DISCUSSION. Smeared Rotating Crack Model for Reinforced Concrete Membrane Elements. Paper by Vahid Broujerdian and Mohammad Taghi Kazemi

Transcription

1 DISCUSSION Disc. 107-S40/From the July-August 2010 ACI Structural Journal, p. 411 Smeared Rotating Crack Model for Reinforced Concrete Membrane Elements. Paper by Vahid Broujerdian and Mohammad Taghi Kazemi Discussion by Rafael Alves de Souza ACI member, PhD, Associate Professor, State University of Maringá, Maringá, Brazil The authors have made significant contributions regarding the analysis of reinforced concrete membrane elements. Their best contributions are undoubtedly related to the importance of considering the gradual yielding of steel bars embedded in concrete and the reinforcement ratio effect in the panels. As shown in the paper, the reinforcement ratio can directly affect the maximum attainable compressive stress and the average cracking strength of concrete. The introduction of the aforementioned effects could explain why some other models have presented some deficiencies for simulating panels containing less than 0.1% reinforcement in one direction or panels that were uniaxially reinforced. Despite the quality of their research and their valuable findings, the discusser found some additional issues that should be addressed to clarify some topics and enhance the overall comprehension of this interesting paper. INTRODUCTION AND RESEARCH SIGNIFICANCE The authors have proposed a new smeared orthotropic rotating crack model for simulating reinforced concrete membrane elements. As mentioned by the authors, the smeared orthotropic models can be classified into fixed or rotating crack models. In the fixed crack model, the direction of the first crack is determined by the direction of the principal tensile stresses that existed before cracking and this direction is maintained fixedly with increasing proportional load. On the other hand, in the rotating crack model, the direction of the subsequent cracks after the first crack may rotate due to the changes in the direction of the principal stresses in the concrete, which in turn are dependent on the amount of steel in the panels. Despite the facilities for implementing a rotating crack model, some researchers argue about the weakness of this model regarding the contribution of concrete, which in turn could be quantified using a fixed crack model. In fact, in the discusser s opinion, the real load-deformation response of a membrane element is supposed to lie between the curves generated by the fixed and rotating crack models. Rotating crack models are supposed to underestimate strength and stiffness, whereas the fixed crack model is expected to overestimate strength and stiffness. Despite the aforementioned observations, the authors presented very accurate predictions of load-deformation responses using their rotating crack angle. In their opinion, have they found an alternative way to include the contribution of concrete in the rotating crack model? MATERIAL MODEL As mentioned by the authors, the behavior of an embedded steel bar in concrete is different from that of a bare bar, and for that reason they have proposed a trilinear stress-strain relationship for a steel bar embedded in concrete. On the other hand, taking into account that increasing the reinforcement ratio increases both the maximum attainable compressive stress and its corresponding strain in concrete increases, the authors have proposed some functions based on the coefficients α and μ. Both the trilinear stress-strain relationship and the coefficients α and μ were determined based on an extensive trial-and-error procedure conducted with a very small number of panels. Do the authors believe that trial-and-error procedures with only a small number of panels are sufficient for describing the complex behavior of membrane elements? The proposed model presented very good accuracy, even for panels with less than 0.1% reinforcement in one direction or panels that were uniaxially reinforced. The discusser suggests to the authors applying their model to a broad databank, however, also taking into account some statistical background. The discusser understands that there are few curves (load-displacement) available in the literature, but a broad databank regarding panel tests can be found in Bentz et al. 33 The authors are to be complimented for the inclusion of some basic concepts of fracture mechanics in their model to extend their observations to any panel dimension. NONLINEAR ANALYSIS PROCEDURE The described equilibrium and compatibility equations, along with the proposed constitutive laws, form a system of nonlinear equations that are suggested to be solved by the flowchart presented in Fig. 6. The meaning of some of the procedures and equations in this flowchart, however, are not very clear. Also, the flowchart only shows how the stress and strain values can be calculated in the elastic range. Could the authors better explain Fig. 6 and how the strains are calculated over the elastic range? At first glance, the proposed model has facilities for computational implementation when compared to the modified compression field theory (MCFT), the softened truss model (STM), and the disturbed stress field model (DSFM). Is that assumption correct, or does the proposed model also demand a great deal of time-consuming work for its implementation? The discusser has also been working on the implementation of rotating and fixed crack models for simulating membrane elements, and this demands a lot of procedures that are usually not provided in the literature. It should be noted that there are no comments regarding the crack widths in the paper. Therefore, crack widths undoubtedly have a major importance for designers, taking into account the verifications under service conditions. How can the authors include the calculation of crack widths in their model? VALIDATION OF PROPOSED MODEL As mentioned previously, the proposed model was validated using only a few test panels. The main reason for 378 ACI Structural Journal/May-June 2011

2 this procedure is found in the limited number of loaddeformation curves available in the literature. The authors are encouraged to apply their model to the tested panels of Bentz 34 and Xie, 35 where it is possible to find relevant information. Also, to compare their results and certify the accuracy of their model, they may use some free available tools, such as Membrane and WWW. 36 The aforementioned tools are available at and respectively. CONCLUSIONS The authors have presented a very interesting paper concerning the analysis of reinforced concrete membrane elements. The main advantages of the proposed model include the consideration of the gradual yielding of steel bars embedded in concrete and the reinforcement ratio effect in the panels. The proposed equations, however, were tested using a trial-and-error procedure with only a few available test panels. Despite this fact, the obtained results have demonstrated a good accuracy, including panels containing less than 0.1% reinforcement in one direction or panels that were only uniaxially reinforced. Therefore, in situations where other prevailing smeared crack models suffered from reduced accuracy, the proposed model has shown a good performance. The authors are to be complimented for their work and are encouraged to extend their research to a broad databank. This way, they could certify the accuracy of their proposed model. REFERENCES 33. Bentz, E. C.; Vecchio, F. J.; and Collins, M. P., Simplified Modified Compression Field Theory for Calculating Shear Strength of Reinforced Concrete Elements, ACI Structural Journal, V. 103, No. 4, July-Aug. 2006, pp Bentz, E. C., Sectional Analysis of Reinforced Concrete Members, PhD thesis, Department of Civil Engineering, University of Toronto, Toronto, ON, Canada, Xie, L., The Influence of Axial Load and Prestress on the Shear Strength of Web-Shear Critical Reinforced Concrete Elements, PhD thesis, Department of Civil Engineering, University of Toronto, Toronto, ON, Canada, Hoogenboom, P. C. J., and Voskamp, W., Performance-Based Design of Reinforced Concrete Panels on the WWW, Proceedings of the Fourteenth International Offshore and Polar Engineering Conference, Toulon, France, 2004, pp Disc. 107-S40/From the July-August 2010 ACI Structural Journal, p. 411 Smeared Rotating Crack Model for Reinforced Concrete Membrane Elements. Paper by Vahid Broujerdian and Mohammad Taghi Kazemi Discussion by Andor Windisch ACI member, PhD, Karlsfeld, Germany The authors promise a smeared rotating crack model that considers equilibrium, compatibility, and constitutive material relationships. Examining Eq. (11) in the loading case of pure shear that is, f x = f y = 0 we find that the tensile stress in the reinforcement is equilibrated through the compressive stress in the concrete. Nevertheless, the compatibility requires that the longitudinal bars and the cracked concrete have the same average longitudinal strain of ε x. This would mean that the average compressive stress in concrete belongs to a tensile strain. Please clarify. Neglecting this quite serious fundamental problem, the discusser arrives to the next one: a trilinear constitutive relation of the average stress-strain relationship for steel embedded in concrete is proposed in Fig. 1(b). The coordinates of the critical points were found in time-consuming, extensive trial-and-error procedures. Nevertheless, the test panels of Vecchio and Collins 4 were reinforced with smooth wires, whereas those of Bhide and Collins 32 were reinforced with deformed wires. As the bond characteristics of these two types of wires must be quite different, the constitutive relations should be different, too. Or, similar to the influence of the concrete specifications, it could have been mentioned that here, too, simplifications have been made. The questionable equilibrium equations explain why studying the available panel test results, it was found that increasing the reinforcement ratio increases both the maximum attainable compressive stress and its corresponding strain in concrete. This means that the softening decreases with the increasing reinforcement ratio, which contradicts with the modification factors such as that of Eq. (5). Please clarify. The proposed model was first validated on Panel PV20 4 loaded in pure shear. Table 1 shows the levels of predicted response. Comparing the corresponding values, some interesting deviations between the measured and predicted values can be detected: In the test with increasing shear loading, the stress in the longitudinal reinforcement f sx was always less than in the transverse reinforcement f sy. In the prediction, the opposite is true at each level. Please clarify. According to Mohr s circle of loading, in the case of pure shear loading, the maximum compressive stress is equal to the shear stress. Comparing the corresponding υ and f c2 values, the latter is approximately double the former value. How is this possible? Please clarify. In the test, the failure was introduced at υ = 3.84 MPa (550 psi) through yielding of the transverse reinforcement. In the prediction, the transverse reinforcement never yielded. How was the failure recognized during the calculation? The directions of the principal strains deduced from the measured strains were from the beginning of the loading approximately 38 degrees; they decreased after yielding of the transverse steel to 30 degrees. In the prediction, θ decreases continuously beginning at 45 degrees with increasing loading, whereas angles θ deduced from the stresses in the test are constant at 45 degrees until the transverse steel begins to yield and then they decrease to 41 degrees. What caused the rotation of the principal directions? The advantages of the proposed model are not evident at all to this discusser. ACI Structural Journal/May-June

3 AUTHORS CLOSURE Closure to discussion by de Souza The authors wish to thank the discusser for his interesting questions and valuable comments. As shown in the paper, using the modified constitutive laws for steel and concrete is the main reason for better predicting the response of reinforced concrete panels relative to other prevailing rotating crack models, such as the modified compression field theory (MCFT). The discusser asked about the reason for using only a few panel test results. As mentioned, all the coefficients of the proposed constitutive laws were determined based on a trialand-error procedure so that the calculated load-deformation responses of the test panels had the best correlation with the experimental results. Thus, the experimental loaddeformation curves of the panels were necessary. This is why some databanks regarding panel tests 33 were not included in the paper. The discusser is thanked, however, for suggesting other resources It must be noted that, in a recent research study, while incorporating the proposed model into a nonlinear finite element procedure, the authors have shown that their model adequately simulates the behavior of lightly reinforced shear-critical test beams. The results will be published soon. The discusser questioned the trial-and-error method used in this study instead of other statistical methods. It must be noted that to perform a nonlinear regression analysis, we need a model expression that combines unknown parameters and known variables as a nonlinear function. In other words, the basic element of a nonlinear regression analysis is an explicit nonlinear model function. In the considered problem, however, there is not such an explicit model. Here, for each set of model variables (specimen properties, loading ratios, and shear strain) and the selected iterative values for model parameters (the coefficients of constitutive laws), a system of nonlinear equations (equilibrium, compatibility, and constitutive laws) forms that needs a numerical method to solve and find the corresponding shear stress. Thus, the practical option in this situation is to calibrate the constitutive laws using the trial-and-error method. The discusser asked about the algorithm used to solve the system of equations governed on the problem of reinforced concrete membrane elements. As mentioned in the paper, the flowchart in Fig. 6 is only for calculating the stress and strain values in the elastic range of steel. As the longitudinal and transverse reinforcement has a trilinear stress-strain relationship, there are several cases for setting the problem. For the sake of brevity, only one case is shown. The discusser asked about the simplicity of the proposed model for computational implementation. As seen in the flowchart in Fig. 6, the computational procedure is very straightforward to use in the elastic range of the constitutive relation of steel. Beyond this range, only the boxes of calculating θ and v in Fig. 6 will be changed. This model can also be simply incorporated into nonlinear finite element procedures, as was done by the authors in a recent work. The discusser also asked about the local crack effects. In this research, the crack-related problems were considered, especially for the failure criteria, but the issue was not included in the paper. This is because the purpose of this paper was to study the parameters affecting the constitutive laws. The crack-related problems will be discussed in a future paper. AUTHORS CLOSURE Closure to discussion by Windisch The discusser stated that in the case of pure shear loading, solving the equilibrium and compatibility equations together results in a contradiction that the tensile strain in the concrete in the x-direction is conjoined with the compressive stress in the same direction. The discusser must note that the direct constitutive relation between strain and stress in concrete is in the coordinate system of principal axes and the mentioned case is not unusual in other coordinate systems. In other words, strains and stresses must be of the same sign in the principal coordinate system and not necessarily in other coordinate systems. The discusser stated that the bond characteristics of the wire mesh used by Vecchio and Collins 4 and Bhide and Collins 32 are different. It must be noted that the assumption of the proposed model is that no overall slip occurred between the concrete and steel. Therefore, the authors selected the test panels for which the overall bond failure did not take place. The discusser asked about Eq. (5). It must be noted that ε c in that equation is a negative value. Thus, increasing the reinforcement ratio that increases the value of ε c also increases the value of β. The discusser also asked a few questions about the predicted values for Panel PV20 4 : 1. In both the prediction and the test, with increasing shear loading up to near the peak load, the stress in the longitudinal reinforcement f sx was always less than the stress in the transverse reinforcement. 2. It must be noted that when the panel loading case (f x, f y, v) is in pure shear, the loading case of the concrete body (f cx, f cy, v) is not in pure shear. 3. According to the test report, 4 as predicted by the presented model, the failure of Panel PV20 was not through yielding of the transverse reinforcement. 4. The rotation of the principal directions in cracked concrete during pure shear loading with constant (f x :f y :v) = (0:0:1) is due to changing the ratio of (f cx, f cy, v). Disc. 107-S41/From the July-August 2010 ACI Structural Journal, p. 419 Shear-Transfer Strength of Reinforced Concrete. Paper by Khaldoun N. Rahal Discussion by Emil de Souza Sánchez Filho Associate Professor at Fluminense Federal University, Rio de Janeiro, Brazil The author has made a considerable contribution to the shear-transfer strength of reinforced concrete. The paper shows a concise method with clear and important conclusions. The author must be congratulated for this work and for his interesting research. The discusser, however, would like to address some comments on relevant issues presented in the text: 380 ACI Structural Journal/May-June 2011

4 1. The upper limit on shear strength given by Eq. (8) should be clearly specified. In other words, it should be made The author has made a considerable contribution to the shear-transfer strength of reinforced concrete. The paper shows a concise method with clear and important conclusions. The author must be congratulated for this work and for his interesting research. The discusser, however, would like to address some comments on relevant issues presented in the text: 1. The upper limit on shear strength given by Eq. (8) should be clearly specified. In other words, it should be made clear that 16 MPa (2300 psi) v 121 MPa (17,550 psi) or κ In Rahal, 25 κ is defined as a maximum allowable shearing stress, but in the paper, it is defined as an upper limit on shear strength, where it is obtained by the adjusted experimental results of reinforced concrete panels for resistances f c 100 MPa (14,500 psi). These names are inconsistent, as Eq. (9) shows that this dimensionless parameter is compared to the geometric ratios of the transverse and longitudinal reinforcements. The justification for adopting Eq. (8) as valid, as is the comparison between data obtained from this expression and the results given by the modified compression field theory (MCFT) in view of only seven experimental results of reinforced concrete panels, the source of which is not mentioned in Rahal Equation (11) was obtained by analyzing the test results of Hofbeck et al., 1 but it was unclear how the author obtained Eq. (12), as he reports that it is valid for normalstrength concretes, yet fails to show which f c values were used to obtain the 2.8 coefficient of this expression and the upper limit 7.9 MPa (11,455 psi). It would be interesting to have Eq. (10) deduced with the data of the other authors listed in Table The analysis of the results of Nagle and Kuchma 8 fails to show how the geometric ratios ρ x and ρ y were adjusted to the inclination α of the reinforcements. What are the equations for this calculation? Which values of the geometric ratio ω x are considered to obtain Eq. (15a)? 5. Figure 4 shows that the experimental results of the precracked specimens are more in line with the results provided by the simplified model for combined stress resultants (SMCS). What is the explanation for this fact? 6. In Fig. 5, the results provided by the SMCS do not seem good for low-level x reinforcement, considering that in this case, f c = 104 MPa (15,080 psi) and α = 25 and 35 degrees. This would seem to indicate that the method adopted to adjust the model for inclined reinforcements is inadequate. What is the plausible explanation for these results? The discusser believes that it is impossible to check the theoretical values given in Table 1. Therefore, the discusser would greatly appreciate if the author could provide some complementary information about the research. The author is encouraged to continue his interesting theoretical research. REFERENCES 25. Rahal, K. N., Maximum Allowable In-Plane Shear Stresses in Reinforced Concrete Membrane Elements, Proceedings of the ACI-KC Second International Conference on the Design and Sustainability of Structural Concrete in the Middle East with Emphasis on High-Rise Buildings, Kuwait, AUTHOR S CLOSURE The author thanks the discusser for his interest in the paper. Comments 3 and 4 seem to indicate that the discusser did not have access to Appendix A, which was not printed in the hard copy of the journal. This Appendix was made available on the ACI Web site, as indicated in the footnote on page 422 of the paper. The author provides the following replies to the discusser s six comments: 1. The discusser is concerned about the range of values of the maximum normalized shear stress κ for the concrete strengths used in the verification. The range was not provided because it can be easily obtained from Eq. (8). 2. The paper clearly refers to Reference 18 for details on the development of the SMCS model in general and Eq. (8) in particular. The 2007 reference 25 was the result of a pioneer work on the method that was further developed to take the current form, where κ is based on a database of 16 overreinforced concrete panels. The 2007 conference paper 25 clearly mentions that the maximum allowable shear stress refers to the maximum stress that can be resisted before concrete crushing. The author agrees with the discusser, however, that the use of the word allowable is not quite consistent with what κ is intended to be. 3. The paper states that Eq. (12) was obtained by substituting the value of the average concrete strength of the Hofbeck et al. 1 specimens into Eq. (11). The details of the individual specimens are listed in Table A1 of Appendix A, which might not have been available to the discusser. The average value can be easily calculated to equal 25.9 MPa (3756 psi). For this value, the factor 0.55 f c is reduced to 2.8. The discusser was interested in simplifying Eq. (10) for the other sets of test data in Table 1. This can be easily achieved by using the same procedure used to obtain Eq. (11) and (12) once the details of the individual specimens in Table A1 are available. 4. The discusser asks how the values of ρ x and ρ y were adjusted for the inclination α of the clamping reinforcement in the Nagle and Kuchma 8 specimens. Reference 8 reports not only the reinforcement details but also the adjusted values (which were adopted as reported). The area of steel perpendicular to the shear-transfer plane is taken as the total amount of clamping reinforcement multiplied by cos(α). The discusser also asks how Eq. (15a) was obtained. This requires knowledge of the average concrete strength of the Nagle and Kuchma 8 specimens, which can be calculated from Table A1 to be 104 MPa (15,080 psi). The value of ρ x f y x for these specimens is 5.85 MPa (848 psi) (refer to Table 1). Using Eq. (9), ω x is the smaller of ρ x f y x /f c (= 0.056) and κ(= 0.218), giving Substituting this value into Eq. (10) leads to Eq. (15a). 5. It is well established that precracking reduces the strength of pushoff specimens. 1 The SMCS model was more accurate in the case of the precracked specimens and relatively more conservative in the case of the uncracked specimens, as indicated by the discusser. This could be due to the conservatism built in the model, which neglects the beneficial effects of: 1) the additional reinforcement in excess of the balanced reinforcement; and 2) the compressive force acting along the x-direction. 6. The author agrees with the discusser that the SMCS method is relatively less accurate in the Nagle and Kuchma 8 tests, and one of the reasons for this could be related to the way the amount of clamping reinforcement was adjusted for the inclination. The author believes, however, that two other factors affected the accuracy. The first is the relatively large scatter in the experimental results, even within the set of specimens with ACI Structural Journal/May-June

5 the same inclination of clamping reinforcement (refer to Fig. 5). The second is the relatively very high concrete strength. The discusser expressed interest in further information to be able to check the results presented in Table 1. This information is provided in Table A1, as referenced in the footnote on page 422 of the paper. The author will gladly supply the discusser with the detailed database upon request via at Disc. 107-S43/From the July-August 2010 ACI Structural Journal, p. 434 Strengthening of Flat Slabs against Punching Shear Using Post-Installed Shear Reinforcement. Paper by Miguel Fernández Ruiz, Aurelio Muttoni, and Jakob Kunz Discussion by Andor Windisch ACI member, PhD, Karlsfeld, Germany The authors apply the critical shear-crack theory for an innovative method for the strengthening of flat slabs. Looking at Fig. 3(b), it seems that deformed bars were certainly used for the shear reinforcement. Please confirm. The rate of the shear reinforcement is characterized by ρ w (refer to Eq. (2)). Looking at Fig. 8 with the (very informative) cracking patterns after they are saw cut, the question arises whether it would be more realistic to take into account the number of stirrups crossing the failure crack instead of calculating with the smeared stirrups. As a matter of fact, in Eq. (7), ΣA swi is defined as the cross-sectional area of the shear reinforcement; it could be read as a reference to the number of shear reinforcing bars. Moreover, the reference to the stress in the shear reinforcement σ si (ψ) in Eq. (7) and the proposed equation for determining its value (refer to Eq. (9)) reveals that not all of these can refer to smeared stirrups. In eliminating the smeared stirrups, another questionable parameter could disappear, too: b 0, the length of the control perimeter. In the case of the critical shear-crack theory, this parameter loses its justification; in the case of the different s 0 distances (refer to Fig. 5 and 8), the control perimeters are certainly different, too. The three different types of flexural reinforcement hotrolled or cold-worked with different bond characteristics and two considerably different levels of yield strength and probably different bond characteristics, too should be taken into account when evaluating the test results. The identical ρ = 1.50% geometrical rates of flexural reinforcement for Slabs PV1 to PV3 and Slabs PV14 to PV17 should result in quite different behaviors of the specimens (the varying concrete strengths diversify these even further). Hence, the mechanical rate of flexural reinforcement could be a better parameter. Comparing the V test values of Slabs PV6 to PV8, the deceptive character of the smeared shear reinforcement ratio ρ w can be perceived. Slab PV8 had half the ρ w value of Slabs PV6 and PV7; nevertheless, the strength was identical. While discussing the failure patterns of Slabs PV14 and PV15 with heavy shear reinforcement, the authors refer to crushing of the compression strut. The following questions/ remarks arise: Are the compression strut and the critical shear-crack model compatible with each other at all? The position of the critical shear crack is quite different in the case of Slab PV14 from Slab PV15. Where is the compression strut situated in these two cases? Slabs PV2 and PV3 have the same ρ values as Slabs PV14 and PV15; nevertheless, even if at dimensioning, flexure 382 and shear are treated independently from one another per their definitions. The compression zone must also fail along the critical shear crack at failure. The authors explain that the larger strength of Slab PV14 was due to the fact that anchorages of the shear reinforcement were placed beyond those of Slab PV15, leading to more limited stress concentrations in the compression-critical region. Please clarify how does the more limited stress concentration in the compressioncritical region let the shear strength increase? The shapes of the failure sections of Slabs PV1, PV2, PV7, PV8, PV14, PV16, PV17, and PV19 shown in Fig. 8 are identical where can the more limited stress concentrations be identified? The discusser means that the failure of the compression strut is in fact a critical shear crack running quite vertical around the column, scarcely intersecting the bars of the shear reinforcement. Increasing s 0 (refer to Fig. 5(a)) also increases the probability of this type of failure. The authors detect progressive smearing of the cracks at the column region as the amount of shear reinforcement increases. It is obvious that increasing tensile reinforcement in any reinforced concrete member in tension decreases the crack distances this is never understood as smearing. How do the bond stresses along the different bars of the shear reinforcement develop/change when successive cracks do occur with increased loading? Compare the first inclined bars near the column (for example, in Slabs PV8, PV14, and PV15). Is a pullout at the upper bond anchorages of the shear bars possible or was it detected at one of the slabs? Based on Eq. (1), (9), and (10), the bond length of the shear reinforcing bars, the opening of the critical shear crack at the level of the shear reinforcement, and the rotation of the slab necessary for the yielding of the 16 mm (0.63 in.) shear reinforcement can be calculated. The necessary bond length is approximately 100 mm (3.94 in.). The necessary crack width at the intersection of the shear reinforcement is approximately 0.25 mm (0.1 in.). Please note that this crack width is far below the allowable crack widths, as stated in the serviceability limits. The necessary rotation ψ in the case of the intersection at a height of 120 mm (4.7 in.) is 0.41%. In the case of a thicker flat slab, the intersection could be at approximately 250 mm (10 in.); here, beyond ψ = 0.2%, the shear reinforcement yields, according to the equations given by the authors. The courses of the load-rotation curves given in Fig. 6 and the ψ test values achieved at failure given in Table 1 fully contradict these calculated values. It would be interesting to learn how Eq. (7) to (11) were applied to calculate V calc. The accuracy of how the rotation ACI Structural Journal/May-June 2011

6 of the slab was determined does not seem to influence the accuracy of the calculated shear force. Examining the conjugated V test /V calc and ψ test /ψ calc values given in Table 1, it can be detected that there is absolutely no interdependence between these pairs of values. The trendline s equation is ( V test V calc ) = ψ test ψ calc ( ) with R 2 = This could indicate that the rotation ψ is not a very strong variable. In the case of Slabs PV3 and PV15, the ψ test /ψ calc values are significantly greater than 1; nevertheless, the calculated shear strength is fairly near the measured value. Please comment. Equation (13) yields the so-called crushing strength of compression struts λ V R,c, where λ > 1. It is not clear why the width of the critical shear crack ( ψ d) should have any influence on the strength of the concrete strut that is situated between the column and this crack. Furthermore, why does the crushing strength depend on f c and not directly on f c, and why does it depend on the aggregate interlock? Even if the model assumptions were correct, the influence of some important parameters such as slab thickness and the maximum size of the aggregate cannot be validated, as these were not varied for this test series. Referring to Fig. 9(b), the authors state that as rotations increase by addition of shear reinforcement, the concrete contribution diminishes. Neither the test results nor the current view in the field concerning the source of the concrete shear contribution that is, the aggregate interlock validate this statement: we all agree that additional shear reinforcement decreases the width of shear cracks (even that of the critical shear crack). This fact supports the impression that was already predicted by the discusser regarding a previous paper 6 ; the rotation of the slab ψ is definitely not the appropriate fundamental parameter of the phenomenon. The coefficient of variation of V test /V calc is very small compared to the coefficient of variation of the basic parameter of the model ψ test /ψ calc, which is quite high. AUTHORS CLOSURE The authors would like to thank the discusser for his interest in the paper and in the critical shear crack theory (CSCT). Detailed replies to his questions are given in the following: As shown in Fig. 3(b), deformed bars were used. This is obvious, as the best bond conditions were sought. The shear reinforcement ratio ρ w was selected as the best representative parameter to compare different reinforcement configurations not a stepwise function, such as the one suggested by the discusser. The same type of steel (hot-rolled or cold-worked) was used for the same flexural reinforcement ratio. The differences in the yield strength were accounted for by the load-rotation behavior of the specimens according to Reference 6 (it can be noted that the CSCT is based on a rational mechanical model and allows the consideration of such influences). The explanation for the measured strength of Slab PV8 is discussed in Fig. 11(c). Failure was governed by bending strength (yield-line mechanism) and not by shear strength. The deformation capacity nevertheless increased as more shear reinforcement was used (in accordance with the CSCT predictions). Details regarding the crushing strength according to the CSCT can be found in Reference 8. Significant cracking developed in the region of the compression strut for Slabs PV14 and PV15 (refer to Fig. 8). Slab PV2 failed slightly differently (pullout of anchorages) and Slab PV3 failed outside the shearreinforced zone. Both failure modes are explained in depth in the paper. To install the bars, holes have to be drilled in the specimens. This disturbs the struts in the soffit (the compression side of the slab) if the holes are too close. This explains the behavior of Slab PV15. In the authors opinion, the term smearing is correct. Shear reinforcement is activated on the top of the specimen only by bond. Measurements on the strains of the bar (not detailed within the paper) taken at the HILT-Schaan Laboratory confirmed this. If the discusser finds a contradiction, he has probably made a mistake in his calculations (perhaps in the loadrotation curve the calculations of the discusser are not detailed and cannot be checked). Please refer to Table 1 for comparisons of ψ calc (a very good agreement was observed). More comparisons can be found in Reference 8. Rotation is indeed a very good variable to calculate the punching shear strength. 6,8 For members with shear reinforcement, however, it leads to some scatter, as rotations may increase at failure (especially for members with large amounts of shear reinforcement, such as Slabs PV3, PV14, and PV15). This increase in the deformation capacity is neglected (on the safe side) with the proposed approach and leads to practically no difference in the estimate of the strength. Details regarding the approach for calculating crushing strength can be found elsewhere. 8 The authors have validated this approach (including size and strain effect) with a specific test campaign in another paper submitted to this journal, which is currently under peer review. The authors respect the discusser s opinion on the pertinence of the rotation as a key parameter but do not share it. It has been validated through extensive research and detailed measurements. 6,8 It is a physical parameter, clearly explaining how this or any other shear reinforcement system works and how to design it. It also leads to an excellent understanding of the mechanics of members without shear reinforcement and allows very accurate strength predictions. 6 It accounts for the various mechanical and geometrical parameters as well as the reinforcing procedure (postinstalling and rotations at the time of prestressing). It constitutes the current state of knowledge (the design method included in the first complete draft of the new Model Code 2010). More refinements can (and probably will) be included, but for the time being, it is, in the authors opinion, the best physical approach to the problem. ACI Structural Journal/May-June

7 Disc. 107-S48/From the July-August 2010 ACI Structural Journal, p. 476 Compression Splices in Confined Concrete of 40 and 60 MPa (5800 and 5700 psi) Compressive Strengths. Paper by Sung-Chul Chun, Sung-Ho Lee, and Bohwan Oh Discussion by Andor Windisch ACI member, PhD, Karlsfeld, Germany Based on test data of 48 columns, the authors supplement their proposed model 2 for compression lap splices in unconfined concrete with the influence of transverse reinforcement. In the Introduction, they report among others about the special details for placing the transverse reinforcement required by the CEB-FIP MC90 8 (Fig. 2) and the updated expression of ACI Committee for a tension splice with transverse reinforcement, which includes c max and c min that is, the maximum and minimum values of concrete covers. Nevertheless, both their test specimens and the proposed design equation did not consider these important influencing factors. During the tests they correctly found that the clear spacing between the bars one of their parameters rarely influences the splice strength. It is remarkable that the longitudinal reinforcement pattern of the D29-specimens is not central-symmetric, hence the intended concentrical loading certainly causes a nonsymmetrical strain distribution in the cross section. This resulted in the numerous premature failures due to eccentricity E c listed in Table 2. Figures 6(a), 7, and 8(a) reveal several important cognitions: The transverse reinforcement index, as defined in Eq. (7), is irrelevant, as the impact of the transverse reinforcement placed at the end of the splice is completely different from that being in the middle of the splice. The position of the hoops just at the ends of the splice in the specimens is not optimum. Here, the sense and function of the concrete failure at the end of the bar must be properly understood and considered. In case of splices in tension, the slip between the reinforcing bar and the concrete, which is necessary for the development of the bond stresses, is governed by the crack at the end of the splice. The incompatibility between the decreasing strains in the ending reinforcing bar and in the surrounding concrete in tension is compensated by the slips. At the end of a compression splice strain, incompatibility prevails between the concrete in compression and the reinforcing bar, which ends there. This strain incompatibility results in the stresses developed by end bearing. The failure mode of the end bearing is a sliding out of the concrete under the bar s end; this reveals the big impact of the side concrete covers and the relative poor influence of the clear spacing. This failure mode clarifies the sense of the reinforcing details of CEB-FIP MC90 8 shown in Fig. 2; one transverse bar must be placed outside the splice, and the rest of the transverse reinforcement is positioned along the outer third of the splice length and never in the central third (compare the hoop pattern in the test specimens and K tr ). The failure of the concrete cover below the bar s end is considered as the failure of the splice for understandable aesthetic reasons, although the splice could resist even higher loads. During the tests, the authors found the following modes of failure: premature 384 failure due to end failure, partial splitting failure, and fully splitting failure. Nevertheless, whether sensible/ practical/economical or not, by putting a compressible shoe on the bar s end, the slips could develop without splitting the concrete cover; one would come to different splice lengths and strengths. For the new design provision, the authors supplement their proposed model 2 for splices in unconfined concrete. According to this model, the mean strength of the splice is proportional to the square root of l s /d b. This remarkable proposal results from the endeavor of the authors to consider all of their previous test results into the regression analysis. The unconfined test specimens had three relative splice lengths l s /d b : 10, 15, and 20. Beyond l s /d b = 10, the splice strength did not increase practically; hence, the authors chose the square root function, which increases little by little beyond l s /d b = 10. Instead, they should have omitted to consider the results of test specimens with l s /d b > 10. All the test specimens with the confined concrete had l s /d b = 10 relative splice lengths; thus, the imperfection of the design provision could not be realized. The design equation and the reinforcing details proposed by the authors are questionable and it is suggested that they be revisited. AUTHORS CLOSURE The authors thank the discusser for his interest in the paper and have provided clarifications to the comments raised. Asymmetric strain distribution in D29-specimens Due to the limitation of the loading machine, D29- specimens were designed, as shown in Fig. 3(b). To prevent asymmetric strain distribution in the D29-specimen, the center of the loading machine was aligned to the center of rigidity of the D29-specimen at the very early stage of the loading process. In the analysis of the test results, three D29- specimens that failed prematurely due to eccentricity were excluded from the analysis. Transverse reinforcement and K tr The details required by CEB-FIP MC90 8 do not seem to be practical for the compression splice in high-strength concrete because required splice lengths are very short. As shown in the paper, some specimens having a splice length of 10d b showed splice strengths higher than the design yield strength of 420 MPa (60.9 ksi). The details of CEB-FIP MC90 8 were not used in the tests. Instead, the authors tried to find the effects of transverse reinforcement evenly placed within the splice length, which is more realistic. The effects of high-strength concrete and transverse reinforcement were evaluated quantitatively in this paper. The authors did not propose special details for spliced or transverse reinforcement, but suggested limitations on the strengths of ACI Structural Journal/May-June 2011

8 concrete and spliced bars based on the material characteristics used in the tests. For compression splices in normal-strength concrete, the current equation of ACI does not have to be amended because it has been practically verified for a long time. Considering the fact that hoops are evenly placed in reinforced concrete columns in practice, recommendations to determine δ and K tr in Eq. (9) were provided to yield a conservative splice in compression. Square root of l s /d b in proposed equation The basic design equation with the square root of l s /d b was derived in the previous study 2 by the authors. The effect of the splice length was examined with three different formulas and it was found that the square root of l s /d b could most suitably represent the characteristics of bond in compression splices in unconfined concrete. An expression using the square root of l s /d b was also proposed in tension splices. 19 The authors conducted tests on compression splices with very short splice lengths of 4d b, 7d b, and 10d b in 80 and 100 MPa (11,600 and 14,500 psi) concrete strengths. Test results are going to be published in an upcoming paper, 20 which will clarify the effect of splice length and provide improved design equations. Concrete cover and spacing: c max and c min As minutely explained in Reference 2, it is common practice in reinforced concrete columns that concrete cover remains the same but the spacing of the main reinforcing bars varies with sectional design. Two things were found from the tests described in this paper: 1) the clear spacing of the main reinforcing bars seemed not contribute to the compression splice strength; and 2) the ratio of c max /c min seemed to not affect the compression splice strength. Consequently, the relative value of c max and c min of ACI Committee was not adopted in the proposed equation. REFERENCES 19. Canbay, E., and Frosch, R. J., Bond Strength of Lap-Spliced Bars, ACI Structural Journal, V. 12, No. 4, July-Aug. 2005, pp Chun, S.-C.; Lee, S.-H.; and Oh, B., Compression Splices in High- Strength Concrete of 100 MPa (14,500 psi) and Less, ACI Structural Journal. (accepted for publication) ACI Structural Journal/May-June