Structural Properties of High Strength Concrete and its Implications for Precast Prestressed Concrete S. P. Shah Professor Department of Civil Engineering Northwestern University Evanston, Illinois Shuaib H. Ahmad Assistant Professor of Civil Engineering Department of Civil Engineering North Carolina State University Raleigh, North Carolina igh strength concrete with a uniaxial ing the first time H compressive strength, f, greater was used for a t than 6000 psi (42 MPa), is experiencing mary of building; increased use and acceptance by de- concretes of h signers and contractors for both rein- strengths have bi forced and prestressed concrete con- in a recent ACI ci struction. 1 2'3 Currently, it is possible to The principa produce concrete with strengths in ex- strength concret cess of 12,000 psi (84 MPa). However, greater compres since not enough information is avail- cost, unit weight able on the structural properties of high as compared to strength concretes, discussion in this cretes. High strei paper is restricted to concretes with greater compress strengths of up to 12,000 psi (84 MPa). cost, is often the Initial use of high strength concrete, of carrying comps f, = 7000 psi (49 MPa), for buildings oc- tion, its greater curred in 1965 during construction of per unit weight a Lake Point Tower in Chicago, Illinois. lighter and more Two years later, this durable building Other advanta material was used to construct the Wil- concrete include lows Bridge in Toronto, Canada, mark- elasticity and incr 92 Increased stiffness is advantageous when deflections or stability govern the Synopsis design, while increased tensile strength is advantageous for service load design Experimental data on the structural in prestressed concrete. properties of high strength concrete (t.' Current ultimate strength design greater than 6000 psi (42 MPa) I are practice is based on experimental in- reported. Based on these findings, as formation obtained from concretes with well as data on normal strength con- compressive strength in the range of crete, empirical expressions are pro- 3000 to 6000 psi (21 to 42 MPa). For de- posed. veloping a satisfactory procedure for the The implications of such parame- design of structures using higher ters as compressive strength, com- strength concretes, additional consider- pressive stress-strain curve, modulus ations, validation or modification of of elasticity, tensile strength, shear existing strength design methods may strength, Poissons ratio, ductility, lat- be necessary. eral reinforcement, as well as In this paper, experimental data on economic considerations for the high strength concrete obtained by the structural design of prestressed con- authors are reported. Based on these crete are studied and design recom- data as well as those reported by other mendations are made. investigators, the authors have proposed empirical expressions to substitute for some of the currently used relation- ships. Note that the details of the exper- stress-strain curve is to load the concrete iments are presented elsewhere. In this cylinders in parallel with a larger diam- paper, the emphasis is on the results, eter, hardened steel tube with a thick- comparison with normal strength con- ness such that the total load exerted by crete, development of empirical for- the testing machine is always increas- mulas and some discussion on structural ing. This approach can be used with design implications. most conventional testing machines. An alternative approach is to use a closed-loop testing machine so that STRESS-STRAIN RELATION specimens can be loaded to maintain a constant rate of strain increase to avoid IN UNIAXIAL COMPRESSION unstable failure. The choice of feedback Several experimental investiga- signal for the closed-loop operation is tions5'la have been undertaken to obtain important and governs the occurrence of the stress-strain curves of high strength stable or unstable post-peak behavior. concrete in compression. It is generally The difficulties of experimentally ob- recognized that for high strength con- taining the post-peak behavior of con- cretes, the shape of the ascending part of crete in uniaxial compression and meth- the curve is more linear and steeper, the ods of overcoming these difficulties are strain at maximum stress is slightly described in a study by Ahmad and higher, and the slope of the descending Shah." For very high strength con- part is steeper, as compared to normal cretes, it may be necessary to use the strength concrete. lateral strains as a feedback signal rather To obtain the descending part of the than the axial strains.'2 stress-strain curve, it is generally neces- For the present study, a closed-loop, sary to avoid the specimen testing sys- servo controlled testing machine was tem interaction. A simple method of used to obtain complete stress-strain obtaining a stable descending part of the curves. The testing was done under PCI JOURNAUNovember-Decembe r 1985 93 • present study o Karr, Hanson and Capell 14 o Nilson and Slate q Ahmad and Shah (Ref ii) e Wischers 12 10 a B-- in Ln 45 I Q) L 30 4 25 7 } ^.vv i jwc v.v v.vv1+ V.wn U.UU1 0.002 0.003 0.004 0.005 strain (in/in) strain (in/in) Fig. 1. Stress- strain curves of high strength concrete under uniaxial compression. strain controlled conditions and a con- the statistical analysis of the experi- stant rate of increase of axial strain was mental data on 3 x 6 in. (75 x 152 mm) maintained throughout the test. Fig. 1 concrete cylinders."•1° These cylinders shows the results of the present investi- were tested in a closed-loop testing gation along with other available exper- machine under strain controlled condi- imental data. From Fig. 1 it can be seen tions and had a compressive strength that the slope of the curve in the post varying from 3000 to 11,000 psi (20 to 75 maximum stress range increases as the MPa). strength of concrete increases. The stress-strain curve in uniaxial compression can be mathematically rep- SECANT MODULUS OF resented by a fractional equation 6"s,'" ELASTICITY A (E/E° ) + (B-1) (E/Eo ) (1) The secant modulus of elasticity is f = ^c 1 + 4-2)(€f€) +B (€J€) defined as a the secant slope of the uni- axial stress-strain curve at a stress level f 4 O.I f,, of 45 percent of the maximum stress. A for post peak region comparison of experimentally deter- mined values4 of the secant modulus of or by a combination of power and expo- elasticity with those predicted by the nential equation:10 expression recommended by ACI 318, Section 8.5,'5 based on a dry unit weight, (2a) W, of 145 lb per cu ft is given in Fig. 2. f=fc[l —^1 — n^ ^^ Also shown is the proposed equation for for ascending part estimating the secant modulus of elas- ticity for low as well as high strength Lu3 I f =fr exp 1-k (E — E° ) (2b) concretes which is: for descending part E, = W2.5 ( vT,)ass = Ws.a ( f^ )o.3u (7a) and wheref is the stress at strain (E), f Note that Eq. (7a) goes through the and E. are the maximum stress and the corresponding strain, and A, B, and K origin and is comparable to the ACI are the parameters which determine the equation for low and normal strength shape of the curve in the ascending and concrete, but it is more accurate for high descending parts, respectively. strength concrete. Other empirical equ- ations proposed for predicting the elas- The value of the parameters A, B and tic secant modulus are:*• s• " K are determined by: E, = 40,000 ^, , + 1.0 x 10 6 psi A = E, E° (3) for (3000 psi f, _- 12,000 psi) (7b) B = 0.88087 - 0.57 x 10-° (f) (4) E, "26W5 ,f'}'e (7c) K = 0.17ff (5) E, = 27.55 W' s V' (7d) Eo = 0.001648 + 1.14 x 10- (f^) (6) The values of the experimentally de- termined secant modulus of elasticity E, = 27.55 W .5 VT (7) depend on the properties and propor- where f f is the compressive strength in tions of the coarse aggregate (for exam- psi and W is the unit weight in lbs per Cu ple, with the same consistency and ft. water-cement ratio, the larger the Eqs. (3) to (6) were determined from maximum size of aggregate and the PCI JOURNAL/November-December 1985 95 CD aD ,MPa ^L) 4 0 i 2.76 10 20 f^ , 60 80 100, 50 7 - MPa 40 range for which ACI code ^ 1 3 formula was derived 40 a a ACI 318, E,= 33w^5 fC psi \^j s_ Q x 2.5 0.65 30 in Ec=w (ft) psi 0x v3 —proposed vl3 tai equation (7a7 , E_= {40,000 fc +1.0x106} (w/145)Lsps point spread M ,psi Fig. 2. Secant modulus of elasticity versus concrete strength. coarser the grading, the higher the mod- of compressive strength. Based on the ulus of elasticity); the wetness or dry- available experimental data of split cyl- ness of the concrete at the time of test inder and beam flexure tests on concretes (the drier the concrete at the time of the of low, medium 19 ' 2 ' 2 ' and high test the lower the modulus of strengths,1s,2E.2a empirical equations to elasticity—wet concrete is stiffer al- predict the average split-tensile strength though often weaker); and the method of (ffp ) and modulus of rupture (f,) for obtaining the deformations (strain gage, concretes of strengths up to 12,000 psi mechanical compressometer, transduc- (84 MPa) are proposed as follows: ers, etc.).