Semianalytical Lower-Bound Limit Analysis of Domes and Vaults

Round 1

Reviewer 1 Report

The paper presents a semi-analytical procedure in order to assess the safety factor of domes under radial pressure. Adding to the large body of literature dealing with this problem, the approach proposed in the submitted manuscript combines a rather straightforward analytical treatment with a numerical one and can be of interest to both scholars and practicing engineers. In particular the manuscript relies upon the classical theorems of limit analysis and on constrained optimization procedures in a fairly direct and coherent sequence, which might offer a basis for further extension. Additionally, a comparison with experimental results available in literature is provided for confirmation of the merits of the study. For all these reasons the present reviewer believes that the manuscript is worth of publication. However, as a minor note, the present reviewers must also point out that: 1) Figure 7 should be resized; 2) Caption of Figure 9 should be corrected.

Author Response

 "Please see the attachment."

Author Response File: Author Response.docx

Reviewer 2 Report

The manuscript applsci-1872399 addresses the important topic of limit resistance of spherical domes made with “No Tension Materials” (the definition “Not tensile Resistant Material” seems not in agreement with the original definition introduced by Di Pasquale and later by Del Piero).

The study is interesting since it presents a solution with much less computational effort than purely optimization-homogenization finite element methods. However, it seems to the present reviewer that the significant and general contribution of Milani and Tralli in Int. J. of Solids and Structures vol. 45 issue 20, 2008 should be included in the references and in the discussion in the introduction.

The following suggestions can be given:

11)     It is not clear if the eigenvalue problem of matrix A is solved analytically or numerically, and what is the relation between this solution and c (is “c” the eigenvector matrix?);

22)     Figure 7 has a wrong ordinate label since the quantity is the vertical elevation of the parallels;

33)     Table 1 lacks the opening angle (or sag) of the domes; if it is a constant value can be cited in the text;

44)     It seems to the present reviewer that the example set is too focused on one type of vault and load; certainly some other examples of hemispherical domes, masonry material, and point load could be added, giving more generality to the capability demonstration of the developed procedure.

Therefore the manuscript is accepted with a major revision request. The authors can fulfil the required modifications and additions to the study before resubmitting it to the journal.

Author Response

 "Please see the attachment."

Author Response File: Author Response.pdf