Probabilistic and Semi-Probabilistic Analysis of Slender Columns Frequently Used in Structural Engineering

Round 1

Reviewer 1 Report

The proposed manuscript deals with the probabilistic analysis of the stability of slender concrete columns. The paper consists of an introduction regarding probabilistic analyses and sensitivity analyses, followed by an overview of the experimental investigations which were at the basis of this research. Next, the input for the reliability analyses is described as well as the outcome of the sensitivity and probabilistic analyses. Finally, the conclusions are presented.

The paper deals with the important topic of reliability assessment of verification formats provided by current standards and codes, with a specific focus on slender reinforced columns. The topic is interesting and is within the scope of Applied Sciences. However, the reviewer thinks that a substantial revision of the manuscript is required before it could be accepted for publication. The (main) comments are provided below:

General remarks:

1. The paper seems too long. Some parts provide too much information (e.g. section 2) regarding aspects that are not required to understand the current manuscript or are apparently even not applied in the subsequent analyses e.g. the Fractile Based Simulation method, section 2.4 'Evaluation procedures', section 4.1 'Standard provisions', section 4.9.2 'Pre NLFEM-Modelling', etc.
2. The structure of the paper should be improved. It appears to the reviewer that the paper has been written by several authors separately and simply merged together afterwards, since several pieces of information are scattered throughout the paper or are repeated/introduced several times.
3. line 80-86: it is not clear whether this research objective has been reached. The authors should consider to restructure and rephrase several parts of the manuscript in order to clearly address this.

Line-by-line comments:

• line 47-48: rephrase, the failure probability and reliability are opposites, not synonyms
• line 134-136: not clear whether this approach has been applied in this manuscript. If not it is confusing to mention this here since it contradicts the information provided in e.g. Table 6
• line 147-150: this statement is false. It seems inappropriate to refer to the content of the forthcoming MC2020 as its content is still under discussion in the different TGs and AGs.
  Furthermore, the different formats indicated in the manuscript are not correct. The current MC2010 mentions 1) the probabilistic method, 2) global resistance format and 3) the partial factor format. The ECOV method is a particular method within the global resistance format. 
• line 179: the statement is unclear.
• line 192: the definition of the coefficient a0 is unclear.
• line 196-209: too much details. Furthermore it is not clear whether this approach has been used in the subsequent analyses.
• line 212: check subscripts.
• line 215-223: a reference regarding LHS should be added.
• line 231-251: not clear whether this approach has been applied in the subsequent analyses, as it appears that simple LHS has been applied. If this is the case, this paragraph should be removed.
• line 288-318: a large part of this text seems to be a more or less exact copy of the text in https://doi.org/10.1016/j.engstruct.2021.112259, which should be acknowledged.
  Furthermore, this approach appears not to be applied in the subsequent analysis (section 4.7), where a FORM analysis and the Kendall Tau algorithm are applied
• line 338 and Table 2: not clear why these parameters are called 'descriptive statistical parameters'. Were any statistical method involved in the derivation of these values? If not, consider rephrasing.
• line 352-363: to the reviewer's knowlegde EN1992-1-1 does not provide a method for deriving model uncertainties.
  Furthermore, it is not clear why the factor 1.06 in the calculation of Md does not correspond to the value 1.01 mentioned in line 355.
  Finally, the derivation of design values seems not to be included in reference [2].
• line 405-407: 'the resistance side is determined by the stochastic properties of the I-D in Equation (19) or the action side substituted' is not clear. Consider rephrasing.
• line 470: replace reference to Section 4.3 by Section 4.2.
• line 471-472: reference to Equations (4-6) seems to be incorrect.
• Table 3:
  • Can the authors provide any reference for the different probabilistic models?
  • The definition of the variables X5-X8 can be clarified by referring to Fig. 7
  • The notation of the distribution type should be clarified. Is 'B' referring to a beta distribution? Then the authors should indicate the range of the beta distribution
  • It is not clear what the '*'-symbol refers to in the standard deviation of X7-X8
  • Why is the standard deviation of X9-X14-X15-X16-X17-X22 'to be defined'? Aren't these quantities not necessary for the subsequent analyses?
  • What is the meaning of variable X27?
  • The authors might consider to more clearly indicate which parameters are involved in which verification format, as it currently appears that more parameters are defined than necessary for the verifications.
• line 514: correct 'hight'
• line 536-537: it seems only the characteristics of C45/55 are indicated in Table 3, while probably other characteristics are necessary to describe the structural behaviour of a column using C100/115. Is the consideration of C100/115 necessary to achieve the research objective in this manuscript?
• Equation 33: is ka considered constant during the analysis? Shouldn't it depend on the applied forces?
• Equation 36: why is ei not included in this equation  (cfr. Equation 24)
• line 557: what is the normalization factor which is used to normalize the normal force?
• line 558: correct reference error.
• line 589-590: too much detail, consider to remove this.
• line 595-...: can the authors comment on the fact that, on the component level, the variables X7 and X8 were not considered, while they have been found of paramount importance for failure considering the cross-sectional analysis?
• line 601: this information (60 LHS) should appear earlier in the text
• line 609-6123: see previous comment regarding the difference between the characteristics of C45/55 and C100/115.
• line 634-644: seems to repeat information provided earlier in the manuscript. Furthermore, check whether reference [25] is correct.
• line 652-654: repeating information provided earlier in the manuscript
• line 660: how is the histogram from the experiments obtained since only 6 tests have been executed?
• Figure 11b: add legend.
• Table 4: it seems not necessary to provide this information in the manuscript itself (could be  added as supplementary material) since the histograms have been included.
• Table 5:
  • Correct the Table caption
  • First row are repeating the information provided in Table 3
  • Characteristics of C100/115: see previous comment regarding the difference between C45/55 and C100/115
  • Why is the mean value of X1 in Table 5 different from the value mentioned in Table 3?
• line 687-...: correct the enumeration, now it says (a), (b), (c), (c), (d), (e) and (f)
• line 692: correct 'siehe')
• line 699-701: this information should already be discussed in section 4.8
• line 706-...: some of the information provided in 4.92. seems to be irrelevant for the proposed manuscript.
• line 754-775: it is not clear how the 'model uncertainty' has been defined in this case as no clear definition is provided. Usually, a model uncertainty is defined as the ratio between the model output and the corresponding experimental observation, see e.g. https://doi.org/10.1016/j.strusafe.2016.08.003
• line 817-820: this statement is extremely important and requires more interpretation and analysis. It appears that the models are not biased and hence this is to be accounted for when using a particular model uncertainty in either the full-probabilistic analysis or the derivation of (global) partial factors.
• Table 7: see comment regarding Table 4.
• Figure 12:
  • extend the range of the normal force (in Figure a not all curves are visible)
  • it is not clear which information is provided by the boxplots. These are not discussed in the text.
  • provide legends to the histograms on the right
• line 837: clarify why these two reliability levels have been selected.
• line 838-844: please see previous comment regarding the model uncertainty.
• Table 8:
  • why are there no partial factors derived for the case where gamma_Rd = 1.06? How is the design resistance derived in that case?
  • how was the partial factor derived for the line 'experiments'? The ECOV method requires two analyses: one using mean values and one using characteristic values. This seems not possible in case of the experiments.
• line 860-862: it is obvious that in case of a higher (targeted) reliability level, the design values of the resistance will decrease.

Author Response

Reply to the reviewer's comments

 Thank you very much for the review, your time and the very valuable comments for the article. We have carefully reflected on all of your comments and have incorporated them into the revision of the article. Enclosed you will find the explanations of the individual changes made.

 

Reviewer N°1 Comment: The paper seems too long. Some parts provide too much information (e.g. section 2) regarding aspects that are not required to understand the current manuscript or are apparently even not applied in the subsequent analyses e.g. the Fractile Based Simulation method, section 2.4 'Evaluation procedures', section 4.1 'Standard provisions', section 4.9.2 'Pre NLFEM-Modelling', etc.

Response of the Authors:

We have revised the first section of the article and revised the second section in order to put it in the context with the following chapters

The manuscript has been revised and many parts have been shortened

 

Reviewer #1 Comment: line 47-48: rephrase, the failure probability and reliability are opposites, not synonyms.

Response of the Authors: Thank you for this note, the original formulation has been replaced by: The failure probability of the considered state results from the system or element reliability.

Reviewer #1 Comment: line 80-86: it is not clear whether this research objective has been reached. The authors should consider to restructure and rephrase several parts of the manuscript in order to clearly address this.

Response of the Authors: Thank you for this observation, the objectives have been detailed and replaced by: “The main objective in this paper is to discuss the probabilistic verification of the stability of slender columns. For this endeavor, details such as sensitivity analysis, probabilistic verification of standard formulations and verification of nonlinear modelling, as well as safety formats such as the ʺEstimation of the Coefficient of Variationʺ of the resistance method are analyzed to validate the numerically determined safety with respect to experimentally tested columns. It will be demonstrated that probabilistic nonlinear finite element analysis (P‐NLFEM) based on advanced sampling techniques can lead to higher column capacity than experimentally tested ones. Such P‐NLFEM results should be considered dangerous.”

Reviewer #1 Comment: line 134-136: not clear whether this approach has been applied in this manuscript. If not, it is confusing to mention this here since it contradicts the information provided in e.g. Table 6.

Response of the Authors: Thank you for your comment. Since these investigations were not performed, this text passage has been deleted.

Reviewer #1 Comment: line 147-150: this statement is false. It seems inappropriate to refer to the content of the forthcoming MC2020 as its content is still under discussion in the different TGs and AGs.

Furthermore, the different formats indicated in the manuscript are not correct. The current MC2010 mentions 1) the probabilistic method, 2) global resistance format and 3) the partial factor format. The ECOV method is a particular method within the global resistance format.

Response of the Authors: Thank you for this observation. The statement has been replaced by: The MC2010 proposes (a) the probabilistic method, (b) global resistance factor format (GRF) and (c) the partial safety factor format (PF). The Estimate of Coefficient of Variation of Resistance (ECOV) method is a particular method within the global resistance format..: the Global Resistance Factor format (GRF), the Par‐ tial Factor format (PF) and the Estimate of Coefficient of Variation of Resistance format (ECOV). The forthcoming fib Model Code 2020 as its content and formats are still under discussion, but should also encompass this concept.

Reviewer #1 Comment: line 179: the statement is unclear.

Response of the Authors: Thank you for this hint, the original statement has been replaced by: In this approach, the sensitivity factor of the resistance side αR, the coefficient of variation VR of the resistance side and the reliability index ß are considered. The descriptive elements of the action side (e.g. partial safety factor E) influences the consideration only indirectly via the interrelation between αE, αR and ß.

Reviewer #1 Comment: line 192: the definition of the coefficient a0 is unclear.

Response of the Authors: Thank you for the comment, the definition of a0 is not relevant for the description of the determination of the failure probability, the statement has been deleted.

 

Reviewer #1 Comment: line 196-209: too much details. Furthermore it is not clear whether this approach has been used in the subsequent analyses.

Response of the Authors: Thank you for this notice. A large part of the description has been shortened. Since the procedure is used in the sensitivity analysis at the component level, a brief description has been retained.

The remaining part is as follows: The correlation between the basic variables, see Figure 1 (right) is set up by a controlled rearrangement of the sample field using simulating annealing. Simulated Annealing (simulated cooling / annealing) is a heuristic approximation method.

Reviewer #1 Comment: Line 212: check subscripts

Response of the Authors: Thank you, the error has been corrected.

Reviewer #1 Comment: line 215-223: a reference regarding LHS should be added.

Response of the Authors: Thank you for this comment. The following literature has been added:

Novák, D., Vořechovský, M., Teplý, B.;

FReET: Software for the statistical and reliability analysis of engineering problems and FReET-D: Degradation module

(2014) Advances in Engineering Software, 72, pp. 179-192.

Reviewer #1 Comment: line 231-251: not clear whether this approach has been applied in the subsequent analyses, as it appears that simple LHS has been applied. If this is the case, this paragraph should be removed.

Response of the Authors: Thank you for this note. In the studies conducted, also the Fractile based sampling algorithm was processed and it was confirmed that it is a method that lies between the ECOV and the LHS - FRBS can also map correlations similar to the LHS. For the sake of completeness, I would therefore like to leave this information in the article and include a reference to it in the appropriate places.

Reviewer #1 Comment: line 288-318: a large part of this text seems to be a more or less exact copy of the text in https://doi.org/10.1016/j.engstruct.2021.112259, which should be acknowledged.

Furthermore, this approach appears not to be applied in the subsequent analysis (section 4.7), where a FORM analysis and the Kendall Tau algorithm are applied

Response of the Authors: Thank you for this observation. Since the FORM based and Kendall Tau based sensitivty algorithm are used, this paragraph has been deleted.

Reviewer #1 Comment: line 338 and Table 2: not clear why these parameters are called 'descriptive statistical parameters'. Were any statistical method involved in the derivation of these values? If not, consider rephrasing.

Response of the Authors: Thank you very much for this recommendation – the statement has been rephrased to:

Figure 6 presents the results of the experiments while Table 2 lists descriptive statistical parameters gained for each of the slender columns.

Reviewer #1 Comment:

1. line 352-363: to the reviewer's knowledge EN1992-1-1 does not provide a method for deriving model uncertainties.
2. Furthermore, it is not clear why the factor 1.06 in the calculation of Md does not correspond to the value 1.01 mentioned in line 355.
3. Finally, the derivation of design values seems not to be included in reference [2].

Response of the Authors: Thank you for this comment. For clarification, the formulations were revised as follows:

10. The model uncertainties of the experimental test results were derived following Achenbach et (2019) https://doi.org/10.1016/j.firesaf.2019.102832 and EN1990 Annex D (Edition:2013-03-15) with Y =Ymean/ Yk. This results for Nmax to Nmax = 1.06, for e2 at Nmax to e2,Nmax = 1.02, and for M at Nmax to M,Nmax = 1.01.
11. The factor does not match because the observations were carried out for Nmax on the vertical axis of the N-M diagram on the one hand and for M on the horizontal axis of the diagram on the other. In the following observations, the unfavourable higher value was used, for instance see (18).
12. The appropriate source is: Cervenka, V (2013) Globale Sicherheitsformate im fib Model Code 2010 für die Bemessung von Betonkonstruktionen. Proceedings of the 11th International Probabilistic Workshop, Brno

Vorsicht in der Antwort steht Achenbach 2019, im text steht aber EN1991‐1‐1. Am ende steht auch nochmal Cervenka 2013 ?

Reviewer #1 Comment: line 405-407: 'the resistance side is determined by the stochastic properties of the I-D in Equation (19) or the action side substituted' is not clear. Consider rephrasing.

Response of the Authors: Thank you for the comment, the following adjustment for clarification has been made: “.., the resistance side (KR · R) in Equation (19) corresponds to the interaction diagram (I-D) (corresponds to the function of the max. permissible N-M values). The action side (KE· (g + q)) of Equation (19) corresponds to the acting N-M load path. (The intersection of the N-M load path with the I-D characterises the max. permissible N-M values),..”

Reviewer #1 Comment: line 470: replace reference to Section 4.3 by Section 4.2.

Response of the Authors: Thank you for your comment, the correction has been made.

Reviewer #1 Comment: line 471-472: reference to Equations (4-6) seems to be incorrect.

Response of the Authors: Thank you for this note, the correction has been made.

Reviewer #1 Comment: Table 3:

• Can the authors provide any reference for the different probabilistic models?
• The definition of the variables X5-X8 can be clarified by referring to 7
• The notation of the distribution type should be Is 'B' referring to a beta distribution? Then the authors should indicate the range of the beta distribution. It is not clear what the '*'-symbol refers to in the standard deviation of X7-X8
• Why is the standard deviation of X9-X14-X15-X16-X17-X22 'to be defined'? Aren't these quantities not necessary for the subsequent analyses?
• What is the meaning of variable X27?
• The authors might consider to more clearly indicate which parameters are involved in which verification format, as it currently appears that more parameters are defined than necessary for the

Response of the Authors: Thank you for these notes

• The different probabilistic models were derived or extracted from the following sources:

Bernhard Krug (2017): Monitoringbasierte, nichtlineare, probabilistische Analyse der Querkrafttragfähigkeit von Spannbetonfertigteilen. Doctoral Thesis - Institut für Konstruktiver Ingenieurbau (IKI), BOKU-Universität für Bodenkultur, pp 256.

Strauss, A; Zimmermann, T; Lehky, D; Novak, D; Kersner, Z. (2014): Stochastic fracture- mechanical parameters for the performance-based design of concrete structures STRUCT CONCRETE. 2014; 15(3): 380-394.

Strauss, A; Ivankovic, AM; Benko, V; Matos, J; Marchand, P; Wan-Wendner, R; Galvao, N; Orcesi, A; Dobry, J; Diab, ME; Nincevic, K; Hauser, M; Srbic, N; Skokandic, D Round-Robin Modelling of the Load-bearing Capacity of Slender Columns by Using Classical and Advanced Non-linear Numerical and Analytical Prediction Tools. STRUCT ENG INT. 2021; 31(1): 118-135

• A footnote has been added to the table which refers to the illustration in 7.
• A footnote has been added to the table which indicates the used distribution The proposed dis tributions for X7-X8 have been verified and adjusted by LN.
• the standard deviation of X9-X14-X15-X16-X17-X22 have been estimated by experts opinion, therefore they have been indicated 'to be defined'. A footnote has been added to the table which indicates that these values have been estimated by
• The variable X27 addresses the properties of the concrete compressive border zone in the course of computing the concrete The variable has been accordingly renamed.
• A footnote has been added to the table that indicates which parameters are involved in which verifica tion

Reviewer #1 Comment: line 514: correct 'hight'

Response of the Authors: Thank you for your observation, the correction has been made.

Reviewer #1 Comment: line 536-537: it seems only the characteristics of C45/55 are indicated in Table 3, while probably other characteristics are necessary to describe the structural behaviour of a column using C100/115. Is the consideration of C100/115 necessary to achieve the research objective in this manuscript?

Response of the Authors: Thank you for this question. The analyses on the component consisting of the material C100/115 are of no less interest in the studies carried out here, as the influence of the material properties on the stability problem of interest can be shown. The input parameters for the probabilistic analyses for the material C45/55 shown in Table 3 were developed in this study in an analogous way for the studies with the material C100/115.

The following text has been included in the footer of Table 3:

Since the analyses on the component consisting of the material C100/115 are of the same interest, as the influence of the material properties on the stability problem of interest can be shown, the input parameters for the probabilistic analyses for the material C100/115 were developed in an analogous way as for the C45/55 in Table 3.

 

 

Reviewer #1 Comment: Equation 33: is ka considered constant during the analysis? Shouldn't it depend on the applied forces?

Response of the Authors: Thank you very much for your observation, that is correct, the Eq. has been adjusted accordingly.

Reviewer #1 Comment: Equation 36: why is ei not included in this equation (cfr. Equation 24).

Response of the Authors: Thank you for this comment. The sensitivity analysis processed in this section focuses on the cross-section level, therefore the ei associated with the geometric imperfection was not taken into account in this formulation.

Reviewer #1 Comment: line 557: what is the normalization factor which is used to normalize the normal force?

Response of the Authors: Thank you very much for this question, the formulation and the axis in the Figs have been adjusted as follows:

Figure 8(a) shows the sensitivity analysis and sensitivity factors, calculated via the First Order Reliability Method (FORM), versus N/Nmax with Nmax = 335.5 kN.

Reviewer #1 Comment: line 558: correct reference error.

Response of the Authors: Thank you for this notice the error has been corrected N/Nmax.

Reviewer #1 Comment: line 601: this information (60 LHS) should appear earlier in the text

Response of the Authors: Thank you for this comment, the information regarding the LHS and the associated sample number has been located at the beginning of those section where the LHS is introduced.

Reviewer #1 Comment: line 589-590: too much detail, consider to remove this.

Response of the Authors: Thank you very much for this notice. This detail has been removed.

Reviewer #1 Comment: line 595-...: can the authors comment on the fact that, on the component level, the variables X7 and X8 were not considered, while they have been found of paramount importance for failure considering the cross-sectional analysis?

Response of the Authors: Thank you for this important comment. The following informationhas been added. “At the component level, the variable X7 and X8 were not taken into account because (a) the exact location of the reinforcement was quarantined by an extraordinary quality control during the fabrication of the columns, and (b) the influence of the material laws, solution algorithms, nonlinear fracture processes and slenderness on the instability process were the focus of interest”

Reviewer #1 Comment: line 601: this information (60 LHS) should appear earlier in the text.

Response of the Authors: Thank you for this comment. The information regarding the LHS and the associated sample number has been located at the beginning of section 4.7.2 where the LHS is used first time. The information is as follows: “The component sensitivity analysis was performed using the advanced Monte Carlo-based Latin hypercube sampling technique with 60 generated column samples of the nonlinear numerical finite element model (P-NLFEM). The P-NLFEM was developed by the University of Natural Resources and Life Sciences using the ATENA Scientific software [22].”

Reviewer #1 Comment: line 609-6123: see previous comment regarding the difference between the characteristics of C45/55 and C100/115.

Response of the Authors: Thank you for this notice. The analyses on the component consisting of the material C100/115 are of no less interest in the studies carried out here, as the influence of the material properties on the stability problem of interest can be shown.

The following observation has been included at the end of the paragraph: “A closer comparison between the sensitivity factor curves of the C45/55 and C100/115 columns shows clear differences. For example, X1(Eci) becomes more important for the normal force analysis with higher strength, see Fig. 9(a) and 10(a). For the horizontal deflection sensitivity analysis, X1(Eci) becomes less important and X13(Gf) becomes more important with increasing strength and load, see Fig. 9(b) and 10(b).”

Reviewer #1 Comment: line 634-644: seems to repeat information provided earlier in the manuscript. Furthermore, check whether reference [25] is correct.

Response of the Authors: Thank you for your observation. This paragraph has been removed.

Reviewer #1 Comment: line 652-654: repeating information provided earlier in the manuscript.

Response of the Authors: Thank you for this observation. These lines have been removed.

Reviewer #1 Comment: line 660: how is the histogram from the experiments obtained since only 6 tests have been executed?

Response of the Authors: Thank you very much for this question. For the estimation of the normal distribution, the 6 test results as well as the NLFEM model adapted in the article [2], with which a probabilistic analysis was carried out, were used. The following sentence was added as an explanation: “For the determination of the PDF's of the test results, the probabilistic results of the optimized NLFEM model [2] has been considered too”.

Reviewer #1 Comment: Figure 11b: add legend.

Response of the Authors: Thank you for this observation, the Legend has been included EN1992‐1‐1 (pink), Experiments (blue).

Reviewer #1 Comment: Table 4: it seems not necessary to provide this information in the manuscript itself (could be added as supplementary material) since the histograms have been included.

Response of the Authors: Thank you for this comment. The table was removed from the manuscript.

Reviewer #1 Comment: Table 5:

• Correct the Table caption
• First row are repeating the information provided in Table 3
• Characteristics of C100/115: see previous comment regarding the difference between C45/55 and C100/115
• Why is the mean value of X1 in Table 5 different from the value mentioned in Table 3?

Response of the Authors: Thank you for these notes, the Table has been modified and corrected.

Reviewer #1 Comment: line 687-...: correct the enumeration, now it says (a), (b), (c), (c), (d), (e) and (f)

Response of the Authors: Thank you very much for this observation, the error has been fixed.

Reviewer #1 Comment: line 692: correct 'siehe')

Response of the Authors: Thank you for this observation, the error has been fixed.

Reviewer #1 Comment: line 699-701: this information should already be discussed in section 4.8.

Response of the Authors: Thank you very much for this comment. This information has been discarded in this section, and the following has been added to the end of the first paragraph of 4.8. “The correlation between the input parameters of the EN1992-1-1 provision was not explicitly discussed, since the provision formulation implements implicitly correlations. For the numerical probabilistic analysis, an explicit definition of the correlations between the input parameters was made according to [19].”

Reviewer #1 Comment: line 706-...: some of the information provided in 4.92. seems to be irrelevant for the proposed manuscript.

Response of the Authors: Thank you for this notice, the section has been shortened to the information that is important for the following probabilistic modelling, for the details the reference to [2] has been included.

Reviewer #1 Comment: line 754-775: it is not clear how the 'model uncertainty' has been defined in this case as no clear definition is provided. Usually, a model uncertainty is defined as the ratio between the model output and the corresponding experimental observation, see e.g. https://doi.org/10.1016/j.strusafe.2016.08.003.

Response of the Authors: Thank you very much for this comment. The section has been shortened to the information that is important. For the traceability of the formulation used to determine the modelling uncertainties from the results of the partners involved, the formulations have been indicated.

Reviewer #1 Comment: line 817-820: this statement is extremely important and requires more interpretation and analysis. It appears that the models are not biased and hence this is to be accounted for when using a particular model uncertainty in either the full-probabilistic analysis or the derivation of (global) partial factors.

Response of the Authors: Thank you very much for these notes. The description has been much more detailed as follows “The probabilistic analyses of most of the partners showed that the calculated normal force mean values are significantly higher than the experimentally determined ones, as can be seen from the box whisker plots (P‐NLFEM results in pink; experimental results in blue) and the histograms of Figs. 12. In these histo‐grams of the normal forces it can also be seen that these differences are smaller in the lower fractile ranges. By considering a model uncertainty of 1.10, an agreement between the normal force mean values of the P‐NLFEM and the experiments can be found, see the graphs in the middle column of Fig.12. Consequently, the lower P‐ NLFEM fractile values shift below the experimental ones, which is on the safe side. Since these deviations appeared in all simulations of the partners and errors can be excluded in the experiments due to the high quality controls, it is important to clarify which effects in the NLFEM lead to this overestimation of the column performance.

Reviewer #1 Comment: Table 7: see comment regarding Table 4.

Response of the Authors: Thank you for this comment, the table was removed from the manuscript

Reviewer #1 Comment: line 817-820: this statement is extremely important and requires more interpretation and analysis. It appears that the models are not biased and hence this is to be accounted for when using a particular model uncertainty in either the full-probabilistic analysis or the derivation of (global) partial factors.

Response of the Authors: Thank you very much for this comment, the description has been much more detailed as follows “The probabilistic analyses of most of the partners showed that the calculated normal force mean values are significantly higher than the experimentally determined ones, as can be seen from the box whisker plots (P‐NLFEM results in pink; experimental results in blue) and the histograms of Figs. 12. In these histograms of the normal forces it can also be seen that these differences are smaller in the lower fractile ranges. By considering a model uncertainty of 1.10, an agreement between the normal force mean values of the P‐ NLFEM and the experiments can be found, see the graphs in the middle column of Fig.12. Consequently, the lower P‐NLFEM fractile values shift below the experimental ones, which is on the safe side. Since these deviations appeared in all simulations of the partners and errors can be excluded in the experiments due to the high quality controls, it is important to clarify which effects in the NLFEM lead to this overestimation of the column performance.

Reviewer #1 Comment: Figure 12:

• extend the range of the normal force (in Figure a not all curves are visible)
• it is not clear which information is provided by the boxplots. These are not discussed in the text.
• provide legends to the histograms on the right

Response of the Authors: Thanks for these hints, in Fig. 12 the following revisions have been made.

• The range of the vertical normal force axis have been extended in order to make all curves visible
• The box plots are described I the text and are included in the discussion of the analysis results.
• Legends have been included in the histograms

Reviewer #1 Comment: line 837: clarify why these two reliability levels have been selected.

Response of the Authors: Thank you for this comment, the following description has been added for clarification.

“These reliability levels have been selected due to the assumption of moderate (ß = 3.8) and low (ß=4.2) relative costs of safety measures and great consequences of failure for a considered classical public building and a reference period of 50 years according to EN 1990”

• line 838-844: please see previous comment regarding the model

Table 8: Please see the comments to your comments to line line 754-775

Reviewer #1 Comment: Table 8:

• why are there no partial factors derived for the case where gamma_Rd = 1.06? How is the design resistance derived in that case?
• how was the partial factor derived for the line 'experiments'? The ECOV method requires two analyses: one using mean values and one using characteristic values. This seems not possible in case of the experiments.

Response of the Authors: Thank you very much for these questions.

• The design resistance is derive acording to Cervenka et al.
• See the explanation in ….
• line 860-862: it is obvious that in case of a higher (targeted) reliability level, the design values of the resistance will decrease.

 

 

Reviewer #1 Comment: line 860-862: it is obvious that in case of a higher (targeted) reliability level, the design values of the resistance will decrease.

 

Response of the Authors: Thank you very this remark. We included:

… it is also obvious that in case of a higher (targeted) reliability level, the design values of the resistance will decrease.

Author Response File: Author Response.docx

Reviewer 2 Report

• Sections 1 and 2 are all well-known concepts. They may be synthetised at all.
• Why the authors chose these dimensions for the column? It seems not a real case.
• How was the sample instrumented?
• Conclusions are too long.

Author Response

Reply to the reviewer's comments

 Thank you very much for the review, your time and the very valuable comments for the article. We have carefully reflected on all of your comments and have incorporated them into the revision of the article. Enclosed you will find the explanations of the individual changes made.

 

Reviewer #2 Comment: Sections 1 and 2 are all well-known concepts. They may be synthetised at all.

• Why the authors chose these dimensions for the column? It seems not a real case.
• How was the sample instrumented?
• Conclusions are too long.

1. The structure of the paper should be improved. It appears to the reviewer that the paper has been written by several authors separately and simply merged together afterwards, since several pieces of information are scattered throughout the paper or are repeated/introduced several times.

Response of the Authors:

Sections 1 and 2 are all well-known concepts. They may be synthetised at all.

We have revised the first section of the article and revised the second section in order to put it in the context with the following chapters

Why the authors chose these dimensions for the column? It seems not a real case.

The selection of the dimensions for the column has been based on the findings of an safety problem for some specific geometrical layouts of the columns. The geometrical dimensions of the investigated column are in some of our buildings in middle Europe used from time to time.

How was the sample instrumented?

The instrumentation of the support is documented in the first paper [2]

Conclusions are too long.

The conclusions were made shorter and clearer.

The structure of the paper should be improved. It appears to the reviewer that the paper has been written by several authors separately and simply merged together afterwards, since several pieces of information are scattered throughout the paper or are repeated/introduced several times.

The manuscript has been revised and many parts have been shortened

Reviewer 3 Report

The paper presents the results of the sensitivity studies of slender columns. The article may be interesting for the readers of the journal, but my main concern is the scientific soundness of the paper. The article is a rather technical note, it contains a lot of wide and detailed descriptions of the well-known approaches as well as the formulations and recommendations from design codes. For this reason, I recommend adding a clear and detailed description at the end of the introduction about the novel elements described in the paper. However, in my opinion, the article contains interesting conclusions.

Below some minor remarks:

1. The Introduction is too brief. The authors cite only two papers to introduce the problem and to justify the necessity to conduct the research and prepare the paper. Please add more references.
2. "The concrete material used to construct the first series of slender columns is C45/55 334 while the steel used is B 500B." - what are concrete parameters? Table 1 contains the parameters of steel. Moreover, these parameters were used in calculations, but were they also determined experimentally? From the text, one can conclude that the reasoning presented in the paper is conducted for columns considered in previous authors' papers. For this reason, the section title "laboratory tested columns" may be misleading. It suggests that some columns were laboratory tested within the conducted study, while they were used as representative cases. I suggest reconsidering the section title in this case.

Author Response

Reply to the reviewer's comments

 Thank you very much for the review, your time and the very valuable comments for the article. We have carefully reflected on all of your comments and have incorporated them into the revision of the article. Enclosed you will find the explanations of the individual changes made.

Reviewer N°3 Comment: The paper presents the results of the sensitivity studies of slender columns. The article may be interesting for the readers of the journal, but my main concern is the scientific soundness of the paper. The article is a rather technical note, it contains a lot of wide and detailed descriptions of the well-known approaches as well as the formulations and recommendations from design codes. For this reason, I recommend adding a clear and detailed description at the end of the introduction about the novel elements described in the paper. However, in my opinion, the article contains interesting conclusions.

Below some minor remarks:

The Introduction is too brief. The authors cite only two papers to introduce the problem and to justify the necessity to conduct the research and prepare the paper. Please add more references.

"The concrete material used to construct the first series of slender columns is C45/55 334 while the steel used is B 500B." - what are concrete parameters? Table 1 contains the parameters of steel. Moreover, these parameters were used in calculations, but were they also determined experimentally? From the text, one can conclude that the reasoning presented in the paper is conducted for columns considered in previous authors' papers. For this reason, the section title "laboratory tested columns" may be misleading. It suggests that some columns were laboratory tested within the conducted study, while they were used as representative cases. I suggest reconsidering the section title in this case.

 

Response of the Authors: Thank you very this remark. We included a clear and detailed description at the end of the introduction about the novel elements described in the paper

The Introduction has been extended and based on much more relevant references that introduce the problem and justifies the necessity to conduct the research and prepare the paper.

"The concrete material used to construct the first series of slender columns is C45/55 334 while the steel used is B 500B." - what are concrete parameters? Table 1 contains the parameters of steel. Moreover, these parameters were used in calculations, but were they also determined experimentally?

"The concrete material used to construct the first series of slender columns is C45/55 334 and the steel parameters are shown in Table 1 – a reference to Table 3 has been included in Table 1 that shows the associated concrete parameters for the indicated concrete strength.

Moreover, these parameters were used in calculations, but were they also determined experimentally?

The parameters used in calculations were determined experimentally and the associated tests and findings are presented in the Round Robin paper 1 [2]

From the text, one can conclude that the reasoning presented in the paper is conducted for columns considered in previous authors' papers. For this reason, the section title "laboratory tested columns" may be misleading. It suggests that some columns were laboratory tested within the conducted study, while they were used as representative cases. I suggest reconsidering the section title in this case.

We adjusted the captions accordingly.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

the paper was improved

Author Response

Thank you

Reviewer 3 Report

Thank you for addressing all reviewer's comments.

Author Response

Thank you