# Review of "The Redundancy Matrix as a Performance Indicator for Structural Assessment"

David Forster, Malte von Scheven, Alexander Popp

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## To cite this version:

David Forster, Malte von Scheven, Alexander Popp. Review of "The Redundancy Matrix as a Performance Indicator for Structural Assessment". 2025. hal-04905865

HAL Id: hal-04905865

https://hal.science/hal-04905865v1

Submitted on 14 Mar 2025

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Distributed under a Creative Commons Attribution 4.0 International License
Identifiers

Open Review

OAI hal-04905865

Reviewed Article

DOI 10.46298/jtcam.13574

Licence

CC BY 4.0

©The Authors

# Review of “The Redundancy Matrix as a Performance Indicator for Structural Assessment”

David Forster<fnref n="1" />*, Malte von Scheven<fnref n="1" />, and Alexander Popp<fnref n="2" />,>E

## Review of version 1

Permalink: arXiv:2405.06294v1

### 1 Reviewer 1 (Anonymous)

**Reviewer** This is an interesting and well-written paper, which I could recommend for publication in the present form. I have just a few comments, which the authors might address before publication.

As a general remark, I have to say that I am quite surprised that the idea of using the redundancy matrix as indicator for robustness, in the sense of criticality of single members for the whole structure, has never been proposed before. I am not doubting on it, the authors apparently have done a very careful literature review. It just seems surprising, since it is basic knowledge that the degree of static indeterminacy is equal to the degree robustness in the sense of local failure modes (e.g. plastic hinges) before global failure, and it seems obvious that the redundancy matrix contains exactly that information. The fact that this had not been studied in detail yet, makes the proposed paper even more important. I believe that using the redundancy matrix for assessing the robustness of a structure as described in the paper can really be of practical use.

**Reviewer** Regarding the use for assessing the assemblability, I think it is a nice and interesting idea, but it seems quite academic, since it does not consider many other factors, which might be much more important for the assemblability. With reference to the example in Fig. 6, it is a two-story building with cross members in each story and cross members spanning both stories. I would think the main question regarding assemblability is, how can all these members be installed without obstructing each other? How is the accessibility with cranes etc.? How are the connections made (also with respect to the imperfections in length)? Of course, these are constructional and operational aspects, but I guess that they are much more decisive than the optimization of residual strains due to some assumed imperfections. Maybe the authors could add some thoughts on this.

**Authors** Thank you for the comment. We changed the manuscript and included the different aspects of the assembly as suggested. Changes in the manuscript: Chapter 4.1

**Reviewer** Regarding eq. (4), the definition of the R matrix, it would be useful in my opinion to show this on a simple example. In general, the concept of redundancy matrices is not so widely known, so I think a basic example could help the readers in understanding better the rest of the paper.

<footnote n="1">¹ University of Stuttgart, Institute for Structural Mechanics</footnote>

<footnote n="2">² Institute for Mathematics and Computer-Based Simulation, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85577, Neubiberg, Germany</footnote>

<footnote>E Editor</footnote>
**Authors** We agree that a basic example helps authors to understand the concept of redundancy. Therefore, we added a simple truss structure along with the redundancy matrix as Figure 2 and edited the explanations in the respective chapter. Changes in the manuscript: Chapter 2.2

## 2 Reviewer 2 (Anonymous)

**Reviewer** The manuscript is concerned with a method to determine the static indeterminacy of structures. Performance indicators with respect to robustness and assemblability are presented. The method is restricted to linear elastic statics. The contribution focus on truss and beam structures.

**Reviewer** The total degree of static indeterminacy of the system in Fig. 4 is given as $n_s=4$. It should be 3 since only 3 boundary constrains are defined and 3 additional diagonal elements are introduced.

**Authors** This is true, thank you. We fixed the typo. Changes in the manuscript: Chapter 4.2

**Reviewer** Overall, the manuscript is well written and organized. It was shown that the design of robust structures can be achieved by distributing the redundancy homogeneously within the structure. The topic is interesting for the readership of JTCAM. It is a nice contribution.

## 3 Editor's assessments (Alexander Popp)

**Editor** The article explores the redundancy matrix as a key performance indicator for assessing structural robustness and assemblability in early design stages. It presents a quantitative approach to measure the distribution of static indeterminacy, which influences a structure's ability to withstand damage and accommodate geometric imperfections during assembly. The paper derives mathematical formulations for these structural performance indicators, validates them through truss structure examples, and suggests potential applications in optimizing resilient and adaptable infrastructure. The initial manuscript underwent a rigorous review process, with two expert referees offering their assessments. Both review reports have been very positive and only requested minor modifications. The authors provided such a minor revision and the manuscript was accepted for publication accordingly.

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