The Serviceability Considerations of HSC Heavily Steel Reinforced Members under Bending

Transcription

1 Amerian Journal of Applied Sienes 5 (9): , 8 ISSN Siene Publiations The Servieability Considerations of HSC Heavily Steel Reinfored Members under Bending 1 Ali Akbar ghsoudi and Yasser Sharifi 1 Department of Civil Engineering, Bahonar University of Kerman, Kerman, Iran Department of Civil Engineering, Vali Asr University of Rafsanjan, Rafsanjan, Iran Abstrat: To investigate the servieability onditions of High Strength Conrete (HSC) beams, the total number of 6 beams (L = m, b =. m, h =. m) heavily reinfored with different ratios of ρ and ρ were ast and tested under bending load. During the test the onrete and steel strains, defletion and rak width are measured at different beam loations. Based on these experimental readings, the bending rigidities (EI) of HSC beams are defined and the results are ompared with the different available theoretial methods. Key words: HSC beams, different ratios of ρ and ρ, servieability onditions, EI INTRODUCTION Despite a large number of investigations [1-6] arried out in the past on flexural behavior of high strength onrete (HSC) beams, ontroversy still remains with regard to some vital design issues. One suh issue is the servieability requirement of raks. Beams tested by several investigators onsistently demonstrated signifiantly larger defletions at servie load than what would be predited by following the ACI 18- [7,8] provisions. Rashid [9] believe that, ever the assumption of raked moment of inertia as the effetive value and use of the representative expressions for the elasti modulus of onrete as reported by ACI ommittee 6 [8] for HSC had failed to bring the preditions on the onservative side. jority of explanations investigations reported are based on the underreinfored HSC, In other words, the servieability onsiderations of HSC heavily steel reinfored members are not investigated. Therefore, must be sought through further investigations on this field. The result of an investigation arried out on flexural behavior of reinfored HSC heavily reinfored beams, with a wide range of variation in ompressive reinforement are presented in this researh. After the raking moment the neutral axis flutuates between raks and ausing the value of I hanges along the beam span from a maximum value of I g for the unraked (gross) setion to a minimum value of I r for the fully raked (transformed) setion. Therefore in raked member, using an effetive moment of inertia, I e that will have a value between raked and unraked setion s value. Design provisions ontained in the urrent ode [8] reommend use of following expression for the alulation of the effetive moment of inertia: Mr Mr Ie = Ig + l I r (1) M a = maximum moment in a member at a stage that defletion is omputed. frig M r = raking moment of beam = y EXPRIMENTAL PROGRAM Test speimens: The program onsisted of testing six heavily reinfored HSC beams tested in flexure. The details of test beams are presented in Table 1 and Fig. 1. Three beams were singly reinfored and the other three were doubly reinfored. Shear reinforements were provided along the beam length exept in the onstant moment region. The variable was the ompressive reinforement ratio,. Table 1 presents the detailed testing program, where one or two letter followed by a number, suh as BC6 or B6, designate the speimens. The letters BC indiated the beams having ompression bars too. The numeral 6 to 8 indiates the variation on and. t Corresponding Author: Ali Akbar ghsoudi, Department of Civil Engineering, Bahonar University of Kerman, P.O. Box , Kerman, Iran 115

2 Am. J. Applied Si., 5 (9): , 8 Table 1: Testing program detail of the tested beam ρ/ρ A s A s d (mm) d (mm) f (MPa) Beam BC B BC B BC B8 Table : Conrete mix proportion Cement Mirosilia Coarse agg Fine agg Super-plastiizer W/C (kg m ) (kg m ) (kg m ) (kg m ) (kg m ) ratio Fig. 1a: Details of test beams Test proedure: The test beams were simply supported and subjeted to four - point loading system over a span of 17 mm, as shown in Fig. 1. The beam midspan defletion was measured with the help of defletion transduers (LVDT S ). Strains in the tension and ompression steel were measured by eletrial strain gauges mounted on them. Compressive strains at the surfae of the onrete beams were measured with eletrial and mehanial (deme) strain gauges fixed at different ritial loating inluding the midspan Fig. 1. The surfae onrete rak widths at onstant moment zone at the enterline near the bottom layer of tensile steel were measured within the entral 8 mm length for any load inrements with an auray of. mm. load was applied by means of a 14 kn hydrauli testing mahine. During test, the measurements were taken by data logger. EXPERIMENTAL RESULTS AND DISCUSSIONS Fig. 1b: Details of beam setions Craking and Yield Moments: The obtained experimental raking and yield moments are presented in Table The experimental raking moments, M r,exp, are alulated and ompared with the orresponding moments alulated by using two different ode approahes, ACI and CSA [8,1] for the beams tested in this researh. Craking moment is estimated using the modulus of rupture as: Fig. 1: Testing arrangement terials: Loally available deformed steel bars having yield strength of 4 MPa were used as flexural reinforement. The mix design is shown in Table. All beams and ontrol speimens were ast in steel molds and demolded the next day and ured under similar humidity onditions for at least 8 days. frig M () y r f r = Modules of rupture of onrete and their values for the two Codes are presented as: f =.6 f MPa (ACI), r r f =.6λ f MPa (CSA) r f =.6 f MPa [5]. y t = Distane of the extreme tension fiber from the neutral axis λ = 1 for onrete with normal density 116 t

3 Am. J. Applied Si., 5 (9): , 8 Table : Experimental raking and yield moments Beam M y(exp) M r(exp) M r(th-aci) M r(th-csa) M r[5] M r(exp) / M r(exp) / M r(exp) / No. (kn.m) (kn.m) (kn.m) (kn.m) (kn.m) M r(th-aci) M r(th-csa) M r[5] BC B BC B BC B Rashid and nsure [9] tested 16 reinfored HSC beams in flexure with onrete strength ƒ, ratios of tensile and ompressive reinforements. ( ρ and ρ, respetively) and spaing of lateral ties as the main parameters. They ompared the obtained experimental raking moments with the orresponding moments alulated by using different approahes [7,11-14] for the beams tested. Different representative expression suggested by [7,11-14] were testified while using Eq. (). These are inlude, modulus of rupture, f r, E and the redued modulus equal to E /, together with gross setion properties. It was found that the ACI ode [7] proedure for servieability requirements of maximum rak width is adequate up to a onrete strength of approximately 1MPa. Conerns However, are expressed regarding the adequay of those for raking moment and servie load defletions. It was shown that [11], however the ACI expressive for f r is highly onservative for HSC. The first author of this researh, tasted another 1 HSC beams in flexure with the main variable ratio of ρ and ρ [5] and it was found that a value of fr =.6 f (MPa) for f r an predit the raking moment with suffiient auray for first rak observed in HSC beams. The omparison of 6 HSC beams of this report with suggested values of [5] are shown in Table. Table 4: Experimental neutral axis depth measured at raking, yield and ultimate loads Beam No. C r (mm) C y (mm) C u (mm) BC B BC B BC B /d /d BC6 B BC7 B7 Neutral Axis Depth: The experimental neutral axis depth of tested beams obtained from the experimentally measured strain values on onrete surfae and tensile steel reinforement. The variation of ratio of neutral axis depth,, to the effetive depth of the setion, d, in the onstant moment zone is shown in Fig. and experimental neutral axis depth at raking, yield and ultimate loads are also shown in Table 4. Craked Moment of Inertia: The value of I exp is assumed to approah I r(exp) when the applied moment approahes M y, whih is a realisti assumption [15]. The alulation of defletion during the servie stage of struture depends mainly on the raked moment of inertia, I r. The experimental moment of inertia I r(exp) is obtained as: 117 /d BC8 Fig. : Behavior of neutral axis depth under load for HSC beams tested B8

4 Am. J. Applied Si., 5 (9): , 8 P y.a (l 4a ) L r (exp l) = 48E exp P y = Load that auses tension reinforement yield A = Shear arm L = Clear span of the beam () Table 5: Theoretial and experimental raked moment of inertia for tested beams Beam No. Ir (th) 1 6 Ir (exp 1) 1 6 Ir (exp ) 1 6 (mm 4 ) (mm 4 ) (mm 4 ) BC B BC B BC B I r raking moment of inertia and it an also be defined as the slope of the line onneting the origin and point of initial yielding of tensile reinforement in moment urvature urve [16,17] and this is given as: I r(exp) My = E ϕ ε + ε ε ϕ y = = d y y sy y (4) ε y = Measured ompression strain in the onrete at yielding stage ε sy = Measured tensile strain in steel reinforement at yielding stage C = Neutral axis depth The traditional theoretial definition of I r based on the raked transformed setion an be given as: Beams with singly reinforement ximum defletion at servie load: To investigate the servie load behavior with respet to defletion, maximum (midspan) defletion, s,al, at servie load are alulated for HSC test beams, using the elasti bending theory as: M a (L 4a ) δ s,al = (5) 4E I To assume the servie load for alulating s,al in Eq. 5, the experimental ultimate load divided by a fator of 1.7 was onsidered. This is similar to suggested value used by [9]. M a = The applied maximum (midspan) moment L = The beam span a = The shear span E = The modulus of elastiity of onrete The value suggested by ACI Code is used as: E = f + 69 b na na d s s + = b Ir = + na s(d ) Beams with doubly reinfored b + (A + A )n (A d + A d )n = s s s s b r = + s + s I na (d ) (n l)a ( d ) n = E s / E E = f + 69 MPa (ACI) The alulated values of theoretial and experimental raked moment of inertia for HSC tested beams are presented in Table MPa (ACI) I = the moment of inertia, is taken as that speified by ode [8] for effetive moment of inertia, I e as: M M I ( ) I [l ( )]I I r r e = g + r g M a = ximum applied moment at a stage that defletion is omputed M r = Craking moment of beam (i.e., Eq. 1) M r is raking moment and the values for ode are presented in Table. The maximum defletion s,al, measured at the midspan with Eq. 5 at the assumed servie load is presented in Table 6. In Table 6 the experimental maximum defletion are ompared with the orresponding predited value, denoted as s,exp. ximum Crak Width at Servie Load: The maximum rak width, w r,exp, measured at the enter of

5 Table 6: Theoretial and experimental maximum defletion at servie load Beam No. s,exp(mm) s,al(mm) F s = P u(exp) /1.7 (kn) BC B BC B BC B Am. J. Applied Si., 5 (9): , 8 Table 7: Theoretial and experimental maximum rak width at servie load Beam First r,exp (mm) r,g&l (mm) F s = P u(exp) / observed rak 1.7 (kn) width (mm) BC B BC B BC B BC6 B6 1 Crak width (mm) BC7 B7 1 4 Crak Width (mm) BC8 B Crak Width (mm) Fig. : Load versus max rak width for HSC test beams 119 Fig. 4: Crak propagation of the beams under servie load the bottom layer of tensile reinforement at the assumed servie load is presented in Table 7. For analytial evaluation, expression suggested by Gergly and Lutz [18] has been hosen for assessment. In Table 7 the experimental maximum rak widths are ompared with the orresponding predited value, denoted as w r,g and L. in Fig. the load versus width rak urve for B and BC beams is showen and in Fig. 4 Behavior and propagation of rak under the servie load is shown. CONCLUSION For HSC with heavily steel reinfored onrete beams the following onlusions an be result: The experimental raking moment is lower than theoretial values two odes ACI, CSA and the suggested value by [5] The neutral axis in doubly reinfored beams in rak, yield and ultimate stages is dereased I r(th) is larger than I r(exp1) and Ir (exp) Defletion at servie load in doubly reinfored beams is larger than singly reinfored beams and s,exp is larger than s,al Width rak at servie load in doubly reinfored beams is larger than singly reinfored beams and r,exp is larger than r,g and L

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