Engineering, Technology & Applied Science Research Vol. 8, No. 2, 2018, 2745-2749 2745 www.etasr.com Ali et al.: Prediction of Corner Columns’ Load Capacity Using Composite Material Analogy Prediction of Corner Columns’ Load Capacity Using Composite Material Analogy Ahsan Ali Department of Civil Engineering Quaid-e-Awam Universityof Engineering, Science & Technology Larkana, Pakistan Pakistanahsanone@gmail.com Zuhairuddin Soomro Department of Civil Engineering Quaid-e-Awam University of Engineering, Science & Technology Larkana, Pakistan zuhairuddin@quest.edu.pk Shahid Iqbal Department of Civil Engineering CECOS University Peshawar, Pakistan shahid.iqbalmce@gmail.com Nadeem-ul-Karim Bhatti Department of Civil Engineering Quaid-e-Awam University College of Engineering, Science & Technology Larkana, Pakistan knadeem_b@yahoo.com Ahmed Faraz Abro Department of Civil Engineering Quaid-e-Awam University of Engineering, Science & Technology Larkana, Pakistan a.faraz.abro@outlook.com Abstract-There are numerous reasons for which concrete has become the most widely used construction material in buildings, one of them being its availability in different types, such as fiber- reinforced, lightweight, high strength, conventional and self- compacting concrete. This advantage is specially realized in high- rise building construction, where common construction practice is to use concretes of different types or strength classes in slabs and columns. Columns in such structures are generally made from concrete which is higher in compressive strength than the one used in floors or slabs. This raises issue of selection of concrete strength that should be used for estimating column capacity. Current paper tries to address this issue by testing nine (09) sandwich column specimens under axial loading. The floor concrete portion of the sandwich column was made of normal strength concrete, whereas column portions from comparatively higher strength concrete. Test results show that aspect ratio (h/b) influences the effective concrete strength of such columns. A previously adopted methodology of composite material analogy with some modifications has been found to predict well the capacity of columns where variation in floor and concrete strength is significant. Keywords-composite material analogy; sandwich columns; corner columns; axial loading I. INTRODUCTION There are many reasons for which concrete has become the most widely used building construction material. Concrete’s ability to shape into any structural form, easy accessibility of its constituent materials and liberty of selecting among its various types, for example, fiber-reinforced, lightweight, high strength, conventional and self-compacting are few worth mentioning reasons. This choice of selection of different grades/types of concrete favors its application also in high-rise building construction. Concrete compressive strength used in construction has been increasing over the years and strengths up to 20ksi (138MPa) and more have been used in the industry, especially in columns of high-rise buildings [1]. The use of high strength concrete column sections along the height, with higher-strength concrete placed in lower stories, results in additional savings associated with repetitive use of formwork. Compared to columns, high strength concrete is not required in floor/slab region of a framed structure. Also, economy and space requirements in high-rise building construction force designers to select concretes of different types/strength classes for slabs and columns. In such a state, presence of two different grades of concrete in slab-column region raises issue of selection of concrete strength 'cf to be used in (2) for estimating column capacity. ACI-318 [2] addresses the issue of variation in strengths of column and floor concretes in its section 10.12, where it recommends no special measures as long as the ratio of column to floor concrete strength ' 'cc csf f is limited to 1.4. Requirements of ACI are based on [3] and state: When ' ' 1.4cc csf f £ (1-a) ' ' ce ccf f= (for interior, corner & edge columns) When ' ' 1.4cc csf f > (1-b) ' ' ce csf f= The maximum concentric load carrying capacity of the column can be obtained by adding the contribution of the Engineering, Technology & Applied Science Research Vol. 8, No. 2, 2018, 2745-2749 2746 www.etasr.com Ali et al.: Prediction of Corner Columns’ Load Capacity Using Composite Material Analogy concrete, calculated by '( )0.85g st cA A f- , and the contribution of the steel ( )st yA f . The value of '0.85 cf instead of 'cf is used in the calculations. ACI recommends this value on the basis of 564 tests on columns carried out during 1927 to 1933 at Lehigh and Illinois universities [4]. The nominal concentric load capacity of a column Po can be expressed as: ( )'0.85o c g st st yP f A A A f= - + (2) Rearranging (2), effective strength of concrete 'cef can be defined as ( ) ' 0.85 o st y ce g st P A f f A A - = - In [3, 5-10], researchers tried to address this subject and proposed different expressions and solutions. Few of these studies are discussed here to justify the proposed solution presented later in the paper. Author in [5] tested six specimens with aspect ratio h/b of 0.7 to understand the load transfer mechanism of high strength concrete column through a layer of lower strength slab concrete and to determine the effects of confinement on behavior of slab concrete. Treating the specimens as composite materials, he used mechanics of materials approach for developing (3) to calculate the effective concrete strength. ' ' ' ' ' 2.0 cc csce G cc cs f f f f f l= + (3) where, 0.9,1.0,1.25Gl = for corner, edge & interior columns respectively. Authors in [11] proposed (4) for computing effective concrete strength of a sandwich column and concluded that current ACI provisions for ' ' 1.4cc csf f > are overly conservative for edge and corner columns. Their results were based on tests conducted on 54 sandwich column specimens. ( )' ' ' 'ce cs cc csf f A f f= + - (4) where 1 0.4 2.66 A h b       . Authors in [7] investigated the effects of aspect ratio h/band column rectangularity on the effective concrete strength 'cef of high strength concrete corner columns intersected by weaker slabs. The aspect ratio varied from 0.3 to 1.14 with maximum 12600psi (87MPa) concrete strength. They concluded that it would be inaccurate to not consider aspect ratio in estimating the effective compressive strength of joint. Using mechanics of material approach like [5], authors in [12] suggest (5), a design expression for prediction of interior column capacity. They are of the opinion that the composite material analogy can be effectively applied for the theoretical analysis of the problem associated with estimating column capacity. However, like [5], their suggested equation also does not acknowledge the effect of aspect ratio. ' '3 3 '3 ' '3 3 2.0 cc csce G cc cs f f f f f l ´ = + (5) where 1.07Gl = . All mentioned studies signify the importance of aspect ratio h/b and composite material analogy approach. Expressions proposed by some researchers are based on this approach but are independent of aspect ratio, whereas expression proposed in[11] is based on regression analysis rather mechanics of material approach. II. EXPERIMENTALPROGRAM AND TEST SETUP The experimental program included the testing of nine sandwiched column specimens in direct compression, as these specimens adequately model the corner column slab joint [5, 7]. Specimens were divided into three groups A, B and C, having three specimens in each group, each group had different ratio of column to floor concrete strength. Specimens in each group had slab/floor layer of 4, 6 and 8 inches (102, 152 and 203mm). Slab portions were sandwiched between two column ends made up of comparatively lower strength concrete than the one used in column ends. Specimen with 4 inch (102mm) thick slab layer had aspect ratio h/b of 0.67 - typical to that of flat plate floor system, whereas those with 6 inch (152mm) and 8 inch (203mm) thick layer developed an aspect ratio of 1 and 1.33 respectively. Figure 1 shows the rest of the features of specimens in all groups. All specimens were tested in axial compression in a 2000kN capacity compression testing machine. First, the test specimens were installed in the testing machine, centered carefully to avoid any flexural stresses resulting from accidental eccentricity. Strain gauges applied to main reinforcement in slab region to monitor their performance under load were connected to the data logger. Three cylinders cast from the column concrete and slab concrete batches were tested first to obtain the axial compressive strength. This was followed by compressive testing of sandwich column specimens. Before testing, elastic pads were placed between specimen and machine loading plates to avoid damage to column ends. The load was applied in increments of 50kN. During the test, specimen behavior was carefully monitored, cracks were marked on their appearance along with load readings. Strain gauge readings were also recorded after each load increment. After specimen failure, the crushed concrete around the failure area was removed to observe the behavior of the reinforcement. A typical test setup is shown in Figure 2(a). III. TEST RESULTS Test results confirm the established behavior of axially loaded columns, specimens in current experimental work failed due to buckling of the longitudinal bars and crushing of slab concrete. The buckling of longitudinal bars and crushing of slab concrete (see Figure 2(b)) took place almost simultaneously and suddenly. Although, at the beginning, sm of cau pro Sp sug thu tes com mo is t beh Co fav [13 (RV ele sim eac 3(c hig asp “b” em bet or as eff req mu dis Engineerin www.etasr maller cracks ap testing machi use of failure ogressed verti pecimens with ggesting that a us confirming st results for al Fig. 1. L IV. Proposed equ mposite mat odifications is that the colum have like com omposites are vorable proper 3]. Figure 3(a RVE) having d ementary mec milarities of R ch other, along c)) with effec ghlighted in F pect ratio (h/b ”. Unlike fibro mbedded by w tween stronge sandwich colu shown in Fi fective transv quires that the ust be equal splacements in Using definit ng, Technology r.com ppeared in the ine, however appeared late ically until a higher aspect aspect ratio do the findings ll specimens ar Longitudinal& cro COMPOSITE uation (3) in terial. The presented her mn with two di mposite materia preferred fo rties - fibrous a) shows the dimensions “b chanics of ma RVE and a san g with equival ctive transvers Figure 3. Ack b), RVE is ass ous composite weaker matrix er column ends umn is subjec igure 3(a), th verse modulu e total transve to the sum n the fibers fyd cybe e= tion of Hook’s ' ' y fy y fy f f E E = ´ y & Applied Sci e column ends the cracks wh er in the floor after spalling ratios (h/b) fa oes influence t of previous s re presented in oss sectional deta E MATERIAL AN [5] is based o same appro re. The basic p ifferent grades al made of tw or application composite is o e representativ b” and simple aterials mode ndwich column lent homogeno se modulus o knowledging signed dimens e (RVE), wher x, weaker sla s in this analo cted to transve he response i us Ey. Geom erse composit of the corres and the matrix fy f my mL Le e+ s Law: ' f my my L f b E ´ + ´ ience Research Ali et al.: Pre s near loading hich were the r concrete are of cover con ailed at lower the column cap studies [7, 10] n Table I. ails of specimens NALOGY on the princip oach with principle or an s of concrete s o kinds of ma n as they res one typical ex ve volume el e states of str els. Comparis n (Figure 3(b) ous material (F f elasticity the significan sions of unit re fibers are h abs are sandw ogy. When the erse normal st s governed b metric compat te displacemen sponding trans x myd . mL myL b ´ V ediction of Corn plates e main ea and ncrete. loads, pacity ]. The ples of some nalogy should aterial. ult in ample ement ess in on or ) with Figure are nce of width held or wiched e RVE tressσy by the tibility nt cyd sverse fibe stre mu mat Sim bec com littl stre ' cef whe com It is colu cor diff AC valu con or e AC Fig prev 318 draw with fou gre new app pre pro exis Vol. 8, No. 2, 20 ner Columns’ L If we assume er are all equal 1 yE b = From Figure esses is valid st be equal fo trix blocks h mplifying and comes: Modulus of e mpressive stren le margin of e ength i.e. cE a ( ' ' cc e cc bf h f f = - ere (h/b≤1). mposite action s believed tha umn slab join rner columns ferent research CI-318 recomm ue of concre ncrete strength equal to 1.4, n Results of ef CI approach an gure 4 shows vious samples 8 and propose wn to these p h overall test t und to be too c ater than 1.5. wly proposed parent strength dicted ration oposed design sting code equ 018, 2745-2749 Load Capacity cy fye e= ´ e that the stres l then above e f m fy L L E b E + ´ ´ 3, it would se because equi or the series a have equal ar d using sand (y c E h E = elasticity is pr ngth. Here for error, it is tak ' cf or ' cf . ) ' ' ' c cs cs cs f f f b+  Condition of n to exist. V. RESU at sandwich co nts. Therefore have been u hers [3, 5-6, 1 mends the us ete strength, i hs ' 'cc csf f exc no measures ar ffective concr nd the propose apparent co s plotted again ed equation. T lots along wit to prediction r conservative, The effective (7) has sho h 'cpf of tested of 1.29 and equation app uation. 9 Using Composi f my L b e´ + ´ ses in the com quation reduce my myE eem that the as ilibrium requi arrangement a reas normal t dwich column ) s cc c s s bE E E E- + roportional to r the sake of s ken proportion ( ' ce c f h f b  = f h/b≤1 is im ULTS ANALYSIS olumns adequa previous data used for ana 11-12, 14]. Fo se of puddle if the ratio o eeds 1.4. If th re suggested. rete strength f ed one are pre oncrete streng nst the calculat The theoretical th the data poi ratio of 1.38, t particularly fo strength calcu own good co samples. With standard devi pears to be m 2747 ite Material An mL b mposite, matrix es to: (6) ssumption of res that the f and both fiber to the y-direc n’s notations b the square ro simplicity and nal to compre ) ' ' ' ' ' cc cs cc cs cs f f f f- + mposed to (7 S ately model c a of sandwich alysis purpose or corner colu concrete or l of column to his ratio is less ' cef , following esented in Tab gth of current ted values by l line at 45o is ints. From Tab the ACI equati or ratios of 'ccf ulated 'cef usin orrelation with h an average t iation of 0.28 much safer tha nalogy x and equal forces r and ction. , (6) oot of d with essive s (7) 7) for orner h and es by umns, lower slab s than g the ble II. t and ACI- s also ble II ion is ' c csf ng the h the test to 8, the an the Engineerin www.etasr S Concre strength psi (MP tP ' cpf ng, Technology r.com Fig. 3. Specimen ete h - Pa) Top column Slab Bottom column lb kN psi MPa ' ' cc csf f ' ' cp csf f h/b y & Applied Sci Fig. (a) . (a) RVE (b) SCA- 4 60 27 60 182700 812.69 3665.47 25.27 1.34 0.67 ience Research Ali et al.: Pre (a) 2. (a) Test se Sandwich colum TABL SCA-6 S 082 (41.93) 725 (18.79) 020 (41.51) 177244 17 788.42 7 3480.81 33 24 2 2.22 1.28 1 Fig. 4. V ediction of Corn etup, (b) Failure o ( mn as composite m LE I. TEST R CA-8 SCB-4 73692 19474 72.62 866.25 360.59 4073 23.17 28.08 1.23 1.81 1.33 0.67 Concrete stren Vol. 8, No. 2, 20 ner Columns’ L f specimen in slab (b) material (c) Equiva RESULTS 4 SCB-6 7754 (53.46) 2249 (15.51) 7105 (48.99) 1 190545 5 847.59 3931 8 27.10 3.3 1.75 1 ngth graphs 018, 2745-2749 Load Capacity b region alent homogenou SCB-8 SCC 187115 171 832.33 761 3814.9 327 26.3 22. 1.696 1.1 1.33 0.6 9 Using Composi (b) (c) s material C-4 SCC-6 5342 (36.84 2857 (19.7) 5556 (38.32 163 165195 .37 734.82 75 3073 59 21.19 1.91 15 1.08 67 1 2748 ite Material An SCC-8 4) ) 2) 163865 728.91 3028 20.88 1.06 1.33 nalogy Engineering, Technology & Applied Science Research Vol. 8, No. 2, 2018, 2745-2749 2749 www.etasr.com Ali et al.: Prediction of Corner Columns’ Load Capacity Using Composite Material Analogy TABLE II. RATIO OF APPARENT TO EFFECTIVE CONCRETE STRENGTH Specimen series ' ccf (psi) ' csf (psi) ' cpf (psi) ACI 318-11 Proposed ' cef (psi) ' ' cp cef f ' cef (psi) ' ' cp cef f A 6051 2725 3666 2725 1.35 3329 1.10 6051 2725 3481 2725 1.28 2725 1.28 6051 2725 3361 2725 1.23 2725 1.23 B 7430 2249 3815 2249 1.70 2921 1.31 7430 2249 4073 2249 1.81 2249 1.81 7430 2249 3931 2249 1.75 2249 1.75 C 5449 2857 3275 2857 1.15 3389 0.97 5449 2857 3073 2857 1.08 2857 1.08 5449 2857 3028 2857 1.06 2857 1.06 Mean 1.38 1.29 Standard deviation 0.28 0.28 VI. CONCLUSIONS Analysis and discussion of test results leads to the following conclusions:  Specimens of all series confirm that the effective strength of an axially loaded column intervened by lower strength concrete floor is influenced by its aspect ratio h/b.  As the aspect ratio increases, the effective strength of the joint decreases.  The ACI 318, Section 10.12, provisions for ' ' 1.4cc csf f > are overly conservative for corner columns.  Mechanics of composite materials can be used to predict the response of slab-column joints to axial loads. The proposed expression (7) can safely be used for predicting the effective concrete strength of axially loaded corner columns. DENOTATION TABLE Ag gross area of column cross section Lf length of fiber Ast area of deformed bar Lm length of matrix b least column dimension Po nominal concentric load capacity of column Ecc modulus of elasticity of column concrete Pt axial test load applied to column Ecs modulus of elasticity of slab concrete ρ reinforcement ratio Ey effective modulus of elasticity in Y-axis direction δcy axial displacement of composite in Y- direction ' ccf compressive strength of column concrete δfy axial displacement of fiber in Y-direction ' cef effective compressive strength of column δmy axial displacement of matrix in Y-direction ' cpf apparent concrete strength of column cy e strain in composite in Y-direction ' csf compressive strength of slab concrete fy e strain in fiber in Y- direction yf yield strength of deformed bar my e strain in matrix in Y- direction h thickness of slab column joint L length of specimen REFERENCES [1] ACI Committee 363, “Report on High-Strength Concrete (ACI 363R- 10)”, in: ACI Manual of Concrete Practice, American Concrete Institute, 2013 [2] ACI 318-14, Building Code Requirements for Structural Concrete and Commentary, American Concrete Institute, 2014 [3] A. C. Bianchini, R. E. Woods, C. E. Kesler, “Effect of Floor Concrete Strength on Column Strength,” ACI Journal, Vol. 31, No. 11, pp. 1149– 1169, 1960 [4] J. K. Wight, Reinforced concrete : mechanics and design,Pearson, 2016 [5] M. K. Kayani, “Load Transfer from High-Strength Concrete Columns through Lower Strength Concrete Slabs”, University of Illinois, 1992 [6] J. H. Lee, Y. S. Yoon, W. D. Cook, D. Mitchell, “Benefits of using puddled HSC with fibers in slabs to transmit HSC column loads”, Journal of Structural Engineering, Vol. 133, No. 12, pp. 1843–1847, 2007 [7] S. C. Lee, P. Mendis, “Behavior of high-strength concrete corner columns intersected by weaker slabs with different thicknesses”, ACI Structural Journal, Vol. 101, No. 1, pp. 11–18, 2004 [8] A. A. Shah, Y. Ribakov, “Estimation of RC slab-column joints effective strength using neural networks”, Latin American Journal of Solids and Structures, Vol. 8, No. 4, pp. 393–411, 2011 [9] I. Shahid, S. H. Farooq, N. A. Qureshi, K. R. 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