Concrete has achieved its status as the most widely

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1 Reinfored geopolymer ement onrete in flexure: A loser look at stress-strain performane and equivalent stress-blok parameters Brett Tempest, Janos Gergely, and Ashley Skipper Geopolymer ement onrete ould revolutionize the onrete industry by merging the benefits of onrete with signifiantly redued greenhouse gas emissions ompared with portland ement onrete. The researh presented in this paper used a ombined axial stress and flexure test developed by Hognestad et al. as a primary means of determining the distribution of stresses in the ompression zone of geopolymer ement onrete in flexure. The results indiated that slightly modified stress blok parameters α 1 and β 1 should be applied to geopolymer ement onrete due to differenes in the stress-strain relationship of geopolymer ement onrete in ompression ompared with portland ement onrete. Conrete has ahieved its status as the most widely used building material in the world beause of its versatility, strength, and durability. However, the prodution of portland ement is an emissions-intensive proess that aounts for approximately 5% of global arbon dioxide emissions. 1 Geopolymer ement, first named and desribed by Davidovits, 2 is an alternative to portland ement as a binder in onrete. Critial analyses of geopolymer and portland ements have estimated the redution in arbon dioxide assoiated with geopolymer ement to be as high as 8% and as low as 9%. 3,4 Other studies have indiated that, depending on the industrial proesses used and the soure material loations, emissions assoiated with geopolymer ement onrete an range from 97% lower to 14% higher than those of portland ement onrete. 5 The potential to redue the arbon dioxide emissions assoiated with onrete prodution is suffiient inentive to motivate the wider-sale adoption of geopolymer ement onrete tehnologies as a limate hange mitigation strategy. Some examples of full-sale failities built with geopolymer ement onrete demonstrate that there has been suffiient advanement of the tehnology to enable real-world engineering and onstrution. 6 Van Deventer has desribed a path to industrialization that inludes demonstration projets and the development of speifi standards for 3 November Deember 216 PCI Journal

2 geopolymer ement onrete. 7 In order to enourage more widespread prodution and adoption of geopolymer ement onrete materials in routine onstrution, their engineering properties and performane in typial strutural omponents must be determined experimentally and doumented. Any signifiant differenes between the performane of geopolymer ement onrete and portland ement onrete must be highlighted so that future editions of building ode requirements an aurately govern the design with geopolymer materials. Similarities in the performane of the two materials ould enable the use of existing odes and provisions. Prior researh works by Sumajouw and Rangan 8 and Yost et al. 9 ompared observations from destrutive beam tests with estimates made using existing design parameters published by the Amerian Conrete Institute (ACI ) 1 and Standards Australia (AS 36) 11 and determined that they provide suffiient auray for design purposes. However, Prahasaree et al. 12 highlighted the need for geopolymer-ement-onrete-speifi design parameters due to differenes in the deformational behavior ompared with that of portland ement onrete. This paper desribes the evaluation of ompressive flexural performane of geopolymer ement onrete using test methods devised by Hognestad et al. 13 to evaluate the stress distribution in onrete beams near ultimate onditions. The results are then applied to predit the strength of a series of reinfored geopolymer ement onrete beams that were tested to failure. Bakground Davidovits 14 desribes four general types of geopolymer ements: slag-based, rok-based, fly-ash-based, and ferrosialate-based. Geopolymer ements soured from fly ash require an ativating solution, often omposed of sodium siliate and sodium hydroxide, in order to develop ementitious properties in the fly ash. 14 The ativating solution and fly ash are ombined with aggregates to produe onrete. Water and superplastiizer may also be added to improve the workability of the onrete mixture. The use of flyash-based geopolymers as a binder typially requires the onrete to be ured at an elevated temperature of 14 F to 176 F (6 C to 8 C) for up to 48 hours. 15,16 Geopolymer ement onrete develops its full ompressive strength through this heat-uring proess. Several reent experimental studies have been performed to evaluate the material properties and strutural performane of geopolymer ement onrete and have shown that these harateristis are similar to those of portland ement onrete. Diaz-Loya et al. 17 studied the stati elasti modulus, ompressive strength, modulus of rupture, and Poisson s ratio of 25 bathes of geopolymer ement onrete. The elasti modulus ranged from 988 to 6219 ksi (6.81 to 42.9 GPa), ompressive strengths ranged from 15 to 11,657 psi (1.3 to 8.4 MPa), the modulus of rupture ranged from 397 to 929 psi (2.74 to 6.41 MPa), and the average Poisson s ratio was.14. Despite these general similarities between the physial harateristis of geopolymer ement onrete and portland ement onrete, there are also signifiant differenes that may affet the deision to use design parameters developed for portland ement onrete. The elasti modulus is generally lower, and shrinkage and reep phenomena our at a redued magnitude. 18 In addition, the tensile strength of geopolymer ement onrete materials may be slightly greater than would be expeted for portland ement onrete with similar ompressive strength. 6 These harateristis and their impats on beam strength and defletion are desribed by Tempest. 18 Thomas and Peethemparan 19 investigated the stress-strain relationship of alkali-ativated ement onretes prepared with either slag ement or high-alium fly ash. Using uniaxial ompression tests, the team measured the stressstrain relationship in the linear elasti, softening, and postpeak loading phases. The performane up to peak stress orrelated well with models for the stress-strain relationship in portland ement onrete, with similar ompressive strength and elasti modulus. A signifiant differene relative to portland ement onrete was the tendeny of alkali-ativated ement onrete to display brittle frature immediately after peak stress was reahed. Cross et al. 2 reported the behavior of reinfored geopolymer ement onrete beams undergoing four-point bending to determine the validity of urrent design methodology for portland ement onrete beams. Three reinfored geopolymer ement onrete beams were designed and fabriated aording to the design methodology in ACI for portland ement onrete. During testing, the beams showed a dutile response, with the tensile steel yielding followed by rushing of the ompression onrete. The observed ultimate moments for all three beams were higher than the moment apaity as alulated using the provisions of ACI Sumajouw and Rangan 8 investigated the flexural behavior of reinfored geopolymer ement onrete beams and evaluated the strength, rak pattern, defletions, and dutility to verify the use of existing portland ement onrete design provisions in AS 36 with geopolymer ement onrete. A series of 12 reinfored geopolymer ement onrete beams were fabriated and tested with variations in the longitudinal tensile reinforement ratio and the ompressive strength of the speimens. The reinfored beams were designed with ompressive strengths of 58, 73, and 1,8 psi (4, 5, and 75 MPa). The ratio of observed apaity to predited apaity averaged 1.11 for all of the speimens, demonstrating that the ode provisions are appliable to estimating the apaity of geopolymer ement PCI Journal November Deember

3 onrete beams. The ratio of observed-to-predited defletion measurements averaged 1.15, whih suggests that the provisions of AS 36 also aurately and onservatively predit the servieability of reinfored geopolymer ement onrete beams. Yost et al. 9 investigated the behavior of reinfored geopolymer ement onrete beams under the influene of four-point bending. As in previously reported studies, the observations showed that the underreinfored geopolymer ement onrete beams behaved similarly to the underreinfored portland ement onrete beams. The geopolymer ement onrete beams demonstrated a more sudden failure and explosive response than the portland ement onrete beams. The geopolymer ement onrete beams also developed a higher onrete strain at ompression failure than the portland ement onrete beams. The average onrete strains were 3147 and 3373 µε for the underreinfored geopolymer ement onrete and portland ement onrete beams, respetively. The overreinfored geopolymer ement onrete beams also showed a more sudden failure in omparison to the similarly designed portland ement onrete beams. The underreinfored geopolymer ement onrete beams had an average observed-to-predited ratio of 1.26, whih was slightly higher than the 1.19 ratio for the underreinfored portland ement onrete speimens. The summary onsensus of studies that have ompared experimental results of beam tests with strength preditions is that existing ACI parameters yield aeptable results. This has been generally true for underreinfored beams with small ross setions that make up the bulk of the beams reported in the literature. The risk of misharaterizing the stress distribution within the ompression zone of a beam in flexure is low for beams with shallow neutral axes. However, beams with greater reinforement ratios ρ or lowerstrength onrete have deeper ompressive stress zones at failure. In these ases, the atual stress distribution, and therefore the more aurate shape of the equivalent stress blok, an ause larger errors if not assumed orretly. Figure 1 illustrates this relationship. The nominal moment apaity of a hypothetial in. (41 61 mm) beam with onrete ompressive strength from 3 to 12, psi (21 to 83 MPa) is plotted with reinforement ratios up to ρ bal (the reinforement ratio at balaned failure onditions). Inreasing or dereasing the value of the stress blok parameter α 1 (that is,.85 for 4 psi [27.6 MPa] onrete) by 1% leads to little hange in the estimated moment apaity for beams with low ρ. However, at ρ bal, the range of the results an be up to approximately 7% of the total beam strength, as in the 3 psi beam. This indiates that more-exat parameters are required for more heavily reinfored beams, espeially if they are signifiantly deep and do not use high-strength onrete. Prahasaree et al. 12 approahed the problem of developing geopolymer-ement-onrete-speifi stress-blok param- Potential error, % f = 3 psi ρ bal =.214 f = 6 psi ρ bal = ρ, in. 2 /in. 2 Figure 1. Potential error from inaurate stress-blok parameters in beams with higher reinforement ratios. Note: f = ompressive strength of onrete; ρ = reinforement ratio; ρ bal = reinforement ratio at balaned failure onditions. 1 in. = 25.4 mm; 1 psi = kpa. eters with analytial methods. The group used data from tests of the elasti harateristis of geopolymer ement onrete to analytially determine the parameters of an equivalent stress blok partiular to geopolymer ement onrete. Using this information, a general stress-strain relationship for geopolymer ement onrete was reated and ompared with researh from other authors. The team found that the stress-blok parameters given in ACI for use in portland ement onrete design were not appropriate for reinfored geopolymer ement onrete design and proposed values based on the tests of geopolymer ement onrete materials. The resulting parameters yielded better estimates of beam apaity. Based on the findings of the initial researh performed by Tempest, 18 a seond study was launhed by Skipper and Tempest to establish stress-strain relationships for geopolymer ement onrete in flexure using bending tests rather than uniaxial ompression. 21 These tests established the stress-blok parameters α 1 and β 1 that are speifi to geopolymer ement onrete of various ompressive strengths. The outome of these tests is presented in the following setions. Researh objetives and methods f = 9 psi ρ bal =.482 f = 12, psi ρ bal =.68 The studies listed in the review of previous researh related to the flexural performane of reinfored geopolymer ement onrete verify the appliability of various portland ement onrete design provisions to geopolymer ement onrete. This paper presents results of experiments onduted to diretly determine parameters α 1 and β 1 that define the equivalent ompressive stress blok that is ommonly used for onrete design purposes. The rosshathed area in Fig. 2 represents the ompression zone of a beam in positive moment flexure. The strain distribution for this segment of the ross setion is linear (Fig. 2); 32 November Deember 216 PCI Journal

4 α 1 f ε b f β 1 /2 = k 2 h d Compression zone of a beam in positive moment flexure ε x F(ε x ) k 3 f x β 1 Resultant = k 1 k 3 f b ompression fore Resultant tension fore Figure 2. Stresses and strains in onrete beams, relationship of k 1, k 2, and k 3 to the resultant ompressive fore. Note: b = width of a retangular onrete setion; = distane from the ompressive fae to the neutral axis in a onrete beam; C = resultant ompressive fore; d = distane from the extreme ompression fiber to the entroid of the ompression reinforing steel group; f = stress in the onrete; f = ompressive strength of onrete; F = fores ating on the setion of the beam olumn; h = depth of beam; k 1 = ratio of average ompressive stress to maximum ompressive stress; k 2 = ratio of distane from top of beam to the resultant ompressive fore C and the depth to the neutral axis ; k 3 = ratio of ylinder onrete strength to beam onrete strength; x = distane from neutral axis to the resultant ompressive fore line of ation; α 1 = stress-blok parameter; β 1 = stress-blok parameter; ε = onrete strain; ε x = unknown onrete strain. however, these strains do not have a linear relationship to stresses after the onrete begins to rak and soften. Beams approahing their apaity in flexure would ontain the stress distribution in Fig. 2. For design purposes, the Whitney stress blok (Fig. 2) is used as an approximation of the area enlosed by the paraboli area. 22 The blok is defined by the fators in Fig. 2, where k 1 = ratio of average ompressive stress to maximum ompressive stress the ompression fae and the neutral axis of the flexural beam is simulated without the effets of tensile stresses and a shifting neutral axis, as would be found in a reinfored beam. Beause this is not possible in onentri tests, the stress and strain gradients that are found in flexural omponents are dupliated in the test piee. Figure 3 shows the test geometry, with P 1 representing the primary axial load and P 2 representing the eentri load. k 2 = ratio of distane from top of beam to the resultant ompressive fore C and the depth to the neutral axis a 1 a 2 P 1 P 2 k 3 = ratio of ylinder onrete strength to beam onrete strength There are several hallenges in determining experimentally the stress-strain relationship in Fig. 2. Although onentri ompression tests an be used to determine the stress-strain relationship through the initiation of rushing, the postpeak behavior is typially obsured by the rapid release of strain energy stored in the testing devie. For the purpose of estimating k 1, k 2, and k 3, as well as measuring the stress-strain relationship, a ombined axial-flexure test was developed by Hognestad et al. 13 In this proedure, a short beam olumn is loaded axially, while an eentri load is applied through two arms attahed to the ends of the speimen (shown ut aross an axis of vertial symmetry in Fig. 3). The eentri load produes a moment that maintains a neutral fae on one side of the beam olumn while the opposite side approahes the ompressive strain limit. In this way, the area between Neutral fae (1 - k 2 ) Beam olumn k 2 Attahed moment arm Compressive fae C = k f 1 k 3 b = P 1 + P 2 Figure 3. Free body diagram of the beam-olumn speimen ut at midheight. Note: a 1 = distane from the neutral fae to P 1 ; a 2 = distane from the neutral fae to P 2 ; b = width of a retangular onrete setion; = distane from the ompressive fae to the neutral axis in a onrete beam; C = resultant ompressive fore; f = ompressive strength of onrete; k 1 = ratio of average ompressive stress to maximum ompressive stress; k 2 = ratio of distane from top of beam to the resultant ompressive fore C and the depth to the neutral axis ; k 3 = ratio of ylinder onrete strength to beam onrete strength; P 1 = primary axial load ating on the beam olumn; P 2 = eentri load ating on the beam olumn. PCI Journal November Deember

5 1, 9 GCC5 GCC2 a 1 = distane from the neutral fae to P 1 8 GCC6 a 2 = distane from the neutral fae to P 2 7 GCC4 f, psi GCC ε, % Figure 4. Relative slopes of stress-strain urves. Note: f = stress in the onrete; ε = strain. 1 psi = kpa. Based on stati analysis of the system, k 1 k 3 and k 2 an be alulated diretly from the beam dimensions and the magnitude of the loads P 1 and P 2 (Fig. 3). The resultant ompressive fore C of the stress in the onrete (Fig. 3) is equal to the sum of the applied fores P 1 and P 2. Equation (1) results from the free body diagram given in Fig. 3. k 2 = 1 P a P a ( P 1 +P 2 ) The relationship between stress and strain must be determined by a proess of numerial integration. It is neessary to assume that the stress in the onrete f is a funtion of ε x, where ε x is a linear distribution aross (Fig. 2). However, beause the funtion F(ε x ) is not known, some substitution of known or measurable quantities must be made to determine f from data olleted during experiments. The resultant ompressive fore C may be defined by Eq. (5). b dx = C = b F ( ε x ) ε F ( ε ) ε x where (4) dε x = P 1 + P 2 = f b (5) F = = k 1 k 3 f b P 1 +P 2 ( ) (1) where F = fores ating on the setion of the beam olumn f b = ompressive strength of onrete = width of a retangular onrete setion ε f = onrete strain = average stress on a ross setion of the beam olumn The moment M is determined by Eq. (6). b 2 xdx = M = b F ( ε x ) ε F ( ε ) ε 2 x = P 1 a 1 + P 2 a 2 = m b 2 ε x dε x (6) = distane from the ompressive fae to the neutral axis in a onrete beam where Solving for k 1 k 3 gives Eq. (2). ( ) k 1 k 3 = P +P 1 2 (2) f b Taking the sum of the moments about the neutral fae of the beam generated by the fores shown in Fig. 5 gives Eq. (3), whih is solved for k 2 in Eq. (4). m = average moment ating on a setion of the beam olumn Equation (7) alulates the average stress on the ross setion f. f P1 P2 = + (7) b where M = = ( P 1 +P 2 )( 1 k 2 ) P 1 a 1 P 2 a 2 (3) M = moment Eq. (8) determines the average moment m. Pa Pa m= 2 b Differentiating the third and last terms of Eq. (5) with (8) 34 November Deember 216 PCI Journal

6 respet to ε results in Eq. (9). Substituting the relationship in Eq. (1), whih is obtained by manipulating the third and fifth terms of Eq. (5) into Eq. (9), where df is approximately equal to f, ε ε d two quantities that are measured during testing. The unknown funtion F(ε x ) has been removed from the analysis, permitting the measured quantities P 1, P 2, and ε to be used to diretly alulate f. ε F ( ε x ) dε x = f ε Using the same strategy gives Eq. (11). f (9) df f= + f dε ε (1) dm = + 2m dε ε (11) Speimen preparation To ondut the flexural test to ollet the quantities desribed previously, five beam olumns and five reinfored beams were onstruted. The beam olumns featured an unreinfored geopolymer ement onrete ross setion that was 7.25 in. (184 mm) deep in the transverse dimension and 7.5 in. (19 mm) deep in the diretion perpendiular to the bending axis. The formwork was onstruted of 3 4 in. (19 mm) oriented strand board and was heavily stiffened with extra framing in order to maintain its geometry under the pressure of the fresh onrete. The forms were also lined with polyethylene sheeting in order to prevent the absorption of water or the alkaline ativator into the wood. Sleeves fabriated from square, hollow strutural steel were ast onto eah end of the speimen. The holes were preisely loated to aommodate the bolting pattern of the moment arms. Passages for the bolts were bloked out with lengths of polyvinyl hloride pipe that were removed after the onrete ured. Bent hoops of Grade 6 (414 MPa), no. 3 (1M) reinforing bar provided reinforing inside of the sleeve. No. 4 (13M) bars extended a short distane beyond the end of the sleeve to transfer fores from the loaded ends of the beam olumn into the unreinfored entral portion of the speimen. Table 1 lists the materials in the onrete mixture design used to ast the reinfored onrete beams and the beam olumns. The fly ash used was marketed as ASTM C618 Class F, whih originated from a steam generation plant in the southeastern United States. The ementitious materials also inluded sodium hydroxide pellets. Speimens GCC1 through GCC3 ontained sodium siliate solution as a soure of soluble silia in the ativating solution. Speimens GCC4 through GCC7 ontained silia fume as the supplemental soure of soluble silia. Coarse aggregates used were a granite type onforming to ASTM C33-16 size 7, with.5 in. (13 mm) maximum partile diameter. The fine aggregate was silia sand, whih also met ASTM C33 16 requirements for onrete appliations. Table 1 also shows the strength of ompanion ylinders ast with the beam olumns. The ylinders were tested at the same time as their assoiated beam or beam olumn. Beause the two types of speimens were tested at different onrete ages, there was typially some strength gain Table 1. Geopolymer ement onrete mixture designs GCC1 GCC2 GCC3 GCC4 GCC5 GCC6 GCC7 Fly ash, lb/yd Water, lb/yd Sodium hydroxide, lb/yd Silia fume, lb/yd Sodium siliate, lb/yd Fine aggregate, lb/yd Coarse aggregate, lb/yd w/m Beam f, psi 32 6 n/a n/a n/a n/a 11,9 Beam olumn f, psi Not tested n/a Note: f = ompressive strength of onrete; n/a = not appliable (not tested); w/m = water ementitious materials ratio. 1 psi = kpa; 1 lb/yd 3 =.593 kg/m 3. PCI Journal November Deember

7 between the beam test and the beam-olumn tests. Test speimens GCC1, GCC2, and GCC3 were prepared in a preast onrete plant setting, and the onrete mixing was provided by a 1 yd 3 (7.6 m 3 ) apaity mixing truk. 6 Speimens GCC4, GCC5, and GCC6 were prepared in a university lab setting and were mixed in a 3 ft 3 (.85 m 3 ) rotary mixer. Speimen GCC7 was prepared in a university lab setting but was mixed in a 1 yd 3 (7.65 m 3 ) apaity mixing truk. 6 The mixture proportions for speimens GCC4 through GCC7 were similar (Table 1), but small variations in the water ontent aused differenes in the ompressive strength of the onrete. After asting, the speimens were allowed a 48-hour aging period at ambient temperature. Following aging, the speimens were ured for 48 hours in a 167 F (75. C) oven onstruted with rigid insulation panels and onditioned by eletri resistane spae heaters. The speimens were instrumented with five onrete strain gauges. Two gauges were mounted on the ompression fae of the beam olumn, and two were mounted on the neutral fae within 2 in. (5 mm) of the enterline. The primary axial load P 1 was applied at a rate of approximately 2 kip/min (89 kn/min). The moment was applied through the arms by an atuator ontrolled by a losed-loop routine. During the testing proess, measurements were reorded by a data aquisition system set to measure twie per seond. The system reorded the loads P 1 and P 2, strain from eah of the five strain gauges, and displaement at the inside and outside of the beam at midspan. The displaement data reorded during the test was used to ompute additional stresses aused by seondary moments related to P 1 and P 2 ating through the eentriity e. These additional stresses were alulated by Eq. (12), whih is a modifiation of Eq. (8). To aommodate a fore limitation in the testing apparatus, the ross setions of beam-olumn speimens GCC2 and GCC3 were slightly redued by saw utting 1 in. (25 mm) vertial slits into the speimen at midspan. Speimens typially failed by initiating rushing at the ompression fae. At the end of the test, suffiient ross setion had been lost from the speimens that the initially onentri P 1 fore beame eentri and the speimens usually failed in shear. Disussion of beam-olumn results The five beam-olumn speimens provided a spetrum of stress-strain response that appears to be related to onrete ompressive strength. The slope of the stress-strain urve inreases as the onrete ompressive strength inreases (Fig. 4). Figure 5 represents the orrelation between the slope of the stress-strain relationship (Fig. 4) and the onrete ompressive strength f. Analogous to portland ement onrete, the relationship between ompressive strength and elasti modulus E an be represented by Eq. (13). where ψ E =ψ = fator fit to the data f (13) For normalweight portland ement onrete, the fator ψ in Eq. (13) is ommonly aepted as equal to 57, (47 for SI units). In the ase of the results presented here, ψ equals 43, (3575 for SI units) and fits the data with oeffiient of determination R 2 equal to.99. This elasti modulus is similar to that of portland ement onrete with lightweight aggregate. Analysis of beam-olumn test data Equations (2) and (4) allow the omputation of k 1 k 3 and k 2, respetively. Table 2 presents the results of these alulations using test data as inputs. The mixtures for speimens GCC1 and GCC6 were not suessfully tested due to equipment malfuntions. The ratio of ylinder onrete strength to beam onrete strength k 3 was found as the ratio of f to the maximum onrete stress f determined during the test. The parameters of α 1 and β 1 were alulated using Eq. (14) and (15). α = kk 2k 2 (14) β 1 = 2k 2 (15) Figures 6 and 7 show the relationship of α 1 and β 1 to the ylinder ompressive strength of the onrete in the beam E, psi 6,, 5,, 4,, 3,, 2,, 1,, GCC3 R 2 =.99 E = 57, f E = 43, , 12, f, psi Figure 5. Relationship of ompressive strength to modulus of elastiity. Note: E = elasti modulus of the onrete; f = ompressive strength of onrete; R 2 = oeffiient of determination. 1 psi = kpa. GCC2 GCC6 GCC4 GCC5 f 36 November Deember 216 PCI Journal

8 Table 2. Calulated values of k 1, k 2, and k 3 for beam olumns Speimen f, psi E, psi k 1 k 3 k 1 k 2 k 3 α 1 β 1 GCC2 7 3,67, GCC3 52 3,9, GCC4 79 3,82, GCC5 9 4,13, GCC6 73 3,76, Note: E = elasti modulus of the onrete; f = ompressive strength of onrete; k 1 = ratio of average ompressive stress to maximum ompressive stress; k 2 = ratio of distane from top of beam to the resultant ompressive fore C and the depth to the neutral axis ; k 3 = ratio of ylinder onrete strength to beam onrete strength; α 1 = stress-blok parameter = kk 1 3; β 1 = stress-blok parameter = 2k 2. 1 psi = kpa. 2k 2 olumns, respetively. All α 1 were in the range of 1., with an upper bound of 1.13 and a lower bound of.89. Although Fig. 6 indiates that α 1 varies with onrete strength, the variation is not pronouned. The preponderane of values above 1. implies that the ompressive strength of onrete in large omponents is greater than the ompressive strength in small test ylinders. This is most likely an indiation of improved uring of onrete in massive omponents over onrete in ylinders. Beause the uring proess is improved by heating, the larger items benefit from their larger heat storage apaity. This phenomenon should be investigated further. Also, differenes in the ompressive strength of the speimens with similar mixture designs ould also be related to temperature variations at different loations in the uring oven. There are not suffiient data to justify proposing a design value of α 1 based on the ylinder ompressive strength until further researh an illuminate the auses of this differene. However, although α 1 is taken as.85 for all ases with portland ement onrete, there may be rea- son to relate α 1 to speimen size or shape for geopolymer ement onrete materials. Alternatively, more sophistiated uring of test ylinders ould be used to better relate the ompressive strength of a ylinder with the ompressive strength of onrete plaed in a strutural omponent. Based on the results of these tests, the relationship shown in Eq. (16) is proposed to relate α 1 to f. α 1 = (7 1-5 ) f (16) Figure 7 plots β 1, whih shows a tendeny to be slightly redued as ylinder ompressive strength inreases. For normal-strength portland ement onrete, ACI provides a range for β 1 of.85 for onrete between 25 and 4 psi (17 and 27 MPa) to β 1 of.65 for onrete above 8 psi (55 MPa). The beam-olumn speimens tested ranged in strength from 52 to 9 psi (36 to 62 MPa); however, the range of β 1 values was not nearly as broad. For the geopolymer ement onrete beam-olumn speimens, β 1 values ranged from.69 for the 52 psi onrete to.46 for the higher-strength onrete. The α 1 β y =.7 f R² = β 1 = -.7 f R² = , f, psi , f, psi Figure 6. Stress-blok parameter α 1 related to ylinder ompressive strength for beam olumns. Note: f = ompressive strength of onrete; R 2 = oeffiient of determination. 1 psi = kpa. Figure 7. Stress-blok parameter β 1 related to ylinder ompressive strength for beam olumns. Note: f = ompressive strength of onrete; R 2 = oeffiient of determination. 1 psi = kpa. PCI Journal November Deember

9 Table 3. Reinforement details, dimensions, and material properties for analysis of beam apaity Beam Soure A s, in. 2 A s, in. 2 d, in. d, in. f y, psi f, psi 1 GCC1-beam , 32 2 GCC1-beam , 32 3 GCC2-beam , 6 4 GCC2-beam , 6 5 GCC7-beam , 11,9 6 Sumajouw , Sumajouw , Sumajouw , Sumajouw , Sumajouw , Sumajouw , Sumajouw , Sumajouw , Sumajouw ,771 11,23 15 Sumajouw ,221 1, Sumajouw ,221 1, Sumajouw ,786 11,23 18 Yost ,221 * Yost ,221 * Yost ,221 * Yost ,221 * Yost ,221 * Yost ,221 * 8253 Soures: Data from Sumajouw and Rangan (26); Yost, Radli ska, Ernst, Salera, and Martignetti (213). Note: A s = area of reinforing steel in the tension zone; A s = area of reinforing steel in the ompression zone; d = distane from the extreme ompression fiber to the entroid of the ompression reinforing steel group; d = distane from the extreme ompressive fiber to the entroid of the tension reinforing group; f = ompressive strength of onrete; f y = yield stress of steel reinforing. 1 in. = 25.4 mm; 1 in. 2 = 645 mm 2 ; 1 psi = 6.89 kpa. * Values estimated using experimental data presented in Yost, Radli ska, Ernst, Salera, and Martignetti (213). dashed line in Fig. 7 represents ACI speifiations. Based on the results of these tests, the relationship shown in Eq. (17) is proposed to relate β 1 to f. β 1 = -(7 1-5 ) f (17) The values for α 1 and β 1 indiate that an equivalent retangular stress blok for geopolymer ement onrete materials is signifiantly smaller than similar bloks representing portland ement onrete behavior. The fator k 1 desribes the ratio of the area defined by the paraboli stress distri- bution in Fig. 3 to the area of a retangle fitted around its border. For a triangular distribution, the geometri fator would be.5, meaning that the triangle oupies half the area of the retangle. Similarly, for paraboli distributions the appropriate fator is.67. The k 1 value for the geopolymer ement onrete materials was.54, indiating that the distribution at failure was nearly triangular. The fator k 2 desribes the distane of the resultant ompression fore C (defined in Fig. 3) from the extreme ompressive fiber. The average omputed value for k 2 was.25, 38 November Deember 216 PCI Journal

10 whih indiates a strongly linear portion to the lower-strain portions followed by a softening near the upper-strain regions of the stress-strain relationship. This is apparent from the plots in Fig. 4. Beam performane Five reinfored geopolymer ement onrete beams were prepared with a subset (GCC1, GCC2, and GCC7) of the onrete mixture designs in Table 1. The beams were reinfored with no. 4 (13M) longitudinal bars and no. 3 (1M) losed stirrups. Eah beam had the same reinforing pattern of two bars in the ompression zone and three in the tension zone. The atual yield stress of steel used in the beams was measured by a tension test of the reinforing steel (Table 3). During the test, equal loads were applied at the third points of the 12 ft (3.65 m) span using a steel beam spreader. Figure 8 shows the results of the beam tests, and Table 4 gives the ultimate apaities. The ultimate moments observed in the beams were similar to the moment apaity omputed using provisions given in ACI , as interpreted in Eq. (18). Calulations to determine the equivalent Whitney stress blok were onduted using indexed fators typially assoiated with portland ement onrete, inluding α 1 of.85 and β 1 of.85 for 32 psi (22 MPa),.75 for 6 psi (41 MPa), and β 1 of.65 for 11,9 psi (82. MPa) onrete. The atual yield strengths of the reinforing steel for the GCC1, GCC2, and GCC4 beams were determined to be 82, psi (565 MPa), 9, psi (621 MPa), and 8, psi (552 MPa), respetively. These measured yield strengths were used in the alulations to estimate the design apaity of the reinfored onrete beams. Table 4 lists the ultimate moments (Fig. 8) observed in eah of the beams. The existing formulas were apable of prediting the beam strength within just a few perentage points of measured values. Only speimen GCC1-beam 1 reahed an ultimate moment that was slightly lower than its estimated moment apaity of 41.6 kip-ft (56.4 kn-m). Table 4 lists the alulated and observed raking and ultimate moments in eah of the beams. Moment, kip-ft GCC1-beam 2 GCC2-beam 2 GCC7-beam 1 GCC2-beam 1 GCC1-beam Defletion, in. Figure 8. Moment-defletion responses for all beams. Note: 1 in. = 25.4 mm; 1 kip-ft = kn-m. The beam tests were also used to verify the appliability of the revised α 1 and β 1 parameters developed by testing the geopolymer ement onrete beam olumns in flexure. The beam apaity alulated by Eq. (18) was estimated using Eq. (16) and (17) for α 1 and β 1. a d AE s s s d d + M = C ε 2 (18) n M n = nominal moment apaity of the beam C = onrete ompressive fore d a A s = distane from the extreme ompressive fiber to the entroid of the tension reinforing group = depth of the equivalent retangular stress blok = area of reinforing steel in the ompression zone E s = modulus of elastiity of reinforing steel ε s = strain at the entroid of the ompression reinforing steel group d = distane from the extreme ompression fiber to the entroid of the ompression reinforing steel group Table 4 shows the results. Beause of the limited number of data points, as well as the fat that the beams have low reinforement ratios, the improvement in apaity estimation auray is small ompared with the α 1 and β 1 values provided by ACI To test the revised parameters against a larger set of experimental results, Tables 3 and 4 present a meta-analysis of the beams reported by Yost et al. 9 and Sumajouw and Rangan. 8 The values in these tables were omputed using speimen details for geometry, onrete ompressive strength, and steel yield strength. The ultimate apaity of the beams was again estimated using α 1 and β 1 parameters defined in ACI Two differenes are notable between the estimated beam apaity presented in the original douments and the omputed values in Table 3. First, Sumajouw and Rangan used provisions of AS to ompute beam apaity, 8 while the work presented in this paper used ACI Seond, Yost et al. did not speifially measure the yield strength of the reinforing steel used to onstrut the beams. Instead, apaity was omputed using 6, psi (414 MPa) as the estimated yield strength of the reinforing steel. 9 As Sumajouw and Rangan and Yost et al. onluded, the existing equivalent stress-blok parameters α 1 and β 1 yield satisfatory estimates of beam apaity. In researh settings, where individual material harateristis and omponent geometries are known with good auray, the estimated apaity of the beam an usually be predited PCI Journal November Deember

11 Table 4. Calulated and observed moments in flexural members Beam ρ Measured ultimate apaity, lb-in. Estimate using ACI , lb-in. Differene from measured, * % Capaity estimate using proposed k 1, k 2, k 3, lb-in. Differene from measured, % ,4 499, , ,8 499, ,4 56, , ,2 56, , , 586, , ,297 41, , , , , ,34,21 1,26, ,42, ,42,545 1,338, ,362, ,441 48, , ,435 75, , ,53,239 1,52,718. 1,68, ,493,121 1,395, ,433, , , , , , , ,122,275 1,81, ,93, ,592,692 1,492, ,516, ,1 257, , ,37 258, , , , , , , , , , , ,493 73, , Note: k 1 = ratio of average ompressive stress to maximum ompressive stress; k 2 = ratio of distane from top of beam to the resultant ompressive fore C and the depth to the neutral axis ; k 3 = ratio of ylinder onrete strength to beam onrete strength; ρ = reinforement ratio. 1 lb-in. =.113 N-m. * Average error = 1.1% Average error = 9.3% within 5% of the measured value. Sumajouw and Rangan attributed the great overestimate of strength for beams 6, 1, and 14 in Table 4 to the ontribution of strain hardening, whih is not aounted for in the model. 8,9 The experimental results from the beam-olumn tests indiate that there are signifiant differenes in the α 1 and β 1 parameters for geopolymer ement onrete and portland ement onrete. Using β 1 parameters devised for portland ement onrete ould lead to an overestimate of geopolymer ement onrete beam strength. The underreinfored beams tested in this study do not exhibit this differene. At failure, the depth of the ompression zone is small and the differene in different stress distributions is redued. Conlusion Geopolymer ement onrete is a more sustainable building material that an be used as an alternative to portland 4 November Deember 216 PCI Journal

12 ement onrete. Fly-ash-based geopolymer ement onrete redues arbon dioxide emissions and makes use of a waste byprodut from oal-burning power plants. Researh on geopolymer ement onrete has shown that it an produe mixtures with similar mehanial properties to portland ement onrete, inluding ompressive and flexural strengths, Poisson s ratio, and elasti modulus. Five flexural beam-olumn speimens were prepared and tested to evaluate the stress-strain relationship in the ompression area of a flexural member. The beam-olumn speimens were subjeted to axial and eentri fores that simulate the ompression stresses that our in a beam in flexure. Results from these tests indiate that the stress-strain response in geopolymer ement onrete behaves similarly to that of portland ement onrete. The stress-strain urve shows a positive linear slope in the elasti region. The slope dereases slightly as the ultimate strength is reahed, and the stress redues slightly before failure. Most of the tests in this researh did not learly show the post-peak response of the onrete, suggesting a rather brittle failure more typial of high-strength portland ement onrete. The results from these tests were used to evaluate the α 1 and β 1 parameters of the Whitney stress blok, whih were ompared with the values provided in ACI These were signifiantly different for geopolymer ement onrete, and their relationship has been expressed in terms of the ompressive strength of onrete. To verify the validity of these parameters, several flexural speimens were built and tested to failure. These beams were signifiantly underreinfored and had a relatively shallow ompression blok. Therefore, the improvement in estimating the ultimate flexural apaity is inremental. However, the ability to predit apaity would be improved for deeper or heavily reinfored members, as well as prestressed setions. Referenes 1. Hasanbeigi, A., L. Prie, and E. Lin Emerging Energy-Effiieny and CO 2 Emission-Redution Tehnologies for Cement and Conrete Prodution: A Tehnial Review. Renewable and Sustainable Energy Reviews 16 (8): Davidovits, J Geopolymers. Journal of Thermal Analysis and Calorimetry 37 (8): Duxson, P., J. L. Provis, G. C. Lukey, and J. S. J. van Deventer. 27. The Role of Inorgani Polymer Tehnology in the Development of Green Conrete. Cement and Conrete Researh 37 (12): Turner, L. K., and F. G. Collins Carbon Dioxide Equivalent Emissions: A Comparison between Geopolymer and OPC Cement Conrete. Constrution and Building Materials 43: MLellan, B. C., R. P. Williams, J. Lay, A. Van Riessen, and G. D. Corder Costs and Carbon Emissions for Geopolymer Pastes in Comparison to Ordinary Portland Cement. Journal of Cleaner Prodution 19 (9): Tempest, B., C. Snell, T. Gentry, M. Trejo, and K. Isherwood Manufature of Full-Sale Preast Geopolymer Cement Conrete Components: A Case Study to Highlight Opportunities and Challenges. PCI Journal 6 (6): Van Deventer, J. S. J., J. L. Provis, and P. Duxson Tehnial and Commerial Progress in the Adoption of Geopolymer Cement. Minerals Engineering 29: Sumajouw, D., and B. Rangan. 26. Low- Calium Fly Ash-Based Geopolymer Conrete: Reinfored Beams and Columns. Researh report GC3, Curtin University of Tehnology, Perth, Australia. 9. Yost, J. R., A. Radli ska, S. Ernst, M. Salera, and N. J. Martignetti Strutural Behavior of Alkali Ativated Fly Ash Conrete. Part 2: Strutural Testing and Experimental Findings. Materials and Strutures 46 (3): ACI (Amerian Conrete Institute) Committee Building Code Requirements for Strutural Conrete (ACI ) and Commentary (ACI 318R-14). Farmington Hills, MI: ACI. 11. Standards Australia Committee BD Conrete Strutures. AS Sydney, Australia: Standards Australia. 12. Prahasaree, W., S. Limkatanyu, A. Hawa, and A. Samakrattakit Development of Equivalent Stress Blok Parameters for Fly-Ash-Based Geopolymer Conrete. Arabian Journal for Siene and Engineering 39 (12): Hognestad, E., N. W. Hanson, and D. MHenry Conrete Stress Distribution in Ultimate Strength Design. Journal of the Amerian Conrete Institute 52 (12): Davidovits, J Geopolymer Cement: A Review. Saint-Quentin, Frane: Geopolymer Institute. 15. Sindhunata, J. S. J. van Deventer, G. C. Lukey, and H. Xu. 26. Effet of Curing Temperature and Siliate Conentration on Fly-Ash-Based Geopolymerization. Industrial & Engineering Chemistry Researh 45 (1): PCI Journal November Deember

13 16. Van Jaarsveld, J. G. S., J. S. J. van Deventer, and G. C. Lukey. 22. The Effet of Composition and Temperature on the Properties of Fly Ash- and Kaolinite- Based Geopolymers. Chemial Engineering Journal 89 (1 3): Diaz-Loya, E. I., E. N. Allouhe, and S. Vaidya Mehanial Properties of Fly-Ash-Based Geopolymer Conrete. ACI Materials Journal 18 (3): Tempest, B. 21. Engineering Charaterization of Waste Derived Geopolymer Cement Conrete for Strutural Appliations. PhD dissertation, University of North Carolina at Charlotte. 19. Thomas, R. J., and S. Peethamparan Alkali- Ativated Conrete: Engineering Properties and Stress-Strain Behavior. Constrution and Building Materials 93: Cross, D., J. Stephens, and J. Vollmer. 25. Strutural Appliations of 1 Perent Fly Ash Conrete. Paper presented at World of Coal Ash, Lexington, Ky. 21. Skipper, Ashley Performane of Geopolymer Cement Conrete in Flexural Members. Master s thesis, University of North Carolina at Charlotte. 22. Whitney, C. S Design of Reinfored Conrete Members under Flexure or Combined Flexure and Diret Compression. Journal of the Amerian Conrete Institute 33 (3): Notation a = depth of the equivalent retangular stress blok a 1 = distane from the neutral fae to P 1 a 2 = distane from the neutral fae to P 2 A s A s = area of reinforing steel in the tension zone = area of reinforing steel in the ompression zone d d e E E s f f f f f y F h k 1 k 2 k 3 L m M M n = distane from the extreme ompression fiber to the entroid of the ompression reinforing steel group = distane from the extreme ompressive fiber to the entroid of the tension reinforing group = eentriity = elasti modulus of the onrete = modulus of elastiity of reinforing steel = stress = average stress on a ross setion of the beam olumn = stress in the onrete = ompressive strength of onrete = yield stress of steel reinforement = fores ating on the setion of the beam olumn = depth of beam = ratio of average ompressive stress to maximum ompressive stress = ratio of distane from top of beam to the resultant ompressive fore C and the depth to the neutral axis = ratio of ylinder onrete strength to beam onrete strength = length of beams used in the experiments = average moment ating on a setion of the beam olumn = moment = nominal moment apaity of the beam b = width of a retangular onrete setion = distane from the ompressive fae to the neutral axis in a onrete beam P 1 P 2 = primary axial load ating on the beam olumn = eentri load ating on the beam olumn C = resultant ompressive fore R 2 = oeffiient of determination C = onrete ompressive fore w/m = water ementitious materials ratio 42 November Deember 216 PCI Journal

14 x α 1 = distane from neutral axis to the resultant ompressive fore line of ation = stress-blok parameter = kk 2k β 1 = stress-blok parameter = 2k 2 ε = strain ε s ε x ρ ρ bal = strain at the entroid of the ompression reinforing steel group = linear distribution aross = reinforement ratio = reinforement ratio at balaned failure onditions ε = onrete strain ψ = fator fit to the data About the authors Brett Tempest, PhD, is an assoiate professor in the Department of Civil and Environmental Engineering at the University of North Carolina at Charlotte. Janos Gergely, PhD, SE, PE, is an assoiate professor in the Department of Civil and Environmental Engineering at the University of North Carolina at Charlotte. dimension, underreinfored beams with fairly shallow ompression zones. The researh presented in this paper used a ombined axial stress and flexure test developed by Hognestad et al. as a primary means of determining the distribution of stresses in the ompression zone of geopolymer ement onrete in flexure. The results indiated that slightly modified stress blok parameters α 1 and β 1 should be applied to geopolymer ement onrete due to differenes in the stress-strain relationship of geopolymer ement onrete in ompression ompared with portland ement onrete. Although these parameters do not signifiantly improve the auray of alulations for small-dimension beams, they are more appropriate for general design onditions, whih might inlude deeper beams, heavily reinfored setions, and prestressed setions. Ashley Skipper, MS, earned her master s degree from the Department of Civil and Environmental Engineering at the University of North Carolina at Charlotte. Keywords Beams, flexural design parameters, geopolymer ement onrete, greenhouse gas, sustainability, stress-strain urve. Abstrat Geopolymer ement onrete ould revolutionize the onrete industry by merging the benefits of onrete with signifiantly redued greenhouse gas emissions ompared with portland ement onrete. Several authors have verified the appliability of equivalent stress-blok design parameters to estimating the apaity of reinfored geopolymer ement onrete beams. These verifiations have been made primarily by testing small- Review poliy This paper was reviewed in aordane with the Preast/Prestressed Conrete Institute s peer-review proess. Reader omments Please address reader omments to journal@pi.org or Preast/Prestressed Conrete Institute, /o PCI Journal, 2 W. Adams St., Suite 21, Chiago, IL 666. J PCI Journal November Deember