Discussion: Recommendations for nonlinear finite element analyses of reinforced concrete columns under seismic loading up to collapse

While the discusser appreciates the work of Dolati et al. (2023), which helps the engineering community to develop non-linear finite-element (FE) models of reinforced concrete columns using ATENA, there are some points of discussion that are necessary to clarify the work. The work reported by Dolati et al. (2023) is novel and innovative, and clearly required needed dedication, time and effort. However, the discusser has some minor concerns regarding the data collected and used in modelling and some major concerns regarding the results discussed in the paper. This discussion corrects the inaccuracies in the paper and suggests possible solutions for the problems whenever possible. The results are thoroughly discussed, raising some serious questions that need answers to better understand the work. The major points regarding the details of the work and the results are discussed first, and then the minor points are addressed.

This article corrects mistakes in the paper by Dolati et al. (2023), which should help engineers better understand the work and model FE models of columns under cyclic loads using ATENA. The results presented are elaborated upon by criticising crucial points, with the aim of helping readers better understand and apply the outcomes of the original paper.

When the authors stated that additional information on the columns can be found in the literature, they cited Li and Hwang (2017). The paper by Li and Hwang (2017) is an analytical study on some tests they carried out, which are documented by Li et al. (2014). This is misleading as instead of Li and Hwang (2017), the reference should have been Li et al. (2014). Furthermore, they state that ‘While lateral drift is imparted to the column, axial load for these tests was kept constant (Figure 1)’. In the paper, Figure 1 consists of three distinct undefined figures without any distinct captions. The figure on the left contains numbers 1, 2 and 3, without any definition.

Dolati et al. (2023) present data related to the examined columns in Table 1. However, a large portion of the numbers are reported incorrectly if they are compared with the properties of the specimens tested in the original papers. These errors are not from unit conversions as the real numbers in the original papers differ from those reported by Dolati et al. (2023).

For instance, the tie spacings of specimens 3CLH18, 3CMH18, SC-2.4-0.2, SC-2.4-0.5, Specimen#1 and Specimen#2 are reported by Dolati et al. (2023) to be 457.2, 457.2, 124.9, 124.9, 457.2 and 203.2 mm, respectively. In the original papers, the spacings for these specimens are reported to be 457, 457, 125, 125, 457 and 203 mm, respectively. Also, the column dimensions of SC-2.4-0.2 and SC-2.4-0.5 in the discussed paper are stated to be 350.5 mm × 350.5 mm, while the dimensions in the original paper (Tran, 2010) are 350 mm × 350 mm. Additionally, Dolati et al. (2023) reported the longitudinal reinforcement ratio of SC-2.4-0.2 to be 0.021, while it is 0.0205 when calculated based on the data given by Tran (2010).

Moreover, the clear height of columns 1NL, 2NL and 2NH is reported as 497.8, 1001 and 1001 mm, respectively, in the discussed paper. However, Li et al. (2014) reported the clear height of the same columns to be 500, 1000 and 1000 mm, respectively. It is not obvious why 19.7 inches in the column dimensions of 2NL and 2NH was converted to 500 mm while the same 19.7 inches for the clear height of specimen 1NL was converted to 497.8 mm in the same table. The same applies for the conversion of the dimensions of columns 3CLH18, 3CMH18, Specimen#1 and Specimen#2, in which 18 inches is converted to 457 mm while for the tie spacings of 3CLH18, 3CMH18 and Specimen#1, the same 18 inches is converted to 457.2 mm in the same table.

The authors claim that they used the equations of ACI 318-19 (ACI, 2019) to calculate the modulus of elasticity (MoE) of the concrete. However, they only used the imperial system equation then converted it to SI units. Because when the SI equation is used to check the data in Table 2, it yields different numbers than those presented. Despite that, the reported numbers also have inconsistencies. For example, in the discussed paper, the MoE of specimens 3CLH18, SC-2.4-0.2 and SC-2.4-0.5 is reported to be 3559, 3262 and 3376 ksi, respectively. However, the calculated MoE for these same specimens based on the compressive strength of the concrete and the equation provided in the discussed paper is 3122, 3224 and 3372 ksi, respectively. Therefore, the difference between the calculated MoE and the reported values of the MoE is in the range 4–437 ksi.

In reporting the material properties of the columns, Table 2 in the discussed paper also shows some discrepancies between the reported data and the data in the original works. For instance, the concrete compressive strengths of specimens 3CLH18, SC-2.4-0.5 and Specimen#1 are reported to be 3.9 ksi, 24.1 MPa and 19.9 MPa respectively – in the original papers they are 3.71 ksi (Lynn et al., 1996), 24.2 MPa and 20 MPa respectively. Additionally, the longitudinal bar diameter of SC-2.4-0.2 is reported as 19.9 mm while the original paper states 20 mm. The tensile strength of longitudinal bars of the same specimen is reported as 606 MPa while it is 606.6 MPa in the original paper. Moreover, the yielding and tensile strengths of the ties for the same specimen are reported as 392 MPa and 580 MPa, respectively, while they are stated as 392.6 MPa and 579.7 MPa in the original papers.

The loading is presented in Table 3 in the discussed paper. However, there are substantial differences between the numbers reported by Dolati et al. (2023) and the numbers in the original papers. For example, the maximum load ratios (P/(f′_cA_g)) of columns 3CLH18, 3CMH18, Specimen#1 and Specimen#2 are reported to be 0.08, 0.26, 0.36 and 0.37, respectively – in the original papers they are 0.12, 0.35, 0.37 and 0.38, respectively. Therefore, the question is: Were the ratios reported in Table 3 or the actual values used for applying axial loads in the modelling?

Regarding the maximum applied lateral load (V_peak), the reported numbers in Table 3 are also incorrect when compared with the original papers. For instance, the values of V_peak for specimens 3CLH18, 3CMH18, SC-2.4-0.2, SC-2.4-0.5, Specimen#1, Specimen#2, 1NL, 2NL and 2NH are reported to be 62.6 kips, 73.7 kips, 218.7 kN, 237.2 kN, 566.2 kN, 521.6 kN, 600.1 kN, 408 kN and 457.1 kN respectively. In the original papers, the values are stated to be 61 kips, 76 kips, 218.9 kN, 237.6 kN, 565 kN, 520 kN, 660 kN, 402 kN and 460 kN. Therefore, the question is: Were the loads stated in Table 3 used in calculating errors or the actual lateral loads?

Additionally, the entire column labelled “Peak shear stress” in Table 3 of the discussed paper yields incorrect numbers if the equation provided in the column heading is used. All the numbers in that column are at least multiplied by ten if the provided equation is used. For example, the peak shear stress of specimen 3CLH18 is 0.33 if the SI unit properties are used in the equation, while using the same equation and material properties in imperial units yields a value of approximately 0.13. In both cases, the result is far from the value of 3.1 reported in Table 3. This is true for all the other specimens. Furthermore, in the same table, the displacement at initiation of axial degradation for specimens 2NL and 2NH is reported as 2.27  inches and 1.16 inches and 67.6 mm and 40.6 mm, respectively. If the displacements in inches are converted to millimetres, the values should be 57.66 and 29.46 mm. respectively. The source of all these inaccuracies is not clear.

Regarding the results presented by Dolati et al. (2023), there are several points to be discussed.

• The authors tried to simulate the experimental drift ratio against lateral load of the columns. However, in doing so, for specimens SC-2.4-0.2 and SC-2.4-0.5, they removed some of the cycles without telling their readers about it. Figure 7 in the paper is a reconstruction of the graph for (SC-2.4-0.2), but when compared with the graph in the original paper, the number of cycles was reduced dramatically.

• The caption for Table 4 is ‘Mesh sizes used for sensitivity study on Specimen_1’, but it shows the data for column SC-2.4-0.2.

• The authors state that ‘The stress at the onset of non-linear behavior in concrete in compression (f′_c0) is kept at the software default of two times the tensile strength. Similarly, the tensile strength of concrete (f_t) is kept at the software default at 2 MPa (290 psi), from the range that is reported in Table 6’. However, it is unclear if a constant 4 MPa was used for the onset of the non-linear behaviour of the concrete for all specimens or the values from Table 6 of the paper were used. Additionally, the authors claimed that (f′_c0) is just twice the tensile strength, but the reported values in Table 6 are approximately 2.1 times the tensile strength for all the specimens.

• The authors claim that w_d can be taken as 5 mm for slender columns but not for short columns – for short columns, the authors gave a range of 0.5–10 mm. The question then is: If 5 mm is within that range provided for short columns and gives accurate results for slender columns, then what is the decisive factor in selecting a number that is smaller than 5 mm or bigger? How should a user know not to select only 5 mm for wd for short columns while that number is within the range provided by the authors? Is it the only number that users should avoid in modelling short columns?

• In Table 7 of the discussed paper, where the errors for final model calibration are presented, in calculating the error in maximum lateral strength, it is apparent that the authors calculated the error based on the positive Y-axis of the graphs of lateral load against drift ratio, ignoring the negative side. In Table 7 of the discussed paper, for specimens 3CLH18 and 3CMH18, they report that the experimental results were more than the simulated results, by 12 kN and 17 kN, respectively. However, from Figure 18, it is obvious that the simulated values were more than the experimental values by approximately 50 kN and 100 kN, respectively. This is also true for specimen SC-2.4-0.2 – the authors report that the experimental result was higher than the simulated value by 26 kN, while Figure 19 of the discussed paper shows that the simulated result was approximately 25 kN more than the experimental result. The authors also claim that the experimental result for 1NL was 9.5 kN more than the simulated value. However, from Figure 21, it is clear that the experimental result of this column was greater than the simulated value by approximately 200 kN. Why are all these details not discussed in the paper? What is the reason behind the difference between pushing and pulling the specimens that lead to that big difference?

• Why did the authors not calculate the error for the maximum drift of the specimens? They only compare the errors for the drift at the maximum load, while the experimental maximum drifts of some of the specimens (e.g. 1NL and 2NL) were greater than the simulated values by more than 70%.

• Both Tables 3 and 8 in the discussed paper present the applied lateral loads of the specimens. All of the data in Table 3 has been shown to be incorrect. However, when comparing Tables 3 and 8 in the same paper, the lateral loads of specimens 3CMH18, Specimen#2 and 1NL are listed as, respectively, 327.8 kN, 521.6 kN and 600.1 kN in Table 3, and 327.9 kN, 521.9 kN and 600.0 kN, in Table 8. The source of the error is unknown as the same lateral load for even the imperial system is different in both tables. Additionally, in Table 3, the lateral loads of Specimen#2 and 1NL are reported to be 117.2 ksi and 134.9 ksi respectively, while the lateral loads of the same specimens in Table 8 are 117.3 ksi and 134.8 ksi, respectively. The source of these errors is not known.

• Table 8 of the discussed paper indicates the FE error for specimen SC-2.4-0.2 to be −2.6%; however, the authors reported an error of only −2%.

• In calculating shear capacities using the equations provided in standards and codes, the authors have not disclosed any equations to guide readers how they used the equations. The transverse reinforcement provided in each of the specimens might be less than the minimum required by standards and codes. Therefore, the authors should have given the equations and the assumptions they made in calculating the shear strengths of the columns. However, the authors omitted these, which made cross-checking their results an indispensable task. If equation (a) provided in Table 22.5.5.1 of ACI 318-19 (ACI, 2019) was used to calculate the capacity of column 3CLH18 (even though the shear reinforcement might be less than the minimum required by the code), it yields 229.27 kN without taking a strength reduction factor. However, the authors reported 292.2 kN. This could be a typo, with 292 mistakenly written instead of 229. Further comparison is not possible without knowing the equations used by the authors.

• Two types of ties are used in the discussed paper – one with hooks of 90° and one with 135° hooks. The authors do not provide an explanation on the modelling of the two ties. They state that ‘This study recommends the following modeling parameters for rectangular shear-critical columns simulated to collapse with shear span to depth ratios within the range of 0.6 ≤ a/d ≤ 1.1 for both 90-degree and 135-degree tie hook angles, and with a variety of diameters and yield strength for reinforcement’. This can be interpreted that, for short columns, the end hooks of the ties would not make a difference. Is this justifiable? If there is no difference between 90° and 135° degree tie hooks, why does ACI 318-25 (ACI, 2025) require the use 135° tie hooks in the hinge regions?

• Figures 22 and 23 in the paper show the failure of the columns, but each figure consists of three figures without any explanation on them.

• Further, how did the authors define the stress–strain of the bars, given that this property is missing in the original papers? What was the fracture strain of the bars? Was it assumed? How did they define that in their modelling? What methodology did they employ to define it?

• Figure 22 of the discussed paper shows the failure mode of SC-2.4-0.2. Tran (2010) reported the rupture of transverse bars along the diagonal shear crack. However, from Figure 22, there are several ties on the path of the diagonal crack where their strain had not reached even the maximum strain of 10% based on the legend. Conversely, there are ties with their strains reaching 10%, which are not on that path. This suggests a contradiction between the reported fractures of the ties by Tran (2010) and the discussed paper. Further discussion on this is difficult due to absence of the fracture strain of the bars.

• Figure 23 of the discussed paper shows the failure mode of Specimen#2. The legend shows the threshold of the axial strain on the ties to be 0.9–27%. However, Henkhaus et al. (2013) stated that in all columns there was a decay in lateral load capacity after the maximum lateral force which ‘was accompanied by the formation of critical inclined cracks and yielding in one or more ties’. On that particular specimen, Henkhaus et al. (2013) reported that, at axial failure, the column experienced the opening of the tie along with longitudinal bar buckling. It is apparent from Figure 23 that longitudinal bars in the real column tested in the lab buckled in two directions (−x and +x) axis, but this is not the case in the model in the discussed paper. This contradicts the conclusion reached by Henkhaus et al. (2013) who reported buckling of the longitudinal bars. Also, no opening of the ties was reported by Dolati et al. (2023); rather, they reported that the strain in one of the ties in the middle of the column reached 27%, which is implausible as the concrete could not transfer the load at that strain level. Also, in the absence of the stress–strain of the bars defined in the model, it is difficult to verify the fracture strain especially for a bar of diameter 6.35 mm. Additionally, based on Figure 23, it is unclear why the lower threshold is set at 0.9%, which is beyond the yielding of the steel bars. This makes it difficult to understand any anomaly in the model.

In the first paragraph, the authors state that many buildings in the USA are at risk of exhibiting low seismic behaviour, citing Inel et al. (2008). However, the cited document is on re-evaluation of buildings in Turkey. For the same statement, Dolati et al. (2023) also cite Galvis et al. (2017), who actually studied buildings in Mexico City, Mexico. Next, they cite Tran (2010) for reasoning that those buildings in the USA were designed not following modern building codes; however, Tran (2010) emphasise that buildings in Singapore lack sufficient confinement. Moreover, in the same section, Ghannoum and Sivaramakrishnan (2012) is cited for a database on rectangular columns; however, based on the bibliography provided in the discussed paper, there are more than two authors for that database, so the citation should be written as Ghannoum et al. (2012). The authors claim that a database of 689 concrete column tests was developed by Suselo (2021); however, the database was actually developed by Ghannoum and Sivaramakrishnan (2012) as the work of Suselo (2021) is a PhD dissertation. Additionally, the sentence ‘Out of a database of 689 concrete columns tests developed by Suselo (2021) and Ghannoum and Sivaramakrishnan (2012), the effect of different lateral loading protocols, such as monotonic pushover and fully reversed cyclic loading protocols, with varying the number of cycles, were explored on only eight experimental tests, despite evidence that axial and lateral load histories can influence significantly the seismic behaviour of non-ductile concrete columns (Nakamura and Yoshimura, 2002)’ lacks clarity as it is not obvious who conducted the eight experimental tests. Are the authors referring to Suselo (2021) or Nakamura and Yoshimura (2002)?

In the second paragraph, the authors introduce FEA without definition, although the abstract reveals that FE refers to finite elements. In this paragraph, the authors cite two papers that are not directly relevant to the work (Khedmatgozar Dolati et al., 2021, 2022) – the former is on the application of rubber bearing pads for bridges and the latter is on the application of VD-LRBP system for bridges.

In the third paragraph, the authors state that the modelled columns, including the columns studied by Tran (2010), were full-scale columns. However, Tran (2010) state that they tested ten half scale columns. Additionally, the sentence ‘Also, the comparison of shear capacity derived from the FE models and estimated by standards are compared (ASCE/SEI 41-17, ACI 369.1-17 (American Concrete Institute (ACI) Committee 369 2017))’ lacks clarity. Is the comparison compared? Or the shear capacity from the FE models and the estimated shear capacities from the standards? Also, why are the standards cited at the end of the sentence? Is this statement mentioned in those standards or were these standards used to estimate the shear capacity?

The authors state that ‘numerous studies have looked at’ – the word choice of ‘looked at’ is informal and, when used, it means the study examined, analysed or reviewed an existing study, result or data. Also, the sentence ‘that not only depends on columns material and geometric properties but also on loading history’ should have been ‘that depends on not only columns material and geometric properties but also on loading history’. Additionally, the authors cite Haselton and Pacific Earthquake Engineering Research Center (2008), but this is a report by Haselton et al. (2007). Moreover, they also cite Rajae et al. (2022), which is on the inspection of bridges using digital image correlation (DIC) systems and it is not directly related to the topic of the paper. Moreover, the authors cite Hagen (2012) to justify that columns that tend to yield in flexure prior to failure generally have larger deformation before shear degradation. However, the work of Hagen (2012) is concerned with shear walls not columns.