Prestressed Concrete Design [CBDG]

CBDG Design Guide

Prestressed 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, structure, increasing the load carrying carrying capacity and durability of the concrete. 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 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 i s 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 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.

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CBDG Design Guide Precast members will generally be pretensioned with tendons bonded to the concrete, or used in segmental construction where members are formed from precast segments, which are subsequently stressed together. Precast segmental structures in the UK have to use external tendons because of doubt s over the efficacy of the duct joints between segments. In situ members will be  post-tensioned with either bonded or unbonded tendons. Table 2 lists factors affecting the choice of bonded or unbonded tendons. When a concrete member is prestressed it will deflect and shorten. If the tendon profile is such that th e deflected shape of the isolated member is compatible with the restraints acting on the member, the profile is said to be concordant. This will always  be the case for a statically determinate member. However, tendon profiles in statically indeterminate members will not generally be concordant.

Table 1 Comparison of pre- and post-tensioning Type of construction

 Ad van tag es

Dis adv ant ages

Pretensioned

no need for anchorages

heavy stressing bed required

tendons protected by concrete without the need for grouting or other protection

more difficult to incorporate deflected tendons

prestress is generally better distributed in transmission zones Post-tensioned

no external stressing bed required

tendons require a protective system

more flexibility in tendon layout and profile

large concentrated forces in end blocks

draped tendons can be used easily

When the tendon profile is concordant, 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. These are the primary prestressing forces.

Table 2 Comparison o f bonded and unbonded const ruction Type of construction

 Ad van tag es

Dis adv ant ages

Bonded

tendons are more effective at the ultimate limit state

tendons cannot be inspected or replaced tendons cannot be re-stressed once grouted

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

less efficient at ultimate limit state

reduced friction losses

relies on the integrity of the anchorages and deviators

generally faster construction

effects of any damage are more widespread

tendons can be re-stressed

less efficient in controlling cracking

thinner webs

When the tendon profile is non-concordant, additional forces and moments will be induced in the member during prestressing  by the restraints acting on it. These are known as the secondary or parasitic effects. Other common nomenclature associated with prestressed concrete is defined in Fig. 2.

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CBDG Design Guide

Concrete is stronger in compression than in tension. Prestress is introduced to pre-compress the areas of concrete, which would otherwise be in tension under service loads. The concrete section is therefore stronger and behaves more as a homogeneous section, allowing elastic methods of analysis to be used, although the concrete compressive stresses can be high. When the tendons are bonded to the concrete, their high ultimate strength can be mobilised, which generally means that the ultimate flexural capacity of a prestressed concrete member is much greater than the applied ultimate design moment. Therefore, limiting the maximum compressive stresses and crack widths under service loads is generally critical in the d esign 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. Therefore, flexural design is normally carried out at the serviceability limit state and then checked at the ultimate limit state. Shear design is carried out at the ultimate limit state. 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;

•

losses due to friction, and

•

wedge slip in the anchorages.

The value of the prestressing force will continue to reduce with time due to: •

relaxation of prestressing steel;

•

creep of the concrete

•

shrinkage of 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, and in service, after all losses have occurred. Prestress can be considered as a load or as a resistance. At the serviceability limit state, it i s normally considered as a load whilst, at the limit state, it is considered as a combination of a load and a resistance. When considered as a load, 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. Such an analysis automatically takes account of both primary and secondary effects. When prestress has been considered as a load, the contribution of prestressing tendons to the resistance of a section is limited to their additional strength beyond prestressing. This can be calculated by assuming that the origin of the stress-strain relationship of the tendons is displaced by the effects of prestressing. For bonded tendons, this is illustrated in Fig. 3. The o rigin of the stress-strain relationship is taken as being at point A, corresponding to a prestress force, Pt, and the contribution of the tendons to the resistance of the section is ∆f  pA p. When the whole of the prestress is considered as a resistance, the origin is taken as point B.

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CBDG Design Guide For unbonded and external tendons, the additional strain in the tendons, ∆ε p, is determined taking into account the deformations of the concrete member

Pt

=  prestressing force at time t

E p

= Young's Modulus of tendons

A p

= area of tendons

ε p0

= the mean strain in the tendons at the time they are bonded to the concrete, (i.e. the initial strain in the tendon, allowing only for losses due to friction and draw, + ∆ε p0)

∆ε p0

= 0, for pretensioned members; = the strain in the concrete due to stressing the tendon (or to stressing the first tendon when a number of tendons are stressed successively), for post-tensioned members

∆ε p

= the additional strain in the tendons (i.e. the tensile strain in the concrete at the centroid of the tendons).

∆f   p

= the additional stress in the tendons

f  p

= 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, some of which are listed at the end of this chapter of the Design Guide. The following sections give advice and information on particular aspects of the design of  prestressed concrete bridges.

Prestressin g wi th External Tendons [Section to be written giving advice of details /materials for sheathing, grouting, strategies for replacement of tendons] [Photograph of bridge deck with external tendons]

Segmental Constructi on [Section to be written describing the issues to be considered in prestressed concrete segmental bridge design, e.g. design methods for glued and dry joints, continuity of sheathing across joints between segments, commonly used methods of erection, staged transfer of dead load from falsework to prestressed section (see also ref 3 below)]. [Include photograph of segmental bridge and diagrams as appropriate]

Precast Beams [Section dealing with stability issues during transport, erection & casting of deck concrete – what loads should be allowed for, etc.]

End Block Design [Section explaining the principles of end block design using “strut-and-tie” models and bending theory. When each methods is appropriate. Particularly good references should be reviewed and included in the list of references at the end of this chapter.] [Include photographs of good and (if possible) bad end block detailing]

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Precast Shells and Composi te 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, prestressed concrete provides one of the most versatile materials to design and construct with. Unusual shapes and structural arrangements may be readily adopted with either insitu or precast constructions, while using prestressed concrete allows the designer to adopt more slender and longer spans than would be possible with just reinforced concrete construction. Prestressing is used in many different way in bridgeworks. It can be in the form of longitudinal tendons to cater for the longitudinal moments and shears in a deck or column, or as transverse tendons prestressing the top slab of a deck to cater for the local wheel loads. Occasionally it is also used as vertical prestress to enhance the deck web shear capacity or to distribute forces with-in the deck diaphragms. Often contactors will use the prestressing in the temporary condition to support the bridge during the construction stages. For the innovative designer its uses are endless, although it must be said that in general the British designers do not use prestressing as often as French and other continental designers. 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. However, in practice the design is more complex than for simple reinforced concrete and the interaction between the structural behaviour, the concrete properties and the prestressing tendons has to be carefully considered by the designer. The  prestressing force causes the concrete to creep while the creep and shrinkage in the concrete reduces the force in the prestress. The prestress secondary moments, sometimes referred to as parasitic moments, may also be redistributed by creep within the concrete and the designer has to combine all these effects into the design. With prestressed concrete bridges, the designer must always take into account the construction sequence and the way the  bridge is going to be built. This quite often has more influence on the prestress tendon arrangement and profile than do the forces and moments applied to the sections. With balanced cantilever construction the prestress tendons are arranged in groups of cantilever and continuity tendons. 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. 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. When choosing which type of prestressing to use, whether it be strand, wires, bars, internal or external, the designers decision is usually based on economics, ease of construction and maintenance. Strands are usually the cheapest type of prestressing tendon when considered in terms of £ per kN o f force, while prestressing bars can be simpler to install, especially for short lengths. External tendons can simplify concreting and reinforcement fixing as well as future inspection and maintenance, but internal tendons are usually less expensive and offer a greater level of protection against accidental damage. The design process that the designer uses for concrete bridges depends on the type of prestressing used. For internal tendons, the design of the prestress is usually g overned by the SLS conditions. The prestress quantity and layout needs to ensure that the stresses within the structure are within the acceptable limits. In this case, the ultimate moment capacity is not usually critical while the shear design is usually a case of having sufficient concrete width and depth, and adequate reinforcement. With external tendons the longitudinal design may be governed by the ULS condition. The amount of prestress needed at any section is dictated by the Ultimate Moments applied with the SLS stresses usually less critical. Designers have a range of software available to them for the analysis of prestressed concrete bridges. 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. Creep and shrinkage of the concrete and friction, draw-in and other prestress losses should also be modelled within the analysis. Software programmes that combine all of these aspects include ADAPT, RM2004, Sofistik, LARSA and Midas. Other software is also available and as the power of computers increase, even the most complex of structures can be analysed in a short time. 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, prestressed concrete has its own set of detailing rules that need to be carefully followed. Space within the concrete is needed for the anchorages and couplers and the extra reinforcement associated with these areas. The required duct spacing and cover is dependent on the force in the tendon and the tendon radius. The structure must also  provide sufficient room to locate the jack and stress the tendons. Ducts clashing with reinforcement can challenge both the detailer and site team. 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, 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. Where external tendons are employed, there should be good access for inspection and for moving the equipment for restressing and grouting around.

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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. Where a project warrants the use of precast concrete, prestressing often simplifies the construction details across the connections. By prestressing the connection the need for insitu connections and complex reinforcing details can be minimised, or eliminated. 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 o f 330m. This shows that  prestressed concrete can rival steel and arch construction for spans up to this length, 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.

Recomm ended Sources of Reference for Prestressed Concr ete Bridge Design  A Gui de t o t he Desig n o f Anc ho r B lo cks for Post-t ens io ned Prestr essed Co ncret e, Gui de No . 1, CIRIA,

London

1976. John L Clarke Provides guidance on the flow of forces and the calculation of reinforcement in end blocks of post-tensioned construction. Prestressed Concrete Bridges, Birkhäuser, Christian Menn

General text on prestressed concrete bridge design. Section 4.6.4 discusses detailing to resist local forces from curved tendons (in curved or straight bridges). Chapter 7 is devoted to the design and construction of special bridges and section 7.6 is  particularly helpful in covering the design of curved prestressed concrete girders. Standard Method of Detailing Structural Concrete, The Institution of Structural Engineers & The Concrete Society, 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. Concrete Box Girder Bridges, Jorg Schlaich & Harmut Scheef.

This book contains good practical examples which are linked with theory. FIP Handbook o n Practical Design .

This book gives practical examples of the design procedures for a variety of prestressed concrete bridges Design of Bridges with External Prestressing, A.F.Daly & P.Jackson

[commentary still to be written] Collection of papers on external prestressing, M.Virlogeux

[precise references and commentary to be provided] Concrete Bridge Construction (?), W.Podlony

This book is very helpful in discussing important construction details which the designer should take into account when developing his designs.

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