A New Concept For Prestressed Concrete - PCI

A new conceptfor prestressed concrete By T. Y. Lin*IntroductionWhen prestressed concrete wasfirst conceived, essentially by EugeneFreyssinet of France, it was visualized as the transformation of a brittle material into an elastic material.Concrete which is weak in tensionand strong in compression was precompressed by steel under high tension so that the brittle concretewould be able to withstand tensilestresses. Thus prestressed concretewas dealt with in terms of internalstresses, with "no-tension" being thegeneral criterion for design and construction. This approach might properly be termed the "stress-concept.'As prestressed concrete becamewidely produced and adopted, asecond concept was formulated,commonly known as the ultimatestrength theory. Under that concept,prestressed concrete is treated as acombination of h\Ph strength concrete and high strength steel, withconcrete to carry the compressionand steel to carry the tension. Design formulas and code requirementswere proposed as a result of that"strength-concept", and they werebasically similar to those of conventionally reinforced concrete.More recently, a third concept hasbeen developed, chiefly by the author, but undoubtedly also utilized0Professor of Civil Engineering,University of CaliforniaAs published in the Australian Constructional Review, Sept. 1961.36by other engineers. In the overalldesign of a prestressed concretestructure, prestressing is primarilyintended to balance a portion of thegravity loads so that flexural members, such as slabs, beams and girders, will not be subjected to flexuralstresses under a given loading condition. This transforms a memberunder bending into a member underaxial stress and thus greatly simpifiesthe design and analysis of otherwisecomplicated structures. For convenience in discussion, we will termthis the "balanced-concept."Life-History of Prestressed MemberUnder FlexureThe life-history of a pre-stressedmember under flexure is brieflyshown in Fig. 1. There are severalcritical points as follows:1. The point of no-deflection2.3.4.5.which usually indicates a rectangular stress block across allsections of a beam.The point of no-tension whichindicates a triangular stressblock with zero stress at eitherthe top or the bottom fiber.The point of cracking whichgenerally occurs when the extreme fiber is stressed to themodulus of rupture.The point of yielding at whichthe steel is stressed beyond itsyield point so that ·complete recovery will not be obtained.The ultimate load which represents the maximum load carPCI Journal

LOADINGS AT VARIOUS STAGESGL GIRDER LOADDL DEAD LOADLL LIVE LOAD---------"U!!J.L-"!!TIMATEk 1DL LLJ - - 10 t0.Jf----CRACKINGDL LLDL--GL---CAMBERDEFLECTIONFig. 1-Life history of a prestressed member under flexure.ried by the member.If the load deflection or the moment-curvature relationship is of adefinite shape, it is then possible todetermine all five of the above pointswhenever one point is known. Actually, on account of the difference inthe shape of the section, the amountand .location of prestressed and nonprestressed steel, as well as differentstress-strain relationships of both theconcrete and the steel, these loaddeflection or moment-curvature relationships may possess widely divergent forms. Thus it is often necessaryto determine more than one of theabove five points in order to be surethat the beam will behave properlyunder various loading conditions.Under the elastic stress concept,the point of no-tension or the pointwith a limited amount of tension istaken as the important criterion. Under this concept, Fig. 2, concrete istreated as an elastic material and afamily of formulas are derived taking the shape ofMeF IDecember, 1961These formulas yield stresses in thebeam under various loading conditions with special emphasis on thedesign live load.Under the ultimate strength concept are developed a second familyof formulas, Fig. 3, taking the shapeofMA.f.jdwhich is the familiar formula for reinforced concrete design. These formulas have also been extended toinclude elastic design by expressingthe internal resisting moment as aT-C couple.The concept of load balancingdeals essentially with the first criticalpoint, in Fig. 1, i.e. the point of nodeflection. Based on this concept thedownward gravity load is balancedby the upward component of theprestressed steel. That upward component can be a concentrated forcefor a sharp bend, Fig. 4, or can be adistributed load for a curved cable,Fig. 5. A third family of formulascan be derived for the computationof these components. Thus for acable with a parabolic curve, wewould have a uniform upward load 37

1 1llIlI1 - -;------------ 1 Concept !-Prestressed concrete as an elastic ma·!erial.Figure 2 I I h FA PRESTRESSING STEEL FeeISTRESS 0MeICOMPUTATIONSrI,Concept 2-Prestressed concrete as a combinationof steel and concrete.Figure 3PORTION OF CONCRETE--),----- J}!cjdT" A,;f, PRESTRESSINGSTEELRESISTING-f ------A-------t-Wi) PRESTRESSING "" PRESTRESSINGCABLEBEAM!MOMENT:Fig. 4-Beam with bent cable.FORCE r- GRAVITY FORCE Vil! i i f-1-l - -L - -L- J Fig. 5-Beam with parabolic cable. CONCRETEBEAM PRESTRESSINGFORCEI PRESTRESSING jSTEELFOR PARABOLICLOAD w,CABLEWITHSAGh, SPAN2F Sh38PCI JournalL,

w, Fig. 5,8Fhw -L2where F the prestressed force, h the cable sag and L the spanlength.If the point of no-deflection, thepoint of non-tension, and the ultimate load are all determined for abeam, its life history is generallypretty well described. If the shapeof the load-deflection relationship isknown, it is necessary only to determine one of these three criticalpoints. For convenience in designand analysis, it is possible to pickany one of the three critical pointsas a control. When properly designed for this controlling criticalpoint, it may not be necessary tocheck for the remaining two criticalpoints.It should be pointed out that fordifferent prestressed elements andstructures, the best control can beobtained sometimes by using onepoint and sometimes by another.Since the behaviour of many elements under their sustained load isoften most significant, it becomes apparent that the criterion of no-deflection could often be the best controlling point.The Loading to be Balancedby PrestressUsing this new concept of loadbalancing, an important question is:what should be the loading to be balanced by the prestress? The answerto this question may not be simple.As a starting point, it is often assumed that the dead load of thestructure or element be completelybalanced by the effective prestress.This would mean that a slightamount of camber may exist underthe initial prestress. In the course oftime, when all the losses of prestressDecember, 1961have taken place, the structure orelement would come back to a levelposition.Although it seems logical to balance all the dead load, such balancing may require too much prestress.Since a certain amount of deflectionis always permitted for a nonprestressed structure under dead load,it is reasonable to also permit a limited amount of deflection for a prestressed one, if it would not becomeobjectionable. However, there is agreater tendency in prestressedstructures to increase their deflections as a result of creep and shrinkage. Hence the deflections should belimited to a smaller value at thebeginning.When the live load to be carriedby the structure is high compared toits dead load, it may be necessary tobalance some of the live load as wellas the dead load. One interesting approach is to balance the dead loadplus one half the live load, ( DL 1/zLL). If this is done, the structurewill be subjected to no bendingwhen one half of the live load is acting. Then, it is only necessary to design for one-half live load acting upwhen no live load exists, and forone-half live load actin

As prestressed concrete became widely produced and adopted, a second concept was formulated, commonly known as the ultimate strength theory. Under that concept, prestressed concrete is treated as a combination of h\Ph strength con crete and high strength steel, with concrete to carry the compression