Analytical and Numerical Study of the Axial Stiffness of Fiber-Reinforced Elastomeric Isolators (FREIs) under Combined Axial and Shear Loads
Round 1
Reviewer 1 Report
This paper presents analytical methods to derive a function to account for the additional vertical deformation of the elastomeric bearings when shear loads are present. The manuscript provides sufficient literature and flows nicely with the analytical and numerical analyses. Overall the manuscript is well-written and organized. The reviewer suggests improving the conclusions to include the thresholds or the limits where the new function is most accurate and well-suited based on their analyses and comparisons.
Lastly, the paper has a few typos that should be copyedited before publication. Examples are given below for some of these typos:
Line 49 -- replace "in order the bearing to be stable" with "in order for the bearing to be stable"
Line 58 -- replace "different level of axial pressure" with "different levels of axial pressure"
Line 418 -- replace "account" with "account for"
Author Response
Kind Reviewer,
I appreciate the time and effort you have dedicated to provide insightful feedback on my work. The comments contributed to improve the quality of the paper. Attached you can find the response to each of your comment.
Author Response File: 
Author Response.docx
Reviewer 2 Report
The paper entitled “Analytical and Numerical Study of the Axial Stiffness of Fiber Reinforced Elastomeric Isolators (FREIs) Under Combined Axial and Shear Loads” provides a very interesting research work about a presented procedure for real practice applications for the evaluation of the axial stiffness of FREI devices. The manuscript is well written, easy to read and provides very useful information. However, a number of revisions are suggested, in order to increase the value of the manuscript.
1. In the whole document numerical values of shape factors S1 and S2 in some cases look out of the ordinary ranges usually adopted in real practice. Additional explanations are needed, with reference to some recent research work:
De Luca, A.; Guidi, L.G. State of art in the worldwide evolution of base isolation design. Soil Dyn. Earthq. Eng. 2019, 125, 105722.
2. Page 10: “In all the FEMs, the horizontal displacement is imposed on the top of the bearing up to a shear strain of 200%, as done in Section 3.3.”. Authors are suggested to explicitly mention that the performed analyses have the aim to simulate what is generally done through dynamic experimental tests, for instance in agreement with the European Standard Code for Anti-Seismic devices UNI:EN15129:2018, by applying radial sinusoidal motions, since radial motions can be representative of bidirectional movements, as reported in the following documents:
CEN. 2018. Comité Européen de Normalisation TC 340, European Code UNI EN 15129:2018 Anti-seismic devices. Brussels, Belgium: European Committee for Standardization.
Furinghetti M., Pavese A. [2017] “Equivalent Uniaxial Accelerogram for CSS-Based Isolation Systems Assessment under Two-Components Seismic Events”, Mechanics Based Design of Structures and Machines, 2017, DOI: 10.1080/15397734.2017.1281145.
3. A graphical representation of the FEM model for all the six devices is needed, in addition to numerical details shown in Table 4.
4. Page 11: “In each FEM, the top and the bottom surfaces are modeled as rigid lines and a contact 345 "touch" type has been set between bearing and supports with Coulomb friction coefficient 346 equal to 0.9 [55].” Does this number mean 90% of friction coefficient? What is the material assumed for supports, in agreement with the cited reference? Did Authors find sliding movements during the analyses? Additional details are needed.
Author Response
Kind Reviewer,
I appreciate the time and effort you have dedicated to provide insightful feedback on my work. The comments contributed to improve the quality of the paper. Attached you can find the response to each of your comment.
Author Response File: Author Response.docx
Reviewer 3 Report
This paper analyses the response of FREIs in unbonded configuration under combined axial and shear loads. The authors provide an analytical solution to evaluate the increase in vertical displacement of FREIs due to lateral deformations when calculating the vertical stiffness and the corresponding effective compressive modulus. A parameter y<1 is calibrated by evaluating how it is affected by changes of the main geometric and mechanical parameters. Different analytical formulations are considered for the effective compressive modulus and for the buckling load of the bearing. The analytical study is then validated using Finite Element Analyses, showing how the proposed analytical formula provides good results when estimating the reduction of the vertical bearing capacity of FREIs subjected to combined vertical and horizontal loads.
The paper is very interesting and the analyses are rigorous. It can be accepted under following minor revisions:
#1: in Section 3.3 the authors are encouraged to provide 2D plots of the y function for the most relevant geometric and mechanical properties of the bearings, in addition to the 3D plots presented throughout the paper.
#2: In section 3.3 the authors claimed a transition value of the secondary shape factor of 2.5 between stable and unstable response. The reduction due to y function corresponding to this value could be discussed adopting equation (15) within the paper.
#3: Further developments of this work should be highlighted within the conclusions, including the variability of reinforcement properties and rubber compound (i.e. recycled and reclaimed rubber) that may affect the reduction in vertical bearing capacity of FREIs.
#4 In Section 4.2, explain the limitation of the proposed constitutive model, which does not account for energy dissipation/viscous behavior, and justify the choice (e.g. a single parameter, G, needed for controlling the stiffness and evaluating its effects on the mechanical behavior of the device)
#5 Clarify that the material is treated as incompressible in the FE analyses.
#6 In section 4.3, please explain why the percentage differences between analytical and numerical results depend on analytical formulations adopted for buckling load and effective compressive modulus.
#7The following research papers dealing with axially flexible rubber isolators could be acknowledged:
- Orfeo A., Tubaldi E., Muhr AH, Losanno D. (2022). Mechanical behaviour of rubber bearings with low shape factor. Engineering Structures, 266, 114532.
# Check symbols in the paper, many are not italic.
# Check the English throughout the manuscript…e.g.“To account the further vertical” should be “To account for the increased vertical”
Author Response
Kind Reviewer,
I appreciate the time and effort you have dedicated to provide insightful feedback on my work. The comments contributed to improve the quality of the paper. Attached you can find the response to each of your comment.
Author Response File: Author Response.docx
Round 2
Reviewer 2 Report
Authors have significantly increased the overall quality of the manuscript. Therefore, the article can be accepted for publication in its revised form.
