Strength Evaluation of Reinforced Concrete Beam-Column Joints

Transcription

1 Strength Evaluation o Reinorced Concrete Beam-Column Joints H. Y. Choi & J. Y. Lee Dept. o Architectural Engineering, Sungkyunkwan University, Korea SUMMARY Joint research by three countries (America, Japan, and New Zealand) has made remarkable improvements in joint design. In spite o this cooperative eort, the joint shear strength predictions o the ACI Recommendations and the AIJ Guidelines (Architectural Institute o Japan) are based on the concrete arch mechanism, while the prediction o the NZS (New Zealand Standard) Code is evaluated by means o both arch and truss mechanisms. In this study, a method was provided to predict the strength o reinorced concrete beam-column joints that ail in shear beore the plastic hinges occur at both ends o the adjacent beams. In the proposed method, the sotening eect o concrete in the joint area was evaluated by using both arch and truss mechanism. In order to veriy the proposed method, the predicted results o the proposed equation were compared with experimental results o RC beam-column joints, as reported in the technical literature. Comparisons between the observed and calculated shear strengths o the tested beam-column assemblies, showed reasonable agreement. Keywords: RC beam-columns joint, shear strength, J-ailure, reinorcement steel, sotening eect.. INTRODUCTION Since the mid-960s, the perormance o reinorced concrete beam-column joints has been recognized as a actor that inluences the behavior o ductile moment rames. Thereore, many theoretical and experimental studies have been carried out to evaluate the perormance o beam-column joints subjected to lateral loading. Reinorced concrete beam-column joints are important structural members that should assure structural stability when the members are subjected to cyclic loading, such as gravity loading and seismic lateral loading. In seismic lateral loading, proper and sae behavior is possible, because energy dissipation ability and corresponding deormability are large when the plastic hinges o beams are well designed. Otherwise, joints show much more brittle ailure in shear, and the ailures cause severe damage o the overall structure. Thereore, it is important that ailure in the joint should not occur until the deormation reaches the designed deormability, through producing plastic hinges in adjacent beams and providing adequate energy dissipation ability. In United States and Japan, the shear strength o beam-column joints has been evaluated by the ACI Recommendations (ACI 352-R02 (2003)), and by the AIJ Guidelines (Architectural Institute o Japan (200)). The ACI Recommendations divide joints into two categories: Type or structures in non-seismic hazard areas and Type 2 in seismic hazard areas. The shape o joints is relected in deining the capacity o beam-column joints or Type, in that ductility o joints is not particularly considered, and or Type 2, in that energy dissipation capacity is important because o strong seismic loading. Also, the AIJ Guidelines have a similar design purpose to the ACI Recommendations, and in ensuring that the structure remains enough deormation, even ater developing yielding mechanisms. The strength evaluation o reinorced concrete beam-column joints could be distinguished by the methods used, whether based on arch mechanism or truss mechanism. In the ACI Recommendations and the AIJ Guidelines, the prediction o joint shear strength is based on the concrete arch mechanism while both arch and truss mechanisms are applied to joint shear strength estimation in the NZS (New

2 Zealand Standard (995)) Code. The method based on arch mechanism is relatively simple to evaluate the shear strength with, but it is diicult in the estimation to relect the eect o shear reinorcement in the joints and bondage. On the other hands, an equation or evaluation can be complicated, when arch and truss mechanisms are used simultaneously. In this study, a method was provided to predict the strength o reinorced concrete beam-column joints that ail in shear beore the plastic hinges occur at both ends o the adjacent beams. In the proposed method, the sotening eect o concrete in joint area was evaluated by using both arch and truss mechanisms, and the equation including two mechanisms was suggested relecting the compressive strength o concrete in the beam-column joints. In order to veriy the shear strength o the proposed method, the predicted results were analyzed and compared with 54 experimental specimens that had been perormed previously. 2. EXISTING DESIGN STANDARD OF BEAM-COLUMN JOINTS In spite o cooperative research eorts between the United States, Japan and New Zealand, the three countries have proposed dierent views on shear mechanisms and joint strength, and uniied design method does not yet exist. The standard o the ACI Recommendations is an empirical method based on experiments, and only concrete compressive strength is considered, even though the equation is simple and accurate, because o using a concrete compressive strut in the beam-column joint, as shown in Fig. (a). In the AIJ Guidelines, similar to the ACI Recommendations, shear orce in the joint is resisted by concrete, and the amount o the reinorcement is determined according to shear stress in the joint. In the NZS Code, the arch and truss mechanisms (Fig. (b)), which consists o horizontal and vertical steel and concrete compressive strut, are relected in the design standard to evaluate joint shear strength. The predicted results in this study are compared with the values estimated by the ACI Recommendations and the AIJ Guidelines because, in the NZS Code, the required amount o reinorcement in the joint is evaluated by taking into account the yield strength o plastic hinges in the beams. In addition, the direct method to calculate joint strength has not been proposed in the NZS Code. is the compressive orce o the arch mechanism, and D s is that o the truss mechanism. b a is the strut width, and α is the crack angle. b a D s α α D s Figure. (a) Arch action (b) Truss action 2. ACI-ASCE Committee 352 In ACI-ASCE Committee 352, beam-column joints are classiied into two groups. Type is or members without signiicant inelastic deormation, and Type 2 is or members that should have enough ductility in the inelastic range with energy dissipation. The shear strength is deined by applying a correction actor to the basic equation, which considers concrete compressive strength as in Eqn. 2..

3 V = γ b h (2.) j ck j c bj + bc mhc bj = min(, bb +, bc ) (2.2) 2 2 Where, V j : joint shear strength, γ : actor dependent on shape o beam-column joint and seismic zone or non-seismic zone, ck : concrete compressive strength (MPa), b j : eective width o the joint and value satisying Eqn. 2.2, h c : column depth, b b : beam width in longitudinal direction, b c : joint width, m : 0.3 or the joint that eccentricity between center o beam and column exceeds b c /8 and 0.5 or other cases. 2.2 AIJ 200 The Architectural Institute o Japan recommends a nominal joint shear strength equation that is based on databases o experiments perormed or interior and exterior connection assemblies rom 996 to 988. Test results indicate that in shear ailure, the eect o concrete compressive strength on the shear strength o beam-column joints is larger than that o the amount o transverse reinorcement. Thereore, the nominal joint shear strength is deined by considering the compressive strut mechanism in shear resistance mechanisms in the orm o Eqn V = kφf b h (2.3) ju j j j F = N mm (2.4) j ck ( / ) b = b + b + b (2.5) j b a a 2 where, k: the actor dependent on the shape o joints (.0 or shape, 0.7 or ト and T shape, 0.4 or L shape) φ:.0 or when transverse beams exist on both sides and 0.85 or the others, F j : modiied concrete compressive strength expressed as Eqn. 2.4, b j : eective width o beam-column joint according to Eqn. 2.5, h j : joint depth (0.75h c or ト and L type and h c or and T type), b b : beam width, b ai : the distance between column aces and both beam aces. 3. PROPOSED EQUATION OF JOINTS SHEAR STRENGTH The horizontal shear strength resists the extent o the dierence between tensile orce and compressive orce in adjacent beams. Each researcher has a dierent opinion about the nominal strength o beam-column joints, thereore, the ACI-ASCE Committee 352R-02 and the AIJ Guidelines consider the arch mechanism only, while the NZS Code considers the arch and truss mechanism. In this study, the horizontal shear strength is calculated according to Eqn. 3., which combines the arch and truss mechanisms. The study is based on the NZS Code being able to compare and evaluate shear and bond strength. V jh = V ch + V sh (3.) V jh is the horizontal shear strength o the beam-column joint. V ch and V sh is the shear strength by the arch and truss mechanisms. V ch is deined in Eqn. 3.2 as using compressive orce in Fig. (a). is expressed with concrete stress ( a ) and area o cracked concrete compressive strut, given by Eqn V ch = a (b s x b a ) cosα (3.2) where, b s : beam width, b a : strut width, α : strut angle Fig. 2 shows the stress model o truss mechanism in the beam-column joint. Shear stress, τ bc rom the horizontal shear stress V sh allows equilibrium equations o orce based on Fig. 2, such as Eqn. 3.3, 3.4, 3.5.

4 2 c τ bc b τ bc Figure 2. Stress o truss model in beam-column joint = cos α + sin α + ρ (3.3) c 2 c 2 b 2 b bs = sin α + cos α + ρ (3.4) c 2 c 2 c 2 c cs c c τ bc = ( 2 + )sinα cosα (3.5) where, b, c : direct stress in beam and column direction, c, 2 c : principle tensile and compressive stress o concrete, ρ b, ρ c : reinorcement ratio o beam and column, bs, cs : steel stress o beam and column. The ollowing assumptions are used to apply equilibrium equations (Eqn. 3.3, 3.4, 3.5) o orce to the truss model o the beam-column joint: ) The directions o the principle compressive stress and diagonal crack o the concrete are identical. 2) The diagonal angle in the concrete within joint is constant, and the angle is deined by the geometric conditions o joints, and given by Eqn. 3.6, where, h b : beam depth, h c : column depth α = sin hb hb hc α = + (3.6) 2 2 cos hc hb hc 3) The tensile stress in the concrete joints ater cracking is so small that it can be ignored. ( c =0) 4) Dowel action and aggregate interlock are not directly considered. According to Assumption 3), V sh is deined, as show in Eqn. 3.7, when the eective area o the joint is relected on the shear stress, τ bc. V = ( h b )sinα cosα (3.7) c sh 2 c j The beam-column joint ails when the concrete stress o the compressive strut ( a ) and that o the truss mechanism ( 2 c ) reach the eective compressive strength (ν ck ) o the concrete given by Eqn ν = + (3.8) ck a c 2 This concept is also used by Nielsen (975) in the study o beam shear strength analysis, but the shear resistance ratio o the arch and truss mechanism is computed by the strength when the shear reinorcement yields. There are many cases where compressive ailure occurs in the beam-column joint beore the reinorcement yields, because o transverse reinorcement o the column and longitudinal reinorcement o the beam and column. Thereore, the connection between the horizontal shear strength by the arch mechanism and the total horizontal shear strength is expressed by Eqn. 3.9, because the portion o shear contribution by the two mechanisms cannot be calculated.

5 V ch = 0.3( n) V (3.9) jh c = ( n) h c (3.0) Park (992) suggested Eqn. 3.9, based on experimental results to estimate the shear capacity o a beam-column joint to which a concrete strut contributes. The compression zone o cross section in the beam and column varies with the axial orce ratio, thus Eqns. 3.9 and 3.0 consider the depth o the compression area, c and axial orce ratio, n. Fig. 3 indicates that depth o compression zone, c, gets deeper as the axial orce ratio, n increases. I axial orce ratio is 0, /4 o the column depth is eective depth o the compression zone according to Eqn Also, the column depth corresponds to the depth o compression area when axial orce ratio is. c = 4h c n = 0 c = h c n = b a b a α α Eqn. 3. can be suggested rom Eqns. 3. and 3.9. Figure 3. Depth o compression zone V jh Vsh = 0.3( n) (3.) In Eqn. 3.2, V jh is expressed by substituting Eqn. 3.7 in Eqn. 3.. V = jh ( ck a ) hcb j sin cos 0.3( n) ν α α (3.2) Eqn. 3.3 is the compressive strength by the arch mechanism, and is computed by substituting Eqn. 3.9 in Eqn Eqns. 3.2 and 3.9 are equations or horizontal shear strength. a 0.3( n) Vjh = (3.3) b b cosα s a Finally, Eqn. 3.4 or V jh is proposed by substituting a, rom Eqn. 3.3 in Eqn V jh bsba ν ckhcb j sinα cosα = ( 0.3( n)) b b + 0.3( n) h b sinα s a c j (3.4) To calculate Eqn. 3.4, the reduction actor, ν, o the eective compressive strength o the concrete cracked and subjected to biaxial stress (compressive and tensile stress) is important. The compressive strength o the concrete strut diers depending on whether the joint is subjected to uniaxial stress or biaxial stress. When biaxial stress loads on the joint, the concrete compressive strength decreases because o the tension orce in a perpendicular direction; that is the sotening eect.

6 In Euro Code-2, the sotening actor, ν is deined by the ollowing Eqn. 3.5, by inversely analysing the beam shear strength rom experimental results. In the Rotating Angle Sotened Truss Model (RA-STM) o Belarbi and Hsu (988) and Modiied Compression Field Theory (MCFT) o Vecchio and Collins (989), the sotening actor is determined by relection o the principle tensile strain, ε which is perpendicular to the concrete crack, as shown in Eqns. 3.6 and 3.7. In addition, the eective concrete compressive strength is deined as ν c. ck 2,max = ν ck = ck (3.5) ν = ν = ε ' c 5.8 ( MPa) ' ( c 4.5 Mpa) + 400ε (3.6) ' ( c > 4.5 MPa) ν = ε (3.7) According to Kim et al. (200), the study results in Fig. 4 when the eective compressive strength is computed by Eqns. 3.6 and 3.7. The eective concrete strength decreases as the principle tensile strain increases, and the compressive strength declines by nearly hal when the tensile strain becomes about twice the steel yield strain. In normal practice, it is known that Eqns. 3.6 and 3.7 estimate the eective compressive strength more precisely than do other equations, because Eqns. 3.6 and 3.7 use concrete tensile strain. c 2,max ck 3 ε c (x0 ) Figure 4. Steel tensile strain vs. sotening actor However, the results o the three equations are very similar, as presented in Fig. 4. Kim et al. suggest Eqn. 3.8, which considers a reinorcement ratio based on comparison and estimation o existing models, and Eqn. 3.8 is applied to the sotening actor, ν o Eqn. 3.4 that is proposed in this study. ρx xy ν = (0.85 (0.85 ν 0)) (3.8) ρ y yy ck ν 0 = 0.6( ) 250 ρ x is the sum o the longitudinal beam reinorcement ratio and transverse column reinorcement ratio

7 reerred to the x direction, and ρ y is the longitudinal column reinorcement ratio reerred to the y direction. xy is the yield strength o x direction reinorcement, and yy is that o y direction reinorcement. Between ρ x xy and ρ y yy in ρ x xy /ρ y yy the larger one is the denominator, and the smaller one is the numerator. 4. SHEAR ESTIMATION OF THE PROPOSED EQUATION 4. Shear estimation results by the proposed equation In this study, the proposed estimation results are compared with the experimental shear strength based on 54 specimens rom preceding studies that ailed in shear beore adjacent beams yield occurred (J-ailure). Collected data and results are presented in Table., and V test /V cal shows to what extent test and calculation result correspond each other. There is more than a 30% dierence between V test and V cal in Teraoka (996) s specimens, which is relatively high dierence, but the dierence is less than 20% in most cases. Fig. 5 shows the relationship ck, ρ x xy, and ρ y yy and V test /V cal to know which actor inluences the results o estimation by the suggested method. V test /V cal has a similar tendency or concrete compressive strength and reinorcement ratio in Fig. 5(a), (b), and (c) and is inluenced by the reinorcement ratio. In Fig. 5(d) and (e), a tendency is not evident, because the range o x direction reinorcement ratio is smaller than y direction reinorcement ratio. The proposed equation evaluates lesser shear strength when ρ x is larger than 0.04, and when ρ y is larger than V test /V cal tends to decrease as the concrete compressive strength increases in Fig. 5(a), and increases as the x and y direction reinorcement ratio increases in Fig. 5(d) and (e). Thereore, the result shown in Fig. 5(b) and (c) is appropriate. Estimation by the proposed method or experimental value (V test /V cal ) results in.4 or the average, and 20% or the coeicient o variation. ck (MPa) ck / xx xy ck / y yy (a) Concrete compression strength (b) x-direction reinorcement index (c) y-direction reinorcement index ρ x (d) x-direction reinorcement ratio ρ y (e) y-direction reinorcement ratio Figure 5. Eect o reinorcement ratio in shear strength

8 Table. Shear strength estimation and comparison Teraoka Shiohara Specimen Beam Column V test /V cal section section ck Axial orce Proposed (Mpa) ratio, n ACI AIJ (mmx mm) (mmxmm) equation X X j j j j X X j j j j Meinheit X X X OKJ Noguchi OKJ X X300 OKJ OKJ A Fuji A X X220 A A Kawasaki JS X X285 JS Hatamoto S X X425 S S Danaka S X X L HNO Teraoka, HNO Kanoh & Tanaka HNO X X HNO HNO Watanabe WJ- 200 X X Watanabe WJ X X300 WJ Average Coeicient o variation

9 4.2 Comparison between the proposed equation and the existing equation Shear strength estimation o the beam-column joint is compared with the results by existing joint design standards, such as ACI and AIJ, to veriy whether evaluation by the method suggested in this study is appropriate or not. Shear strength based on the ACI Recommendations is computed by Eqn. 2., and the coeicient γ or a non-seismic hazard area (Type ) is used in the calculation. In addition, the coeicient γ includes the eect that there are not transverse beams, except in Meinheit (98) and Hatamoto (96) specimens. The shear strength in the AIJ Guidelines is estimated by Eqn. 2.3, and k, which reers to the shape o the joint, is.0 or all specimens. φ is.0 or Meinheit and Hatamoto specimens that have transverse beams, and 0.85 or the others. b j is deined according to Eqn. 2.5, and h j also ollows the AIJ Guidelines. Shear strength estimations by the ACI Recommendations and the AIJ Guidelines that consider only concrete strength show a larger average o V test /V cal than that proposed method shows. The coeicient o variation is 22% or the ACI Recommendations and 25% or the AIJ Guidelines, both o higher value than 20% or proposed method. Thereore, it is concluded that the proposed equation makes a reasonable estimates o the shear strength o beam-column joints. Fig. 6(a) indicates the results o V test /V cal by the ACI Recommendations, the AIJ Guidelines, and the proposed equation or concrete compressive strength. The x-direction reinorcement index (Fig. 6(b)) is included to help visualize which method closely estimates shear strength against the experimental results. The three methods tend to evaluate shear strength as smaller than the experimental results presented, and Fig. 6 conirms that the proposed equation is appropriate or shear strength estimation o J-ailure beam-column joints. In the suggested method, the eects o both the concrete compressive strut and the truss mechanism on the horizontal and vertical reinorcement are considered. Additionally, the inluence o the reinorcement is taken into account in deining a sotening actor, ν which determines the eective compressive strength in the development o shear strength. Finally, the proposed method shows relatively close results to experimental values. (a) Concrete compressive strength ck ρ ck xx xy (b) x-direction reinorcement index Figure 6. Result comparison o each equation 5. CONCLUSION In this study, the shear strength is estimated or interior beam-column joints that ail in shear, beore beam reinorcement yields (J-ailure). A new equation or estimating shear capacity is suggested based on the arch and truss mechanisms, and the equation evaluates shear strength using the sum o stress by the arch and truss mechanisms. To veriy the perormance o the proposed model, 54 specimens rom previous research are used. The proposed equation results in improved perormance, when it is compared with the calculation results by the ACI Recommendations and the AIJ Guidelines. Each coeicient o variance is 20% or the proposed equation (Eqn. 3.4), 22% or the ACI

10 Recommendations (Eqn. 2.), and 25% or the AIJ Guidelines (Eqn. 2.3). It is expected that this new equation could evaluate the strength and ductility o a beam-column joint that ails in bondage reasonably well, because the equation takes into account both the arch and truss mechanisms. REFERENCES Joint ACI-ASCE Committee 352. (2003). Recommendations or Design o Beam-Column Connections in Monolithic Reinorced Concrete Structures. American Concrete Institute. Farmington hills, Michigan. AIJ Standard or Structural Calculation o Reinorced Concrete structures. (revised 200) NZS 30: part. (995). Concrete structures standard (NZS 30:995), Standard association o New Zealand, Willington, New Zealand. M. P. Nielsen and M. W. Braestrup. (975). Plastic Shear Strength o Reinorced Concrete Beams. Bygningsstatiske Meddelelser. Denmark. Vol. 46, No. 3, T. Paulay and M. J. N. Priestley. (992). Seismic Design o Reinorced Concrete and Masonry Buildings. Jogn Wiley and Sons. New York T. T. C. Hsu. (988). Sotened Truss Model Theory or Shear and Torsion. ACI Structural Journal 85:6, F. J. Vecchio and M. P. Collins. (989). The Modiied Compression-Field Theory or Reinorced Concrete Elements Subjected to Shear. ACI Structural Journal 83:2, K. Hayashi and M. Teraoka. (96). The Study or the Mechanical Properties o Reinorced Concrete +Type Beam-Column Joints. Architectural Institute o Japan K. Oka and H. Siohara. (992). Tests o High-Strength Concrete Interior Beam-Column Joint Subassemblages. Earthquake Engineering D. F. Meinheit and J. O. Jirsa. (98). Shear Strength o R/C Beam-Column Connections. Proceedings o the ASCE 07:ST, H. Noguchi and T. Kasiwazaki. (992). Experimental Studies on Shear Perormances o RC Interior Column-Beam Joints with High-Strength Materials. Earthquake Engineering. Tenth World Conerence S. Fujii and S. Morita. (99). Comparison between interior and exterior RC beam-column joint behavior. American Concrete Institute. SP-23, K. Kawasaki et al. (99). Experimental Study on the Shear Perormance o R/C Interior Beam-Column Joints with Ultra High-Strength materials. Architectural Institute o Japan H. Hatamoto et al. (96). Earthquake Resistant Design o a 30 Story Reinorced Concrete Building. Architectural Institute o Japan M. Teraoka, Y. Kanoh, S. Sasaki and K. Hayashi. (996). An estimation o Ductility in Interior Beam-Column Subassemblages o Reinorced Concrete Frames. The Society o Materials Science 45:9, K. Watanabe, K, Abe, J. Murakawa and H. Noguchi. (988). Strength and Deormation o Reinorced Concrete Interior Beam-Column Joints. Transactions o the Japan Concrete InstituteVol.0,