Nonlinear Dynamic Analyses Utilising Macro-Models of Reinforced Concrete Building Structures and Site-Specific Accelerograms
Round 1
Reviewer 1 Report (Previous Reviewer 1)
Thanks for addressing all my comments. I still have reservations on the assumptions of the method, but I'm happy to see some caveats added. It should also be noted that the roof drifts shown in Figure 13 are all less than 0.5%, which indicates that the degree of damage in the building is likely quite low. Nevertheless, I'm happy for this manuscript to be published as is.
Author Response
Dear Reviewer,
We sincerely appreciate the time and effort you have invested in improving the quality of our paper.
In the current version of the manuscript, the spell check and grammar has been corrected.
Your insightful feedback and meticulous review have greatly enhanced its strength and clarity. The revisions we made, guided by your expertise, have bolstered the paper's contributions. We are grateful for your valuable input, which has played a crucial role in sha** the final version of our manuscript. Thank you for your invaluable efforts.
Sincerely,
Authors
Reviewer 2 Report (New Reviewer)
The paper is nice, my unique comment is about the quality of Figures which is rather poor. Please improve the resolution or the quality, especially for Fig. 7
Author Response
Dear Reviewer,
We sincerely appreciate the time and effort you have invested in improving the quality of our paper.
In the current version of the manuscript, the quality of the figures has been improved. The Figure 7 has been replaced with a new figure which is of higher quality compared to the previous one. Moreover, the spell check and grammar has been corrected.
We are grateful for your valuable input, which has played a crucial role in sha** the final version of our manuscript. Thank you for your invaluable efforts.
Sincerely,
Authors
Reviewer 3 Report (New Reviewer)
This paper presents an interesting work regarding the application of rapid nonlinear time history analysis in earthquake engineering. The introduction is clear and presents a brief summary of the previous work by other authors. The authors presented the results in a clear exhibition in which all aspects were discussed and assessed. The graphs point out the advantages here proposed and are lucid enough to understand the breakthrough in research. The authors compare it with classical pushover analysis and present the main advantages, and also compared dynamic non-linear analysis.
1st in the introduction, the authors should clearly state, if they are using in-house software, or commercial software. If so, the name of the software should be in the introduction.
2nd the conclusions must present some “future research” section, otherwise all the work in here is lost.
3rd the reviewer analyzed all the previous comments, provided by the authors, regarding the previous questions, and these were all successfully answered, which was enriched the final version of the manuscript.
Author Response
Dear Reviewer,
We sincerely appreciate the time and effort you have invested in improving the quality of our paper.
In the current version of the manuscript, in the introduction, the following sentence is added to clarify the use of in-house software, or commercial software.
".. the results are compared with the sophisticated finite element analysis. For analysing the case study building, RNLTHA algorithms were implemented using MATLAB Version R2022a [13] and SeismoStruct Version 2021 [14] was used for conducting the finite element analysis."
Similarly, in the conclusions, the following sentence is added to present the recommendation on the “future research”.
"Future research is suggested to extend the procedure for structures supported by frame actions or a combination of walls and frames, to include additional case studies to assess the method's suitability for analyzing buildings with complex core walls and coupled walls, and to develop the multi-degree-of-freedom system based macroscopic model."
Your insightful feedback and meticulous review have greatly enhanced its strength and clarity. We are grateful for your valuable input, which has played a crucial role in sha** the final version of our manuscript. Thank you for your invaluable efforts.
Sincerely,
Authors
This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.
Round 1
Reviewer 1 Report
. The method RNLTHA proposed in the paper seems interesting, but it suggests that only the first mode would experience an inelastic response. It is a rather tricky assumption that would not be general enough for multi-story buildings. The responses shown in Figures 10 and 11 are primarily governed by the first mode. They are not necessarily good examples to validate the method. It would be interesting to see what may happen (particularly the order of errors) if the responses are not just governed by the first mode.
. The method assumes that all the mode shapes and the frequencies of higher modes stay the same after yielding occurs. It is not correct. All modes experience inelastic response whenever yielding occurs. Using elastic responses for all the higher modes is problematic. The responses shown in Figures 10 and 11 are displacements, which are primarily governed by the first mode. They would not be enough to evaluate the performance of the method and the effects of higher modes. I can see the merit of this method, but I believe it is only applicable for estimating roof displacements. It would not work for other responses that would depend on higher modes. If this is the intention, it should be clarified in the paper.
. How was the model set up in SeismoStruct? Figure 7 shows many shell elements, but the sentences in lines 382-384 indicate that the model is a 3D line model using beam-column elements. A line model is not suitable for representing a multistorey building. By using a line model, the responses have been restricted to a response primarily governed by the first mode, which is rather insufficient.
. Table 5 shows the discrepancies between RNLTHA and SeismoStruct in less than 7%, some essentially zero, with a mean of 3%. It looks too good to be true. Some discussions and evidence need to be presented to explain and justify such a small discrepancy using this crude approximation for modeling. It may not be surprising if the SeismoStruct model is simply a cantilever column. However, the cantilever column is a crude model for a multi-story building. Comparing two crude models would not do justice to evaluating the accuracy of the proposed method. Consider using a more detailed FEM model for comparison.
. Step 8, both linear addition and SRSS methods are used to combine displacement responses, with the linear addition method for time histories and the SRSS method for the peak response. It is confusing. Shouldn't the peak response be directly obtained by taking the maximum of the total time histories? How could the two numbers (peak of time histories and the SRSS of peak) reconcile?
. In terms of dam**, although using the Rayleigh model with tangent stiffness would reduce dam** forces, there could still be an overestimation of the dam** forces. According to Figure 5, the Rayleigh dam** curve is concave upwards. A reduction in the first mode frequency would lead to a significant increase in the dam** ratio of the first mode, which cannot be justified. The Rayleigh model should not be used. There are better models.
. Are the equations in Appendix A based on the Newmark method? Is anything new? Please highlight new improvements with justifications, or consider removing Appendix A otherwise. Providing a reference will suffice for old work.
. The units of height in Figures 10 and 11 are mm, which is way too small. Is it a typo? Please check.
Reviewer 2 Report
Paper is clear and well written.
1. Suggest title is reworded to more concisely reflect the contents of the paper. I consider main purpose of the paper is to consider use of RNLTHAs.
2. In the first paragraph of section 2, are the authors sure that the citation of articles 14 and 15 is correct in this context? Please check citations for all references.
3. Please correct typo in the breakdown of Routine 3 where, in Step 5, the instructions say to “Step 5: Multiply the… displacement as calculated in Step 5…”
4. The review considers the approach reasonable for an estimation of the displacement demands on structures and indeed, that is what is highlighted in the paper. However, the authors haven’t clarified clearly enough the limitations of the method in relation to other response parameters. In my opinion, it is fine if the method is only used to provide indications of displacements and storey drift demands. However, note that the method doesn’t respect equilibrium at plastic hinge locations because it appears that the characteristics of higher modes are evaluated using elastic structural characteristics and only the 1st mode considers the strength limitation at the hinge location. Thus, if one combines the base moments associated with say a cantilever wall, it would emerge that the base moment significantly exceeds the plastic hinge resistance – which suggests loss of equilibrium. In the text, the authors claim that the RNLTHA approach can be used to determine the “structural response”. In line with the above, this should be re-worded to clarify that it can be used to estimate the displacement and drift response. Alternatively, to overcome the issue with equilibrium considerations, the researchers could consider alternative modal superposition approaches that address this, such as the transitory inelastic modal superposition approach of Sullivan et al. (2008).
Sullivan, T.J., Priestley, M.J.N. and Calvi, G.M., (2008) “Estimating the Higher Mode Response of Ductile Structures” Journal of Earthquake Engineering, Vol.12, No. 3, pp456–472.P
Reviewer 3 Report
Thank you for your interesting manuscript outlining a proposed simplified analysis procedure. However, I do not believe it is suitable for publication at this time. It would appear the proposed procedure is very similar (or is an exact application) to the widely used uncoupled modal response history analysis and NL-RHA method often credited to Chopra and Goel. The paper in its current form also contains a large portion of basic structural dynamic material presented, which detract from the original contribution of the research.
There also appears to be confusion about the premise of various analysis techniques available to the structural designer; thus, the justification of a "new" procedure is unclear. What is evidently valuable is the resource available at quakeadvice.org.
I also have reservations about the details of the SeismoStruct model as a verification of proposed method.
Below is a list of more specific comments and queries for the paper
Section 1, para 1: There seems to be a blurring of boundaries between the purpose of design procedures versus analysis techniques. The former is the development of a recipe (with force reduction/behaviour factors/overstrength) to adequately predict a reliable lower-bound Capacity of a system. Whilst analysis techniques aim to produce accurate response of a system subject to prescribed condition; analysis techniques are often used to establish Demand in the design process to ensure Capacity exceeds Demands.
Line 51: suggest replace about computation time with effort and cost. Rarely do I think computation time is the foremost barrier in practicing engineers' mind. Also, it is not about the lack of guidance, at many times there is impossible to have guidance, rather it is the uncertainty in material performance, construction quality and etc.
Line 53: Remove "in the writing", "the need"
Paragraph starting on line 57 is poorly written and should be rewritten.
Line 61: There's confusion here about the objectives of NLTHA vs PO in the design process. PO is often viewed as establishing the Strength side of the equation and validating mechanism.
Line 63: The premise of pushover analysis cannot capture strength, stiffness degradation and geometric nonlinearity is rather artificial. One can simply conduct a cyclic pushover (with P-Delta) if indeed that aspect of the performance is of interest? It is a false dichotomy argument. Pushover is perhaps overall superior for design in a way as it considers a lower bound case where dam** is not involved, and that strain-rate related performance enhancement of material is not incorporated.
Line 65: NLTHA more often is for validation of likely performance for a particular excitation input, or for seeking design demand (e.g. maximum drift). One will have to repeat this a number of time before arriving at statistically sounded input for the design process. NLTHA, as a tool for designing for strength, is also often predicated on cyclic performance properties prescribed to elements, so performance prediction is dependent on what is assumed.
Line 75 to Line 78, the computation requirement seems to be overstated. The increase of meshing and complexity of models do not translate to more accurate prediction (more precise maybe but that is of little use to designers.)
Line 101: What is the justification that multi-modal behaviour occurs only when a building exceeds 30m? To be precise, a model of any height will need multiple masses to develop a multi-modal response. I suspect many factors are involved, e.g. structural type, boundary conditions and etc.
Line 140, angular frequency not angular velocity
Line 163, It is not clear where you are applying the SRSS method. What do you mean by peak response in each vibration mode? Is it the peak response for each different site period? If you actually mean structural period and SRSS is not used then don't include this statement. The reader does not need a structural dynamics 101.
Line 165, I am not sure what the justification is for taking the mean of peak displacement for a number of site periods as the design assessment. What is proposed here seems to be to use conditional mean scaled ground motion records as earthquake inputs rather than using uniform hazard spectrum compatible ground motion records. However, for design, you have a defined site with a definitive site period (albeit with small variation), and to stack the analyses with GM records scaled to other site periods simply detune or statistically reduce the peak response (by averaging). There would neither be a rational justification for this in pursuing a more realistic or lower bound estimate of structural performance.
Line 185, I recommend adding the underlying assumption to arrive at the 70%/17%/7% modal mass participation. For example, is it a three uniformly lumped mass system simplified to a single lumped mass at 0.7H.
Line 213, the hysteresis model adopted is simply modified Takeda with specific parameters. Just list the values used and no need to explain further.
Line 217, something weird with typesetting happening here.
Line 227, Not sure a reference other than [17] is required here.
All of section 2.3 is redundant, it is widely understood structural dynamic concepts.
Suggest removing section 3 or at least significantly removing s3.1-3.3. No value to the research community.
Line 341, 2% exceedance probability in 50 years is 2450 years return period according to Poisson distribution.
Line 343, subscript VS30
Line 375, Table 4, rationalise some of the rounding here.
Section 4, kPa not Kpa
Figure 7. May you please elaborate more on the development of your SeismoStruct model? It would appear that you may have idealised the walls as 1D equivalent frame elements with a nonlinear material, pinned at the base. Does this still accurately trigger nonlinear material properties, wall type behaviour or would that simply be based on equivalent gross I, A section properties. How do you ensure that these elements behave like in-plane and out-of-plane walls and track their distributed plasticity behaviour.
This may be an explanation of the improbably good matching between your FE analysis and the simplified modal time history, as your FE model may really reflect a uniformly distributed cantilever as per your "NLTHA" idealisation. Perhaps presenting the stress-strain-displacement distribution along wall heights over time from the FE model will clear up any concerns.
