FORCE DISTRIBUTION OF REINFORCED CONCRETE COUPLING BEAMS WITH DIAGONAL REINFORCEMENT
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1 FORCE DISTRIBUTION OF REINFORCED CONCRETE COULING BEAMS WITH DIAGONAL REINFORCEMENT Yenny Nurhasanah Jurusan Teknik Sipil, Fakultas Teknik, Universitas Muhammadiyah Surakarta Jl. A. Yani Tromol os 1 abelan Kartasura Telp yn.hasanah@gmail.om Abstrak The strutural behaviour of reinfored onrete ouple shear walls is greatly influened by the behaviour of their oupling beams. The behaviour of the oupling beams themselves depends on the geometry of the beams and the strength harateristis of the onrete and reinforement. Behaviour harateristi of deformation and mode of failure at oupling beams that happened is the existene of ompression area at diagonal diretion oming in ontat with tip of fore, tension area at opposite diagonal diretion whih will have rak till split at diagonal area ompress, and the beam will attain its maximum load arrying apaity when small portion of the onrete in the ompression orners rush. Mode of failure that happened is shear failure. The proposed method of analysis of reinfored onrete oupling beams based on the equilibrium of fores of a triangular half of the beam at failure gives a satisfatory predition of fore in the main bars. The distribution of fore in the main bars of the beams at failure is showed using the proposed onept, when the diagonal splitting mode of failure ours, is tensile. The fore varies linearly along the span with a smaller value at he tip of the triangular half of the beam to its full apaity at the support. Although it was not possible to ompare the fore diretly with the experimental result, the observed behavior agrees with the proposed onept. The distribution of fore in the bars based on the onventional onept of flexural deformation of reinfored onrete oupling beams differs drastially with the atual behavior. Key words : Coupling beams; CRT Bar ; dutility ; diagonal reinforement; fore distribution Introdution Multistory shear walls with openings present a number of problems. If the openings are very small, their effet on the overall stress minor. However, large openings have muh more pronouned effet. Opening (windows, doors, and the like) normally our in regularly spaed vertial rows throughout the height of the wall. So, their must to provide a struture that ould be funtion to transfer the fore between the vertial walls. For that purpose, hene provided a beams to onneting the walls. The strutural behaviour of reinfored onrete ouple shear walls is greatly influened by the behaviour of their oupling beams. The behaviour of the oupling beams themselves depends on the geometry of the beams and the strength harateristis of the onrete and reinforement. Many beams with oupling fore have been designed as onventional flexure members with stirrups and with some shear resistane alloated to the onrete are oftentimes will inevitably fail speially at diagonal areas, hene for beams with oupling fore is reommended that the beams are reinfored with diagonal systems (bi-diagonal reinforement) Analysis Reinforement Design : Gravity load effets on these beams are negleted. It is reommended that in oupling beams of strutural walls, the entire seismi design shear and moment should be resisted by diagonal reinforement in both diretions. Maximal allow shear stress : V max = 0,1. l n. f ' / h (Ma) f ' V max = 1,2. (l n / h). (psi) Minimum allow shear stress : V min = Q u / (. b w. d) ; = 0,85 S-79
2 If v min > v max, diagonal reinforement should be used in all oupling beams to resist the entire earthquake-indue shear fore. Fig 1. Fore diretion and notation of oupling beams Fig. 1, from this, it is seen that the diagonal fore are : C u = T u = Q / (2.sin ) The area of diagonal steel required is : A sd = T u / (.f y ) ; = 0,9 = Q / (2..f y.sin ) (Ma) Transverse reinforement area required is : A te = Ab. f y. (mm) 16. f yt s 100 where, s 100 mm s 6. d b (D-diagonal) s 24 x D-sengkang Development length required is : l db = 1,38. Ab. f y (mm). f ' Fig 2. Flexural deformation of beam and fore where, 2 s is enter-to-enter distane between bars in the vertial plane. The development length of this group of four bars is, however, to be inreased by 50%. l d = 1,5 x l db (mm) When transver ties are also used within the wall, the development length may be redued with : k tr = Atr. f yt 10. s with redution fator : k tr and thus, l d = redution fator x 1,5 x l db (mm) Deformation The true deformation of the oupling beams is a ombination of the flexural and shear deformations. But in any partiular ase, either flexure or shear will govern. When flexure governs, the overall deformation of the beam is still aurately represented by flexure type deformation (Fig. 2) and as in (1) is reasonably aurate for estimating the ultimate strength of the beam. u = 2 h. A st. f y (1) a Shear Deformation A pure shear deformation and the ations produed in the beam are shown in Fig. 3a and Fig. 3b. The pure shear deformation requires both top and bottom surfaes of the beam all along the length to be tension. There is ompression along the diagonal AC and tension along BD. An element of the beam near the mid span is subjeted to a biaxial ompression tension state of stress. The onrete rak when the tensile stress in the onrete along the diagonal BD reahed the limiting tensile strength of onrete. The mode of failure in shear is haraterized by the extension of the diagonal rak up to the position of the main reinforement diagonally opposite and by the rushing in the ompression orners (Fig. 3b) When the behavior is governed by shear, the overall deformation of the beam is muh more omplex. The flexural deformation ausing the beam to bend in double urvature, with tension along one-half of the beam hanging into ompression along the other half on both top and bottom surfaes, onflit with the shear deformation whih auses the beam to go into tension on both surfaes along entire length. S-80
3 Diagonal Split Crush Fig. 3a. Initial stage : element under biaxial stage Gbr. 3b. Final stage : Diagonal splitting and rushing of onrete Dutility Deformation Dutility defines the ability of a struture and seleted strutural omponent to deform beyond elasti limits without exessive strength or stiffness degradation (aulay-riestly, 1992). The most onvenient quantity to evaluate the dutility imposed on struture by an earthquake, or the struture s apaity to develop dutility, is displaement. The displaement dutility is : y Where, = y + p. The yield ( y ) and fully plasti ( p ) omponent of the total lateral tip defletion. Coupling Beams Analysis (N.K. Subedi, 1988) The analysis of oupling beams subjeted to flexural and shear stress ations, and in whih the strutural behaviour is governed by shear, may be arried out by onsidering the fore system in a triangular half of the beam as shown in Fig. 4. Fig. 4. idealized diagram : equilibrium of triangular half of the beam The following equation may be written : Vertial equilibrium : u = 2.V + f t.b.a + v (2) Horizontal equilibrium : st = f t.b.h + h + C (3) momen about 0 (M=0) : 2 2 st h = V.a + f t. b.( h' a ) + h. h ' + v. a (4) From eqns. (2) to (4), the ultimate load for the beam may be expressed as = (f t.b.h + 2.C + h ). h' (5) a u In proposing equation (5) the most important riteria for the failure of oupling beams is assumed to be the rushing of the onrete of depth (h-h ) / 2 in highly stressed ompression orners. The ompressive fore, C = 0,67.f u.b.(hh ) / 2 The quantity f t.b.h and ontribution of h depends on whether the web strength is ontrolled by onrete or by reinforement. Control of Web Strength and Contribution of Web Reinforement The web reinforement onsists of horizontal web bars plaed in the entral part of the beam between the top and the bottom main bars and vertial stirrups. The ontrol of web strength and ontribution of the web bars S-81
4 depends on the relative apaities of the onrete splitting fore and the web reinforement. The following riteria tests may be applied : When the web strength I ontrolled by reinforement, h = 1.A h.f sy, v = 2.A v.f sy and f t will not ontribute. Here, 1. 2 = 1. When the web strength is ontrolled by onrete, h = A h.f s, v = A v.f s and f t will ontribute. Here, f s = modular ratio x f t and 1 and 2 are fators whih depend on the geometri parameters. Test f f.b.h + A h.f s f t.b.a + A v.f s Web strength is ontrolled by (a) < A h.f sy < A v.f sy reinforement (b) > or > A h.f sy or < > or > A v.f sy or < onrete The riteria tests indiate learly that, for the web reinforement to be effetive, suffiient amount must be provided in both diretions, i.e. horizontal and vertial. If suffiient reinforement is present in one diretion only, e.g. losely spaed vertial stirrups but no additional horizontal bars, the effetiveness of the reinforement will be small. The introdution of fators, 1 and 2, suggests that, for a better utilization of the web reinforement must be provided in the same proportion as the omponents of the onrete splitting fore. When the web strength is governed by the reinforement and also when the proportion of the reinforement in the horizontal and the vertial diretions is in the ratio. ( f t.b.h + A h.f s ) / ( f t.b.a + A v.f s ) 1 = 2 = 1. That represents an effiient use of the web bars. Contribution of Main Reinforement The ontribution of the main bars may be examined from equation (3). Sine the ompressive fore, C, is assumed to be equal to 0.67 f u.b.(h-h )/2 at failure, st an alulated. Now, if st is less than the apaity of the main bars, A st.f y, it is assumed that the main bars will not yield at the failure of the beam. If st is greater than A st.f y, the main bars will yield at failure. Fore Distribution in Main Bars It is assumed that the fore in the main bars varies linearly from T o at the tip of the triangular half (Fig. 4.) to T a at the support. For the evaluation of T o, equation (2) is expressed as V = ½. ( u2 f t. b.a v ) (6) in whih u2 is alulated from equation (5) and the ontribution of the other quantities is obtained as appropriate, i.e. based on whether the ontrol of web strength is by onrete or by reinforement. Then, referring to Fig. 4., the fore in the main bar near the tip of the triangle may be obtained from V a T o = h' the fore in the bar at the support, T a, is evaluated from equation (3), as disussed earlier. Researh Method This researh pertained experimental laboratory researh where the parameters used to be based to the theoretial analysis. The analysis are: Theoretial analysis whit using some parameters that relevant to predit the deformation behavior of oupling beams. This analysis will produe the theoretial values. Experimental analysis, where the data from analysis theoretial to be treated to the speimens (oupling beams). This analysis will produe the experimental values. Failure roess. Deformation that happen on oupling beams in this experiment is a ombination of the flexural and shear deformation Behaviour harateristi of deformation and mode of failure at oupling beams that happened is the existene of ompression area at diagonal diretion oming in ontat with tip of fore, tension area at opposite (7) S-82
5 diagonal diretion whih will have rak till split at diagonal area ompress, and the beam will attain its maximum load arrying apaity when small portion of the onrete in the ompression orners rush This behaviour requires fresh explanation and may be desribed as follows (see Fig. 6): (i). At early stage of loading, the beam starts to deform in ommon flexural type behaviour (Fig. 6a). At this stage, the beam has double urvature with a line of ontraflexure at the enter of the span. A line of ontraflexure is defined as the line passing through the points of ontraflexure of the horizontal layers of the beam. But soon after, when the shear fore is large enough to initiate a diagonal rak, the double urvature (flexure) behaviour hanges. (ii). As the rak opens up beause of inreasing diagonal tension ompression effet, the outer onave part of the urvature on both top and bottom surfaes of the beam pushes outward gradually. This is equivalent to a shift in the position of the points of ontraflexure in reinforement from their original position at the enter towards the supports in the opposite diretion. It an be visualized from Fig. 6b that the line of ontraflexure rotates antilokwise as the diagonal rak in the onrete spreads outwards from the enter (iii). The shift in the position of the point of ontraflexure in the reinforement will stop near the fixed end support where the onfliting deformation required for the bending and shear ation ause the reinforement to kink (Fig. 6). At this stage, the onrete will have raked most of the way diagonally showing a marked separation near the middle. The reinforement, both top and bottom, will be in tension along most of its length exept near the kink where the loal affet will influene the behaviour. (iv). The beam will attain its maximum load arrying apaity when small portion of the onrete in the ompression orner rush, thus marking the failure of the beam (Fig. 7). Line ontraflexure Fig. 6a. Early stage : flexural behaviour Fig. 6b. Diagonal splitting and rotation of the line of ontraflexure Crak attern and Split The diagonal split wide values of oupling beams with diagonal reinforement plaing (Deform and also of CRT Bar) is 1,35 m, and the diagonal split wide value of onventional oupling beams is 2,75 m. from this data proved that oupling beams whit diagonal reinforement an lessen widely of split up to 50,91% ompared to is wide of split at onventional oupling beams. This result an be enabled to happened beause with the existene of diagonal reinforement addition in one group (four bars) hene will be formed a onrete ore that an resist the tension stress at diagonal stress areas. The diagonal stress areas will be ontrary diretion with diagonal ompress areas. But, wide of diagonal split among usage both types of the steel bar do not show differ far. C T As d T Soure : Experiment Diagonal Split C Fig. 6. Final stage at failure : Final deformed shape S-83
6 Referring to Table. I. two values for the ultimate strength, u1, based on the flexural mode of failure are given. The seond row of u1 value were alulate from equation (1) in whih the flexural strength is based on the apaity of the main reinforement alone. The fifth row of u1 values was extrated from equation (5). These values represent the atual strengths based on the total horizontal bars in the ross setion. It is lear that the flexural strengths are underestimated in the ase of beams with the additional horizontal bars. Therefore, it is reasonable to take into aount all the horizontal bars in alulating the flexural strength of the setion. Comparing the theoretial, u1 and u2.. it is evident that in all ases, u1, is smaller. Hene the predited mode of failure in all ases is shear or diagonal splitting with the rushing of the onrete at highly stressed ompression orners. rushing kink Detail A rak Fig. 7. Kink area Soure : Experiment rushing The experimental observations of the modes of failures agree well with this predition. The ultimate loads for the beams were predited using equation (5). The ratios in the last row of Table 5. u analysis / u test, suggest that the predited values agree well with the test result. Displaement Dutility Defletion value measured at the tip area of the beam that opposite with bak part area that getting the fore (load). Read of defletion use the LVDT. The displaement dutility values is : ( ) = u. Where, u y y = dutility = defletion at ultimate load = defletion at yield load TABLE I COMARISON ANALYSIS OF CONVENTIONAL COULING BEAMS BETWEEN EXERIMENTAL AND THEORETICAL RESULT f ' N/mm 2 21,073 Experimental Result (BK) Mode of Failure Shear, major diagonal rak, onrete and steel stresses seriously disturbed at the ompression orners. Theoretial Result u, experimental kn 114,84 f u N/mm 2 26,341 f t N/mm 2 1,254 u, flexural failure kn 217,8410 u, Shear failure kn 112,1181 redited mode of failure Shear, diagonal splitting and rushing of onrete at the ompression orners. Ultimate load u, analysis kn 112,1181 u, analysis u, experimental 0,9763 S-84
7 Defletion at yield ( y ) took at first rak moment. Defletion at ultimate ( u ) took if the beams reah maximum load that marked with split moment. Strutures response at six speimens shown that the dutility response inluded in Restrited dutility, beause the struture have value of maximum displaement dutility ( ) in interval 1,5 to 3,5. The proposed method of analysis, as in (1) to (5), was used to analyze the beams. In eah ase the first step was establish whether the web strength was ontrolled by onrete or by reinforement. It is obvious that, in beams with only vertial stirrups, the ontrol of web strength is by onrete, beams 1 is example. In beam 2 the proportion of web horizontal reinforement is small, and the overall ontrol is governed by onrete. In beam 3, 4, 5 & 6, there is adequate reinforement in both the horizontal and vertial diretion. Therefore the web strength is ontrolled by the reinforement. The proportions are suh that the strengths due to reinforement are similar to those due to onrete. Therefore, in pratie either an ontrolled the web strength. Fore Distribution in Main Bars The distribution of fore in the main bars of the beams at failure is shown in Fig. 8. using he proposed onept, the fore in the main bars, when the diagonal splitting mode of failure ours, is tensile. The fore varies linearly along the span with a smaller value at he tip of the triangular half of the beam to its full apaity at the support. Although it was not possible to ompare the fore diretly with the experimental result, the observed behavior agrees with the proposed onept. The distribution of fore in the bars based on the onventional onept of flexural deformation of reinfored onrete oupling beams differs drastially with the atual behavior (Fig. 8) Flexural Ation Diagonal Splitting Ation 0 Compression Tension Span= 1m Fig. 8. Theoretial distribution of fores in the main bars Conlution Behaviour harateristi of deformation and mode of failure at oupling beams that happened is the existene of ompression area at diagonal diretion oming in ontat with tip of fore, tension area at opposite diagonal diretion whih will have rak till split at diagonal area ompress, and the beam will attain its maximum load arrying apaity when small portion of the onrete in the ompression orners rush. Mode of failure that happened is shear failure. Ratio between u (analysis of N.K. Subedi method) with u (experiment) is equal to 0,98, this number indiate that analysis with N.K. Subedi method an be used to predit the value and behaviour of dutility at oupling beams. The distribution of fore in the bars based on the onventional onept of flexural deformation of reinfored onrete oupling beams differs drastially with the atual behavior. The proposed method of analysis of reinfored onrete oupling beams based on the equilibrium of fores of a triangular half of the beam at failure gives a satisfatory predition of fore in the main bars. Referene ACI Committee 318, (2002), Building Code Requirements for Reinfored Conrete (ACI ), Amerian Conrete Institut, Detroit Nawy, G Edward, (1985), Reinfored Conrete a Fundamental Approah, seond Edition. rentie-hall In. New Jersey ark. R, aulay T., (1975), Reinfored Conrete Struture, Seventh Edition. John Willey & Sons In. Canada aulay, T. riestley M.J.N., (1992), Seismi Design of Reinfored Conrete Struture and Massonary Building, Third Edition. John Willey & Sons In. Canada Wang, C.K. and Salmon, Charles, (1985), Reinfored Conrete Design, Fourth Edition. Happer & Row, In. New York Nurhasanah, Y., (2006), Dutility Behavior of Reinfored Conrete Coupling Beams with Diagonal Reinforement between Deform type with CRT Bar type. Gelagar, Jurnal Teknik UMS S-85
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