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Structural Propertiesof High Strength Concrete
and its Implications forPrecast Prestressed Concrete
H igh strength concrete with a uniaxialcompressive strength, f,' greater
than 6000 psi (42 MPa), is experiencingincreased use and acceptance by de-signers and contractors for both rein-forced and prestressed concrete con-struction. 1 2 '3 Currently, it is possible toproduce concrete with strengths in ex-cess of 12,000 psi (84 MPa). However,since not enough information is avail-able on the structural properties of highstrength concretes, discussion in thispaper is restricted to concretes withstrengths of up to 12,000 psi (84 MPa).
Initial use of high strength concrete,f, = 7000 psi (49 MPa), for buildings oc-curred in 1965 during construction ofLake Point Tower in Chicago, Illinois.Two years later, this durable buildingmaterial was used to construct the Wil-lows Bridge in Toronto, Canada, mark-
92
S. P. Shah
ing the first timewas used for a tmary of building;concretes of hstrengths have biin a recent ACI ci
The principastrength concretgreater comprescost, unit weightas compared tocretes. High streigreater compresscost, is often theof carrying compstion, its greaterper unit weight alighter and more
Other advantaconcrete includeelasticity and incr
ProfessorDepartment of Civil Engineering
Northwestern UniversityEvanston, Illinois
Shuaib H. AhmadAssistant Professor of Civil EngineeringDepartment of Civil EngineeringNorth Carolina State UniversityRaleigh, North Carolina
Increased stiffness is advantageouswhen deflections or stability govern thedesign, while increased tensile strengthis advantageous for service load designin prestressed concrete.
Current ultimate strength designpractice is based on experimental in-formation obtained from concretes withcompressive strength in the range of3000 to 6000 psi (21 to 42 MPa). For de-veloping a satisfactory procedure for thedesign of structures using higherstrength concretes, additional consider-ations, validation or modification ofexisting strength design methods maybe necessary.
In this paper, experimental data onhigh strength concrete obtained by theauthors are reported. Based on thesedata as well as those reported by otherinvestigators, the authors have proposedempirical expressions to substitute forsome of the currently used relation-ships. Note that the details of the exper-iments are presented elsewhere. In thispaper, the emphasis is on the results,comparison with normal strength con-crete, development of empirical for-mulas and some discussion on structuraldesign implications.
STRESS-STRAIN RELATIONIN UNIAXIAL COMPRESSION
Several experimental investiga-tions5'la have been undertaken to obtainthe stress-strain curves of high strengthconcrete in compression. It is generallyrecognized that for high strength con-cretes, the shape of the ascending part ofthe curve is more linear and steeper, thestrain at maximum stress is slightlyhigher, and the slope of the descendingpart is steeper, as compared to normalstrength concrete.
To obtain the descending part of thestress-strain curve, it is generally neces-sary to avoid the specimen testing sys-tem interaction. A simple method ofobtaining a stable descending part of the
Synopsis
Experimental data on the structuralproperties of high strength concrete (t.'greater than 6000 psi (42 MPa) I arereported. Based on these findings, aswell as data on normal strength con-crete, empirical expressions are pro-posed.
The implications of such parame-ters as compressive strength, com-pressive stress-strain curve, modulus
of elasticity, tensile strength, shearstrength, Poisson's ratio, ductility, lat-eral reinforcement, as well aseconomic considerations for thestructural design of prestressed con-crete are studied and design recom-mendations are made.
stress-strain curve is to load the concretecylinders in parallel with a larger diam-eter, hardened steel tube with a thick-ness such that the total load exerted bythe testing machine is always increas-ing. This approach can be used withmost conventional testing machines.
An alternative approach is to use aclosed-loop testing machine so thatspecimens can be loaded to maintain aconstant rate of strain increase to avoidunstable failure. The choice of feedbacksignal for the closed-loop operation isimportant and governs the occurrence ofstable or unstable post-peak behavior.The difficulties of experimentally ob-taining the post-peak behavior of con-crete in uniaxial compression and meth-ods of overcoming these difficulties aredescribed in a study by Ahmad andShah." For very high strength con-cretes, it may be necessary to use thelateral strains as a feedback signal ratherthan the axial strains.'2
For the present study, a closed-loop,servo controlled testing machine wasused to obtain complete stress-straincurves. The testing was done under
PCI JOURNAUNovember-Decembe r 1985 93
• present study
o Karr, Hanson and Capello Nilson and Slateq Ahmad and Shah (Ref ii)e Wischers
a
in
Ln 45
30
25
^.vv i jwc v.v v.vv1+ V.wn U.UU1 0.002 0.003 0.004 0.005strain (in/in) strain (in/in)
Fig. 1. Stress- strain curves of high strength concrete under uniaxial compression.
14
12
10
B--
I
Q)L
4
7
}
strain controlled conditions and a con-stant rate of increase of axial strain wasmaintained throughout the test. Fig. 1shows the results of the present investi-gation along with other available exper-imental data. From Fig. 1 it can be seenthat the slope of the curve in the postmaximum stress range increases as thestrength of concrete increases.
The stress-strain curve in uniaxialcompression can be mathematically rep-resented by a fractional equation 6"s,'"
A (E/E° ) + (B-1) (E/E o ) (1)f = ^c 1 + 4-2)(€f€) +B (€J€)
f 4 O.I f,,for post peak region
or by a combination of power and expo-nential equation:10
f=fc[l —^1 — n^ ^^
(2a)
for ascending part
f =fr exp 1-k (E — E° )Lu3 I (2b)
for descending part
and wheref is the stress at strain (E), f
and E. are the maximum stress and thecorresponding strain, and A, B, and Kare the parameters which determine theshape of the curve in the ascending anddescending parts, respectively.
The value of the parameters A, B andK are determined by:
A = E, E° (3)
B = 0.88087 - 0.57 x 10-° (f) (4)
K = 0.17ff (5)
E o = 0.001648 + 1.14 x 10-' (f^) (6)
E, = 27.55 W' .5 VT (7)
where f f is the compressive strength inpsi and W is the unit weight in lbs per Cu
ft.Eqs. (3) to (6) were determined from
the statistical analysis of the experi-mental data on 3 x 6 in. (75 x 152 mm)concrete cylinders." •1 ° These cylinderswere tested in a closed-loop testingmachine under strain controlled condi-tions and had a compressive strengthvarying from 3000 to 11,000 psi (20 to 75MPa).
SECANT MODULUS OFELASTICITY
The secant modulus of elasticity isdefined as a the secant slope of the uni-axial stress-strain curve at a stress levelof 45 percent of the maximum stress. Acomparison of experimentally deter-mined values4 of the secant modulus ofelasticity with those predicted by theexpression recommended by ACI 318,Section 8.5,' 5 based on a dry unit weight,W, of 145 lb per cu ft is given in Fig. 2.Also shown is the proposed equation forestimating the secant modulus of elas-ticity for low as well as high strengthconcretes which is:
E, = W2.5 ( vT,)ass = Ws.a (f^ )o.3u (7a)
Note that Eq. (7a) goes through theorigin and is comparable to the ACIequation for low and normal strengthconcrete, but it is more accurate for highstrength concrete. Other empirical equ-ations proposed for predicting the elas-tic secant modulus are:* • s• "
E, = 40,000 ^,' ,' + 1.0 x 10 6 psi
for (3000 psi f,' _- 12,000 psi) (7b)
E, "26W5 ,f'}'e (7c)
E, = 27.55 W' s V' (7d)
The values of the experimentally de-termined secant modulus of elasticitydepend on the properties and propor-tions of the coarse aggregate (for exam-ple, with the same consistency andwater-cement ratio, the larger themaximum size of aggregate and the
PCI JOURNAL/November-December 1985 95
CDaD
,MPa^L) '4 0
i
7 -2.76 10 20 f^ , MPa 40
60 80 100,
range for which ACI code ^ 1
3 formula was derived
ACI 318, E,= 33w^'5 fC psi \ j
2.5 0.65Ec=w (ft) psi
—proposedequation (7a7 , E_= {40,000 fc' +1.0x106} (w/145)Lsps
point spread
aQ
xin
v3
tai
50
40a
s_
30 0x
vl3
M
,psi
Fig. 2. Secant modulus of elasticity versus concrete strength.
coarser the grading, the higher the mod-ulus of elasticity); the wetness or dry-ness of the concrete at the time of test(the drier the concrete at the time of thetest the lower the modulus ofelasticity—wet concrete is stiffer al-though often weaker); and the method ofobtaining the deformations (strain gage,mechanical compressometer, transduc-ers, etc.).
In view of the possible variability ofexperimental data on modulus, it islikely that any of the above equationscan be used for estimating the secantmodulus of elasticity and the develop-ment of a more accurate equation isperhaps unwarranted.
TENSILE STRENGTHThe tensile strength of concrete can
be experimentally determined in threedifferent ways: (1) uniaxial tensile test;(2) split cylinder test; and (3) beam testin flexure. The first method of obtainingthe tensile strength may be referred toas "direct," and the second and thirdmethods may be referred to as "indi-rect."
In the direct test for tensile strength,the specimen is gripped at its ends andpulled apart in tension; tensile strengthis the failure load divided by the areaexperiencing tension.
In the splitting tension test, a cylinderis loaded in compression on two diamet-rically opposite sides, and the specimenfails in tension on the plane between theloaded sides.
In the beam flexure test (modulus ofrupture test), a rectangular beam isloaded at the center or third points andfails in bending; the computed tensilestress at failure load is called modulus ofrupture.
Many engineers assume that the di-rect tensile strength of concrete is about10 percent of its compressive strength;splitting tensile strength is about thesame, or perhaps 1 percent stronger; andmodulus of rupture is about 15 percent
of compressive strength. Based on theavailable experimental data of split cyl-inder and beam flexure tests on concretesof low, medium 19 ' 2 ' 2 ' and highstrengths, 1s,2E.2a empirical equations topredict the average split-tensile strength(ffp ) and modulus of rupture (f,) forconcretes of strengths up to 12,000 psi(84 MPa) are proposed as follows:
fSP = 4.34 (J c )0.55
(8)
fr = 2.30 (ff) 3(9)
where ff is the compressive strength ofconcrete in psi.
Note that Eq. (9) is the same expres-sion proposed by Jerome," which wasdeveloped on the basis of data for con-cretes of strengths up to 8000 psi (56MPa). Figs. 3a and 3b show the plot ofthe experimental data and the proposedequations for predicting the split cylin-der strength (fe p ) and modulus of rup-ture (f.) of concretes with strengths upto 12,000 psi (84 MPa).
Also shown in Figs. 3a and 3b are theequations proposed by ACI Committee363 which appear to overestimate thevalues of tensile strengths as comparedto Eqs. (8) and (9). However, theseequations4.16 have the same functionalform as currently used by the ACT Code(also shown in Fig. 3b). For design pur-poses, the equations proposed to predictthe average results may be unsatisfac-tory. Design equations which are lowerbound for the experimental data are alsoshown in Figs. 3a and 3b.
The complete stress-strain curve ofconcrete in tension is difficult to obtain,primarily because of the inability tocorrectly monitor the strains after tensilecracking. Due to the difficulties in test-ing concrete in direct tension, only lim-ited and often conflicting data are avail-able. Recent work at Northwestern Uni-versity25 points out that due to thelocalized nature of post-peak defor-mations, no unique tensile stress-strainrelationships exist.
According to this study:"
PC1 JOURNAL1November-Decereber 1985 97
•w•
4.34 (fC)o.a5 0.
(mean)800
f5, =7.40r bb —^(Ref. 4) --
O O -00
O ^0 q qQ a4
600 Jr .^ . c r °
0 ff• • s^ r. fyp = 6 fC
U9 400 0°p • (lower bound)A .o e •rn
, c • a'i • Walker and Bloem (6"x 12" cylinders)a Houk (6 ` x6"square prisms)200` • Grieb and Werner (6x12 cylinders)o Carrasqui l to (4"x S " cylinders)
° o Ahmod (6'x12"cylinders)
0 2000 4000 6000 8000 10000 12000compressive strength (psi)
Fig. 3a. Split cylinder tensile strength of plain, normal weight concrete.
1. A unique tensile stress versus crackwidth relationship exists in the post-peak region,
2. The uniaxial strength can be pre-dicted by the expression, 6.5 ^+' f,, wheref, is the uniaxial compressive strengthin psi,
3. The tangent modulus of elasticity isidentical in tension and compression.
4. The prepeak stress-strain curve intension is relatively less nonlinear thanin compression,
No data in uniaxial tension is reportedfor higher strength concretes. However,some unpublished data at NorthCarolina State University on tensilestress-strain curves, as obtained fromsplit cylinder tests, indicate that tensile
strains corresponding to maximum ten-sile stress increase with high tensilestrengths (i.e., higher strength con-cretes).
POISSON'S RATIOPoisson's ratio under uniaxial condi-
tions is defined as the ratio of lateralstrain to strain in the direction of load-ing. In the inelastic range due to volumedilation resulting from internal mi-crocracking, the apparent Poisson's ratiois not constant but is an increasing func-tion of axial strain. However, experi-mental data on the values of Poisson'sratio for high strength concrete are verylimited.' '27
98
o a0
Na
LL
a
0N
0E
o -'0
0 ^-11.7 f, ^.^ 2.3(f'.3(f2/(Ref. 4) \ i (mean)
a0
o ^- 0 2i • (lower bound)
p vV
/ v aC^a f,= 7.5v0 /^vy^ • (ACI code)
> a/ p q ° a
> 9
°a 6r/ V
v va^^°r ■ri p • Gonnerman and Shuman (7"x10 " beams)
7
r°• Walker and Bloem (6^x 6' beams)c Houk (6 "x6" beams)
v v Grieb and Werner (6'x6"x 21" beams)o Corrasquillo (4"x4"x14"beams)o Kha loo (6 "x 6"x 20" beams)
0 2000 4000 6000 8000 100compress!ve strength (psi)
Fig. 3b. Beam flexural tensile strength of plain, normal weight concrete.
Based on the available experimentalinformation, Poisson's ratio of higherstrength concretes in the elastic rangeappears comparable to the expectedrange of values for lower strength con-cretes. In the inelastic range, the rela-tive increase in lateral strains is less forhigher strength concretes as comparedto concretes of lower strengths. 14 That is,higher strength concretes exhibit lessvolume dilation than lower strength
PCI JOURNAL'November-December 1985
concrete (Fig. 4). This implies lessinternal microcracking for concretes ofhigher strengths."
The lower relative expansion duringthe inelastic range may mean that theeffects of triaxial stresses will be pro-portionally different for higher strengthconcretes. For example, the effective-ness of hoop confinement is reportedto be less for higher strength con-crete S.14
99
Q1L
N
V)asLa.E0U
10 El
6 circumferential strainmeasuring device
4-
2
0 p
0 0.002 0.004 0.006 0 0.004 0.008 0.012 0.016 0.020axiom strain tin / in) lateral stroin (in/in)
Fig. 4. Axial stress versus axial strain and lateral strain for plain, normal weight concrete.
MULTIAXIAL STRESSESExperimental data on the behavior of
high strength concrete under multiaxialstresses are not yet available. In a re-cent paper,"' an orthotropic model forpredicting the behavior of concreteunder uni, bi and triaxial stresses hasbeen proposed. This model incorporatesthe lower volume dilation of highstrength concrete in the inelastic range.
EFFECT OF STRAIN RATESome experimental information is
available on the effect of strain rate onthe behavior of concretes with strengthsin the range of2000 to 5500 psi (14 to 39MPa). 2 Very little information isavailable on the behavior of concretes ofhigher strengths under high strain rates(such as those that would be experi-enced during earthquakes). Ahmad andShah" have tested concretes withstrengths up to 7000 psi (49 MPa) under
high strain rates (up to 30,000 mi-crostrains per see).
On the basis of experimental results'and the other available data,$94 empiri-cal equations to predict the secant mod-ulus of elasticity, maximum strength andthe corresponding strain under highstrain rates are proposed: The secantmodulus of elasticity (at 0.45f) underfast strain rates is given by:
(Er ) j = (Er ). 1 0.962 + 0.038 loto ]L g s
(l0a)
where (Er )8 = 27.55, .,i fr and Iog Ee = log(32 microstrains per see) are the valuesat the usual static loading rate, and (E, )iis the corresponding secant modulus ofelasticity at a desired strain rate.Compressive strength under fast strainrates (fore > 16 microstrains/sec) is:
(f^ )E = f [0.95 + 0.27 to E]
(lob)
100
where f' is the compressive strengthmeasured at the usual static rate and a isthe shape factor to account for the dif-ferent shapes. The shape factor is givenby:
a=0.85+0.09(4)-0.02 (h)for h ^5
(10c)where
d = diameter or least lateral dimen-sion (in.)
h = height (in.)
and
(Eq } f = 1938.46 + 11.138(i) + 0.272 ffl ,8
(l Od)
where f, is in psi and f3 is the shape fac-tor given by:
0.80+0.143(4)- 0.033(h)
for -a5 (l0e)
From these equations, it can be seenthat (1) the secant modulus of elasticityincreases with increase in strain rate; (2)the strength enhancement (increase)due to higher strain rates is less for con-cretes of higher strengths as comparedto normal strength concretes; and (3) thestrain corresponding to the maximumstress increases with the increase instrain rate.
It should be noted that the studyn islimited in scope and more research isneeded in this area to quantify the ef-fects of very fast strain rates on highstrength concretes. Such information iscurrently being obtained by using an in-strumented impact testing system atNorthwestern University 36
MATERIAL ANDSECTIONAL DUCTILITY
It is generally accepted that highstrength concrete is less ductile thannormal strength concrete. It is not pos-sible to express the relative ductility (or
brittleness) in a quantitative mannersince no rational method of measuringthis quantity currently exists. Attemptsusing nonlinear fracture mechanics todefine fracture toughness are beingmade 37,38
Ductility can be quantitatively ex-pressed, in a crude manner, from theslope of the post-peak response of con-crete subjected to uniaxial compression;for example, if the slope is zero, then thematerial is perfectly plastic, while forperfectly brittle material, the slope isinfinity. From Fig. 1 it can be seen thathigh strength concrete has a greaterslope than that for normal strength con-crete.
According to the above definition, un-reinforced high strength concretes aremore brittle than normal strength con-crete; however, the same is not neces-sarily true for reinforced high strengthconcrete structural elements. Consider,for example, a typical under-reinforcedconcrete beam moment versus midspandeflection relationship shown in Fig. 5a.If ductility is defined as the ratio of thedeflection at ultimate to that at yieldingof the tensile steel, then this ratio de-pends not only on the compressivestress-strain curve of concrete but alsoon the amount of longitudinal rein-forcement, shape of the beam cross sec-tion and the loading conditions (thirdpoint loading versus single central pointloading, presence of axial loads, as wellas many other factors).
Moment versus midspan deflectioncurves of the beam shown in Fig. 5awere theoretically calculated for threereinforcement ratios and five compres-sive strengths. The amount of longitudi-nal steel was varied such that the ratiobetween the actual steel content, p, andthe balanced steel content, pb (definedand calculated according to the ACICode' s ) remained essentially the samefor beams with five different concretestrengths.
The moment-curvature relationshipfor a section was calculated assuming
PCI JOURNAL/November-December 1985 101
that plane sections remain plane, using analytically expressed as outlined byEq. (1) for the stress-strain curve of con- Wang et al. 39 Note that the tensilecrete, while the stress-strain curve of the strength contribution of concrete wassteel was as shown in Fig. 5a and was ignored.
mid span deflection (in)0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7
stress stress
fc f
fc' (MPa) fc (ksi) concrete steel 1800
700B5 34.5 5.0 strain strain7B 9 6 7.0.0 E 0.003 13
B9 62.0 90B 11 89.6 110
=0.0042 1600180 g13 89.6 13.0
16 c = 0.003
811 1400c0.0042
-0.003/E 1200E B9
1Y 20 Fcu=O,OO42 2= 0.003 -1000'.-_
C B7 11 100 Cc= 0.0042 EEoE /EL =0.003 0
800 EB5
BO E,„ = 0.004 6
600fy -414 MPa (60ksi)60 b=17.8 mm{7in) P =0.50
h 40040
E
E _
EEE.^ P P
a NLq
Foldf7 N 200
2 -k___O 0 101.6mm 01,6mm 101.6mm
f4in1
0 I I I 07.5 15,0 22.0 30.0 37.5 45.0 52.5 60.0
mid span deflection (mm)
Fig. 5a. Analytical moment versus midspan deflection for a singly reinforced beam withdifferent concrete.
102
0- fy= 60 ksi
g • p/p6 0.3
a P/pb = 0.5
6 A p/pb = O.7
7
6
5-
4-
I
3
2
1
00 1 2 3 4 5 6 7 8 9 10 11 12 13f, (ksi)
Fig. 5b. Effect of concrete compressive strength on the deflection ductilityof a singly reinforced beam under third point loading.
4)
41U
D
C0ZUas
The moment-deflection relationshipswere calculated from knowing the mo-ment field and integrating the curvaturealong the beam. This procedure as-sumes that there are no discontinuitiesin the distribution of the curvatures.This may be a correct assumption Forclosely spaced narrow cracks. For widercracks, curvatures may he computed byeither discrete deformation summationor by using nonlinear strain distributionacross the depth of the member.
The curves shown in Fig. 5a are forbeams made with five different com-pressive strengths and reinforced suchthat they all had the same pip,,. It can beseen that the ductility ratio is the sameregardless of compressive strength. Thisis also true for other values ofplp b as canbe seen in Fig. 5b. From the theoreticalresults (Fig. 5b), it can be seen that theductility ratio is essentially independentof the compressive strength of concrete,if the ratio ofp/pa is kept constant.
Table 1 compares the results of thetheoretical predictions with the experi-mental results of research conducted atCornell University and reported in theACI report. 4 The dimensions of thesingly reinforced beams tested' are thesame as shown in Fig. 5a and yieldstrength of steel was 60,000 psi (414MPa). It is seen that except for Beam A3in Table 1, the theoretical prediction isclose to the experimentally observedvalues, Note that in the testing of thebeams, the shear failure was avoided byusing the stirrups in the shear span.
SHEAR STRENGTHThe shear strength of concrete has
been experimentally studied in twoways: by testing solid or hollow con-crete cylinders in pure torsion and bytesting beams under third point loadingand studying the shear and diagonaltension strength.
PCI JOURNALlNovember-December 1985 103
Table 1. Comparison of analytical and experimentaldeflection ductility ratios A,, / w .
BeamNo.
f(ksi) n ano P p'/p Analytical Exp. (Ref. 4)
Al 3.7 0.51 0.0135 0 3.96 3.54A2 6.5 0.52 0.0219 0 2.16 2.84A3 8.5 0.29 0.0145 0 6.31 2.53A4 8.5 0.64 0.0321 0 1.91 1.75AS 9.3 0.87 0.0481 0 1.35 1.14A6 8.8 1.11 0.0565 0 1.02 1.07
Note: 1 ksi 6.895 MPa.
Fig. 6 shows the shear stress-shearstrain and shear stress-axial tensilestrain curves for concretes of differentcompressive strengths. These curveswere obtained by testing solid 3 x 9 in.(76.2 x 228.6 mm) cylindrical concretespecimens under pure torsion. Theshear strains were simultaneously ob-tained by the strain gages on the surfaceof the concrete and by measuring thechange in are length (as shown sche-matically in the subset of Fig. 6) withthe help of a very sensitive, linear volt-age direct transducer (LVDT). The re-sults obtained from these methods werevery comparable to each other.
In these tests, the lateral loads (togenerate the torsion) were appliedthrough a pair of horizontal jacks placed24 in, (610 mm) apart. The axial tensileextension induced because of shear wasalso recorded through a LVDT placedbetween the top of the test specimenand the platten of the machine. The re-lationship between the shear stress (cal-culated by using the elastic torsion for-mula) and axial tensile strain is a mea-sure of the shear dilation phenomenonin concrete (note that for metals this di-lation is assumed to be zero).
The relatively lower axial tensilestrain observed for high strength con-crete may indicate that microcracks inhigh strength concrete are less rough.This may influence the so-called shear-aggregate-interlock phenomenon.9'
The current shear design philosophy
is to provide the total shear resistance inexcess of shear imposed (required) byconditions using factored loads. Thetotal shear resistance is made up of twoparts: V, provided by the concrete and V,provided by the shear reinforcement.The value of V, recommended by theACI Code15 includes the contributionsof the uncracked concrete at the head ofa hypothetical crack, the resistance pro-vided by the aggregate interlock alongthe diagonal crack face, and the dowelresistance provided by the main rein-forcing steel.
In a recent paper, Frantz`' reportedthat the current ACI formulas for cal-culating V, are applicable to highstrength concrete, However, unpub-lished data by Nilson indicates that cur-rent design methods are not conserva-tive for higher strength concretes.
Recently, fifty-four singly reinforcedbeams were tested at North CarolinaState University'' to study the flexure-shear interaction of high strength con-crete beams. All the beams were with-out web reinforcement and were 5 in.wide x 10 in. deep (127 x 254 rum), Thebeams were tested under third pointloading with different shear span todepth (aid) ratios. Some of the beamswere designed to fail in flexure andothers were designed to fail in shear.Only the results of beams which failedin shear are presented in Figs. 7a-7b.
The Ioad which produced the first di-agonal crack was defined as the diagonal
M1
T(psi )422
900 6 3"
SOO T//"/700
B600
/B
500
A A400
300
200
A- low strength concrete (f^-5.3ksi)B - high strength concrete (f, =12 ks i )
200 100 100 200 300 400 500axial tensile strain (Et ) shearing strains (y) microstrain
microstrainsFig. 6. Shear stress versus shear strain and axial tensile strain for plain, normal weightconcrete.
cracking load and was used to calculatethe shear stress at diagonal cracking(ar , ). Note that the magnitude of thecracking load (and thus the crackingstress) is sensitive to both the actual lo-
cation of the initiating flexural crack andto the observer's judgment.
The ultimate shear stress (au ) was cal-culated by dividing the failure(maximum) load by the cross-sectional
PCI JOURNAL/November-December 1 985 105
a/d >2.50 o Ahmad and AlvaroCL400— a/d = 2.7 3.0 and 4.0
e Andrew and FrantzN a/d = 3.6
300L
rsZsutty2Q0 vr=59If^Pa,
L_U
0
000 e O
0
ao o0
e Q e
proposed designequation id '3 psiv«=40(fcpa}
2 3 4 5 6iifcpa)IFig. 7a. Cracking shear stress of slender beams without web reinforcement.
area of the beam. Figs. 7a and 7h showthe experimental data for beams withoutweb reinforcement42 • 43 along with theequation recommended by Zsutty" forlow strength concretes.
From these figures it appears thatZsutty's equation gives a good averageestimate for the cracking and ultimateshear stress. However, it may prove tobe unconservative for design purposes.On the basis of experimental data, de-sign equations which are lower boundfor the experimental data are proposed.The proposed design equations to esti-mate cracking and the ultimate shearstress are:
vc, = 40 (f, pd/a)' rs (Ila)
vaz = 50 (f,pdia)"3 (11b)
whereucr = cracking shear stressVCR = ultimate shear stressp = longitudinal steel contentd = effective depth of the beama = shear span
BENEFICIAL EFFECTOF LATERAL CONFINEMENT
In compression dominant structuralelements like columns, it is advanta-geous to confine the concrete by pro-viding lateral steel in the form of con-tinuous spirals or ties. The beneficialeffects of lateral confinement of con-crete on column behavior are:
1. It increases the strength of the coreconcrete inside the spiral by confiningthe core against lateral expansionunderload.
2. It increases the axial strain capacityof concrete, thereby permitting a moregradual and ductile failure.
Currently, no research data are avail-able regarding the behavior of highstrength concrete confined by rectan-gular ties. Recently, three research re-ports' 4 - 4 46 on the beneficial effects ofcontinuous spirals for low and highstrength concretes have been published.From these reports, it can be observedthat for high strength and lightweightaggregate concretes, the beneficial ef-
106
a
VIVI
LUi
aE
0 1 2 3 4 5 6d 1/3tfCpa?
Fig. 7b. Ultimate shear stress of slender beams without web reinforcement.
fects horn lateral confinement are differ-ent than those for normal strength con-cretes. This difference can be attributedto the different (less) volume dilation inthe inelastic range for higher strengthconcretes 14 (Fig. 4).
Using the constitutive properties ofconcrete and the stress-strain relation-ships of the confining steel, an analyticalmodel was proposed by Ahmad andShah14 to predict the beneficial effects ofhoop confinement for low as well ashigh strength concrete. This workshowed that adequate ductility can beobtained for high strength concrete byincreasing the amount of confiningreinforcement or by increasing the yieldstrength of hoop reinforcement. Similarconclusions have been reported fromexperiments with high strength, normalweight concrete conducted by Japaneseresearchers and for lightweight, highstrength concrete.'
This conclusion was also reached in arecent study at Northwestern Univer-sity1e Moment-curvature relationshipswere calculated for confined concretecolumns subjected to a constant axialload and increasing amount of lateralload. The current practice of providingconfinement as suggested by AC1 15 forround columns is given by:
Tea = 0.45 (Aa /A. – 1) flll fvh (12a)
Pa = 0.12 ff I.f,,h (12b)
wherep, = ratio of spiral reinforcementAo = gross area of the cross sectionA„ = area of core of spirally reinforced
column measured to outside di-ameter of the spiral
f„h = yield stress of the hoop steelNote that the higher the compressive
strength, the higher the amount of con-fining reinforcement required by the
PCI JOURNALJNovember-December 1985 107
11000i0000--------- -----^AC1
C 5 f' = 9000 ps i
9000 Po=Agfc=4072 kipsP„=1018 kips
8000 P,/Po 0.25spiral reinforcement: ps =0.031spacing = 2,75in
confined concrete (cor
steel
T Csteel hardeningC=compressive steelT= tensile steel
I
unconfined concrete (cover) I0Q0 0.01 0.02 0.03 c04 e 0.05
strain
Fig. 8. Diagram of moment versus maximum core compressive strain.
6000
500CE0E 400C
1200
1100
1000
900
800
700
600
500
400
300
200
100
ACI Code. It was observed' that Eqs.(12a) and (12b) adequately compensatefor the inherently poor efficiency of theunit confinement for high strength con-crete by increasing the confinement forincreased compressive strength.
This can be seen in Fig. 8 where thetheoretically calculated moment versusmaximum core compressive strain for around, high strength column'" is shown.The column was subjected to increas-ing bending moment and a relativelyhigh constant axial load. It was con-fined using the ACI Code requirement.
Even for a relatively high value ofaxial strain, the column is seen to main-tain the ACI predicted value of themaximum load. As shown in Fig. 8, the
contribution of confined core and thelongitudinal steel compensates for theloss of cover capacity. The theoreticallycalculated curves could not be corn-pared with the experimental results ofhigh strength concrete columns since nodata are available. However, a satisfac-tory comparison was obtained with theavailable results for normal strengthconcrete.''
ECONOMICS OFHIGH STRENGTH CONCRETE
To examine the possible savings inengineering costs of using high strengthconcrete, a 79-story high rise buildingsimilar to Water Tower Place in
108
Table 2. Cost comparison of using normal strength concreteand high strength concrete for a 79-story building (Ref. 49).
Materials
Compressive strength
Up to12,000 psi 4,000 psi
Cost per 25 x 25 ft panelConcrete $ 45,035 $ 88,836Forms 35,729 54,606Longitudinal steel 34,449 87,161Spirals 1,441 1,930
TOTAL $116,654 $232,533Total cost for 33 columns = $3,849,582 $7,673,589
Note: 1 ft = 0.3048 m; E psi = 0.006895 MPa.
Table 3. Unit cost of materials and placing for various levels
of concrete compressive strength.
Materials and
Compressive strength
placing 4,000 psi 9,000 psi 12,000 psi
Concrete per cu yd $50.00 $68.62 $96.60Placing per cu yd 16.00 1.6.00 16.00Forms per sq ft 2.8 2.8 2.8Steel in place per lb 0.38 0.38 0.38
Note: 1 en yd = 0.77 nrl ; 1 sq ft = 0.093 m'; 1 psi = 0.006895 MPa.
Chicago, Illinois was examined by Shahet a1. The total cost of constructing col-umns using high strength concrete withcompressive strengths of up to 12,000psi (84 MPa) was compared with thatusing concrete with a compressivestrength of 4000 psi (28 MPa).
With the high strength concrete, col-umn dimensions were kept constant andwere calculated so that the lowest storycolumns can be made with a 12,000 psi(84 MPa) concrete and 1 percent lon-gitudinal steel. The dimension of thecolumn and the percentage of the lon-gitudinal steel was maintained constantfor all 79 stories. Note that, in general,the smaller the percentage of steel, thelower the column cost per unit load car-rying capacity. 55 The advantage ofkeeping constant dimension for the en-
tire height of the building is that thesame forms can he used repeatedly forall stories.
For the computations a typical interiorcolumn was considered. Columns weredesigned for only axial loads and nomoments were considered, since only apreliminary estimate was attempted.For the high strength concrete, the top29 floors were designed with 4000 psi(28 MPa), the next 31 floors with 9000psi (63 MPa), while the bottom 19 floorswere designed with 12,000 psi (84 MPa).
For normal strength concrete, allfloors had concrete with a compressivestrength of 4000 psi (28 MPa). However,to maintain a 1 percent ratio of thelongitudinal steel, the dimensions of thedesigned circular columns were in-creased from about 55 in. (1400 mm) at
PCI JOURNAL/November-December 1985 109
girder length (ft)0 50 100 150 200
Bulb Tee
AASHTO-PCIType VI
W S DOT120 series
Colorado
spacing 8' Or
Bulb Tees
.J
a 150NXa
100
60 B.T. 8 ksi72F B.T. 6 ks i48 Br. 10 ksi
4
6 8 10 12girder spacing (ft)
Fig. 9. Effect of concrete strength on span capabilities and depthvariations of different types of solid prestressed girders.
the top to 116 in. (2950 mm) for the bot-tom story. The total number of columnsfor a spacing of 25 ft (7.6 m) and floorplan dimensions of 94 ft x 220 ft (28.6 x67 m) was 33.
A cost comparison of these two designalternatives is shown in Table 2. The
cost of concrete, longitudinal steel, spi-ral steel and the formwork were takenfrom the 1983 Chicago area cost esti-mate and are shown in Table 3.
A total savings of $3,824,007 is ob-tained when using a high strength con-crete option for the columns. This
110
48„4 .. 1,.
i1.T 3„
191/2
2" 2' R=_^ry a6
M
9 1/2 5" 91/z 5'
26" 24"
WSDOT Girders Bulb Tee
42
jIj/241 N^ 92
Qa 2as N
10 8 (".1 O/1 II
8 ^^
2824"
Type V & V1(AASHTO-PCI) 72" Colorado Girder
Fig. 10. Cross section of solid section girders.
amount is very approximate; the actualsavings may he less. On the other hand,this amount does not include the savingsdue to an increase in rental space of66,000 sq ft (6131 m 2 ). The 1983 rentalcost in downtown Chicago was ap-proximately 520 sq ft (1.86 m2) per year.
IMPLICATIONS FORPRESTRESSED CONCRETE
1. The compressive strength in uni-axial compression does not substantiallyinfluence the resisting capacity offlexural systems because of the desir-
PCI JOURNAL/November-December 19B5 111
A
ability of the under-reinforced condi-tions in design. The location and theamount of steel are predominant in de-termining the ultimate capacity of suchsystems. For prestressed flexural sys-tems the use of high strength concretemay not produce cost effective benefitsin terms of ultimate capacity. However,if the design is governed by serviceabil-ity limit states, then high strength con-crete can be beneficial. This was illus-trated by robse and Moustafa.17
For cast-in-place decks the benefitsof high strength concrete in increasingthe span capabilities of four types of gir-ders (see Fig. 9) are shown in Fig. 10. It
can be seen from this figure that for theAASHTO-PCI Type VI girder of 72 in.(1830 mm) depth, the increase of con-crete strength from 6000 to 10,000 psi(42 to 70 MPa) increases the span capa-bility approximately from 140 to 165 ft(43 to 50 m)—an increase of 18 percent.
The potential for using shallow mem-bers with increasing concrete strengthsis also shown in Fig. 10. For cast-in-place decks, the potential for reducingthe depth from 72 to 48 in. (1830 to 1220mm) and increasing concrete strengthsfrom 6000 to 10,000 psi (42 to 70 MPa)can be realized for all girder spacings.
2. The use of high strength concrete
n
330_ 1
fpu = 270000 ksifpe = 154.9 ksig=0.7 b
present study/f,=13ksi, p=0.005
PCI£cuA = 0.003428: 0.00362C: 0.00322
A': 0.002920 ` = 0.00321C'= 0.00264
present studyf,=5ksi, p=0.005
PCIA'
C' C B'
2400
21
750 1500 2250 3000 3700 4500 5250moment (kip-in)
Fig. 11. Effect of concrete strength on the load-moment interaction curve of prestressedconcrete beam-column element.
112
PK-
f^
5.5 bf.ff0.4
u
bt
03
curve no. A p = 0.005B p=0.007
0.2-7 0.7
0.1- BA
f,=13 ksife=5ksi
O0 2 4 6 8 10 12 14 16 18 20 22 24 26
Li
Or
Fig. 12, Effect of concrete strength and level of axial load and amount of prestressingreinforcement on the sectional ductility of prestressed concrete beam-column element.
can, in general, speed-up constructiontime. Since given strength is attainedearlier, post-tensioning and stresstransferring operations can be per-formed earlier.
3. The use of high strength concreteshows a definite advantage in structuralelements which predominantly carrycompressive forces. The effect of higherstrength concrete on the load-momentinteraction, and the comparison of re-sults obtained by using the PCP' proce-dure and a nonlinear computerized pro-cedureS2 is shown in Fig. 11. The non-linear computerized procedure assumesplane sections remain plane, uses Eq. (1)
for the stress-strain curve of concreteand uses a polynomial equation to ex-press the stress-strain relationship of a270,000 psi (1890 MPa) seven wire pre-stressing strand. This comparison indi-cates that the current PCI method forstrength computations is appropriate forbeam-column members of higherstrength concretes.
The PCI method is sufficiently accu-rate for high strength concrete, despitethe approximate rectangular stressblock, a constant value of ultimate strain(Ely ), and an approximate equation forthe stress (fr.) in prestressing steel atthe ultimate condition.
PCI JOURNALJNovember-December 1985 113
In Fig. 11 the values of the compres-sive strain in concrete at the maximumresistance of the section (E,y ) are alsoshown and they are not constant. Asimilar conclusion was reached 38 forreinforced concrete. The analysis resultspresented in Fig. 11 do not include thelong term effects due to lack of informa-tion on time effects on high strengthconcrete columns.
4. The modulus of elasticity of con-crete is an important considerationwhen calculating the cambers and de-flections of prestressed concrete mem-bers. The ACI equation for elastic mod-ulus overestimates by as much as 20percent the modulus for concretes withstrengths of about 12,000 psi (84 MPa).The modulus of concrete is also an im-portant parameter in computating pre-stress losses and buckling of slender,compression-dominant members suchas columns. The reported creep andshrinkage of high strength concretes' arelow, therefore, prestress losses will bereduced for high strength concrete ele-ments.
5. A large number of design parame-ters in current practice are implicitlyrelated to the tensile strength of con-crete, such as development length,minimum reinforcement for flexure,shear and torsion, and maximum stressfor shear and torsion. Whether these de-sign parameters are applicable to highstrength concrete remains to beexamined.
The tensile strength of concrete isoften relied upon in working stress de-sign. The AC1 Code's permissible ex-treme fiber tensile stress in the precom-pressed tensile zone for prestressedflexural elements, 6 y+7, can be usedwith an acceptable degree of conser-vatism for concretes of higher strengthsif split cylinder tests are considered tobe representative of the tension in thebottom flange of a prestressed beam.However, from beam flexural tests theresults of flexural modulus indicate that6 ,+ , may be too conservative,
6. Poisson's ratio of normal and highstrength concrete is comparable in theelastic range; hence, there should not bea difference in the behavior of biaxiallyloaded members such as slabs and tri-axially loaded members such as pilesand columns, under service load condi-tions.
7. AIthough at a material level, highstrength concrete is relatively morebrittle than normal strength concrete,the same is not the case for sectionalductility. Fig. 12 shows the variation ofcurvature ductility (/) with thelevel of axial load, the amount of long-itudinal prestressing and the compres-sive strength of concrete. The computa-tions were carried out using the straincompatibility and force equilibriumequations, assuming plane sections re-main plane and using Eq. (1) for stress-strain curve of concrete. The stress-strain curve of 270,000 psi (1890 MPa)for the seven wire prestressing strandwas expressed through a polynomialequation.
Prestressed beam-column members ofhigher strength concrete show similarsectional ductility capability in the re-gion of loads below balanced condition.For low axial loads (k < 0.1) the sectionwith higher strength concrete showsrelatively more ductility as compared tonormal strength concrete sections. Fig.12 shows that if the amount of pre-stressing steel is kept constant, then in-creasing the strength of concrete in-creases the ductility ratio especially atlow values of axial loads.
This analytical observation of in-creased sectional ductility for beam-column members of high strength con-crete (for the same amount of longitudi-nal steel) should he substantiated withexperimental results. The comparison ofanalytical results for strain at ultimateresistance of the section and the com-puted curvature ductilities for low andhigh strength concrete with differingamounts of prestressing steel is pre-sented in Table 4.
114
Table 4. Analytical results of strain at ultimate and curvature ductility for low and highstrength concrete.
f p K" K'°^^
ata,.
= 0.003
0.007 0.000 0.118 0.00328 0.617 0.0875 7.051 6.3500.085 0.128 0.00335 0.5108 0.1121 4.557 3.9790.170 0.131 0.00298 0.3663 0.1360 2.694 -0.255 0.132 0.00323 0.3447 0.1677 2.056 1.875
5,000 0.340 0.127 0.00284 0.2528 0.2046 1-236 1.319
p5i 0.009 0.000 0.131 0.00277 0.4227 0.0918 4.606 -0.080 0.140 0.00348 0.4640 0.1146 4.048 3.3830.161 0.140 0.00343 0.3920 0.1473 2.662 2.6260.241 0.136 0.00298 0.2886 0.1712 1.686 1.7020.322 0.129 0.00312 0.2698 0.2227 1.211 1.147
0.007 0.000 0.041 0.00312 1.1086 0.0777 15-255 14.2120.097 0.076 0.00340 0.7253 0.1169 6.204 5.1320.194 0.100 0.00344 0.5236 0.1626 3.221 2.5500.291 0.111 0.00358 0.4245 0.2069 2,052 1.552
13,000 0.388 0.162 0.00347 0.3268 0.2555 1,2789 1.017psi 0.009 0.000 0.072 0.00324 0.9425 0.0812 11.610 10.241
0.940 0.096 0.00333 0.6272 0.1207 5.198 4.4690.188 0.112 0.00375 0.5455 0.1639 3.329 2.3690.282 0.119 0.00346 0.3820 0.2084 1.833 1.4270.376 0.119 0.00349 0.3193 0.2565 1.245 0.982
K _ P,f,hI
Note 1. The above values are for:fp„ = 270,000 psi f,, = 154.9 ksi,E„ =0.00 and g=0.7.
Note 2. 1 psi = 0.006895 MPa;1 ksi = 6.895 41 Pa.
e
gt
8. The beneficial effects of the confin-ing reinforcement on the stress-straincurve of concrete depends on thestrength of concrete. The effect of thelateral confining reinforcement be-comes predominant only after sufficientlateral dilation has taken place; forexample, after the concrete has under-gone large strain in the most com-pressed direction. In the inelastic rangethe lateral dilation of higher strengthconcrete is relatively less. Thus, to en-
sure adequate sectional ductility, addi-tional lateral confining reinforcementwill be necessary.
9. Additional considerations for use ofhigh strength concrete for precast andprestressed concrete applications aredetailed in a recent ACI Special Publi-cation.s ' For examples, see papers byAswad and Hester, Moksnes and Jakob-sen, and Fafitis and Shah in the ACIpublications Further information isgiven in the list of references.
PCI JOURNALJNovember-December 1985 115
CONCLUSIONS ANDRECOMMENDATIONS
On the basis of the results of thiswork, the following conclusions can bedrawn:
1. There are significant differences inthe compressive stress-strain curves ofnormal and high strength concretes. Thecurve for higher strength concrete is muchmore linear to a much higher fraction ofthe compressive strength. The slope ofthe post maximum stress range increasesas the strength increases.
2. The ACI equation for estimatingthe secant modulus of elasticity, E, =33W'•5 f,', predicts values as much as20 percent too high for concretes withcompressive strengths in the vicinity of12,000 psi (84 MPa).
3. The split cylinder strength for lowand high strength can be conservativelyrepresented by the expression, f,. =6,T
4. The ACI Code's current expressionfor modulus of rupture, f, = 7.5 Y ,' maybe too conservative for high strengthconcrete and an alternate expression, f,.= 2 (f f ? 3 , appears to be more repre-sentative of the test data.
5. In the inelastic range, high strengthconcrete exhibits less volume dilation,therefore, the effectiveness of confininglateral reinforcement is relatively lesscompared to normal strength concrete.
6. The effect of high strain rate on thestrength increase is less for higherstrength concretes.
7. The current PCI procedure forstrength computation is adequate forbeam-column members using highstrength concrete.
8. At material level, high strengthconcrete is less ductile than normalstrength concrete, but at the sectionallevel for reinforced concrete elements,if the ratio p/pa is kept constant, the de-flection ductility is essentially indepen-dent of the strength of concrete. For pre-stressed concrete beam-column mem-bers, the analytical results indicate thatfor high level axial loads there is noloss in the curvature ductility with theuse of high strength concrete. For lowaxial load levels (i.e., predominantlyflexural behavior) the curvature ductil-ity of high strength concrete prestressedelements is superior to that of normalstrength concrete prestressed beam-column members.
9. The test results of solid torsionalcylinders and reinforced concretebeams subjected to shear suggest thatshear strength appears to be related tocompressive strength through a 0.333power.
10. The use of high strength concretecan increase the span capabilities ofprestressed concrete bridge girders andmay also reduce the overall depth of thegirders.
ACKNOWLEDGMENTThe research reported in this paper
has been partly supported by a Pre-stressed Concrete Institute ResearchFellowship and National Science Foun-dation Grant NSF-CEE-830-7532 to thefirst author (S. H. Ahmad) and NSF-CEE 8203100 to the second author (S. P.Shah). The NSF Program Manager forboth NSF grants is Dr. M. Gaus.
NOTE: Discussion of this paper is invited. Please submityour comments to PCI Headquarters by July 1, 1986.
116
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APPENDIX - NOTATION
f = stressE = strain
= uniaxial compressive strength(peak stress)
e o = strain corresponding to peakstress
A, B, K = calibrating constantEr, (E, ), = secant modulus of elasticity
at 0.45 ff under static strainrate
W = unit weight in lb per cu ftfg p = split cylinder strengthf, = modulus of rupture of con-
crete(E )F = secant modulus of elasticity
at strain rate eE = strain ratee, = static strain rate = 32 micro-
strains per sec(f )E = compressive strength at strain
PCI JOURNAL)November-December 1985
rate ea, = shape factors(eo )i = peak strain at strain rate ea = shear spanV" = shear stress at diagonal crack-
ingyr = ultimate shear stressp = longitudinal steel ratiod = effective depth, i.e., distance
from extreme compressive fi-ber to center of gravity of ten-sile reinforcement
A. = gross area of sectionA,, = area of core of spirally rein-
forced column measured tooutside diameter of spiral
f„n = yield stress of hoop steelph = reinforcement ratio produc-
ing balanced strain conditionp. = ratio of spiral reinforcement
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