant of the forces applied to the edge of the flwr.
Betwen the edge and the above plane the lines of force are curved and give rise to transverse tensile suesses in both directions perpendicular to the applied force direction.
Figures 36 and 37, adapted from reference 18, illusbate the varying proportions of the presoessing force manifesting itself as a splitting tensile force of magnitude depending on the anchorage and floor relative geometries. Where a group of anchorages exist, as is often the case for 'banded' slab tendons. Care should also be taken to ensure that the phasing of the application of prestress to anchorage groups does not create a bursting condition which may be critical.
If this condition is unavoidable, reinforcement should be added accordingly. BS, Part 1. Section 4. At Ultimate Limit State for unbonded tendons only, reinforcement requirements should be checked in accordance with BS, Clause 4.
This Ultimate Limit State check is unlikely to be governing. Where anchorages are grouped, or where the distribution of anchorages does not reflect the distribution of concrete in the cross-section, it may be necessary L include o 'equilibrium' reinforcement to prevent splitting between anchorages. Also when anchorages occur within the plan area of the floor rather than at the perimeter, it may be necessary u, include 'following' reinforcement This reinforcement runs parallel to the tendon past the anchorage to limit cracking adjacent to the anchorage.
Post-tensioning system suppliers often test their anchorage systems in concrete prisms. Such tests may be deemed under BS, Part 1. Section 2. Two examples showing the calculation of, and the detailing of, bursting reinforcement are given in Appendix E.
Reinforcement between lendon anchomges Figure 43 shows an area of slab between tendon anchorages which require reinforcement to span the unstressed zones. Any presuessed tendons which pass through this zone, parallel to the slab edge, may be included with the relevant rcinforccmcnt, provided it is in the local tension zone.
This reinforcement should be evenly disnibuled across a width equal to 0. The area of reinforcement placed perpendicular to the slab edge should be the greater of 0. It should be placed evenly between anchorages, and extend the greater of I, or 0. Deflection This is a Serviceability Limit State relating to the complete structure.
The deflections of a structure, or of any pans of a structure, should not adversely affect appearance or performance. The final calculated deflection including the effects of tempmure, creep and shrinkage, and camber , measured below the line between the supports of the flwr and roof, should not in general exceed s p d 5 0.
In addition. Vibration Prestressed flwrs are usually thinner or span funher than unpresuessed floors. They herefore lend to have lower natural frequencies and greater consideration must be given to their dynamic performance. The Steel Construction Institute has published a design guide on the vibration of floorsm'.
This guide covers sources of vibration excitation in buildings. Although it was written primarily for checking the acceptability of lightweight concrete composite floors on steel beams, most of the guide is relevant for any floor system. Appendix G gives a procedure, based on the guide for checking presnessed flwrs with a rectangular grid.
Vibration should not k a problem for general office buildings if the total slab depth is greater or equal to the values given in Table 1. For more sensitive locations, or for slabs shallower than the above criteria.
Lightweight aggregate concrete Additional considerations on the use of lightweight aggregate concrete are given in BS, Part 2, Section 5'4', and the Guide to the Structural Use of Lightweight Aggregate Concretem1. The allowable tensile stresses given in Sections 6. In BS, Part 2, Clause 5.
These values are 0. X times the values given for normal weight concrete. In the view of h e Working P r y h e Limitations for normal weight at concrete, the lesser of 0.
These are discussed in Section 2. It is therefore recommended that a minimum of two tendons should pass through this section. For ribbed slabs or beams, the dishibution of tendons is dictated by the spacing of members. Tendon s g The maximum spacing of uniformly distributed tendons should not exceed six times the slab depth for unbonded tendons or eight times the slab depth for bonded tendons. Unbonded tendons may be placed in groups if required.
It is recommended that grouped tendons are laid side by side and do not exceed four lendons per group. The minimum horizontal distance between ducts or groups of tendons shouid be the greater of 75mm or the gmuplduct width. Should it be necessary to arrange the tendons in vertical layers in beams or ribs, then it is recommended that the gap between the layers should be at least the venical dimension of the lendon or duct In the case of bonded tendons where oval metal ducts are used, it is recommended that their positions are staggered to ease the placing of concrete.
If tolerances on tendon pasitions are not staled, the values in Table 3 should be adopted. Tendon notation The accepted standard notation or tendons on drawings is shown in Figure It is recommended that this legend Figure is included on all tendon layout drawings. Note: When more than one symbol appears on a tendon group the number o f rtrandr equal the rum o f the symbol derignarionr. Figure Method of notation for use on tendon layout drawings. Figure 39a shows an example using the legend showing groups of tendons and anchorages types, together with the tendon sequence, detailed.
This Figure is based upon reference 24 modified along Lines recommended in this document. Tendon profiies in the longitudinal and transverse directions are shown using an exaggerated scale for the vertical dimensions. These are usually given from the soffit of the slab to the centreline of the ducvsheath and are plotted at intervals of lm. Closer centres may be necessary for sharp vertical curves. For ease of placement on site, shop drawings are detailed giving the vertical tendon position from soffit m underside of tendon.
It is therefore recommended that the support centres do not exceed lm. For ribbed stabs or beams, support bars can be adequately held by f wire ties. Spot welding can be used but m this makes any adjustment difficult. Figure 39b shows a typical support bar layout. The actual layout may be modified by the contractor depending on the support system adopted, so that the specified tendon profiles are attained and adequate suppon is provided.
Note: 1. Height given is from soffit of slab to underside 2. Diameter of support bar is 10mm. Typical tendon pmfie and support bar layout for a flat slab. Layout of un-tcmswned reinforcemni Figure 40 shows an example of the reinforcement that is always required at edges and in the top of flat slabs at columns. It also shows the reinforcement needed in the boaom of the slab at midspan for some design applications. S e Section 6. At columns Reinforcement should be placed in the Lop of the slab over columns.
The design of such reinforcement is described in Section 6. Figure 41 shows a typical arrangement of tendons and un-tensioned reinforcement amund a column. Figure Reinforcement arrangement a t a column. Shear reinforcement Shear reinforcement in flat slabs. Fabricated steel shear heads may also be used. See Figures 41 and'42 and Section 6. At a n d between anchorages An adequate amount of reinforcement should be placed at anchorage end blocks to avoid splitting of the concrete.
A sample calculation m determine the amount of this reinforcement is given in Appendix F. Reinforcement should be provided in the 45" wedge area between the anchorages Figure The change of direction of the tendon should occur away from the opening, and trimmer bars should be provided to avoid possible cracking at the comers. Figure Unbonded tendons diverted around an opening.
The oval sheathing used in bonded tendons is very rigid in the transverse direction, and cannot be bent around openings. In this instance, openings should t confined to e the areas between tendons.
Gmuted tendons, providing the gmut is effective, can be cut without significant loss of prestress. However, when unbonded tendons have been used, care must be taken to lotate the tendons before concrete removal. Tendons can be cut and reinstated but it is recommended that this work be carried out by a specialisr. Extent of pours With bonded tendons, friction losses usually restrict fhe length of single end stressed tendons to 25m, and double end stressed to 5Om.
The lower friction values for unbonded tendons extend these values to 35m and 70m respectively. Longer lengths are achievable but the friction losses should be carefully considered. These limitations usually determine the extent of pours. Prestressing tendons may be continuous thmugh construction joints allowing larger areas without any permanent joints. Allowances should be made in accordance with good practice to accommodate temperature variations by the provision of expansion joints on larger slabs.
Consmction joints Generally consmction joints should be made in the vicinity of quaner and third points of the span from supports. Shear provision in accordance with good practice should be made by the introduction of expanded mesh, by roughening the previously poured surface or by the introduction of a shear key. In long slabs, intermediate anchorages may be introduced which allow the stressing to be continuous through the construction joint see Figure Alternatively infill skips can be used, but it should be noted that fhese will nor be prestressed.
These suips are cast after the stressing of the adjacent sections is complete see Figure This operation should be delayed for as long a period as is reasonable to reduce the effects of creep and shrinkage.
Figure Infill rip for jack access. In assessing the movement of slabs at expansion or confraction joints from the time of polning concrete, a strain of x 10"should be. The drying out effect of air conditioning can increase this to 1WO x lo4. Generally dowels should be avoided in slabs saessed in two directions.
Protection qf anchomges Tendons are normally anchored within the middle third of the slab to ensure adequate edge cover to the anchorage. Pocket fonners at anchorages should be large enough lo allow adequate trimming of the tendons after stressing, thus ensuring good end cover to the sirand.
Trimming should be. In no circumstances should the tendon be trimmed by flame cutting. Pocket formers are normally proprietary plastic or polystyreneinits which make up part of the anchorage fuings. Our customer product and service solutions span four major areas of information: energy, product lifecycle management, environmental and security.
By focusing on our customers first, we deliver data and expertise that enable innovative and successful decision-making. Customers range from governments and multinational companies to smaller companies and technical professionals in more than countries. IHS has been in business since and employs more than 3, people in 35 locations around the world.
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