Analysis of geopolymer concrete columns

Transcription

1 Analysis of geopolymer onrete olumns Prabir Kumar Sarker, Leturer, Department of Civil Engineering, Curtin University of Tehnology, Perth, Western Australia, Phone: , Fax: , p.sarker@urtin.edu.au Abstrat Ordinary portland ement (OPC) has been traditionally used as the binding agent in onrete. However, it is also neessary to searh for alternative low-emission binding agents for onrete to redue the environmental impat aused by manufaturing of ement. Geopolymer, also known as inorgani polymer, is one suh material that uses by-produt material suh as fly ash instead of ement. Reent researh has shown that fly ash-based geopolymer onrete has suitable properties for its use as a onstrution material. Sine the strength development mehanism of geopolymer is different from that of OPC binder, it is neessary to obtain a suitable onstitutive model for geopolymer onrete to predit the loaddefletion behaviour and strength of geopolymer onrete strutural members. This paper has investigated the suitability of using an existing stress-strain model originally proposed by Popovis for OPC onrete. It is found that the equation of Popovis an be used for geopolymer onrete with minor modifiation to the expression for the urve fitting fator, to better fit with the post-peak parts of the experimental stress-strain urves. The slightly modified set of stress-strain equations was then used in a nonlinear analysis for reinfored onrete olumns. A good orrelation is ahieved between the predited and measured ultimate loads, load-defletion urves and defleted shapes for twelve slender test olumns. Keywords: Column; geopolymer onrete; fly ash; stress-strain relationship. 1

2 1. Introdution Conrete is the most widely used onstrution material in the world. Ordinary portland ement (OPC) has been traditionally used as the binding agent for onrete. The worldwide onsumption of onrete is estimated to inrease due to the inrease of infrastruture espeially in ountries suh as India and China [1]. The amount of arbon dioxide released during the manufaturing proess of OPC is in the order of one ton for every ton of OPC produed. Globally, the OPC prodution ontributes about 7% of the world s arbon dioxide. This is adding about 1.6 billion tons of arbon dioxide into the atmosphere [1]. Sine it has now beome a priority to ontrol the trend of global warming by reduing the arbon dioxide emission, it is appropriate to searh for alternative low-emission binding agents for onrete. Geopolymer, also known as inorgani polymer, is one suh alternative material that ats as the binding agent in onrete. The geopolymer binder uses by-produt materials instead of ement and thus its use by the onstrution industry will redue the arbon dioxide emission and the environmental impat of the manufaturing of ement. Geopolymer is a type of alumino-siliate produt obtained from the geohemistry proess [2]. The geopolymer binders show good bonding properties and utilize a material suh as fly ash or metakaolin as the soure of Silion and Aluminium for reation by an alkali. In fly ashbased geopolymer binder, fly ash is reated with an alkaline solution to reate an aluminosiliate binder. Geopolymer binders are used together with aggregates to produe geopolymer onrete. Fly ash based geopolymer onrete is a reently developed onrete in whih no portland ement is used and the geopolymer paste ats as the only binder. The basi ingredients of fly ash-based geopolymer onrete are fly ash, sodium hydroxide, sodium siliate, fine aggregates and oarse aggregates. However, water and super plastiizer an be added to improve workability of the onrete mixture. Reent researh works [3-9] have studied the properties of heat ured fly ash based 2

3 geopolymer onrete. The results of these studies have shown potential use of geopolymer onrete as a onstrution material. The studies have shown that geopolymer onrete has the properties of high ompressive strength, very little drying shrinkage, low reep, good bond with reinforing steel, good resistane to aid, sulphate and fire. It was also found from the experimental and analytial works that the performane of geopolymer onrete strutural members suh as beams and olumns was similar to that of OPC onrete members. Other reent studies [10-12] have also reported similar engineering properties of geopolymer onrete whih are favourable for its use as a onstrution material. Computations of the load-defletion behaviour and the ultimate load apaity of reinfored onrete members need the stress-strain relationship of onrete. Past researh works [10, 11, 13, 14] have determined the experimental values of modulus of elastiity of geopolymer onrete. The experimental results of omplete stress-strain behaviour of geopolymer onrete were reported by Hardjito et al. [14]. While the strength development in OPC onrete is beause of the hydration reation of ement with water, the strength development in geopolymer onrete is beause of the geopolymerisation reation between the soure of Silion and Aluminium with the alkaline liquids. Beause the strength development mehanism of geopolymer onrete is very different from that of OPC onrete, it is neessary to obtain a suitable expression for the stress-strain relationship of geopolymer onrete. It is also neessary to evaluate the appliation of the onventional methods of analysis used for OPC onrete strutures to geopolymer onrete strutural members. This paper has evaluated the suitability of using an existing stress-strain model originally proposed by Popovis [15] for OPC onrete to geopolymer onrete. The slightly modified set of stress-strain equation is used in a nonlinear analysis of reinfored onrete olumns [16] to analyze the twelve geoppolymer onrete olumns tested by Sumajouw et al. [9]. The alulated ultimate axial loads, load-defletion urves and the defleted shapes of the olumns 3

4 are ompared with the orresponding experimental results. 2. Material properties 2.1 Modulus of elastiity of geopolymer onrete The modulus of elastiity (E ) of geopolymer onrete was determined by testing ylinder speimens and reported in literature by Fernandez-Jimenez et al. [10], Sofi et al. [11], Hardjito et al. [14]. These test results are shown in Fig. 1 and ompared with the preditions by different empirial equations. There were some variations in these reported test results in terms of the ingredients of the test speimens and the test methods used. The test results of Fernandez-Jimenez et al. [10] were measured in aordane with the Spanish Standard UNE These speimens were made using low alium fly ash, 12.5 molar NaOH, Na 2 SiO 3 of SiO 2 to Na 2 O ratio of 3.4, and oarse and fine aggregates. The test data by Sofi et al. [11] and Hardjito et al. [14] were measured in aordane with the Australian Standard [17]. The test speimens of Sofi et al. [11] were made by using low alium fly ash from three different soures, slag ontaining 40% CaO by mass and a ombination of NaOH or KOH and Na 2 SiO 3 as the alkaline liquid. The speimens did not have any oarse aggregates exept the one orresponding to ompressive strength of 39 MPa. The test speimens by Hardjito et al. [14] used low alium fly ash, 14 molar NaOH, Na 2 SiO 3 with SiO 2 to Na 2 O ratio of 2, and oarse and fine aggregates. The type of oarse aggregates used in these speimens was granite. It is known that the mehanial properties of geoplymer vary with the hemial omposition of the produt obtained after the reation. It was found in the previous studies [10, 11] that geopolymer showed different mehanial properties depending on the type of fly ash, and the type and onentration of the alkali used. Usually a higher onentration of the alkali 4

5 dissolves a higher proportion of the fly ash partiles. Thus a higher degree of geopolymerisation ours and a denser mirostruture is ahieved in the geopolymer matrix. The denser mirostruture of the matrix provides better mehanial properties to geopolymer onrete. Also, the mehanial properties of geopolymer are found to improve with the inrease in the ratio of Si to Al of the reation produt. It an be seen that the ingredients and the mixture proportions varied in the test speimens. Beause of the variation in the ingredients and their mixture proportions, satter is observed in the test data presented in Fig E (GPa) f (MPa) Test - Sofi et al. [11] Test - Hardjito et al. [14] Test - Fernandez-Jimenez et al. [10] Predition Hardjito et al. [14] Predition - ACI 363 [18] Predition - AS 3600 [19] Predition - Carrasquillio et al. [20] Predition - Ahmad & Shah [21] Fig. 1 Modulus of elastiity of geopolymer onrete While the modulus of elastiity of onrete varies depending on the paste and the type of aggregates, simplified empirial equations in terms of onrete ompressive strength (f ) and onrete density (ρ) are often used for normal-weight onretes. The values of the modulus of 5

6 elastiity alulated by the empirial equations are ompared with the test results of geopolymer onrete. Some empirial equations proposed for OPC onrete (Eqs. 1-4) and for geopolymer onrete (Eq. 5) are given below. Amerian Conrete Institute, ACI 363 [18]: E 3320 f 6900 (1) Australian Standard, AS 3600 [19], within ± 20%: E f m (2) Carrasquilo et al. [20]: 1.5 E ( 3320 f 6900)( 2320) (3) Ahmad and Shah [21]: E 3.38 ( f ) 10 (4) Hardjito et al. [14]: E 2707 f 5300 (5) The predition equations for the modulus of elastiity of OPC onrete reommended by the Australian Standard AS 3600 [19], Carrasquillo et al. [20] and Ahmad & Shah [21] are funtions of the density of onrete and the onrete ompressive strength. The equation proposed by Hardjito et al. [14] for geopolymer onrete is similar to that given by the ACI 363 [18] with different values of the onstants. These equations are relatively simple to use sine they are expressed as funtion of onrete ompressive strength only. The trend lines through the predited values of the test results by the five equations (Eqs. 1-5) are shown in Fig. 1. It an be seen that the equations of the ACI 363 [18], AS 3600 [19], Carrasquillo et al. 6

7 [20] and Ahmad & Shah [21] overestimate most of the test results of geopolymer onrete. The predition of the modulus of elastiity by Eq. (5) is lose to the test results and is onsidered reasonable taking the variations of test speimens into onsideration. Therefore, this equation is used to alulate the modulus of elastiity required for the stress-strain relationship of geopolymer onrete, presented in the next setion. 2.2 Stress-strain relationship of geopolymer onrete Experimental data on the stress-strain urves of geopolymer onrete are very limited in literature. Hardjito et al. [14] reported the experimental stress-strain urves of three different mixes of heat ured fly ash-based geopolymer onretes using granite aggregates. These results are shown in Figs. 2 to 4. The expression for the omplete stress-strain response of onventional OPC onrete ylinders proposed by Popovis [15] was subsequently modified by Thorenfeldt et al. [22] by introduing a fator k in the equation to ensure a steeper desending part of the urve for high-strength onrete. This expression of Thorenfeldt et al. is seleted here to evaluate the suitability of its use for geopolymer onrete by omparing with the experimental stress-strain urves. The stress-strain relationship of Popovis, modified by Thorenfeldt et al. is given by the following expression: f f n. n 1 nk (6) where f = onrete ompressive stress, = strain in onrete, f = maximum ompressive stress in onrete, = strain when f reahes f and n = urve fitting fator. The fator k equals 1 when / is less than 1. Collins and Mithell [23] suggested that k is given by Eq. (7) for / is greater than 1 and the urve fitting fator n is estimated by Eq. (8). 7

8 f 0.67 k when 62 >1 in MPa unit (7) f n 0.8 in MPa unit (8) 17 Collins et al. [24] reommended that the strain at peak stress an be found from Eq. (9) by knowing the value of the modulus of elastiity (E ). f n. (9) E n 1 Equations 6 through 9 were used to alulate the stress-strain urves for the test speimens of Hardjito et al. [14]. Equation 5 was used to alulate E. The alulated stress-strain urves are shown in Figs. 2 to 4. It an be seen from the figures that when the urve fitting fator n is alulated from Eq. (8), the strains orresponding to peak stress ( ) alulated by using Eq. (9) are slightly higher than the measured values and the post peak parts of the alulated stress-strain urves are pushed to the right from the measured urves for all the three ases. It was therefore attempted to obtain a similar modified equation for the urve fitting fator for a better fit between the alulated and the measured stress-strain urves. Equation 10 was thus obtained from trials. f n 0.8 in MPa unit (10) 12 The stress-strain urves alulated by using the urve fitting fator given by Eq. (10) are also shown in Figs. 2 to 4. From the omparison between the alulated and measured stress-strain 8

9 Stress (MPa) urves, it an be seen that Eq. (10) provides a better estimation of the urve fitting fator for the fly ash-based geopolymer onrete. Therefore, Eq. (10) is used to determine the stressstrain relationship of geopolymer onrete ylinders. However, the strength of onrete in a olumn differs from that in a ylinder due to their differenes in size, vibration during asting, uring, loading rate et. To take into aount these differenes, a fator k 3 is usually applied to the ylinder stress to obtain the onrete stress in a olumn. ACI ommittee 363 [25] reommended a onstant value of 0.85 for k 3. Ibrahim and MaGregor [26] analyzed the test results of 49 eentrially loaded olumns for k 3, whih showed a variation of k 3 from 0.82 to 1.12, for f of 40 to 130 MPa. Their analysis showed that a value of 0.85 ould reasonably be used as a lower bound value of k 3 for eentrially loaded olumns. MaGregor and Wight [27] used a value of 0.90 for k 3. This value k 3 is used in the present analysis to aount for the differene in onrete strengths between the ompressive ylinder and the olumn Cal. - n by Eq. 10 Test - Hardjito et al. [14] Cal. - n by Eq Strain Fig. 2 Stress-strain urve of geopolymer onrete (f = 41 MPa) 9

10 Stress (MPa) Stress (MPa) Cal. - n by Eq. 10 Test - Hardjito et al. [14] Cal. - n by Eq Strain Fig. 3 Stress-strain urve of geopolymer onrete (f = 61 MPa) Strain Cal. - n by Eq. 10 Test - Hardjito et al. [14] Cal. - n by Eq. 8 Fig. 4 Stress-strain urve of geopolymer onrete (f = 64 MPa) 10

11 2.3 Stress-strain relationship of reinforing steel The reinforing steel is assumed to be elasti-perfetly plasti and the stress-strain relationship in tension and ompression is taken as follows: f when s < y (11) s E s s f s f y when s y (12) where f s = stress in steel, E s = modulus of elastiity of steel, s = strain in steel, y = yield strain of steel and f y = yield strength of steel. 3. Column analysis A method of analysis was developed for reinfored onrete olumns under ombined ompression and uniaxial bending with equal or unequal load eentriities at the ends. It is based on the ommon assumptions for reinfored onrete members suh as preservation of plain setions after bending, perfet bonding between onrete and steel, negligible tensile strength of onrete and initial straightness of the member with prismati setion along the length. The analytial method determines the ultimate axial load apaity of a olumn using the usual axial load-moment interation diagram. The setion apaity line and the loading line in the interation diagram are onstruted using the moment-thrust-urvature relationship of the ross-setion and the load-defletion relationship of the olumn. The priniples used for the development of moment-thrust-urvature and load-defletion relationships are similar to those generally used for reinfored onrete olumns [28, 29, 30]. The analytial method uses the atual nonlinear stress distribution in the ross-setion to alulate the setion apaity. The load path of the olumn is obtained by alulating the atual defleted shape using the load eentriities and olumn slenderness, and is not based on any simplified assumption about the defleted shape. Thus, both material and geometri nonlinearities are taken into 11

12 aount to determine the ultimate load apaity of the olumn. Sine the method needs iterations, it is onveniently solved by writing a omputer program. The method of analysis is desribed below. 3.1 Development of the moment-urvature relationship The analysis requires moment-urvature (M i - ) relationships of the ross setion for different axial loads. For this purpose, the olumn ross setion is first divided into number onrete strips of equal height and reinforement layers, as shown in Fig. 5. The strain and stress distributions, and the alulated axial fore and internal moment in the ross-setion are also shown in Fig. 5. For a nominated value of axial load N, a value of the strain at the extreme ompressive fibre of onrete is first assumed. For the assumed value of, a value of the neutral axis depth, d n is guessed. Then the stress in the onrete strips and reinforing steel layers are obtained using the material onstitutive laws desribed in the previous setions. The stress at the entroid of a onrete strip is assumed to be onstant throughout its depth. The fores in all the onrete strips and the steel layers are summed up algebraially to obtain the net axial fore P ating on the setion. d n y D P M i b Cross-setion Strain distribution Stresses in onrete strips Stresses in reinforement layers Axial fore and moment Fig. 5 Cross-setion analysis 12

13 The net axial fore P is then ompared with the nominated value N. If the differene between them is not within a presribed tolerane, a new position of the neutral axis is guessed and the proess is repeated. When the orret position of the neutral axis is obtained, the internal moment of the ross-setion M i for the urrent N is alulated. The internal moment of the setion is obtained by summing up the moments of the fores of individual onrete strips and reinforement layers about the plasti entroid. The orresponding urvature is alulated, whih is equal to the slope of the strain profile aross the ross-setion. The omplete moment-urvature relationship for the nominated value of the axial load is thus established by inrementing the extreme ompressive fibre strain and alulating the orresponding values of moments and urvatures. The moment-urvature relationship is used later to alulate the defleted shape of the olumn. 3.2 Column defleted shape The olumn is assumed to be hinged at both the ends and any side sway of the supports is restrited. Therefore, the lateral defletions at the ends are zero. For the purpose of alulating the omplete defleted shape for a nominated value of the axial load at a presribed set of load eentriities, the olumn length is divided into a number of rigid segments. The points where two segments are onneted to eah other are alled nodes. Defletion at every node is alulated and thus the omplete defleted shape of the olumn is obtained. Calulation of the node defletions ould start from the either end, where the defletion is zero. The provision that the defletion at the other end is also zero is used as a boundary ondition for meeting the onvergene of the iterative solution. In the analysis, the slope of the first rigid segment from the starting end is used as a ontrol value and is inremented in every iteration. With the assumed value of the ontrol slope 1, defletion of the seond node is alulated simply by multiplying the slope with the length of 13

14 the rigid segment. Defletions of the subsequent nodes are alulated using the developed moment-urvature relationship of the ross-setion for the nominated value of the axial load. Curvature of the defleted olumn at any node is defined as the rate of hange of slope at that node and it an be shown that defletion at any node an be expressed by the following equation [31]: v (13) j 2 j 1 ( L) 2v j 1 v j 2 where v j = defletion at any node j, j = urvature at node j and L = length of rigid segment. For the assumed values of ontrol slope and nominated values of axial load, the node defletions are alulated using Eq. (13) and when the alulated defletion at the last node is lose enough to zero, the value of axial load is taken as the orret value for the assumed ontrol slope. Thus the orret values of axial loads and the orresponding node defletions are alulated for the inremented values of ontrol slopes. This gives the defleted shape of the olumn for an axial load and given load eentriities. 3.3 Axial load-moment interation The total external moment (M ej ) at any node j for equal load eentriities (e) at the olumn ends is then alulated by the following equation: M ej N e v ) (14) ( j The maximum external moment in the olumn with equal load eentriities ours at mid height of the olumn. The maximum moment apaity (internal) of the ross-setion for the nominated axial load is obtained from the moment-thrust-urvature relationship. Thus the load moment interation diagram of the olumn is onstruted using the maximum values of external and internal moments orresponding to eah axial load. The iterative alulation ontinues until the maximum external moment reahes the moment apaity of the ross- 14

15 Load (kn) setion. The maximum value of the axial load until reahing this point is taken as the ultimate load apaity of the olumn. If the maximum value of axial load ours before the loading line reahes the setion apaity line, it indiates a bukling failure. Otherwise it is a material failure. 15 mm 8N mm 15 mm 100 mm / 175 mm Fig. 6 Typial ross-setion of test olumns [9] Setion apaity e = 15 mm e = 35 mm e = 50 mm Moment (kn-m) Fig. 7 Load-moment interation diagrams for GCII-1, GCII-2 and GCII-3 15

16 Load (kn) GCII-1 al. GCII-1 test GCII-2 al. GCII-2 test GCII-3 al. GCII-3 test Mid-height defletion (mm) Fig. 8 Load-defletion diagrams for GCII-1, GCII-2 and GCII-3 16

17 Height (mm) GCII-1 al. (1420 kn) GCII-1 test (1455 kn) GCII-2 al. (990 kn) GCII-2 test (1030 kn) GCII-3 al. (758 kn) GCII-3 test (827 kn) Defletion (mm) Fig. 9 Defleted shapes at ultimate load for GCII-1, GCII-2 and GCII-3 4. Comparison of predition with experimental results The analytial method presented in the previous setion is implemented in a omputer program to perform the olumn analysis. Sine the use of geopolymer in reinfored onrete appliation is relatively new, very limited test data on reinfored geopolymer onrete is available in literature. The twelve geopolymer onrete olumns tested by Sumajouw et al. [9] are analyzed by using the method and the material onstitutive laws desribed in the previous setions. A typial ross-setion of these test olumns is shown in Fig. 6 and the test 17

18 parameters are given in Table 1. The longitudinal reinforement of the olumns onsisted of either 4 or 8 Australian N12 deformed bars. The nominal ross-setional area of N12 bar is 110 mm 2 and the yield strength was 519 MPa, as found from tensile strength tests. The lateral losed ties onsisted of 6 mm diameter (W6) hard-drawn steel wires at 100 mm spaing. Effetive length of the olumns is taken as the entre to entre distane between the knifeedges, whih is equal to the olumn length plus twie the distane from the olumn end to the entre of the knife-edge. Length of the test olumns was 1500 mm and the effetive length was found to be 1684 mm. Table 1 Details of the Test Speimens [9] Speimen f (MPa) Longitudinal reinforement e (mm) GCI N12 15 GCI N12 35 GCI N12 50 GCI N12 15 GCI N12 35 GCI N12 50 GCII N12 15 GCII N12 35 GCII N12 50 GCII N12 15 GCII N12 35 GCII N12 50 The olumn is divided into twenty rigid segments in this analysis. Typial load-moment interation diagrams developed in the analysis, from whih the ultimate axial loads are obtained, are shown in Fig. 7. Typial alulated load-defletion diagrams and defleted shapes at the ultimate load are also shown in Figs. 8 and 9 respetively. Table 2 shows the omparison of the alulated and measured values of ultimate load and orresponding midheight defletions for eah test olumn. The mean value of the ratio of test to alulated 18

19 ultimate loads for these twelve olumns is 1.03 with a standard deviation of 5%. The mean value of the test predition ratios of orresponding mid-height defletions is 1.14 with a standard deviation of 11%. The measured and alulated olumn load-defletion diagrams and the defleted shapes at ultimate load orrelated well, as shown in Figs. 8 and 9. Table 2 Comparison of Calulated and Test Results Speimen Test [9] Predition Test-predition ratio Ultimat e load (kn) Midheight defletion Ultima te load (kn) Midheight defletion Ultimate load (kn) Midheight defletion (mm) (mm) (mm) GCI GCI GCI GCI GCI GCI GCII GCII GCII GCII GCII GCII Average Standard deviation Conlusions The objetive of this study was to find a suitable expression for the stress-strain relationship of geopolymer onrete and to determine the suitability of a nonlinear method for alulation of strength and defletion of reinfored geopolymer onrete olumns. From the analytial works, the following onlusions are drawn: 1. Popovis equation for OPC onrete an be used to alulate the stress-strain urve of low-alium fly ash-based geopolymer onrete with some modifiation. Use of Eq. 19

20 (6) with Eqs. (5), (7), (9) and (10) has provided good orrelation with the experimental stress-strain urves. 2. The alulated values of the ultimate loads using the desribed nonlinear method of olumn analysis have orrelated very well with the test results. The mean value of test-predition ratio is 1.03 and standard deviation is 5% for the 12 test olumns. 3. Calulated mid-height defletions at ultimate load orrelated reasonably well with the orresponding test values, with the mean test-predition ratio of 1.14 and standard deviation of 11%. The alulated load-defletion urves and defleted shapes also orrelated well with the orresponding diagrams obtained from tests. 4. Therefore, the analytial method for onventional OPC onrete olumns an be used for geopolymer onrete olumns with the appropriate stress-strain relationship of geopolymer onrete. 6. Referenes [1] Mehta PK (2001) Reduing the environmental impat of onrete. Conrete International 23(10):61-66 [2] Davidovits J (1994) High-alkali ements for 21 st entury onretes. Conrete Tehnology Past, Present and Future. ACI Speial Publiation, SP 144, Farmington Hills, Mihigan, pp [3] Hardjito D, Wallah SE, Sumajouw DMJ et al (2004) On the development of fly ashbased geopolymer onrete. ACI Mater J 101(6): [4] Hardjito D, Wallah SE, Sumajouw DMJ et al (2005) Fly ash-based geopolymer onrete. Aust J Strut Eng 6(1):77 86 [5] Rangan BV (2006) Studies on low-alium fly ash-based geopolymer onrete. Indian 20

21 Conrete Institute J Otober Deember: 9-17 [6] Sarker PK (2004) Making geopolymer onrete using Sarawak fly ash. In: Proeedings of The First International Conferene of Asian Conrete Federation, Chiang Mai, Thailand, Otober 2004, pp [7] Sarker PK, Grigg A and Chang EH (2007) Bond strength of geopolymer onrete with reinforing steel. In: Zingoni A (ed) Reent Developments in Strutural Engineering, Mehanis and Computation, CD ROM, Millpress, the Netherlands, pp [8] Sarker PK and demeillon T (2007) Residual strength of geopolymer onrete after exposure to high temperature. In: Zingoni A (ed) Reent Developments in Strutural Engineering, Mehanis and Computation, CD ROM, Millpress, the Netherlands, pp [9] Sumajouw DMJ, Hardjito D, Wallah SE et al (2007) Fly ash-based geopolymer onrete: Study of Slender Columns. J Mater Si 42 (9): [10] Fernandez-Jimenez AM, Palomo A and Lopez-Hombrados C (2006) Engineering properties of alkali-ativated fly ash onrete. ACI Mater J 103 (2): [11] Sofi M, van Deventer JSJ, Mendis, PA et al (2007) Engineering properties of inorgani polymer onretes (IPCs). Cem and Con Res 37: [12] Sofi M, van Deventer JSJ, Mendis PA et al (2007) Bond performane of reinforing bars in inorgani polymer onretes (IPCs) J Mater Si 42: [13] Hardjito D and Rangan BV (2005) Development and properties of low alium fly ashbased geopolymer onrete, Researh Report GC1, Faulty of Engineering, Curtin University of Tehnology, Western Australia. available via 21

22 [14] Hardjito D, Wallah SE, Sumajouw, MJ et al (2005) The stress-strain behaviour of fly ash-based geopolymer onrete. Developments in Mehanis of Strutures and Materials. A A Balkema Publishers, The Netherlands, pp [15] Popovis S (1973) A numerial approah to the omplete stress-strain urve of onrete. Cem and Con Res 3: [16] Sarker PK Rangan BV (2003) Reinfored onrete olumns under unequal load eentriities. ACI Strut J 100 (4): [17] AS (1997) Determination of stati hord modulus of elastiity and poisson s ratio of onrete speimens. Standards Assoiation of Australia, Sydney, Australia [18] ACI Committee 363(1993) State of the art of high strength onrete, Amerian Conrete Institute, Detroit, USA [19] AS 3600 (2001) Conrete strutures. Standards Assoiation of Australia, Sydney, Australia [20] Carrasquillo RL, Nilson AS and Slate FO (1981) Properties of high strength onrete subjeted to short term loads. ACI J 78: [21] Ahmad SH and Shah SP (1985) Strutural properties of high strength onrete and its impliation for preast pre-stressed onrete. PCI J 30: [22] Thorenfeldt E, Tomaszewiz A and Jensen JJ (1987) Mehanial properties of high strength onrete and appliation in design. Proeedings of the Symposium of on Utilization of high strength Conrete, Tapir, Trondheim, 1987, pp [23] Collins MP, Mithell D (1991) Prestressed onrete strutures. Prentiee-Hall In., Englewood Cliffs, New Jersey [24] Collins MP, Mithell D and MaGregor JG (1993) Strutural design onsiderations for 22

23 high-strength onrete. Conrete International 15(5):27-34 [25] ACI Committee 363 (1984) State of the art report on high strength onrete. ACI Pro 81(4): [26] Ibrahim, HHH, and MaGregor JG (1997) Modifiation of the ACI retangular stress blok for high-strength onrete. ACI Strut J 94(1):40-48 [27] MaGregor JG and Wight JK (2006) Reinfored onrete mehanis and design, 4 th ed. In SI units, Prentie Hall [28] Pfrang EO, Siess CP and Sozen MA (1964) Load-moment-urvature hararistis of reinfored onrete ross-setions. ACI J Pro 61(7): [29] Warner, RF, Rangan BV, Hall AS et al (1998) Conrete strutures, Addison Wesley Longman, Australia [30] Kilpatrik AE (1996) The behaviour of high strength omposite onrete olumns. PhD Thesis, Curtin University of Tehnology, Western Australia [31] Sarker PK (2001) Study of high strength onrete olumns. PhD Thesis, Curtin University of Tehnology, Western Australia 23