E. Booth, Edmund Booth Consulting Engineer, London; R. Fenwick, University of Canterbury, New Zealand; and R. S. Narayanan, Clark Smith Partnership, London
The findings and conclusions of the paper need to be treated with some caution for a number of reasons, as follow.
The authors propose limiting ratios of beam to column depth, longitudinal column steel, and transverse joint confining steel, beyond which it is claimed joint shear strength is influenced to a negligible extent. While the general trends noted by the authors for the effect of these factors on joint shear strength are accepted as valid, the number of samples tested is far too small to support definitive values for the limits, which will in any case depend on a number of supplementary factors.
The hysteretic curves of Fig. 5 represent the results of deformations in the beams and columns as well as the joints. Although the authors draw conclusions from these figures on ‘joint ductility’, these become much less clear cut when the beam’s nominal flexural capacity is approached or exceeded, because some of the apparent ductility may be attributable to flexure in the beam.
On the basis of results shown in Table 3, the authors conclude that the seismic design codes overpredict joint shear strength. The comparison is not, however, accepted as valid because the joints tested do not satisfy seismic code requirements in a number of very important respects, including detailing and quantity of joint confinement steel, beam longitudinal bar diameter and (in some cases) provision of intermediate longitudinal column bars.
The shear strength formula quoted for NZS 3101 (equation (4)) represents only one of a number of aspects that must be checked, namely concrete diagonal compression failure, which is an unusual failure limit to reach. Sufficient confinement of the joint concrete by joint ties and intermediate column bars must be demonstrated. Thus, for the low ductility requirements of NZS 3101, minimum horizontal shear reinforcement is required to carry 35% of the joint shear force; in addition some intermediate vertical reinforcement is required in the column joint zone. In addition, bond and anchorage of longitudinal beam bars must be checked, an aspect that may well have been critical in the tests reported, judging from the photographs of failure mode.
The shear strength formula quoted for Eurocode 8 (equation (5)) is not recognised as appearing in the code. In fact, for low ductility (DCL) members, there are no requirements beyond those of Eurocode 2, for moderate ductility (DCM) members, joint design depends on satisfying minimum detailing requirements and for high ductility (DCH) members, a series of checks for various failure modes, similar to those in NZS 3101, are presented.
The authors’ conclusion that BS 8110 predicts joint shear strength relatively well must be tempered by the fact that it appears to overpredict strength by around 50% for the test specimen with a high beam-to column depth ratio (BS-L-600).
The authors state that beam-to-column depth ratio is generally ignored by current codes when assessing joint shear strength. While it may be true that this ratio does not appear as an explicit, independent parameter, the joint geometry (and hence this ratio) is a crucial factor when assessing the required quantity of joint confinement and requirements for anchorage of the longitudinal beam steel, both in NZS 3101 and in Eurocode 8.
The authors’ equations (6) and (7) relate to column shear requirements in BS 8110 and Eurocode 2 respectively. In fact BS 8110 and Eurocode do not require an explicit check of joint shear strength. The authors’ equation (6) is similar (but not identical) to equation (6a) in BS 8110. The authors’ equation (7), while apparently based on equation (6·2a) in Eurocode 2, contains some significant differences and there is a dimensional inconsistency in the authors’ definition of the (dimensionless) variable k. While equation (6·2a) in Eurocode 2 is for sections without shear reinforcement, the authors have added an additional term for reinforcement. Equation (6·9) is appropriate for maximum shear resistance in the presence of axial load. In any case the region being considered is a ‘discontinuity’ region. As such, strut and tie models such as those in Annex J of Eurocode 2 for frame corners would be more appropriate.
The beam flexural capacity is incorrectly shown as 151 kN in Fig. 5(g). It should presumably be 139 kN.
Authors’ reply
The authors agree with the discussers that the sample numbers to be tested should be increased. In fact, a number of the specimens have recently been tested by the authors and the results support definitive values for the limits.
The authors agree with the discussers that the apparent ductility may be attributable to flexure in the beam. The ‘ductility of beam–column joint’ drawn from Fig. 5 may not fully refer to the joint itself.
The authors believe that the seismic design codes used in Table 3 should be reasonably good for predicting the shear strengths of joints designed for earthquake resistance. The purpose of these comparisons in the table is not, however, to show the accuracy of the code predictions, which is intended to indicate that the current seismic and non-seismic design codes may not be used for predicting the shear strength of beam–column joints that are designed and detailed without seismic consideration under seismic action. This is particularly useful when assessing the shear capacity of non-seismically designed and detailed joints subjected to seismic loading; there is therefore a need to develop a method of analysis for predicting the shear strength and designing beam–column joints with non-seismic details under low-to-moderate earthquakes. Similar code comparisons for non-seismically designed joints were also made by other researchers.19–21
The simplest failure mode of a beam–column joint without shear reinforcement would be a diagonal compression one.22 This is why comparisons should be made between the experimental results and 0·2f′c, which is a value of the limit, to avoid diagonal compression failure in joints by shear, as stated in NZS 3101. A similar comparison has also been made.21
Equation (5) represents only the horizontal shear force applied to the joint rather than the joint shear strength, and the equation was inadvertently expressed in the paper as it is not recognised as appearing in the code. All the results predicted by Eurocode 8 in the paper are, however, obtained from the formula quoted for Eurocode 8, given by
where Ash is the amount of horizontal links; hjw and hjc are the distances between reinforcement at two faces in beam and column, respectively; λ is 1·2 for DC’M’; τRd is the basic design shear strength of concrete in N/mm2; and νd = Nsd/(Acfcd). For the comparison purpose, all factors of safety in the expression have been removed.8In this particular case, BS 8110 overpredicts the shear strength of the joint with a high beam-to-column depth ratio, which is 2, for about 50%. Nevertheless, the conclusion drawn was based on the average predictions in the study.
In NZS 3101 and Eurocode 8, when assessing the required quantity of joint confinement and requirements for anchorage of the longitudinal beam steel, the beam and column depths are considered, where the limiting shear of a joint is directly related to the diagonal compression failure of concrete. The joint aspect ratio (beam–to-column depth ratio) would, however, have an effect on the strut angle, thus affecting the value of maximum joint shear strength. A similar point of view has also been addressed by Scott et al.19 While the effect of the joint aspect ratio on the limiting shear of joints has not been considered directly in NZS 3101 and EC8, ACI 318 considers that the shear strength of a joint is directly related to the concrete strength only and is not sensitive to the amount of shear reinforcement. From the results of this study, the amount of transverse reinforcement determined by ACI 318 may be less conservative for the joints with a high beam-to-column depth ratio as compared to those determined by NZS 3101 and Eurocode 8.
In non-seismic codes, such as BS 8110 and Eurocode 2, while there is no design requirement for beam–column joints, a beam–column joint can be treated as the portion of a column within the depth of the beams that frame into it.8 To compare the experimental results with the predictions from the non-seismic codes, column shear strength is considered. For BS 8110, equation (6a) of the code is adopted for the comparison, where the factors of safety have been removed.19 This is why equation (6) in the paper appears in a different form to that in the code. Similarly, for Eurocode 2, the standard method is adopted to calculate the shear strength of a column, given by
where9In the paper, the factors of safety are removed from the above equation;20 thus it appears in a different form from that in the code. For the dimensionless variable k, it is defined by k = (1·6 – d) where d is the effective depth of member in metres. At the same time, k should not be less than 1.10It should be 139 kN.
