Structural Analysis of Self-Weight Loading Standing Trees to Determine Its Critical Buckling Height

Round 1

Reviewer 1 Report

This article presents several methods (three) to obtain the critical buckling height of a tree. The calculation results from the three methods are compared to obtain each tree's critical height and safety level against buckling. The following points are suggested to make the article easier to understand:

·       The text does not explain the main questions that researchers in this study will answer.

·       Does the variable L in equation 10 have to be defined as the effective length value?

·       The text does not explain the data source or the places for collecting data analyzed in this study.

·       In conclusion, it is not explained what variables significantly affect unsafe, safe, and very safe conditions (e.g., tree height, tree diameter, etc.)

·       Conclusions should be presented in the form of concluding points and not in the form of paragraphs.

Author Response

Responses to the Reviewers’ comments

Dear Editors and Reviewers

Thank you for your letter and for the reviewers’ comments concerning our manuscript “Structural Analysis of Self-weight Loading Standing Trees to Determine Its Critical Buckling Height.” Those comments are all valuable and very helpful for revising and improving our paper. We have studied the comments carefully and made corrections accordingly, hoping to make the paper clearer. The  responses to the reviewers’ comments are below.

Best Regards,

Authors

Author’s response to Reviewer 1:

This article presents several methods (three) to obtain the critical buckling height of a tree. The calculation results from the three methods are compared to obtain each tree's critical height and safety level against buckling. The following points are suggested to make the article easier to understand:

1. The text does not explain the main questions that researchers in this study will answer.

Author’s responses:

We agree to revise the text to add the main question that this study will answer.

This study promotes the structure’s stability analysis following the standardized methods provided by the building code to answer the question of tree safety planted in a built environment. Although a tree may receive more external loads, this study delimitated its scope to the tree receiving the self-weight only and ignoring the external load to simplify the analysis.

2. Does the variable L in equation 10 have to be defined as the effective length value?

Author’s responses:

Yes it does, L is the effective length. We agree to revise the text.

The determination of critical buckling stress (s_cr) is based on a general formula for Euler buckling, as shown in Equation 10.

                                                                                (10)

where ? is a moment of inertia,  is the effective length, and ? is the cross-sectional area.

3. The text does not explain the data source or the places for collecting data analyzed in this study.

Author’s responses:

We add the location of the tree specimens:

The sample size (n) is 73 trees, including 50 rain trees and 23 agathis located in IPB Campus Dramaga (6.54° - 6.56° S, 106.71° - 106.73° E). The altitude is 145-195 masl.

4. In conclusion, it is not explained what variables significantly affect unsafe, safe, and very safe conditions (e.g., tree height, tree diameter, etc.)

We agree to write some variables that significantly affect the tree safety condition.

The critical buckling height value was inputted into the tree structure stability analysis to determine the tree safety factor (S_f). Every tree can be categorized based on three safety conditions: unsafe, safe, and very safe. The safety condition is affected by the stem’s structural (mechanical) properties [i.e., modulus of elasticity (E) and compressive strength parallel to the grain (F_c)], section properties [i.e., area (A), static moment (Z), and moment of inertia (I)], slenderness ratio (length to diameter ratio), and the self-weight (i.e., stem weight and canopy weight).

5. Conclusions should be presented in the form of concluding points and not in the form of paragraphs.

Author’s responses:

Many published articles on Sustainability presented the conclusion as a paragraph. We prefer to present the conclusion in the form of a paragraph.

Author Response File: Author Response.pdf

Reviewer 2 Report

This is an article in the field of stability of structures, in this case trees. The article presents purely theoretical considerations with little connection to practice. Nevertheless, they are interesting.
My comments:
1. in the introduction you should describe exactly what is the purpose of the research conducted. There is a lack of illustration (preferably pictures) of the failure of trees as a result of pure buckling.
2. what is the relationship between the critical buckling height of trees shown in Fig.5 with the real height of these trees. An analysis of these relationships is needed.
3. what is the "n" in Table 3.
4. there is a lack of conclusions about the buckling capacity of existing trees.
5. too many self-citations (14). Should be reduced.

Author Response

Responses to the Reviewers’ comments

Dear Editors and Reviewers

Thank you for your letter and for the reviewers’ comments concerning our manuscript “Structural Analysis of Self-weight Loading Standing Trees to Determine Its Critical Buckling Height.” Those comments are all valuable and very helpful for revising and improving our paper. We have studied the comments carefully and made corrections accordingly, hoping to make the paper clearer. The  responses to the reviewers’ comments are below.

Best Regards,

Authors

Author’s response to Reviewer 2:

This is an article in the field of stability of structures, in this case trees. The article presents purely theoretical considerations with little connection to practice. Nevertheless, they are interesting.

My comments:

1. in the introduction you should describe exactly what is the purpose of the research conducted. There is a lack of illustration (preferably pictures) of the failure of trees as a result of pure buckling.

Author’s responses:

We agree to write the purpose of this study explicitly. We also agree to state the deformed shape of a buckled column. We add the sketch of an original straight tree and its bucking deformed shape.

This study exemplified the structural instability analysis of a tree to investigate its safety in a built environment. Unlike building construction [9–18], the structural analysis practices of the tree based on the engineering mechanics approaches have rarely been conducted before because a tree is not a construction. Dargahi et al. [19] suggested a finite element method to analyze the tree stability to reduce the risk of damage. The measured and scientific safety justification should doubtlessly advise people to plant some trees in their neighborhood and convince them to avoid casually felling the tree; thus, it may support the recent increasing environmental awareness to implement more ecological practices for developing a sustainable and environmentally friendly city. The commitment to sustainability is the primary indicator to appraise a construction company’s performance in the built environment project developments [20].     .    

This study aimed to analyze the safety factors related to the critical buckling height of decurrent and excurrent trees modeled as slender round columns using three different methods.

When buckling occurs, a column structure can no longer maintain its original straight shape; the deformed shape resembles an arch curvature-like bending deflection (Figure 1), leading to the tree stem's instability failure.

Figure 1. Sketch of an original straight tree and its buckling deformed shape.

2. what is the relationship between the critical buckling height of trees shown in Fig.5 with the real height of these trees. An analysis of these relationships is needed.

Author’s responses:

We agree to redraw Fig. 5 (revised to become Fig.6) to compare the critical buckling height with the tree actual height.

Figure 6. Critical buckling height with three different methods compared with the tree actual height

Figure 6 shows that the tree’s actual heights are generally shorter than its critical height, which indicates the trees are reliably receiving their self-weight. All agathis trees’ critical buckling heights are higher than their actual height, exhibiting safety. All rain trees are also safe when ignoring the canopy weight (Method 2). On the contrary, if the canopy weight is also considered the self-weight load (Methods 1 and 3), the error bar of the rain tree’s actual height has a small intersection range with its critical height, indicating some trees may be unsafe, although most of them are safe. 

3. what is the "n" in Table 3.

Author’s responses:

“n” is number of tree. We replace the n notation with the phrase “number of tree”.

4. there is a lack of conclusions about the buckling capacity of existing trees.

Author’s responses:

Thank you very much for your kind suggestion related to the buckling capacity. Your advice enlightens us to calculate the additional load the tree may receive safely. It is interesting to determine how much the dead load (i.e., tree house building), occupancy load, live load, wind load, and snow load can be applied. Your suggestion encourages us to study the possibility of building a reliable and safe construction on the tree.

However, this recent study was limited to the boundary condition of a tree receiving its self-weight only; therefore, we did not calculate the buckling capacity of the existing tree. We will consider calculating it in the following study.

5. too many self-citations (14). Should be reduced.

Author’s responses:

All citations are directly related to this study; therefore, we prefer to keep them up. We agree to add some references to reduce the percentage of self-citation.

Author Response File: Author Response.pdf

Reviewer 3 Report

The authors have proposed a Building Code, to check the tree dimension adequacy resisting the load. Their study simplified the case by focusing only on the self-weight and ignoring the external loads. Therefore, the buckling analysis of a slender tapered round column subjected to compression is advocated. The Euler and Ylinen's buckling stress analysis (Method 1) calculated the tree safety with a 95% confidence level. This study also applied the Greenhill formula (Method 2) to determine the critical height of a tree receiving the stem weight, then modified it to include the crown weight into consideration (Method 3). The three methods calculated the critical height to determine safety factor, that is, the ratio of the actual tree height to the 95% confidence level estimated critical height.

In my opinion the work is well presented and can be accepted after following minor revisions:

1-    The literature review denotes that there are lots of studies about buckling analysis of different structures under self-weight loading. What is the novelty of present work? The authors must present novelties and research highlights of their study point by point in the last paragraph of introduction section.

2-    Very limited Refs have been reviewed in the introduction section. The authors must improve the literature review by adding and discussing more Refs. The authors can review deeply about Refs related to buckling of structures under self-weight loading.

3-    It is better that the authors verify their results with previous published papers.

4-    The authors must present some of their main results in the conclusion section.

Author Response

Responses to the Reviewers’ comments

Dear Editors and Reviewers

Thank you for your letter and for the reviewers’ comments concerning our manuscript “Structural Analysis of Self-weight Loading Standing Trees to Determine Its Critical Buckling Height.” Those comments are all valuable and very helpful for revising and improving our paper. We have studied the comments carefully and made corrections accordingly, hoping to make the paper clearer. The  responses to the reviewers’ comments are below.

Best Regards,

Authors

Author’s response to Reviewer 3:

The authors have proposed a Building Code, to check the tree dimension adequacy resisting the load. Their study simplified the case by focusing only on the self-weight and ignoring the external loads. Therefore, the buckling analysis of a slender tapered round column subjected to compression is advocated. The Euler and Ylinen's buckling stress analysis (Method 1) calculated the tree safety with a 95% confidence level. This study also applied the Greenhill formula (Method 2) to determine the critical height of a tree receiving the stem weight, then modified it to include the crown weight into consideration (Method 3). The three methods calculated the critical height to determine safety factor, that is, the ratio of the actual tree height to the 95% confidence level estimated critical height.

In my opinion the work is well presented and can be accepted after following minor revisions:

• The literature review denotes that there are lots of studies about buckling analysis of different structures under self-weight loading. What is the novelty of present work? The authors must present novelties and research highlights of their study point by point in the last paragraph of introduction section.

Author’s responses:

We agree to explicitly state the novely of this study:

This study exemplified the structural instability analysis of a tree to investigate its safety in a built environment. Unlike building construction [9–18], the structural analysis practices of the tree based on the engineering mechanics approaches have rarely been conducted before because a tree is not a construction.

• Very limited Refs have been reviewed in the introduction section. The authors must improve the literature review by adding and discussing more Refs. The authors can review deeply about Refs related to buckling of structures under self-weight loading.

Author’s responses:

We agree to add more references in the introduction section.

Unlike building construction [9–18], the structural analysis practices of the tree based on the engineering mechanics approaches have rarely been conducted before because a tree is not a construction. Dargahi et al. [19] suggested a finite element method to analyze the tree stability to reduce the risk of damage.

• It is better that the authors verify their results with previous published papers.

Author’s responses:

We agree to compare this study’s results with previous published papers.

The results from this study, as presented in Table 3, showed that 10 excurrent-agathis trees were safe and 13 were very safe. Meanwhile, 5 unsafe trees were found among the decurrent-rain trees, while 31 and 14 trees were safe and very safe trees, respectively. The unsafe trees showed deformation from the straight to the arch curvature form (Figure 1), similar to 15 years old buckled shape Pinus radiata in New Zealand studied by Dargahi et al. [19]. The safety condition was related to the critical tree height, and this value was affected by the stem’s modulus of elasticity (E). Watt et al. [71] mentioned that an increase in E could increase the critical compressive stress the stem can withstand before buckling occurs. Despite the value of the slenderness excurrent tree being higher, which generally means the tree stem’s stability is low, this tree model is quite good at estimating critical height and safety conditions. Furthermore, Putz et al. [72] reported that trees with stem failure in windstorms usually have lower wood density, strength, and E than uprooted trees. In terms of its crown characteristic effect, the crown weight becomes the dominant influence on the buckling capacity of the column [19]. Further, Watari et al. [73] concluded that critical buckling height increases with crown/stem mass ratio reduction.

• The authors must present some of their main results in the conclusion section.

Author’s responses:

We agree to write the main results of this study in the conclusion section:

This study advocated the Euler and Ylinen buckling stresses method (Method 1) following SNI 7873:2013 Building Code for Wood Construction to determine the tree stem's critical buckling height rather than the Greenhill buckling method (Method 2) and the modified Greenhill buckling method (Method 3).

Author Response File: Author Response.pdf

Reviewer 4 Report

Dear authors

This study aimed to evaluate the safety of standing tree using analytic methods based on self- weight of tree. The arrangement and writting of this paper are quick clear and well. However, some critical points were also existed. See followings.

1) As known, the external loads, i.e., wind, rain, storm, are critical risk for trees. Whereas, in this study, the external loads were not considered. It is recommended that you furteher study it using  computer numerical simulation method.

2) Just as mentioned, the three methods you used were all referred from previous study, then what's new in this paper? Just application, a case study?

3) How did you get the 95% confidence level estimated critical height, How many trees you measured?

4) In page 132-134, You measured the dynamic elastic moudulus and cited some study to validate that the dynamic E is higher than the static one. It is suggested that more references added to support this point of view. DOI: 10.15376/biores.16.4.7101-7111.

5) Figure 6 seemed interesting, are there mathmatic model available to simulating the crown shap. That's also a intersting point.

6) The significance of this paper must be reclamed clearly to make the paper in the scope of sustainability.

Author Response

Responses to the Reviewers’ comments

Dear Editors and Reviewers

Thank you for your letter and for the reviewers’ comments concerning our manuscript “Structural Analysis of Self-weight Loading Standing Trees to Determine Its Critical Buckling Height.” Those comments are all valuable and very helpful for revising and improving our paper. We have studied the comments carefully and made corrections accordingly, hoping to make the paper clearer. The  responses to the reviewers’ comments are below.

Best Regards,

Authors

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

I accept the authors' responses and the corrections and additions made to the manuscript. 

Author Response

Dear reviewer

Thank you very much for your support.

Best regard,

Author