INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 1, No 3, 2010

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1 Volme 1, No 3, 21 Copyright 21 All rights reserved Integrated Pblishing services Research article ISSN Moment Crvatre Characteristics o ordinary grade Fly Ash Concrete beams Dakshina Mrthy 1, Sdheer Reddy 2 1 Proessor, Faclty o Civil Engineering, Kakatiya Institte o Technology and Science, Warangal 56 15, Andhra Pradesh, India 2 Proessor, Faclty o Civil Engineering, Kakatiya Institte o Technology and Science, Warangal 56 15, Andhra Pradesh, India nrdmrthy@yahoo.com ABSTRACT The characteristic eqations o the stress strain crve or ly ash concrete (ordinary grade M3Grade) are sed to stdy the M Ø characteristics o beam sections. The theoretical procedre has been validated by condcting an experimental investigation on nder reinorced ly ash concrete beams. The correlation between experimental and analytical vales o moments and crvatres arrived at based on the above procedre is ond to be good. The cement was replaced by1, 2, 3 and 4% ly ash obtained rom near by thermal power station. Keywords: Ordinary Grade Concrete, Moment, Crvatre, eective depth. 1. Introdction The concrete indstry is responsible or the economic and sae disposal o millions o tons o indstrial by prodcts sch as ly ash and slag. De to their highly pozzolanic and cementitios properties, ly ash and slag can be sed in large amonts as cement replacement materials in concrete. It is obvios that large scale cement replacement in concrete with these indstrial by prodcts will be highly advantageos rom the stand point o cost economy, energy eiciency, drability and overall ecological proile o concrete. The small size and the essentially spherical orm o low calcim ly ashes particles inlences the rheological properties o cement pastes, casing a redction in the water reqired or an increase in workability compared with that o an eqivalent paste withot ly ash. Fly ash diers rom other pozzolona which sally increase the water reqirement o concrete mixtres. A complete stress strain crve is needed or the analysis and rational design o concrete strctres. The strctres bilt in severe environment need drable concrete becase o hge amont o constrction expenses and diiclty in concrete repairs. A stress strain crve is a graph derived rom measring load vs strain or a sample o a material. In concrete the rate o increase o stress is less than that o increase in strain becase o the ormation o micro cracks, between the interaces o the aggregate and the cement paste. The stress strain behavior o concrete is a prime parameter in designing, prediction o lexral behavior and estimating the toghness o concrete. The present work was taken p to stdy the rotational capacity o reinorced concrete sections and ly ash concrete sections. De to large constrction activity all over the world, the scarcity o the constrction materials is becoming an obstrction or the expansion. With a 497

2 Volme 1, No 3, 21 Copyright 21 All rights reserved Integrated Pblishing services Research article ISSN view to tilize the mineral by prodcts like ly ash, to stdy its (behavioral) capacity in redistribting the moments and minimize cement content, An experimental investigation was carried on beams o nder reinorced sections. 2. Models or Stress Strain Crves Many researchers developed varios models or the prediction o stress strain behavior o concrete. Some o the models are given below. 2.1 Desayi and Krishnan s model For Normal strength concrete, the stress strain relationship is given by Ax = 1 + Bx 2 Where = The Normalized stress (Stress/ltimate stress) X = Normalized strain(strain/strain at ltimate stress) A, B are the constants and they can be ind ot by sing bondary conditions. This model is valid only p to ascending branch o stress strain crve. 2.2 Saenz Model With reerence to Desayi s model, Saenz proposed a model by taking into accont both the ascending and descending portions o the stress strain crve. This model is in the orm o Ax Y = 1 + Bx + 2 Cx Where y = ( / o) and x = o = Ultimate stress and Є o = strain at ltimate stress. 2.3 Hognested s Model For Normal strength concrete p to ascending portion, the stress strain model is c = compressive strength Є o = strain at peak stress.=.78 ( c ) ¼ 2.4 Wang et.al. Model c = c {2 (Є / Є o ) (Є / Є o ) ²} 498

3 Volme 1, No 3, 21 Copyright 21 All rights reserved Integrated Pblishing services Research article ISSN The model sed by Wang et.al. is in the orm o A( / ) + B ( / ) 2 ' o o c = c C( / o) + D ( / o ) However instead o sing one set o the coeicients A, B, C, and D to generate the complete crve, Wang et.al, sed two sets o coeicients one or the ascending branch and the other to the descending branch, the respective coeicients being obtained rom the relevant bondary conditions assigned to each part o the crve. 3. erimental Investigation In this phase o investigation the cylindrical specimen molds o size 15mm dia x 3mm length were selected (M3 Grade o concrete). The proportions or the mix are 1:1.42:3.9 with a W/C ratio o.46. The Cement content or one cbic meter o concrete was 38 kgs. First the molds were cleaned with kerosene, the inner srace o the molds were lbricated with grease. The concrete was illed in the molds in layers. To achieve ll compaction 25 mm needle vibrator was sed. The molds were de molded ater 24 hors o casting. A two lettered designation is given to the specimens. PL, Letters represent the ordinary grades o concrete. The third letter indicates % o ly ash added. For ex: PH indicates ordinary grade concrete with % ly ash. The designation o the specimen was done with indelible water proo ink. The de mold specimens were kept nder water or cring prpose. Ater cring or a period o 28 days the specimens are removed rom the water and kept nder shade. The cred specimens were capped with plaster o paris to provide smooth loading srace, as the casting and testing has to be done on the same ace. The capping was done with the help o glass a plate and spirit level. The excess paste on the sides was removed sing a ctting edge. 4. Testing Procedre The capped specimen was attached with abricated compressometer with three dial gages and was placed on the movable cross head o the Tins Olsen Testing machine and centered correctly. Strain rate control was adopted to get the complete stress strain diagram inclding the post ltimate descending portion. The dial gages having a least cont o.2mm were sed. The average o the three dial reading was taken. A niorm movement was achieved by adjsting the inlet valve o the testing machine, throghot the period o testing with the help o control dial gage attached to the cross head o the testing machine and the stopwatch. For the satisactory recording o strains the crosshead movement o 1mm per minte was sggested by the previos investigators. The stressstrain crves or conventional ly ash concretes were developed by the athor in the orm Ax = 1 + Bx 2 Where = The Normalized stress (Stress/ltimate stress) 499

4 Volme 1, No 3, 21 Copyright 21 All rights reserved Integrated Pblishing services Research article ISSN X = Normalized strain(strain/strain at ltimate stress) The stress strain crves are shown in igres 1. to 5. or varios ly ash percentage replacements. The vales o the constants were derived sing bondary conditions. A, B and A, B vales or varios % o ly ash are Tablated in Table 1.The area nder the stress strain crves were calclated and are tablated in Table Development o M Ø Diagrams or Beam Sections In order to generate the M Φ diagram or any cross section, it can be seen that or any concrete strain ( Є ), in the extreme ibre : C c = a.b(n.d) Where a 1 = d M c nd = b c 2 d The corresponding crvatre can be obtained by Ø = ( Є c / nd ) The evalation o integrals c d leads to the expressions : C c = a.b(n.d ) a 1 = c d a M a = 1 = = c ck A d B ( / ) c ( A / 2 B ) log ( + B / ) ck ( Bn d / )( A / ){( / B ) ( / B ) B Tan ( B / )} ck 5

5 Volme 1, No 3, 21 Copyright 21 All rights reserved Integrated Pblishing services Research article ISSN b c a nd C c d D A st T S s Figre 1: Stress Block Diagram or RCC. For obtaining the complete moment crvatre relationship or any cross section, discrete vales o extreme ibre concrete strains(є ) were selected sch that the even distribtion o the points on the plot, both beore and ater the maximm moments were obtained. The procedre sed in the comptation is as ollows. For a selected vales o Є c, the extreme ibre concrete strain, a netral axis depth nd is assmed initially. For the assmed vale o nd the compressive orce Cc and the vale o moment M c o this resltant compressive orce abot netral axis is calclated. The strain in tension steel Є s is calclated on the basis o strain compatibility. The tensile orce T s, in the tension steel is arrived at by taking the corresponding stress rom stress strain diagram o steel and mltiplying with the area o steel. The corresponding moments M s abot the netral axis is M s = T s (d nd). The vales o C c and T s are compared. I C c and T s are same, then the assmed position o netral axis is correct. Then moment M c and crvatre Ø c are calclated or a particlar ibre strain. I C c is not eqal to T s a new vale o netral axis depth is assmed based on jdgment whether C c is greater or smaller than T s.the above procedre is repeated ntil the eqilibrim condition C c = T s is satisied. The above analytical procedre enables the assessment o lexral strength o ly ash Concrete sections. The assmption made is a) Variation o strain across the section is linear p to ailre. In addition to above assmption, the ollowing three basic relationships Eqilibrim o orces, C c = T s Compatibility o strains(є c /nd= Є s /d nd ) and Stress strain relationship o the material. 51

6 Volme 1, No 3, 21 Copyright 21 All rights reserved Integrated Pblishing services Research article ISSN Present work Reslts derived rom the above proposed analytical procedre are compared with the experimental data. The beams have shown very good reslts in comparison. All the beams were tested nder symmetrical two point loading on a simply spported span o 17 mm. Figre11 shows simply spported beam testing arrangements. Specially abricated extensometer and compressometers were sed in addition to delectometers. The delections were taken at 5 dierent points over the entire span o the beam. Displacement control was sed to obtain the complete proile o moment crvatre behavior, especially in the post ltimate moment region. Moment crvatre diagram were generated or all the beams based on the characteristic stress strain diagram. The experimental vales o moments and crvatres are plotted as discrete points on the moment crvatre diagrams. The experimental ltimate moments and theoretical moments compted based on the characteristic stress strain crve o reinorced concrete are represented on correlation diagrams. Normalised Stress Graph show ing Nor. Stress Vs Nor. Strain For % Fly Ash in Ordinary Grade Concrete Normalised Strain r A= Normalised Stress Graph show ing Nor. Stress Vs Nor. Strain For 1% Fly ash in Ordinary Grade Concrete A= B= Normalised Strain Graph Show ing Nor. Stress Vs Nor. Strain For 2% Fly ash in Ordinary Grade Concrete Graph Show ing Nor.Stress Vs Nor. Strian For 3% Fly ash in Ordinary Grade Concrete Normalised Stress Normalised Strain A= Normalised Stress Norm alised Strain A=

7 Volme 1, No 3, 21 Copyright 21 All rights reserved Integrated Pblishing services Research article ISSN Normalised Stress Graph Show ing Nor. Stress Vs Nor.Strain For 4 % Fly Ash in Ordinary Grade Concrete Normalised Strain A= B= Normalised Stress Graph showing Nor. Stress Vs Nor. Strain For Avg. Fly Ash in Ordinary grade Concrete A= B= Normalised Strain Figre 2: retical erimental Stress Strain Crves Table 1: Vales o constants or Stress Strain Crves or M3 Grade Fly Ash Concretes Designation A B A 1 B 1 Area nder the crve(units) PL PL PL PL PL A, B are constants in ascending portion o the Normalized stress strain crve A 1, B 1 are constants in descending portion o the Normalized stress strain crve Beam Desig Nation Table 2: Perormance Details o M3 Grade Fly Ash Concrete Beams Strain Delectio Max. Strain Load in Strain Delectio n Momen at at Concret in n at max. t Extrem First e Steel at irst Load (kn. e crack at max. crack (mm) M) ibre (kn.) Load Max. Load kn. Delection at Service Loads (mm) PLU PLU 1 PLU 2 PLU 3 PLU

8 Volme 1, No 3, 21 Copyright 21 All rights reserved Integrated Pblishing services Research article ISSN where A st = 2 mm 2 (provided) σs y = 415 N/mm 2. b = 1 mm. D = 2 mm. Cover = 25 mm. Shear reinorcement = 6 mm 1 mm c/c. One replication or each beam specimens. Average o three specimens (reading) or stress strain behavior. 16 PLU Moment KN M E+ 2.E 5 4.E 5 6.E 5 Crvatre 2 PLU1 Moment KN M E+ 2.E 5 4.E 5 6.E 5 Crvatre 54

9 Volme 1, No 3, 21 Copyright 21 All rights reserved Integrated Pblishing services Research article ISSN PLU2 Moment KN M E+ 3.E 5 6.E 5 9.E 5 Crvatre Moment KN M PLU3.E+ 2.E 5 4.E 5 6.E 5 Crvatre 2 PLU4 Moment KN M E+ 2.E 5 4.E 5 6.E 5 Crvatre 5.2 Correlation Figre 3: retical erimental Moment Crvatre Graphs It can be seen that the procedres developed or obtaining the complete proile o moment crvatre diagram o Fly Ash Concretes sections based on the characteristic stress strain crves or Fly Ash Concrete predict the experimental behavior satisactorily (Figs2 to 6). There is a good agreement between the analytical and experimental ltimate moments, as can 55

10 Volme 1, No 3, 21 Copyright 21 All rights reserved Integrated Pblishing services Research article ISSN be seen rom the correlation diagram (Figs7 to 11). The lack o very good correlation in crvatres may be attribted to the act that, the analytical crvatre at a section compted to satisy the eqilibrim and compatibility conditions, where as the experimental crvatre is the crvatre measred over a gage length o 2 mm and hence represents the average crvatre over gage length inclding localized high crvatres at the cracks. Figre 12: Failed beam specimen ater testing Figre 13: Test arrangement or the beam 56

11 Volme 1, No 3, 21 Copyright 21 All rights reserved Integrated Pblishing services Research article ISSN Figre 14: Image showing the testing arrangement Notations: D,b = Lateral dimensions o beams. d = Eective depth., Є=Stress and corresponding strain. C c =Compressive orce in ly ash concrete beams. ck = Concrete cbe strength at 28 days M e =erimental ltimate moment M t =retical ltimate moment Ø e = erimental crvatre at ltimate load Ø t = retical crvatre at ltimate load Ts=Tensile Force Cc=Force in compression zone 6. Conclsions 1. An analytical model was developed or obtaining the complete moment crvatre diagram or Fly Ash ordinary grade Concrete. 2. The ltimate moments obtained rom the proposed analytical procedre are ond to be in good agreement with the experimental vales. 3. Fly ash replacement (p to 3%) in concrete has shown good improvement in lexral strength. 7. Reerences 1. Chava Srinivas., Gopala Krishnayya. and Raj.P.S.N. 24 Eect o FA addition on Compressive Strength, stress strain behavior and drability o concrete exposed to 57

12 Volme 1, No 3, 21 Copyright 21 All rights reserved Integrated Pblishing services Research article ISSN slphric acid. ICACC 24. Proceedings o International Conerence on Advances In Concrete and Constrction December, Vasavi College o Engineering, Hyderabad. India. pp Hs, L. S. M. and Hs, T.T. (1994), Stress Strain Behavior o Steel Fiber High Strength Concrete nder compression, ACI Strctral Jornal, V. 91, No. 4, Jly Agst, pp Papworth, F. and Ratclie, R. (1994), High Perormance Concrete The concrete Ftre, Concrete International, V. 16, No. 1, pp Pendyala.R.S., (1997). The behavior o High strength concrete lexral members Ph.D Thesis, The niversity o Melborne. 5. Reddi. S.R. (1974) Behavior o concrete in rectanglar binders, and its application in lexre o reinorced concrete strctres Ph.D Thesis J.N T.University, Hyderabad. 6. Sesh. D.R., et.al.(24) Compressive strength o high volme ly concretes o dierent grades, Proceeding o National work shop on Advances in materials and mechanics o concrete strctres, pp Jly 2 nd & 3 rd, IIT Chennai 7. K.Ramesh et.al.(23). Moment crvatre characteristics o hybrid erro iber cocretre (HFFC) beams Jornal o Ferro cements volme 33, No.1, Janary, pp Bozobaa.N and Fornier.B.(23). Optimization o FA content in concrete. Part I. Non air entrained concrete made withot Sperplastizer. Cement and Concrete Research., Vol.33, pp Hongsted,F.et.al.(1955), Concrete stress distribtion in ltimate strength design,jornal o ACI Proc.vol.52,No.4, Dec, pp