Design and Uses of Prestressed Concrete Columns by Raymond Itaya*

PROCEEDINGS PAPER

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-prestressed reinforcement does not appreciably 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 theoretical 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 ultimate strength method or a combina- POSSIBLE DESIGN APPROACHES tion of both may be used. For the design engineer, prestressed 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 section is given by F P Mc PAc f =— At -.At — It — It where F = effective total prestress including all losses, except elastic shortening due to superimposed load. P = superimposed load. M = external moment at the section; = Pe in Fig. 4. c = distance to the extreme fiber J from the centroid of the section. At = area of the transformed section. It = moment of inertia of transformed section. A = deflection of the column at the section. For a pin-ended column with uniform 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 becomes 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,

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 prestress 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. Computer analysis, such as the one rg carried out at the University of The 60% is based on the decrease in North Carolina will help, but will prestress at the ultimate load. have to be extended to include more For short columns subjected to variables. As more data becomes axial load and bending and con- available, it may be possible to de- trolled by compression, the ACI rive simple design rules. However, Code interaction formula is sug- the task is a highly complicated one gested: including many variables. Recent less than unity. work shows promise, but may re- Fa -} F ' + Fby quire many more years of verifica- The allowable Fa is computed as tion. in the ACI Code, F=.34(1+pg m) f0 MODIFICATION OF THE ACI CODE The axial stress f,, is computed for Now we come to a practical pro- external load only, unless the effec- posal which may enable the design tive prestress exceeds .15 f', in which of prestressed concrete columns to case 15% of the excess is added to be immediately accepted. This will the computation of f,,. The 15% is not give a perfect solution since it based on the 60% of the prestress at will be based on the 1963 ACI Code ultimate, multiplied by the factor for Reinforced Concrete Columns. 0.25 as for axial load only. On the other hand, it contains allow- For short columns subjected to able factors of safety which are ac- axial load and bending and con- cepted for reinforced concrete and trolled by tension, an ultimate should, therefore, be acceptable for strength approach, is proposed. The prestressed concrete. interaction curve may be assumed For short columns under axial to vary linearly between Mo when load, the ACI Code formula for the the section is under pure flexure, to allowable axial load on spiral col- M b when the axial load is N b. The umns is proposed: value Mo is computed as for any P = A,(.25f+f$p,,) prestressed section under flexure. where f8 and p, refers to the non- Further study is needed for the 74 PCI Journal determination of Mb and Nb at bal- CONCLUSION anced failure. Limited tests . and In conclusion, it may be stated computer analyses indicate that at that prestressed concrete columns ultimate load, the value of Nb can will be found useful and economical be obtained from the following under certain conditions, such as formula for rectangular sections': columns with high slenderness ratios,

Nb = (.45 f c —fce) A columns subjected to appreciable where fee = effective unit prestress bending moments, and precast col- in the concrete, consid- umns. Since prestressed concrete col- ering only the case of umns can be rationally analyzed, any uniform prestress. engineer who possesses a basic un- The eccentricity eb at balanced derstanding of structural mechanics failure varies from about 0.25d for should be able to design any pre- sections with no non-prestressed re- stressed concrete column based on inforcement, to about 0.5d for 3% first principles, provided he has the non-prestressed reinforcement for a time to perform the necessary calcu- 12 inch thick column. "d" is the lations. Hence, it is only reasonable column thickness. How these values that prestressed concrete columns should be used for working stress de- should be permitted when rational sign is yet to be determined. analysis can be presented. For slender columns, reduction In lieu of a rational analysis, ap- factors outlined in Chapter 9 of the proximate and safe methods of de- ACI Code may be followed. Article sign can be made using the 1963 912 of the Code, limiting the dimen- ACI Code for reinforced concrete sion to eight inches, should not be columns with certain modifications. applied to prestressed concrete col- Additional research, both theoretical umns since very often thin, pre- and experimental, is urged to deter- stressed columns are desirable and mine the effects of many variables reliable if properly designed. For on these columns. The formulation very long columns, the Euler load of simple design rules and formulae should be checked. based on these studies will lead to The PCI Committee on Columns wider adoption and applications. will soon have to make a decision Some of the variables to be con- as to which approach among the sidered are: aforementioned three should be rec- 1. The amount and location of ommended for prestressed concrete prestressed steel columns. Clearly, the rational ap- 2. The amount and location of proach is the most logical, but it is non-prestressed steel not the easiest. If the second ap- 3. The shape of column proach is taken, it is conceivable 4. Spiral prestress and tri-axial that a simpler set of design rules prestress may be set up than the ACI clauses 5. Types of steel and concrete for reinforced concrete columns. 6. Variation of moment However, there will be the practical 7. Eccentricity ratio problem of getting the method ac- 8. Slenderness ratio cepted by the public, whereas if the In addition, the types of column third approach is taken, a proposal connections, the joints between col- can be made within a few months umns and girders, temperature, if the effort is made. shrinkage and creep effects all re- June 1965 75 quire additional research. 5. Hall, A. S., `Buckling of Prestressed Columns", Construction Review, Syd- Indeed, there remains a great deal ney, Australia, June, 1963. to be done. But, we already have 6. Lin, T. Y., Design of Prestressed Con- sufficient knowledge to produce safe crete Structures, Second Edition, John designs, though not always optimum Wiley & Sons, Inc., New York, 1963. ones. 7. Lakhwara, T. R., "Ultimate Strength of Partially Prestressed Concrete Columns Under Eccentric Loading", Graduate REFERENCES Student Research Report No. 94, Divi- 1. Breckenridge, R. A., "A Study of the sion of Structural Engineering and Characteristics of Prestressed Concrete Structural Mechanics, University of Cal- Columns", University of Southern Cali- ifornia, Berkeley, 1963. fornia, Los Angeles, 1953. 8. Sandrini, L. M., "Ultimate Strength of 2. Jernigan, A. M. and Ozell, A. M., "Some Partially Prestressed Concrete Columns Studies on the Behavior of Prestressed Under Eccentric Loads—A Computer Concrete Columns", University of Flori- Analysis", Graduate Student Research da, Gainesville, 1956. Report No. 146, Division of Structural 3. Zia, P., "Ultimate Strength of Slender Engineering and Structural Mechanics, Prestressed Concrete Columns", Univer- University of California, Berkeley, 1964. sity of Florida, Gainesville, 1957. 9. Moreadith, F. L., "An Analytical Study 4. Lin, T. Y. and Itaya, R., "A Prestressed of Ultimate Load Capacity of Long Concrete Column Under Eccentric Hinged Prestressed Concrete Columns", Loading", Journal of the Prestressed Doctoral Thesis, Department of Civil Concrete Institute, Vol. 2, No. 3, De- Engineering, University of North Caro- cember 1957. lina, Raleigh, 1964.

Presented at the Tenth Annual Convention of the Pre- stressed Concrete Institute, Washington, D.C. September 1964.

76 PCI Journal