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In the last few decades, important attention was given to infill masonry panels due to their worldwide uses. Many experimental and numerical studies were conducted to study their effect on the behavior of RC frames. In general, three modeling strategies are widely applied to model infill masonry, namely, micromodels, mesomodels, and macromodels. This study investigates the accuracy of the width models to predict the behavior of masonry infills using the mesomodeling technique. To this aim, the masonry infills are modeled as an equivalent homogenized diagonal element in order to represent the diagonal action of masonry infills. The width models used to determine the width of the diagonal strut are used in mesomodeling. In addition, the study contains comparisons between different modeling techniques to predict the global behavior of the infilled frames. Experimental tests conducted on two infilled frames from the literature are considered to calibrate the numerical simulations. The results indicate that the micromodeling approach gives a good agreement with the experimental tests in terms of lateral force and deformation shapes, the related errors varying between 0.12 and 2.8%. Using single strut models, the differences between numerical and experimental results vary from 1.1 to 20%. On the other hand, the errors obtained from multiple strut models are varying between 9 and 40%.
Infill masonry panels are used worldwide for reinforced concrete buildings. This heterogeneous material is used for internal and external separations, which provide thermal and acoustic insulation. During earthquakes, infill panels are subjected to inplane lateral forces received from the frameinfill connections. These forces imply different failure modes to a masonry infill. According to the experimental investigation conducted by
During the last few decades, important attention is given to the effect of masonry infill walls on responses of steel and reinforced concrete (R/C) frames. Experimental studies demonstrated that the existence of masonry infills affects the global response of structures by increasing the strength and the stiffness. The effect of masonry infills is directly affected by several parameters such as the existence of openings, the frameinfill connection, type of units (solid or hollow), and type of mortar (weak or strong).
Furthermore, numerical studies are introduced to investigate the inplane and outofplane behaviors of masonry infills using different modeling techniques.
The previous method takes into account all masonry infill details by modeling each component as a separate element. This approach makes the modeling process more complex and difficult to realize. Alternatively, the mesomodeling approach treats the masonry infills as one single element. The masonry infill components are smeared out as one equivalent element using the homogenization technique. This technique is based on selecting a periodic unit cell that includes all component types. The periodic unit cell should be selected in a way where its repetition generates the entire masonry panel [
The macromodeling strategy adopts different modeling techniques. A simplification comprises the use of a single strut or multidiagonal struts. The first appearance of this technique is established based on the observation made by
The first main contribution proposed in this study is the use of the mesomodeling approach to investigate the accuracy of several width models proposed in the literature. To this aim, the masonry infills are modeled as an equivalent homogenized diagonal element. The width in mesomodeling is calculated according to several models selected for macromodeling. The equivalent properties are defined from the experimental behaviors of masonry infills.
In addition, this study contains a comparison between the accuracy of micro, meso, and macromodeling techniques. In micromodeling, the infills are modeled with the simplified approach where the units are extended to the halfthick of joints in each direction. In macromodeling, the diagonal strut is modeled with a 3D spar element that works only in compression and has no tension or bending resistance. The numerical simulation is carried out using the finite element software ANSYS. Two specimens experimented by
From the literature, three different modeling techniques can be classified to model masonry infills, known as micro, meso, and macromodeling. These techniques are different in terms of complexity, computational time, and accuracy. The micromodeling technique is more accurate among the two other methods. The consideration of details in the modeling process makes this method more useful for research purposes which can capture the local phenomena and the failure modes of the interaction between the different components. The complexity and the computational time make micromodeling inappropriate in large structures. The mesomodeling approach is less complicated than micromodeling. These modeling techniques are based on modeling the masonry infill as one homogenized element. This simplification is useful to study the frameinfill contacts. A more practical method is known as macromodeling. The simplicity makes this method more appropriate for large structures.
Micro and meso modeling approaches
In mesomodeling, the masonry infills are considered homogenized elements. This method required the definition of equivalent material properties that can produce the same behavior as the masonry infill. To this aim,
The previous method is a complex task. The long computational time needed to solve the models made it inappropriate in engineering practice. Otherwise, the macromodeling approach simplifies the contribution of the masonry infill on the global behavior based on its physical acting when the surrounded frame is subjected to lateral loads (
Macro models:
Several equations proposed to calculate the width of the diagonal strut are reported in this section. The selected equations relate the width of the strut to the diagonal length and inclination, the thickness, and the mechanical properties of the masonry and concrete materials. In addition, the dimensions and the type of brick units can affect the width of the strut, where larger brick units will affect the total arrangement of the masonry infill, which implies an effect on the diagonal behavior of the masonry wall. The first expression suggested is that proposed by
According to
As mentioned by
Based on a numerical study using ABAQUS
Other researchers improved the macromodeling technique to account for both the inplane and the outofplane behaviors.
Moreover,
Comparison between difference strut width equations according to the variation of the relative stiffness for the frame of Specimen 9 (
Twelve experimental tests on onestory, onebay, 1/2 scale R/C frames infilled with concrete masonry units are tested by
Details and results of specimens 8 and 9 (units in N and mm):
The concrete material is modeled using the SOLID65 element available in the ANSYS library. This element has cracking and crushing capabilities in case of tension or compression, respectively [
The failure surface used in ANSYS for brittle materials is that proposed by
Adopted nonlinear Stressstrain relationships for:
The reinforcements are modeled with a LINK180. This element is used to model trusses, cables, springs, and links. It has the capability to represent the tension and/or compression elements with no bending resistance [
The masonry infills are modeled using the simplified micro modeling approach where the mortar thickness is halved and assigned to the adjacent unit. The element and procedure used to model the concrete material are used to model the masonry material. The tensile stress of masonry is considered to be 10% the compressive strength [
The frameinfill interactions and that between masonry units are modeled with contact elements. Surfacetosurface contact elements CONTA174 combined with a target element TARGE170 are used. The contact elements are used to represent the contact and sliding between two element surfaces. The elements are defined with six or eight nodes depending on the shape of the contact surface. These elements support isotropic and orthotropic Coulomb friction, shear stress friction. In ANSYS, the cohesive zone material model (CZM) is combined with contact pairs to define the separation between two elements. The CZM model (
In the macromodeling approach, the masonry infills are modeled with the LINK180 element from ANSYS library. This element is a 3D spar that can be used in a variety of engineering applications (
Modeling techniques of masonry infill:
In mesomodeling, the masonry infills are modeled as a single homogenized diagonal element using the SOLID65 element. The diagonal element is modeled in the same direction of the stresses and strain distributions obtained.
The mechanical properties of the diagonal elements are defined from the behavior of the masonry infill. The masonry infill response is subtracted from the behavior of the infilled frame based on the hypotheses that consider the behavior of the infilled frame as a combination of its two components frame and infill [
The total width and the contact length in
Strut width values for specimen 8–9 (units in mm).
Author  Specimen 8  Specimen 9  Number of strut (s) 


855  855  1 

167  159  1 

552  520  1 

463  413  1 

427  427  1 

323  314  1 

92  87  3 
The results obtained from this analytical study are presented and discussed in this section. The dissection is split into two phases: 1) before reaching the maximum lateral load and 2) after reaching the maximum lateral load. Before the peak load, the results are compared in terms of maximum force (
Results obtained from micro modeling:
The diagonal distributions of the stresses and the strains in the infilled frames, when the systems reach their peak strength, are illustrated in
Distribution of stresses and strains:
The results obtained from modeling specimen 8.
Modeling method  Strut models 




Micromodel  —  184  54.5  9.10 
Macromodel  All models  183  102  27.5 
Mesomodel 

160  81.2  18.0 

177  75.3  19.1  

170  77.9  17.6  

172  78.2  18.3  

173  78.1  18.7  

175  78.2  18.9 
The results obtained from modeling specimen 9.
Modeling method  Strut models 




Micromodel  —  292  207  33.6 
Macromodel  All models  297  115  20.9 
Mesomodel 

288  90.8  33.8 

273  88.8  32.5  

265  95.0  30.6  

270  93.3  32.1  

269  93.3  32.0  

272  92.1  32.4 
The results of the multistrut model.
Models  Modeling method  Specimen 8  Specimen 9  








Micromodel  184  54.5  9.10  292  207  33.6  

Mesomodel  179  71.0  14.5  278  79.5  18.4 
Macromodel  179  58.0  11.0  250  69.7  13.3  

Mesomodel  197  83.6  18.2  261  84.1  26.3 
Macromodel  203  69.4  16.8  272  72.0  25.5 
As indicated in
The results obtained from mesomodeling indicate that the width models of
The maximum forces record from
The width models used to model specimen 8 are used for specimen 9. The results obtained from the numerical analyses are summarized in
Using macromodels, the numerical force is 297 KN, which reached at a displacement of 14.2 mm. The stiffness obtained at the peak force is around 2 times lower than the experimental value. In terms of initial stiffness, the numerical value is 28% lower. Using mesomodeling, the width models proposed by
In terms of initial stiffness, the model of
The results obtained from modeling the masonry infills with threestrut models are presented in
In terms of stiffness, both models overestimate the initial stiffness and stiffness at the peak load of the specimen 8 with difference varying between 0.5 and 35%; only in macromodeling of
Comparison between experimental and numerical macro models for specimen 8:
Comparison between experimental and numerical macro models for specimen 9:
Comparison between experimental and multistrut models:
In macro and mesomodels, the curves obtained from analyzing specimen 8 (
This work contains a numerical investigation on the accuracy of width strut models using mesomodeling. The homogenized concept is used to model the masonry infill as a diagonal element. In addition, the work contains a comparison between micro, meso, and macromodeling techniques of infills surrounded by reinforced concrete frames using the finite element software ANSYS. Two experimental specimens with weak and strong infill panels subjected to monotonic increasing lateral loading are selected to calibrate the numerical study.
First, seven width models are selected. The variation of the strut width equation according to the relative stiffness indicates that the selected equations can be classified according to the relative stiffness to dependent and independent equations. The dependent equations show constant width values during the variation of the relative stiffness. Otherwise, the independent equations show a reduction of width values during the increase of the relative stiffness.
Next, the masonry is modeled using a simplified micromodel. The global responses of the infilled frames of the experimental test are well predicted using the simplified micromodeling approach (in terms of strength and stiffness). The deformation shapes of the numerical models can capture the shear sliding in specimen 8. While in specimen 9, the numerical model can capture the diagonal and sliding cracks. In macromodeling, the masonry infills are modeled using a 3D spar, known as LINK180. In mesomodeling, the masonry infills are modeled as an equivalent homogenized diagonal element using SOLID65. The width is calculated according to the models used in macromodels.
In general, the macromodeling with a singlestrut model indicates the capability of the single strut to capture the global behavior of the infill frames. The forcedeformation curves obtained from different macromodeling show the same curve. Using mesomodeling, the singlestrut models are more predictable to the global response by using
The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.
MB was responsible for writing, methodology, software, and validation. ZB carried out the methodology, writing, and supervision.
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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