CBDG Design GuidePrestressed Concrete Design When prestressing was first introduced into bridgeworks in the 1930’s it revolutionised concrete bridges. Prestressing made longer spans and slender decks possible. It is used during the construction and erection of the bridge as well as in the permanent structure, increasing the load carrying capacity and durability of the concrete. Today, prestressed concrete is used for simple supported spans a few meters long to cable-stayed bridges with spans of 500m. It has become the material of choice for medium and long-span bridges and viaducts around the world. The following sections describe the features of prestressed concrete bridges. The advantages and disadvantages are highlighted, and key design issues discussed while the list of references includes the essential reading for any designer of prestressed concrete bridges. Introduction Prestressed concrete is different from ordinary (non-prestressed) reinforced concrete because the tendons apply loads to the concrete as a result of their prestress force, whilst in reinforced concrete the stresses in the reinforcement result from the loads applied to the structure. A proportion of the external loads is therefore resisted by applying a load in the opposite sense through the prestressing whilst the balance has to be resisted by ordinary reinforcement. Prestressing tendons may be internal, i.e. within the concrete either bonded to the concrete or unbonded, or external, i.e. outside the concrete but (generally) inside the envelope of the member, see Fig. 1. It is possible for external tendons to be outside the concrete envelope; as their eccentricity to the centroid of the concrete section increases, the section behaves more as an extradosed cable-stayed structure than a prestressed concrete member and different design rules are appropriate. Prestressed members can be either pretensioned, i.e. the tendons are stressed before the concrete is cast around them and the force transferred to the concrete when it has obtained sufficient strength, or post-tensioned, i.e. sheathing is cast into the concrete to form ducts through which the tendons are threaded and then stressed after the concrete has gained sufficient strength. Table 1 compares the advantages and disadvantages of pre- and post-tensioning. Prestressed Concrete Design Page 1 However. Table 2 Comparison of bonded and unbonded construction Type of construction Bonded Advantages tendons are more effective at the ultimate limit state does not depend on the anchorage after grouting localises the effect of damage Unbonded tendons can be removed for inspection and are replaceable if corroded reduced friction losses generally faster construction tendons can be re-stressed thinner webs less efficient at ultimate limit state relies on the integrity of the anchorages and deviators effects of any damage are more widespread less efficient in controlling cracking Disadvantages tendons cannot be inspected or replaced tendons cannot be re-stressed once grouted When the tendon profile is non-concordant. Prestressed Concrete Design Page 2 .and post-tensioning Type of construction Pretensioned Advantages no need for anchorages tendons protected by concrete without the need for grouting or other protection prestress is generally better distributed in transmission zones Post-tensioned no external stressing bed required more flexibility in tendon layout and profile draped tendons can be used easily tendons require a protective system large concentrated forces in end blocks Disadvantages heavy stressing bed required more difficult to incorporate deflected tendons When the tendon profile is concordant. which are subsequently stressed together. Other common nomenclature associated with prestressed concrete is defined in Fig. the only forces induced at any point in the member by the action of prestressing are an axial compression equal to the prestressing force and a moment equal to the product of the prestressing force and its eccentricity relative to the neutral axis of the member. Table 1 Comparison of pre. or used in segmental construction where members are formed from precast segments. When a concrete member is prestressed it will deflect and shorten.CBDG Design Guide Precast members will generally be pretensioned with tendons bonded to the concrete. These are the primary prestressing forces. This will always be the case for a statically determinate member. Precast segmental structures in the UK have to use external tendons because of doubts over the efficacy of the duct joints between segments. 2. the profile is said to be concordant. In situ members will be post-tensioned with either bonded or unbonded tendons. tendon profiles in statically indeterminate members will not generally be concordant. additional forces and moments will be induced in the member during prestressing by the restraints acting on it. If the tendon profile is such that the deflected shape of the isolated member is compatible with the restraints acting on the member. Table 2 lists factors affecting the choice of bonded or unbonded tendons. These are known as the secondary or parasitic effects. their high ultimate strength can be mobilised. at the limit state. the effects of prestress can be determined by analysing the structure under a system of equivalent loads representing the forces from the prestressing tendons acting on the concrete. It is normal to check the flexural stresses in a prestressed concrete member both when the prestress force is initially transferred to the concrete (at transfer). taking account of the initial losses. Pt. The origin of the stress-strain relationship is taken as being at point A. Prestress can be considered as a load or as a resistance. The concrete section is therefore stronger and behaves more as a homogeneous section. and the contribution of the tendons to the resistance of the section is ∆fpAp. the origin is taken as point B. At the serviceability limit state. allowing elastic methods of analysis to be used. after all losses have occurred. creep of the concrete shrinkage of the concrete. This can be calculated by assuming that the origin of the stress-strain relationship of the tendons is displaced by the effects of prestressing. it is considered as a combination of a load and a resistance. which would otherwise be in tension under service loads. The prestressing force applied to the concrete immediately after tensioning and anchoring (post-tensioning) or after transfer (pretensioning) will be less than the jacking load due to one or more of the following: • • • elastic deformation of the concrete. Prestressed Concrete Design Page 3 . losses due to friction. and in service. Such an analysis automatically takes account of both primary and secondary effects. When the whole of the prestress is considered as a resistance. it is normally considered as a load whilst. 3. and wedge slip in the anchorages. the contribution of prestressing tendons to the resistance of a section is limited to their additional strength beyond prestressing. limiting the maximum compressive stresses and crack widths under service loads is generally critical in the design of prestressed concrete members. although this may not be the case for members with unbonded tendons or members with bonded tendons and large allowable crack widths. For bonded tendons. which generally means that the ultimate flexural capacity of a prestressed concrete member is much greater than the applied ultimate design moment. Therefore.CBDG Design Guide Concrete is stronger in compression than in tension. although the concrete compressive stresses can be high. corresponding to a prestress force. flexural design is normally carried out at the serviceability limit state and then checked at the ultimate limit state. Therefore. Prestress is introduced to pre-compress the areas of concrete. When prestress has been considered as a load. When the tendons are bonded to the concrete. The value of the prestressing force will continue to reduce with time due to: • • • relaxation of prestressing steel. Shear design is carried out at the ultimate limit state. this is illustrated in Fig. When considered as a load. = the additional stress in the tendons = the total stress in the tendons [Insert a paragraph describing partial prestressing with a table listing the advantages and disadvantages] The design of prestressed concrete bridges is described in a number of standard texts. Prestressing with External Tendons [Section to be written giving advice of details /materials for sheathing. the additional strain in the tendons.g. etc.e. for post-tensioned members εp0 ∆εp0 = 0. ∆εp. strategies for replacement of tendons] [Photograph of bridge deck with external tendons] Segmental Construction [Section to be written describing the issues to be considered in prestressed concrete segmental bridge design. grouting. design methods for glued and dry joints. [Include photograph of segmental bridge and diagrams as appropriate] Precast Beams [Section dealing with stability issues during transport. e. + ∆εp0) = the strain in the concrete due to stressing the tendon (or to stressing the first tendon when a number of tendons are stressed successively). ∆εp ∆f p fp = the additional strain in the tendons (i.] End Block Design [Section explaining the principles of end block design using “strut-and-tie” models and bending theory. for pretensioned members. the initial strain in the tendon. continuity of sheathing across joints between segments. is determined taking into account the deformations of the concrete member Pt Ep Ap = prestressing force at time t = Young's Modulus of tendons = area of tendons = the mean strain in the tendons at the time they are bonded to the concrete. When each methods is appropriate. some of which are listed at the end of this chapter of the Design Guide. (i. allowing only for losses due to friction and draw. Particularly good references should be reviewed and included in the list of references at the end of this chapter. the tensile strain in the concrete at the centroid of the tendons).e. erection & casting of deck concrete – what loads should be allowed for. staged transfer of dead load from falsework to prestressed section (see also ref 3 below)]. The following sections give advice and information on particular aspects of the design of prestressed concrete bridges.CBDG Design Guide For unbonded and external tendons. commonly used methods of erection.] [Include photographs of good and (if possible) bad end block detailing] Prestressed Concrete Design Page 4 . the designer must always take into account the construction sequence and the way the bridge is going to be built. Unusual shapes and structural arrangements may be readily adopted with either insitu or precast constructions. The prestress secondary moments. prestressed concrete provides one of the most versatile materials to design and construct with. the designers decision is usually based on economics.CBDG Design Guide Precast Shells and Composite Action [Section discussing appropriate design rules for the design of precast shells filled with insitu concrete and prestressed so that it behaves as a single composite section] [Photograph of Taney Bridge under construction – KRW to provide] The Designers Perspective For the bridge designer. The concept of prestressing is simple in that it is just an external load applied to a section to balance the tensile stresses that occur. The structure must also provide sufficient room to locate the jack and stress the tendons. the ultimate moment capacity is not usually critical while the shear design is usually a case of having sufficient concrete width and depth. Prestressing is used in many different way in bridgeworks. With prestressed concrete bridges. With span-by-span construction the prestress tendons are usually anchored on the construction joints and often have couplers to extend them into the next span cast. Designers have a range of software available to them for the analysis of prestressed concrete bridges. while prestressing bars can be simpler to install. With external tendons the longitudinal design may be governed by the ULS condition. Often contactors will use the prestressing in the temporary condition to support the bridge during the construction stages. The prestress quantity and layout needs to ensure that the stresses within the structure are within the acceptable limits. The amount of prestress needed at any section is dictated by the Ultimate Moments applied with the SLS stresses usually less critical. but internal tendons are usually less expensive and offer a greater level of protection against accidental damage. Software programmes that combine all of these aspects include ADAPT. bars. sometimes referred to as parasitic moments. The required duct spacing and cover is dependent on the force in the tendon and the tendon radius. Other software is also available and as the power of computers increase. or as transverse tendons prestressing the top slab of a deck to cater for the local wheel loads. while using prestressed concrete allows the designer to adopt more slender and longer spans than would be possible with just reinforced concrete construction. wires. Ducts clashing with reinforcement can challenge both the detailer and site team. The prestressing force causes the concrete to creep while the creep and shrinkage in the concrete reduces the force in the prestress. and adequate reinforcement. In this case. When choosing which type of prestressing to use. Where external tendons are employed. Space within the concrete is needed for the anchorages and couplers and the extra reinforcement associated with these areas. There is usually a need to draw up the prestressing tendons and reinforcement in detail to ensure that it all fits within the concrete section. RM2004. the concrete properties and the prestressing tendons has to be carefully considered by the designer. To fully analysis all the aspects of prestressed concrete the software package must be able to handle the stage-by-stage construction that inevitable occurs with this type of construction. Sofistik. Creep and shrinkage of the concrete and friction. LARSA and Midas. there should be good access for inspection and for moving the equipment for restressing and grouting around. although it must be said that in general the British designers do not use prestressing as often as French and other continental designers. Occasionally it is also used as vertical prestress to enhance the deck web shear capacity or to distribute forces with-in the deck diaphragms. Strands are usually the cheapest type of prestressing tendon when considered in terms of £ per kN of force. External tendons can simplify concreting and reinforcement fixing as well as future inspection and maintenance. With balanced cantilever construction the prestress tendons are arranged in groups of cantilever and continuity tendons. For internal tendons. and there is still enough room to get the concrete in! The designer should not forget the need for future inspection and maintenance of the prestressing tendons. internal or external. It can be in the form of longitudinal tendons to cater for the longitudinal moments and shears in a deck or column. For the innovative designer its uses are endless. Prestressed Concrete Design Page 5 . prestressed concrete has its own set of detailing rules that need to be carefully followed. The design process that the designer uses for concrete bridges depends on the type of prestressing used. This quite often has more influence on the prestress tendon arrangement and profile than do the forces and moments applied to the sections. may also be redistributed by creep within the concrete and the designer has to combine all these effects into the design. even the most complex of structures can be analysed in a short time. the design of the prestress is usually governed by the SLS conditions. whether it be strand. ease of construction and maintenance. in practice the design is more complex than for simple reinforced concrete and the interaction between the structural behaviour. especially for short lengths. However. The designer should always be aware that all of these programmes have limitations and a certain amount of interpretation and approximation is still needed to end up with the right answers! As with all forms of bridgeworks. If a bridge deck is fully cast before the prestress is applied then the prestress may consist of single tendons extending from one abutment to the other. draw-in and other prestress losses should also be modelled within the analysis. prestressing often simplifies the construction details across the connections.F. M. CIRIA. John L Clarke Provides guidance on the flow of forces and the calculation of reinforcement in end blocks of post-tensioned construction. Where a project warrants the use of precast concrete. Standard Method of Detailing Structural Concrete. Jorg Schlaich & Harmut Scheef. The Institution of Structural Engineers & The Concrete Society.Jackson [commentary still to be written] Collection of papers on external prestressing. The longest free span in the world for a concrete box girder is currently Stolma Bridge in Norway with a main span of 301m although the Shibanpe Bridge in China currently under construction will have a main span of 330m. Prestressed Concrete Bridges. 1. This shows that prestressed concrete can rival steel and arch construction for spans up to this length. Section 4. Prestressed Concrete Design Page 6 . Guide No. This book contains good practical examples which are linked with theory. Birkhäuser.CBDG Design Guide One of the main advantages of prestressing is the improved long-term durability of the structure by reducing or eliminating cracking within the concrete and a designer can make use of this in vulnerable parts of the bridge. Recommended Sources of Reference for Prestressed Concrete Bridge Design A Guide to the Design of Anchor Blocks for Post-tensioned Prestressed Concrete. London 1976.6 is particularly helpful in covering the design of curved prestressed concrete girders. By prestressing the connection the need for insitu connections and complex reinforcing details can be minimised. Chapter 7 is devoted to the design and construction of special bridges and section 7.Virlogeux [precise references and commentary to be provided] Concrete Bridge Construction (?).6. FIP Handbook on Practical Design. Concrete Box Girder Bridges. 1989 Chapter 7 deals with prestressed concrete and discusses succinctly a number of issues which should be considered when designing and detailing prestressed concrete bridges. or eliminated. This book gives practical examples of the design procedures for a variety of prestressed concrete bridges Design of Bridges with External Prestressing.4 discusses detailing to resist local forces from curved tendons (in curved or straight bridges). A.Daly & P. W.Podlony This book is very helpful in discussing important construction details which the designer should take into account when developing his designs. Christian Menn General text on prestressed concrete bridge design. while with cable-stayed bridges it is common to find prestressed concrete being the material of choice for the deck with spans up to 450m.