PROCEEDINGS PAPER Design and Uses of Prestressed Concrete Columns by Raymond Itaya* SYNOPSIS At the present time, criteria for the design of prestressed concrete columns are not included in the PCI Building Code Requirements nor the ACI Build- ing Code Requirements for Reinforced Concrete. The PCI Prestressed Con- crete Column Committee has been studying the behavior of prestressed concrete columns for nearly two years. This paper attempts to summarize the knowledge to date and outline an approach to the design of prestressed concrete columns. INTRODUCTION cant when bending predominates9 Since columns are generally con- (Fig. 1) . Prestressing yields a homo- sidered as members under compres- geneous member with reliable buck- sion, it might first appear that there ling capacity which is important for is no justification for putting com- slender columns. For precast col- pression into the concrete by pre- umns subjected to transportation and stressing. Upon closer examination, erection stresses, prestressing sup- however, columns are very often sub- plies a higher resistance to cracking jected to tensile stresses when bend- during handling. It is therefore clear ing moments due to wind and earth- that prestressed concrete columns quake forces, eccentric loads, or will be found useful under many frame action are applied to columns. conditions. Figs. 2 and 3 illustrate Prestressing columns then can be the use of such columns where con- considered as an extension of ordi- ventional reinforced columns would nary reinforced concrete columns have been uneconomical, if not im- where reinforcing steel is used to possible. Several possible types of pre- resist tension. Prestressing introduces additional stressed concrete columns should be advantages to concrete columns. It considered. Aside from the fully pre- transforms a cracked section into a stressed concrete columns, the com- non-cracked one, thus enabling the bination of prestressed reinforcement entire concrete section to resist bend- and non-prestressed reinforcement ing moments. This becomes signifi- offers advantages. The non-pre- stressed reinforcement does not ap- preciably strengthen the column *Vice President T. Y. Lin & Associates under bending stresses in the work- Van Nuys, California ing load range, but it is very effective June 1965 69 e=050d 1.8 — p =0.010 ---p =0.020 a=0.15d 1.6 •o" 0 1 2 a=0.50 d L0 A, He =0.l5d a) 0.8 0. ^ , a=0 Q 0.6 ^^o ^^ a=0 - -4--0-- -o-^ 0.2 10 20 30 40 50 60 Slenderness ratio L/d Fig. 1—Comparison of Prestressed and Reinforced Concrete Column Strengths beyond cracking and into the ulti- higher than the cylinder strength. mate load range, both in compressive The spiral reinforcement may be and tensile resistance. Furthermore, non-prestressed; it may be indirectly the addition of non-prestressed rein- prestressed by the Poisson ratio ef- forcement could change the mode of fect resulting from longitudinal pre- failure of the column and increase stressing; or it may be chemically its ductility. Experimental and theo- prestressed by expansive cements. retical studies have already con- Realizing that the lack of knowl- firmed this7'11, although applications edge concerning the design and be- are yet limited. havior of prestressed concrete col- Another possibility is the three- umns was largely responsible for dimensional prestressing of columns, their slow devolopnient, the PCI combining spiral reinforcement with formed a committee on prestressed longitudinal prestressing. As is well concrete columns in 1963. The com- known, tri-axial compressive strength mittee is evaluating the available of concrete can be up to ten times data and theories to formulate cri- 70 PCI Journal Fig. 3—Six-inch Wide Columns major changes have been made in the ACI Code during the last three decades. The 1963 Code incorpo- rated the results of extensive theoret- ical and experimental studies, but it is still far from perfect. A similar evolution may be foreseen for pre- Fig. 2-90-Ft. Prestressed Concrete Columns stressed concrete columns with the exception that our knowledge of re- teria for design of prestressed con- inforced concrete columns may be crete columns. The committee be- utilized when dealing with pre- lieves that sufficient knowledge and stressed ones. data are already available so that Three approaches are possible for safe and reasonable criteria can be the design of prestressed concrete set up to guide the engineer in the columns: design of simple types of prestressed 1. Rational and analytical ap- concrete columns. Additionl study proach. and research, however, are much 2. A new set of code design needed to refine the procedure and clauses to be set up specifically to produce more economical results. for prestressed concrete col- This paper is an attempt to summar- umns. ize the knowledge to date (Ref. 1 to 3. Modification of ACI Code 9). While it represents the opinion clauses for reinforced concrete of only the author, free use has been columns so that they will be made of data and ideas from other applicable to prestressed con- members of the committee and their crete columns. contribution is hereby acknowl- In any of these three approaches, edged. either the working stress or the ulti- mate strength method or a combina- POSSIBLE DESIGN APPROACHES tion of both may be used. For the design engineer, pre- stressed concrete columns present a RATIONAL AND ANALYTICAL METHOD real challenge. It is noted that for It is well known that the stresses reinforced concrete columns, several in a prestressed concrete column can June 1965 71 be rationally analyzed. For example, in Fig. 4 the stresses at any point in eP a prestressed concrete column sec- tion is given by F P Mc PAc f =— At -.At — It — It where F = effective total prestress in- cluding all losses, except elastic shortening due to superimposed load. P = superimposed load. M = external moment at the sec- tion; = Pe in Fig. 4. c = distance to the extreme fiber J from the centroid of the section. At = area of the transformed sec- tion. It = moment of inertia of trans- formed section. A = deflection of the column at the section. For a pin-ended column with uni- form eccentricity, critical stresses - occur at midheight of the column I where the deflection is given by the well known secant formula, tP 0=e( sec Eclt —I) Fig. 4—Column Under Eccentric Load may not be a complicated process. For a given load eccentricity, this Unfortunately, for certain columns, pin-ended column usually represents the elastic stresses are not the best the worst possible condition in any measure of their strength, and plastic building or bridge column unless the analysis is required to determine the column is not laterally supported at deflection and buckling effects. A the ends. Often it will be more eco- complete plastic analysis should in- nomical to take into account the ac- clude the plasticity of both steel and tual moment variation along the concrete, the cracking of concrete, length of the column; but, as a first and the moment curvature relation- approximation and on the safe side, ships of sections under combined the engineer can always resort to axial loading and bending. While the this simpler approach. When the basic theory of analysis is relatively column is short and the deflection, straight forward, the execution be- A, is negligible, the solution be- comes a rather tedious problem. The comes greatly simplified. Thus, the reliability of such an analysis has rational analysis of elastic stresses been proved by tests carried out at 72 PCI Journal the University of California4'7, Uni- By assuming a location for the versity of Florida2,3 and the Univer- neutral axis at ultimate load, setting sity of Southern California'. Com- e0 as the ultimate strain in the con- puter programs have been set up at crete and f ,' as the ultimate stress the University of North Carolina and of the concrete, and by assigning others8'9. ultimate stress distribution curves for concrete, it is possible to com- The basic conditions of static equi- pute the combination of P and M librium and geometrical compatibil- ity for a prestressed column section that results in this ultimate failure. under ultimate load are given by For slender columns, the value of Fig. 56• The static equilibrium of the M just computed should include the section requires that for Y,V = 0, effect of deflection, which can be P=C—T1—T2 computed by a numerical procedure, and for Y.M=0, provided the load-moment curvature relationship of the column section M = (T^ — T2) 2t +Cy,, is known. P M Steel I^ ^ ^Column Fs1 Fc Fs2 Strains at a Section k. column T2 T, fc' yc Stress-Block in Concrete C Fig. 5—Ultimate Strength Under Combined Axial Load and Moment June 1965 73 While the rational analysis will prestressed reinforcement. For tied give stresses and the ultimate columns, 85% of the allowable load strength of prestressed concrete col- for spiral columns may be used. umns under combined axial load and When the amount of prestress is bending, the problem of allowable high, it may appreciably decrease stresses or factors of safety remains the ultimate strength of the columns. a difficult one. Therefore, when the effective pre- stress exceeds 0.15 f the term f NEW DESIGN CODE in the formula should be reduced by Although studies for prestressed 60% of the prestress in excess of concrete columns have enabled the 0.15 f ,' so that for spiral columns, prediction of their behavior and P= strength, we do not yet have enough data to derive simple rules of de- A9l.25 {fe— .6 ' avg—.15f^)] +f8p} sign. Most engineers cannot afford where the time to make a rational analysis, F even though the theory is available.